From 42ccc4d3e95183104030cbc6e10fefbc7c9d8d0d Mon Sep 17 00:00:00 2001
From: jgarnek <jgarnek@amu.edu.pl>
Date: Thu, 23 Mar 2023 17:45:28 +0000
Subject: [PATCH] baza crys dziala; poprawki w coordinates dr; wspolrzednie
 cris prawie dzialaja

---
 sage/.run.term-0.term                         | 16036 +++++++++++++++-
 sage/as_covers/tests/cartier_test.sage        |    11 +
 sage/drafty/draft.sage                        |    14 +-
 sage/init.sage                                |     3 +-
 .../superelliptic_cech_class.sage             |    58 +-
 sage/superelliptic/superelliptic_class.sage   |     6 +-
 .../superelliptic_form_class.sage             |    56 +-
 sage/superelliptic/tests/a_number_test.sage   |     5 +
 .../tests/form_coordinates_test.sage          |    12 +
 sage/superelliptic/tests/p_rank_test.sage     |     6 +
 sage/superelliptic/tests/pth_root_test.sage   |    11 +
 sage/superelliptic_drw/automorphism.sage      |     3 +
 sage/superelliptic_drw/de_rham_witt_lift.sage |    49 +-
 .../decomposition_into_g0_g8.sage             |     7 +-
 sage/superelliptic_drw/second_patch.sage      |     7 +
 .../superelliptic_drw_cech.sage               |    43 +-
 .../superelliptic_drw_form.sage               |     4 +-
 .../tests/decomposition_into_g0_g8_tests.sage |    11 +
 .../tests/superelliptic_drw_tests.sage        |    10 +
 sage/tests.sage                               |     4 +-
 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

diff --git a/sage/.run.term-0.term b/sage/.run.term-0.term
index 8ddfd91..142281a 100644
--- a/sage/.run.term-0.term
+++ b/sage/.run.term-0.term
@@ -34650,4 +34650,16038 @@ superelliptic_drw_cech.sage  superelliptic_drw_form.sage  superelliptic_drw_test
 ]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add sage/superelliptic_drw/superelliptic_witt.sage sage/superelliptic_drw/superelliptic_drw_cech.sage sage/superelliptic_drw/superelliptic_drw_
 superelliptic_drw_cech.sage  superelliptic_drw_form.sage  superelliptic_drw_tests/     
 ]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add sage/superelliptic_drw/superelliptic_witt.sage sage/superelliptic_drw/superelliptic_drw_cech.sage sage/superelliptic_drw/superelliptic_drw_form.sage sage/superelliptic_drw/de_rham_witt_lift.sage sage/superelliptic_drw/automorphism.sage 
-]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ g
\ No newline at end of file
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git addd  -u
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m "superelliptic drw podzielone na wiecej pilikow"
+[master ce0ac0d] superelliptic drw podzielone na wiecej plikow
+ 8 files changed, 442 insertions(+), 421 deletions(-)
+ create mode 100644 sage/superelliptic_drw/automorphism.sage
+ create mode 100644 sage/superelliptic_drw/de_rham_witt_lift.sage
+ delete mode 100644 sage/superelliptic_drw/superelliptic_drw.sage
+ create mode 100644 sage/superelliptic_drw/superelliptic_drw_cech.sage
+ create mode 100644 sage/superelliptic_drw/superelliptic_drw_form.sage
+ create mode 100644 sage/superelliptic_drw/superelliptic_witt.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: 31, done.
+Counting objects:   3% (1/31)
Counting objects:   6% (2/31)
Counting objects:   9% (3/31)
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Counting objects: 100% (31/31)
Counting objects: 100% (31/31), done.
+Delta compression using up to 4 threads
+Compressing objects:   4% (1/24)
Compressing objects:   8% (2/24)
Compressing objects:  12% (3/24)
Compressing objects:  16% (4/24)
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Compressing objects: 100% (24/24)
Compressing objects: 100% (24/24), done.
+Writing objects:   4% (1/24)
Writing objects:   8% (2/24)
Writing objects:  12% (3/24)
Writing objects:  16% (4/24)
Writing objects:  20% (5/24)
Writing objects:  25% (6/24)
Writing objects:  29% (7/24)
Writing objects:  33% (8/24)
Writing objects:  37% (9/24)
Writing objects:  41% (10/24)
Writing objects:  45% (11/24)
Writing objects:  54% (13/24)
Writing objects:  58% (14/24)
Writing objects:  62% (15/24)
Writing objects:  66% (16/24)
Writing objects:  70% (17/24)
Writing objects:  75% (18/24)
Writing objects:  79% (19/24)
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Writing objects:  87% (21/24)
Writing objects:  91% (22/24)
Writing objects:  95% (23/24)
Writing objects: 100% (24/24)
Writing objects: 100% (24/24), 11.54 KiB | 168.00 KiB/s, done.
+Total 24 (delta 17), reused 0 (delta 0)
+remote: . Processing 1 references
+remote: Processed 1 references in total
+To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
+   cc45757..ce0ac0d  master -> master
+]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[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux

+[?7h[?12l[?25h[?2004l[?7hV(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aux.omega

+[?7h[?12l[?25h[?2004l'[?7h((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8((2*C.one/(C.x^2 + C.x))*C.y)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?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[?7lomea0_omega8((C.x)(-2)*C.dx)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega0_omega8((C.x)^(-2)*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[?7la)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)

+[?7h[?12l[?25h[?2004l[?7h(((-x^8 + x^6 - 1)/y) dx, ((-x^8 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[?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[?7lload('superelliptic_drw/de_rham_witt_lift.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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_omega0_omega8(aux.omega)[?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[?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[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1] == aux.omega

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1] == aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l decomposition_omega0_omega8(aux.omega)[1] = aux.omega[?7h[?12l[?25h[?25l[?7l+ decomposition_omega0_omega8(aux.omega)[1] = aux.omega[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: decomposition_omega0_omega8(aux.omega)[0] + decomposition_omega0_omega8(aux.omega)[1] == aux.omega

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] + decomposition_omega0_omega8(aux.omega)[1] == aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l aux.omega[?7h[?12l[?25h[?25l[?7l aux.omega[?7h[?12l[?25h[?25l[?7l- aux.omega[?7h[?12l[?25h[?25l[?7l aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: decomposition_omega0_omega8(aux.omega)[0] + decomposition_omega0_omega8(aux.omega)[1] -  aux.omega

+[?7h[?12l[?25h[?2004l[?7h((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] + decomposition_omega0_omega8(aux.omega)[1] -  aux.omega[?7h[?12l[?25h[?25l[?7l==[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l aux.omega[?7h[?12l[?25h[?25l[?7l aux.omega[?7h[?12l[?25h[?25l[?7l[]aux.omega[?7h[?12l[?25h[?25l[?7l[]- aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]- aux.omega

+[?7h[?12l[?25h[?2004l[?7h0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]- aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[] aux.omega[?7h[?12l[?25h[?25l[?7l[]= aux.omega[?7h[?12l[?25h[?25l[?7l= aux.omega[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom3.reduce()[?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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[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[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?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[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]).reduce().form

+[?7h[?12l[?25h[?2004l[?7h(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]).reduce().form[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.omega[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?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[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux.omega.reduce().form

+[?7h[?12l[?25h[?2004l[?7h(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?2004h[?25l[?7lsage: [?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[?7laux.omega.reduce().form[?7h[?12l[?25h[?25l[?7l(decposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]).reduce().form[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7l(decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]).reduce().form[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega

+[?7h[?12l[?25h[?2004l[?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[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega

+[?7h[?12l[?25h[?2004l[?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[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega

+[?7h[?12l[?25h[?2004l(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y) (-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
+[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecompsition_mega0_omega8(ux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecmposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecompositin_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1][?7h[?12l[?25h[?25l[?7lecomposition_omega0_omega8(aux.omega)[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[?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[?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: decomposition_omega0_omega8(aux.omega)[1].expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t^4 + 2*t^8 + t^12 + O(t^14)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[1].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[?7l0][?7h[?12l[?25h[?25l[?7l] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7l[] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega

+[?7h[?12l[?25h[?2004l(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y) (-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
+[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1]== aux.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: decomposition_omega0_omega8(aux.omega)[0]

+[?7h[?12l[?25h[?2004l[?7h((-x^8 + x^6 - 1)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.omega.reduce().form[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux

+[?7h[?12l[?25h[?2004l[?7hV((((2*x^18 + 2*x^16 + 2*x^14 + 2*x^10 + 2*x^8 + 2*x^4 + 2*x^2 + 2)/(x^13 + x^11 + x^9))*y) dx) + dV([((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.omega.reduce().form[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: aux.h2

+[?7h[?12l[?25h[?2004l[?7h((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(aux.omega)[0][?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lsage: decomposition

+ decomposition                 decomposition_g0_g8_pth_power

+ decomposition_g0_g8           decomposition_omega0_omega8  

+

+

+ [?7h[?12l[?25h[?25l[?7l_omega0_omega8(aux.omega)[0][?7h[?12l[?25h[?25l[?7l

+ decomposition                

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l_g0_g8

+ decomposition                

+ decomposition_g0_g8          [?7h[?12l[?25h[?25l[?7l((2*C.one/(C.x^2 + C.x))*C.y)

+

+

+[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(aux.h2)

+[?7h[?12l[?25h[?2004l[?7h((x^4 + x^2 + 1)*y, ((x^4 + x^2 + 1)/x^6)*y, 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[?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[?7ldecomposition_g0_g8(aux.h2)[?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[?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[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(aux.h2)[0] - decomposition_g0_g8(aux.h2)[1] == aux.h2

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[0] - decomposition_g0_g8(aux.h2)[1] == aux.h2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7l[]decomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7l[decomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7l()decomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7l(decomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h2)[1][?7h[?12l[?25h[?25l[?7lecomposition_g0_g8(aux.h2)[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[?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[?7l[?7h[?12l[?25h[?25l[?7l[?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: decomposition_g0_g8(aux.h2)[1].expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht + t^5 + 2*t^9 + t^13 + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.h2[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega.reduce().form[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: aux.omega

+[?7h[?12l[?25h[?2004l[?7h(((2*x^18 + 2*x^16 + 2*x^14 + 2*x^10 + 2*x^8 + 2*x^4 + 2*x^2 + 2)/(x^13 + x^11 + x^9))*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[?7la[?7h[?12l[?25h[?25l[?7ld[?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[?7lsage: load('super

+ super                  superelliptic_cech     superelliptic_drw_form superelliptic_witt    

+ superelliptic          superelliptic_drw/     superelliptic_form     supersingular_D       

+ superelliptic/         superelliptic_drw_cech superelliptic_function supersingular_j       

+

+ [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

+ super                 

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7lelliptic

+ super                 

+ superelliptic         [?7h[?12l[?25h[?25l[?7l/

+

+ superelliptic         

+ superelliptic/        [?7h[?12l[?25h[?25l[?7l_cech

+ superelliptic_cech    

+

+ superelliptic/        [?7h[?12l[?25h[?25l[?7ldrw/

+ superelliptic_cech    

+ superelliptic_drw/    [?7h[?12l[?25h[?25l[?7l_cech

+

+ superelliptic_drw/    

+ superelliptic_drw_cech[?7h[?12l[?25h[?25l[?7l/

+

+ superelliptic_drw/    

+ superelliptic_drw_cech[?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[?7l

+ sup…rw/automorphism.sage             sup…rw/second_patch.sage             sup…rw/superelliptic_drw_tests/     

+ sup…rw/de_rham_witt_lift.sage        sup…rw/superelliptic_drw_cech.sage   sup…rw/superelliptic_witt.sage      

+ sup…rw/decomposition_into_g0_g8.sage sup…rw/superelliptic_drw_form.sage                                       [?7h[?12l[?25h[?25l[?7lautomorphism.sage

+ sup…rw/automorphism.sage            

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7lsecnd_atch

+ sup…rw/automorphism.sage             sup…rw/second_patch.sage            [?7h[?12l[?25h[?25l[?7luperelliptic_drw_tests/

+ sup…rw/second_patch.sage             sup…rw/superelliptic_drw_tests/     [?7h[?12l[?25h[?25l[?7l

+

+

+

+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7le[?7h[?12l[?25h[?25l[?7lsts/[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_into_g0_g8_tests.sage[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')

+[?7h[?12l[?25h[?2004l(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y) (-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
+1
+True
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')

+[?7h[?12l[?25h[?2004l(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y) (-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)
+1
+True
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/tests/decomposition_into_g0_g8_tests.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[?7li[?7h[?12l[?25h[?25l[?7l(t.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.is_regular()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: eta2

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.is_regular()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta2.r()

+[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.omega[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lux.omega[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.r()

+[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.r()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.r()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?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: eta2 - aux

+[?7h[?12l[?25h[?2004l[?7h(V(((-x^8 + x^6 - 1)/y) dx), [0], V(((-x^8 + x^6 - 1)/y) dx))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2 - aux[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta2 - aux)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?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: (eta2 - aux).omega0.frobenius()

+[?7h[?12l[?25h[?2004l[?7h0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.is_regular()[?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[?7lx[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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 - x^6)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (x^8 - x^6).quo_rem(x^3 - x)

+[?7h[?12l[?25h[?2004l[?7h(x^5, 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^8 - x^6).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7leta2 - aux).omega0.frobenius()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?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[?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: (eta2 - aux).omega0.omega.cartier()

+[?7h[?12l[?25h[?2004l[?7h((-x^3)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-x^8 + x^6 - 1)/y) 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[?7lCx^8 + x^6 - 1)/y) dx[?7h[?12l[?25h[?25l[?7l.x^8 + x^6 - 1)/y) 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[?7lCx^6 - 1)/y) dx[?7h[?12l[?25h[?25l[?7l.x^6 - 1)/y) 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)/y) dx[?7h[?12l[?25h[?25l[?7lC)/y) dx[?7h[?12l[?25h[?25l[?7l.)/y) dx[?7h[?12l[?25h[?25l[?7lo)/y) dx[?7h[?12l[?25h[?25l[?7ln)/y) dx[?7h[?12l[?25h[?25l[?7le)/y) 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[?7lCy) dx[?7h[?12l[?25h[?25l[?7l/y) 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[?7ly) dx[?7h[?12l[?25h[?25l[?7l.y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l* dx[?7h[?12l[?25h[?25l[?7lC dx[?7h[?12l[?25h[?25l[?7l. dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldx[?7h[?12l[?25h[?25l[?7lsage: (-C.x^8 + C.x^6 - C.one)/C.y)*C.dx

+[?7h[?12l[?25h[?2004l  Input In [39]
+    (-C.x**Integer(8) + C.x**Integer(6) - C.one)/C.y)*C.dx
+                                                    ^
+SyntaxError: unmatched ')'
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-C.x^8 + C.x^6 - C.one)/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*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[?7lsage: (-C.x^8 + C.x^6 - C.one)/C.y*C.dx

+[?7h[?12l[?25h[?2004l[?7h((-x^8 + x^6 - 1)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-C.x^8 + C.x^6 - C.one)/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((-C.x^8 + C.x^6 - C.one)/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[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((-C.x^8 + C.x^6 - C.one)/C.y*C.dx).cartier()

+[?7h[?12l[?25h[?2004l[?7h((-x^3)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-C.x^8 + C.x^6 - C.one)/C.y*C.dx).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[?7lC.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x^6 - C.one)/C.y*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x^6 - C.one)/C.y*C.dx).cartier()

+[?7h[?12l[?25h[?2004l[?7h0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.r()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.reduce()

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2 - aux[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: eta2

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l - aux[?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: eta2 - aux

+[?7h[?12l[?25h[?2004l[?7h(V(((-x^8 + x^6 - 1)/y) dx), [0], V(((-x^8 + x^6 - 1)/y) dx))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2 - aux[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?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: eta2.omega0.cartier()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [47], in <cell line: 1>()
+----> 1 eta2.omega0.cartier()
+
+AttributeError: 'superelliptic_drw_form' object has no attribute 'cartier'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega0.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[?7locartier()[?7h[?12l[?25h[?25l[?7lmcartier()[?7h[?12l[?25h[?25l[?7lecartier()[?7h[?12l[?25h[?25l[?7lgcartier()[?7h[?12l[?25h[?25l[?7lacartier()[?7h[?12l[?25h[?25l[?7l.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[?7lsage: eta2.omega0.omega.cartier()

+[?7h[?12l[?25h[?2004l[?7h((-x^3 + x)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.reduce()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ltom(b[0]).coordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(eta2).coordinates()

+[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [49], in <cell line: 1>()
+----> 1 autom(eta2).coordinates()
+
+File <string>:63, in coordinates(self, basis)
+
+File <string>:81, in coordinates(self)
+
+File <string>:87, in coordinates(self)
+
+File <string>:87, in coordinates(self)
+
+    [... skipping similar frames: coordinates at line 87 (1097 times)]
+
+File <string>:87, in coordinates(self)
+
+File <string>:86, in coordinates(self)
+
+File <string>:5, in __init__(self, C, omega, fct)
+
+File <string>:28, in __sub__(self, other)
+
+File <string>:7, in __init__(self, C, g)
+
+File <string>:245, in reduction_form(C, g)
+
+File <string>:216, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:711, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
+    709                     x0, y0, self))
+    710 try:
+--> 711     return self._element_class(self, x, y, coerce=coerce)
+    712 except TypeError:
+    713     if parent(x) is parent(x0):
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:115, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
+    113 if coerce:
+    114     self.__numerator   = parent.ring()(numerator)
+--> 115     self.__denominator = parent.ring()(denominator)
+    116 else:
+    117     self.__numerator   = numerator
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:506, in FractionField_generic.ring(self)
+    503     s = 'FieldOfFractions(%s)' % self.ring()._magma_init_(magma)
+    504     return magma._with_names(s, self.variable_names())
+--> 506 def ring(self):
+    507     """
+    508     Return the ring that this is the fraction field of.
+    509 
+   (...)
+    516         Multivariate Polynomial Ring in x, y over Rational Field
+    517     """
+    518     return self._R
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(eta2).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(eta2).coordinates()

+[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+File <string>:59, in __mul__(self, other)
+
+File <string>:226, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+   1002 try:
+-> 1003     return self(str(element))
+   1004 except TypeError:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:991, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+    990         element = element.replace("^","**")
+--> 991         element = eval(element, d, {})
+    992 except (SyntaxError, NameError):
+
+File <string>:1, in <module>
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+
+During handling of the above exception, another exception occurred:
+
+AttributeError                            Traceback (most recent call last)
+Input In [50], in <cell line: 1>()
+----> 1 autom(eta2).coordinates()
+
+File <string>:23, in autom(self)
+
+File <string>:6, in __init__(self, omega0, f)
+
+File <string>:90, in diffn(self, dy_w)
+
+File <string>:99, in diffn(self, dy_w)
+
+File <string>:84, in __add__(self, other)
+
+File <string>:31, in __add__(self, other)
+
+File <string>:63, in __mul__(self, other)
+
+AttributeError: 'superelliptic_function' object has no attribute 'form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(eta2).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[?7lsage: autom(eta2)

+[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
+    379 try:
+--> 380     z = integer_ring.Z(value)
+    381 except (TypeError, ValueError):
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
+    286 cdef Map m
+--> 287 cdef Element e = method(C)
+    288 if e is None:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:832, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
+    831 self.reduce()
+--> 832 num = R(self.__numerator)
+    833 inv_den = R(self.__denominator).inverse_of_unit()
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
+   1691 for f in self.__list:
+-> 1692     x = f._call_(x)
+   1693 return x
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:1677, in sage.categories.map.FormalCompositeMap._call_()
+   1676 
+-> 1677     cpdef Element _call_(self, x):
+   1678         """
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
+   1691 for f in self.__list:
+-> 1692     x = f._call_(x)
+   1693 return x
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1619 
+-> 1620     cpdef Element _call_(self, _x):
+   1621         """
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1652, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_()
+   1651 if nmod_poly_degree(x._denom) != 0:
+-> 1652     raise ValueError("not integral")
+   1653 if nmod_poly_degree(x._numer) > 0:
+
+ValueError: not integral
+
+During handling of the above exception, another exception occurred:
+
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [51], in <cell line: 1>()
+----> 1 autom(eta2)
+
+File <string>:23, in autom(self)
+
+File <string>:19, in autom(self)
+
+File <string>:13, in autom(self)
+
+File <string>:7, in __init__(self, C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    636 ring_one = self.ring().one()
+    637 try:
+--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
+    639 except (TypeError, ValueError):
+    640     pass
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
+    112 FieldElement.__init__(self, parent)
+    113 if coerce:
+--> 114     self.__numerator   = parent.ring()(numerator)
+    115     self.__denominator = parent.ring()(denominator)
+    116 else:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+   1007 try:
+   1008     # now try calling the base ring's __call__ methods
+-> 1009     element = self.base_ring()(element)
+   1010     _p = p_NSet(sa2si(element,_ring), _ring)
+   1011     return new_MP(self,_p)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
+   1143 """
+   1144 TESTS::
+   1145 
+   (...)
+   1182     True
+   1183 """
+   1184 try:
+-> 1185     return integer_mod.IntegerMod(self, x)
+   1186 except (NotImplementedError, PariError):
+   1187     raise TypeError("error coercing to finite field")
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
+    199         return a
+    200 t = modulus.element_class()
+--> 201 return t(parent, value)
+    202 
+    203 
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:388, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
+    386     value = py_scalar_to_element(value)
+    387 if isinstance(value, Element) and value.parent().is_exact():
+--> 388     value = sage.rings.rational_field.QQ(value)
+    389     z = value % self.__modulus.sageInteger
+    390 else:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
+    536     """
+    537     if x is not None:
+--> 538         self.__set_value(x, base)
+    539 
+    540 def __reduce__(self):
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
+    624 
+    625         elif hasattr(x, "_rational_"):
+--> 626             set_from_Rational(self, x._rational_())
+    627 
+    628         elif isinstance(x, tuple) and len(x) == 2:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:784, in sage.rings.fraction_field_element.FractionFieldElement._rational_()
+    782         1/2
+    783     """
+--> 784     return self._conversion(QQ)
+    785 
+    786 def _conversion(self, R):
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:832, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
+    830 else:
+    831     self.reduce()
+--> 832     num = R(self.__numerator)
+    833     inv_den = R(self.__denominator).inverse_of_unit()
+    834     return num * inv_den
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
+    536     """
+    537     if x is not None:
+--> 538         self.__set_value(x, base)
+    539 
+    540 def __reduce__(self):
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value()
+    624 
+    625         elif hasattr(x, "_rational_"):
+--> 626             set_from_Rational(self, x._rational_())
+    627 
+    628         elif isinstance(x, tuple) and len(x) == 2:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1446, in sage.rings.polynomial.polynomial_element.Polynomial._rational_()
+   1444         TypeError: not a constant polynomial
+   1445     """
+-> 1446     return self._scalar_conversion(sage.rings.rational.Rational)
+   1447 
+   1448 def _symbolic_(self, R):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1391, in sage.rings.polynomial.polynomial_element.Polynomial._scalar_conversion()
+   1389     if self.degree() > 0:
+   1390         raise TypeError("cannot convert nonconstant polynomial")
+-> 1391     return R(self.get_coeff_c(0))
+   1392 
+   1393 _real_double_ = _scalar_conversion
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__()
+    536     """
+    537     if x is not None:
+--> 538         self.__set_value(x, base)
+    539 
+    540 def __reduce__(self):
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:691, in sage.rings.rational.Rational.__set_value()
+    689 
+    690         else:
+--> 691             raise TypeError("unable to convert {!r} to a rational".format(x))
+    692 
+    693     cdef void set_from_mpq(Rational self, mpq_t value):
+
+File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
+    192 except AttributeError:
+    193     return super().__repr__()
+--> 194 result = reprfunc()
+    195 if isinstance(result, str):
+    196     return result
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:340, in sage.rings.fraction_field_FpT.FpTElement._repr_()
+    338     return repr(self.numer())
+    339 else:
+--> 340     numer_s = repr(self.numer())
+    341     denom_s = repr(self.denom())
+    342     if '-' in numer_s or '+' in numer_s:
+
+File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
+    192 except AttributeError:
+    193     return super().__repr__()
+--> 194 result = reprfunc()
+    195 if isinstance(result, str):
+    196     return result
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
+   2688         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
+   2689     """
+-> 2690     return self._repr()
+   2691 
+   2692 def _latex_(self, name=None):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
+   2654 if n != m-1:
+   2655     s += " + "
+-> 2656 x = y = repr(x)
+   2657 if y.find("-") == 0:
+   2658     y = y[1:]
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega0.omega.cartier()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: eta2

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 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[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: load('sa

+ sage          sage_eval     sage_mode     sample        save_session 

+ sage0         sage_globals  sage_wraps    sandpiles                  

+ sage0_version sage_input    sageobj       save                       

+

+ [?7h[?12l[?25h[?25l[?7l

+

+

+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ler

+ super                  superelliptic_cech     superelliptic_drw_form superelliptic_witt    

+ superelliptic          superelliptic_drw/     superelliptic_form     supersingular_D       

+ superelliptic/         superelliptic_drw_cech superelliptic_function supersingular_j       [?7h[?12l[?25h[?25l[?7lelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')[?7h[?12l[?25h[?25l[?7l

+ super                 

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7lelliptic

+ super                 

+ superelliptic         [?7h[?12l[?25h[?25l[?7l_drw/

+

+ superelliptic          superelliptic_drw/    [?7h[?12l[?25h[?25l[?7la

+

+

+

+[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ltomorphism.sage[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/automorphism.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+

+ [?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/automorphism.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(eta2)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom(eta2)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(eta2)

+[?7h[?12l[?25h[?2004l([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])) drw cech
+[(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]) drw form
+((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx form
+(1/(x^2 + 2))*y function
+(1/(x^2 + 2))*y function
+[2/x*y] witt
+2/x*y function
+0 function
+[?7h([(1/(x^2 + 2*x))*y] d[x] + V(((-x^10 - x^7 - x^4 - x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(x/(x^2 + x + 1))*y]), [(2/(x + 1))*y], [(2/(x^4 + x^3 + 2*x^2 + 2*x))*y] d[x] + V(((-x^14 - x^13 + x^11 + x^10 - x^7 + x^6 + x^4 + x^2 - x)/(x^6*y - x^5*y - x^4*y - x^3*y - x^2*y - x*y + y)) dx) + dV([((2*x^4 + 2*x^3 + 2*x^2 + x)/(x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(eta2)[?7h[?12l[?25h[?25l[?7l().coordinates()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(eta2).coordinates()

+[?7h[?12l[?25h[?2004l([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])) drw cech
+[(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]) drw form
+((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx form
+(1/(x^2 + 2))*y function
+(1/(x^2 + 2))*y function
+[2/x*y] witt
+2/x*y function
+0 function
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [55], in <cell line: 1>()
+----> 1 autom(eta2).coordinates()
+
+File <string>:63, in coordinates(self, basis)
+
+File <string>:81, in coordinates(self)
+
+File <string>:87, in coordinates(self)
+
+File <string>:87, in coordinates(self)
+
+    [... skipping similar frames: coordinates at line 87 (64 times)]
+
+File <string>:87, in coordinates(self)
+
+File <string>:52, in coordinates(self)
+
+File <string>:102, in degrees_de_rham0(self)
+
+File <string>:80, in basis_de_rham_degrees(self)
+
+File <string>:5, in __init__(self, C, omega, fct)
+
+File <string>:95, in diffn(self)
+
+File <string>:7, in __init__(self, C, g)
+
+File <string>:245, in reduction_form(C, g)
+
+File <string>:222, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:632, in PolynomialRing(base_ring, *args, **kwds)
+    629     except KeyError:
+    630         raise TypeError("you must specify the names of the variables")
+--> 632 names = normalize_names(n, names)
+    634 # At this point, we have only handled the "names" keyword if it was
+    635 # needed. Since we know the variable names, it would logically be
+    636 # an error to specify an additional "names" keyword. However,
+   (...)
+    639 # and we allow this for historical reasons. However, the names
+    640 # must be consistent!
+    641 if "names" in kwds:
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(eta2).coordinates()[?7h[?12l[?25h[?25l[?7l = C.de_rham_bass()[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = autom(eta1)

+[?7h[?12l[?25h[?2004l([(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])) drw cech
+[(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]) drw form
+((-x^5 + x^3 + x)/(x^2*y - y)) dx form
+(x/(x^2 + 2))*y function
+(1/(x^3 + 2*x))*y function
+V(1/x*y) witt
+0 function
+1/x*y function
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = autom(eta1)[?7h[?12l[?25h[?25l[?7l.coordinates([?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates()[?7h[?12l[?25h[?25l[?7lsage: a.coordinates()

+[?7h[?12l[?25h[?2004l(1, 0)
+omega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+aux before reduce (V(((-x^5 - x^4 - x^3 - x^2 - x + 1)/(x^2*y + x*y + y)) dx) + dV([(2/(x^2 + x + 1))*y]), V((2/(x^2 + x))*y), V(((-x^5 - x^4 - x^3 - x^2 - x + 1)/(x^2*y + x*y + y)) dx) + dV([(1/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
+aux V(smth) (V(((-x^5 - x^4 - x^3 - x^2 - x + 1)/(x^2*y + x*y + y)) dx) + dV([(2/(x^2 + x + 1))*y]), V((2/(x^2 + x))*y), V(((-x^5 - x^4 - x^3 - x^2 - x + 1)/(x^2*y + x*y + y)) dx) + dV([(1/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [57], in <cell line: 1>()
+----> 1 a.coordinates()
+
+File <string>:75, in coordinates(self, basis)
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 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[?7llimit = 10[?7h[?12l[?25h[?25l[?7load('superelliptic_drw/automorphism.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('superelliptic_drw/automorphism.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/automorphism.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/automorphism.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'superelliptic_drw/automorphism.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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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$ qui]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[?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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lell = [89, 983, 839, 43, 31, 167, 103, 40829, 653, 11969][?7h[?12l[?25h[?25l[?7lta2[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l - aux[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lsage: eta2 - aux

+[?7h[?12l[?25h[?2004l[?7h(V(((-x^8 + x^6 - 1)/y) dx), [0], V(((-x^8 + x^6 - 1)/y) dx))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2 - aux[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta2 - aux)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).omega0.omega.cartier()[?7h[?12l[?25h[?25l[?7l().omega0.omega.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[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().omega0.omega.cartier()[?7h[?12l[?25h[?25l[?7lomega0.omega.cartier()[?7h[?12l[?25h[?25l[?7lsage: (eta2 - aux).omega0.omega.cartier()

+[?7h[?12l[?25h[?2004l[?7h((-x^3)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2 - aux[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lta2 - aux[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1.is_regular()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta1.r()

+[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1.r()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2 - aux[?7h[?12l[?25h[?25l[?7l.omega0.omega.cartier()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta2.r()

+[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[1]

+[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(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[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [7], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:22, in <module>
+
+File <string>:29, in de_rham_witt_lift(cech_class, prec)
+
+File <string>:74, in __sub__(self, other)
+
+File <string>:81, in __add__(self, other)
+
+AttributeError: 'superelliptic_form' object has no attribute 'h1'
+[?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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) V(((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx)
+([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
+ 
+ V(((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx)
+([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
+ 
+ [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
+ 
+
+([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
+ 
+ [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
+ 
+
+dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.coordinates()[?7h[?12l[?25h[?25l[?7lutm(eta2).coordinates()[?7h[?12l[?25h[?25l[?7lx.reduce()[?7h[?12l[?25h[?25l[?7lsage: aux

+[?7h[?12l[?25h[?2004l[?7hdV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.reduce()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.frobenius(*)

+[?7h[?12l[?25h[?2004l  Input In [13]
+    aux.frobenius(*)
+                   ^
+SyntaxError: invalid syntax
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.frobenius(*)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: aux.frobenius()

+[?7h[?12l[?25h[?2004l[?7h((-x^6 + x^4 + x^2 - 1)/(x^6*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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
+ 
+ [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
+ 
+ 0 
+ 
+
+dV([((2*x^4 + 2*x^2 + 2)/x^6)*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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.frobenius()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux

+[?7h[?12l[?25h[?2004l[?7h((x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2)/x^6)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.frobenius()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldelta = f.discriminant()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_g8(aux.h2)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_g8(aux.h2)[1].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[?7lsage: decomposition_g0_g8(aux)

+[?7h[?12l[?25h[?2004l[?7h((x^4 + x^2 + 1)*y, ((x^4 + x^2 + 1)/x^6)*y, 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux)[?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[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: decomposition_g0_g8(aux)[1].expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht + t^5 + 2*t^9 + t^13 + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
+ 
+ [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
+ 
+ 0 
+ 
+
+dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
+ 
+ [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
+ 
+ 0 
+ 
+
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.coordinates()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux

+[?7h[?12l[?25h[?2004l[?7h[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.r()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega0.omega.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?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: eta2.omega8 - aux

+[?7h[?12l[?25h[?2004l[?7hV(((-x^8 + x^6 - 1)/y) dx) + dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8 - aux[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta2.omega8 - aux)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?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: (eta2.omega8 - aux).frobenius()

+[?7h[?12l[?25h[?2004l[?7h((-x^6 + x^4 + x^2 - 1)/(x^6*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta2.omega8 - aux).frobenius()[?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: (eta2.omega8 - aux).frobenius().expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2 + 2*t^4 + t^8 + O(t^10)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?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: aux.frobenius()

+[?7h[?12l[?25h[?2004l[?7h((-x^2 + 1)/(x^6*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.frobenius()[?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[?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: aux.frobenius().expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t^8 + 2*t^16 + O(t^18)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux

+[?7h[?12l[?25h[?2004l[?7h[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lreduce()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.r()

+[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta2.omega8 - aux).frobenius().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[?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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
+ 
+ [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
+ 
+ 0 
+ 
+
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc = C.de_rham_basis()[?7h[?12l[?25h[?25l[?7lonvert_superfct_into_AS(a.f)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: compare

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [32], in <cell line: 1>()
+----> 1 compare
+
+NameError: name 'compare' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8 - aux[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: eta2

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta.omega8[?7h[?12l[?25h[?25l[?7leta.omega8[?7h[?12l[?25h[?25l[?7lsage: eta.omega8

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [34], in <cell line: 1>()
+----> 1 eta.omega8
+
+AttributeError: 'function' object has no attribute 'omega8'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta.omega8[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.omega8 - aux[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: eta2.omega8

+[?7h[?12l[?25h[?2004l[?7h[(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?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: eta2.omega8.frobenius()

+[?7h[?12l[?25h[?2004l[?7h((-x^2 + 1)/(x^2*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8.frobenius()[?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: eta2.omega8.frobenius().expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2 + 2*t^4 + O(t^10)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7limit = 10[?7h[?12l[?25h[?25l[?7lft_form_to_drw(a)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?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[?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[?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()()[?7h[?12l[?25h[?25l[?7l([?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: lift2.omega8.frobenius().expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2 + 2*t^4 + O(t^10)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l - aux[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta2.r()

+[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.r()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: eta2

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta2.omega8 - aux).frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7lsage: (lift2 - eta2)

+[?7h[?12l[?25h[?2004l[?7h(V(((x^8 - x^6 + 1)/y) dx), [0], V(((x^8 - x^6 + 1)/y) dx))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(lift2 - eta2)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?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: (lift2 - eta2).omega8.frobenius()

+[?7h[?12l[?25h[?2004l[?7h0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(lift2 - eta2).omega8.frobenius()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(lift2 - eta2)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l().omega8.frobenius()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: (lift2 - eta2).omega

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [43], in <cell line: 1>()
+----> 1 (lift2 - eta2).omega
+
+AttributeError: 'superelliptic_drw_cech' object has no attribute 'omega'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(lift2 - eta2).omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: (lift2 - eta2).omega0.omega

+[?7h[?12l[?25h[?2004l[?7h((x^8 - x^6 + 1)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[1;3S[?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[?7llift2.omega8.frobenius().expansion_at_infty()[?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[?2004lfomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
+ 
+ [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
+ 
+ 0 
+ 
+
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lfor i in range(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[?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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
+ 
+ [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
+ 
+ 0 
+ 
+
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.teichmuller.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lteichmuller().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[?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[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.teichmuller()*C.y.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis[1][?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[1]

+[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l9[?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[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7leC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lcC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7loC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lnC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7ldC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7l_C.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lpC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7laC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7ltC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lcC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lhC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7l(C.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: second_patch(C.de_rham_basis()[1].omega8)

+[?7h[?12l[?25h[?2004l[?7h(x/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.de_rham_basis()[1].omega8)[?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_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?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: second_patch(C.y)

+[?7h[?12l[?25h[?2004l[?7h1/x^2*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.y)[?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[?7lprint(lista_l)[?7h[?12l[?25h[?25l[?7latchC).crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: patch(C)

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = 2*x^3 + x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l.C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7lxC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7ltC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7leC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7liC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7lcC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7lhC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7lmC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7luC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7llC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7llC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7leC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7lrC.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l(C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l()C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l() C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l()*C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x.teichmuler()*C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^.teichmuler()*C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l3.teichmuler()*C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l(3).teichmuler()*C.y.teichmuler.difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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^3).teichmuller()*C.y.teichmuller.diffn()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [8], in <cell line: 1>()
+----> 1 -(C.x**Integer(3)).teichmuller()*C.y.teichmuller.diffn()
+
+AttributeError: 'function' object has no attribute 'diffn'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-(C.x^3).teichmuller()*C.y.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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(.difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: -(C.x^3).teichmuller()*C.y.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7h[(2*x^2/(x^2 + 2))*y] d[x] + V(((x^16 - x^12 - x^10)/(x^2*y - y)) dx) + dV([(2*x^12/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-(C.x^3).teichmuller()*C.y.teichmuller().diffn()[?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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?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[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?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[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ltdifn()[?7h[?12l[?25h[?25l[?7ledifn()[?7h[?12l[?25h[?25l[?7lidifn()[?7h[?12l[?25h[?25l[?7lcdifn()[?7h[?12l[?25h[?25l[?7lhdifn()[?7h[?12l[?25h[?25l[?7lmdifn()[?7h[?12l[?25h[?25l[?7ludifn()[?7h[?12l[?25h[?25l[?7lldifn()[?7h[?12l[?25h[?25l[?7lldifn()[?7h[?12l[?25h[?25l[?7ledifn()[?7h[?12l[?25h[?25l[?7lrdifn()[?7h[?12l[?25h[?25l[?7l(difn()[?7h[?12l[?25h[?25l[?7l()difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: -(C.x^3).teichmuller()*C.y.teichmuller().diffn() + 2*C.y.teichmuller()*(C.x^(-4)).teichmuller()*C.x.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7h[((2*x^6 + 2*x^2 + 1)/(x^6 + 2*x^4))*y] d[x] + V(((x^24 - x^20 - x^18 + x^14 - x^12 + x^10 + x^8 - x^6 - 1)/(x^10*y - x^8*y)) dx) + dV([(2*x^12/(x^2 + 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[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift2.omega8.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lf[?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[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: lift == omega8_lift

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift == omega8_lift[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l omega8_lift[?7h[?12l[?25h[?25l[?7l omega8_lift[?7h[?12l[?25h[?25l[?7l- omega8_lift[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: lift - omega8_lift

+[?7h[?12l[?25h[?2004l[?7h[((x^4 + x^2 + 1)/x^4)*y] d[x] + V(((-x^22 - x^20 + x^16 + x^14 + x^12 - x^10 - x^8 - x^6 - x^4 - x^2 + 1)/(x^8*y)) dx) + dV([((x^16 + x^14 + x^12 + x^10 + x^8 + x^6 + x^4 + x^2 + 1)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift - omega8_lift[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: lift.r()

+[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom3.reduce()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le3[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift([?7h[?12l[?25h[?25l[?7l_lift([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega8_lift.r()

+[?7h[?12l[?25h[?2004l[?7h((-x^6 - x^2 + 1)/(x^3*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift.r()[?7h[?12l[?25h[?25l[?7load('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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+omega8_lift.r() ((-1)/(x*y)) dx
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift.r()[?7h[?12l[?25h[?25l[?7lft.r()[?7h[?12l[?25h[?25l[?7lsage: lift.r()

+[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift.r()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lega8_lift.r()[?7h[?12l[?25h[?25l[?7lga8_lift.r()[?7h[?12l[?25h[?25l[?7lsage: omega8_lift.r()

+[?7h[?12l[?25h[?2004l[?7h((-x^6 - x^2 + 1)/(x^3*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift.r()[?7h[?12l[?25h[?25l[?7load('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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+omega8_lift.r() ((-1)/(x*y)) dx
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift.r()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0.r()

+[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0.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[?7lomega8_lift[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0 - omega8_lift

+[?7h[?12l[?25h[?2004l[?7h[((x^4 + x^2 + 1)/x^4)*y] d[x] + V(((-x^22 - x^20 + x^16 + x^14 + x^12 - x^10 - x^8 - x^6 - x^4 - x^2 + 1)/(x^8*y)) dx) + dV([((x^16 + x^14 + x^12 + x^10 + x^8 + x^6 + x^4 + x^2 + 1)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-(C.x^3).teichmuller()*C.y.teichmuller().diffn() + 2*C.y.teichmuller()*(C.x^(-4)).teichmuller()*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[?7l)[?7h[?12l[?25h[?25l[?7l(.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7ldifn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?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.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.x.difn()[?7h[?12l[?25h[?25l[?7l()*C.x.difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7ldifn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l()*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7lsage: -(C.x^3)*C.y.diffn() + 2*C.y*(C.x^(-4))*C.x.diffn()

+[?7h[?12l[?25h[?2004l[?7h((-x^6 - x^2 + 1)/(x^3*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-(C.x^3)*C.y.diffn() + 2*C.y*(C.x^(-4))*C.x.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(3)*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l-3)*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())*C.y.difn() + 2*C.y*(C.x^(-4)*C.x.difn()[?7h[?12l[?25h[?25l[?7lsage: -(C.x^(-3))*C.y.diffn() + 2*C.y*(C.x^(-4))*C.x.diffn()

+[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-(C.x^(-3))*C.y.diffn() + 2*C.y*(C.x^(-4))*C.x.diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+omega8_lift.r() ((-1)/(x*y)) dx
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0 - omega8_lift[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lga8_lift0 - omega8_lift[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0 - omega8_lift

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly.teichmuller.diffn().frobenius() == (C.y)^2 * C.y.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l().frobenius() == (C.y)^2 * C.y.diffn()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn().r()

+[?7h[?12l[?25h[?2004l[?7h(1/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn().r()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius() == (C.y)^2 * C.y.diffn()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbenius() == (C.y)^2 * C.y.diffn()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lus() == (C.y)^2 * C.y.diffn()[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn().frobenius()

+[?7h[?12l[?25h[?2004l[?7h((x^3 - x)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn().frobenius()[?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[?7lC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l.C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lyC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l.C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7ltC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7leC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7liC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lcC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lhC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lmC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7luC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7llC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7llC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7leC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lrC.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l(C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l() C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2C.y.teichmuler() * C.y.teichmuler().difn() =[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler() * C.y.teichmuler().difn() =[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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(.teichmuler()[?7h[?12l[?25h[?25l[?7l().teichmuler()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC).teichmuler()[?7h[?12l[?25h[?25l[?7l,).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l/).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l.).teichmuler()[?7h[?12l[?25h[?25l[?7lx).teichmuler()[?7h[?12l[?25h[?25l[?7l^).teichmuler()[?7h[?12l[?25h[?25l[?7l3).teichmuler()[?7h[?12l[?25h[?25l[?7l ).teichmuler()[?7h[?12l[?25h[?25l[?7l-).teichmuler()[?7h[?12l[?25h[?25l[?7l ).teichmuler()[?7h[?12l[?25h[?25l[?7lC).teichmuler()[?7h[?12l[?25h[?25l[?7l.).teichmuler()[?7h[?12l[?25h[?25l[?7lx).teichmuler()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 2*C.y.teichmuller() * C.y.teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+True
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
+ 
+ [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
+ 
+ 0 
+ 
+
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn().frobenius()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift.r()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_form_to_drw(a)[?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[?7lomega8_lift0 - omega8_lift[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0

+[?7h[?12l[?25h[?2004l[?7h[2/x*y]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0[?7h[?12l[?25h[?25l[?7l.r()[?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: omega8_lift0.diffn()

+[?7h[?12l[?25h[?2004l[?7h[((x^2 + 1)/(x^4 + 2*x^2))*y] d[x] + V(((x^6 + 1)/(x^4*y - x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(lift2 - eta2).omega0.omega[?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[?7l2)[?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[?7l2*C.y.teichmuller() * C.y.teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l(C.y).teichmuller()* (C.y).teichmuller().diffn(dy_w = C.dy_w()) == (C.x^3 - C.x).teichmuller().diffn(dy_w = C.dy_w())[?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[?7l1[?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().*C.[?7h[?12l[?25h[?25l[?7lt*C.[?7h[?12l[?25h[?25l[?7le*C.[?7h[?12l[?25h[?25l[?7li*C.[?7h[?12l[?25h[?25l[?7lc*C.[?7h[?12l[?25h[?25l[?7lh*C.[?7h[?12l[?25h[?25l[?7lm*C.[?7h[?12l[?25h[?25l[?7lu*C.[?7h[?12l[?25h[?25l[?7ll*C.[?7h[?12l[?25h[?25l[?7ll*C.[?7h[?12l[?25h[?25l[?7le*C.[?7h[?12l[?25h[?25l[?7lt*C.[?7h[?12l[?25h[?25l[?7l(*C.[?7h[?12l[?25h[?25l[?7l()*C.[?7h[?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.[?7h[?12l[?25h[?25l[?7lr()*C.[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()).teichmuler()*C.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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)^(-1).teichmuler()*C.[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?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[?7h[?12l[?25h[?25l[?7l2[?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[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?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[?7lt)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ll)[?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[?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[?7ld[?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[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?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[?7lsage: 2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*(C.x.teichmuller())^(-2) * C.x.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [34], in <cell line: 1>()
+----> 1 Integer(2)*((C.x)**(-Integer(1))).teichmuller()*C.y.teichmuller().diffn() - Integer(2)*C.y.teichmuller()*(C.x.teichmuller())**(-Integer(2)) * C.x.teichmuller().diffn()
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:2195, in sage.rings.integer.Integer.__pow__()
+   2193         return coercion_model.bin_op(left, right, operator.pow)
+   2194     # left is a non-Element: do the powering with a Python int
+-> 2195     return left ** int(right)
+   2196 
+   2197 cpdef _pow_(self, other):
+
+TypeError: unsupported operand type(s) for ** or pow(): 'superelliptic_witt' and 'int'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*(C.x.teichmuller())^(-2) * 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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l() * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C.x.teichmuler() * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().teichmuler() * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^).teichmuler() * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()).teichmuller())* Cx.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l-)).teichmuler() * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l1)).teichmuler() * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: 2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7h[((x^3 + 2*x + 2)/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 - x^4 - x^3 - x^2 - x - 1)/(x*y)) dx) + dV([(2/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*((C.x^(-1)).teichmuller()) * 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[?7lomega8_lift0.diffn()[?7h[?12l[?25h[?25l[?7lsage: 2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn() == omega8_lift0.diffn()

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn() == omega8_lift0.diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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*(C.x)^(-1).teichmuler()*C.y.teichmuler().difn() - 2*C.y.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r()

+[?7h[?12l[?25h[?2004l[?7h((x^3 - x - 1)/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).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[?7lomega8_lift0.diffn()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0.diffn().r()

+[?7h[?12l[?25h[?2004l[?7h((x^2 + 1)/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0.diffn().r()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la8_lift0.diffn().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[?7lsage: omega8_lift0

+[?7h[?12l[?25h[?2004l[?7h[2/x*y]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0[?7h[?12l[?25h[?25l[?7l.diffn().r()[?7h[?12l[?25h[?25l[?7l(2*((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() - 2*C.y.teichmuller()*((C.x^(-1)).teichmuller()) * 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- 2*C.y.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn().r()[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)).teichmuler()*C.y.teichmuler().difn() - 2*C.y.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn().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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?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.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn().r()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn().r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn().r()[?7h[?12l[?25h[?25l[?7lC.y.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn().r()[?7h[?12l[?25h[?25l[?7l+C.y.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn().r()[?7h[?12l[?25h[?25l[?7l C.y.teichmuler()*(C.x^(-1).teichmuler() * C.x.teichmuler().difn().r()[?7h[?12l[?25h[?25l[?7lsage: (((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r()

+[?7h[?12l[?25h[?2004l[?7h((x^3 - x + 1)/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r()[?7h[?12l[?25h[?25l[?7lomega8_lift0[?7h[?12l[?25h[?25l[?7l.diffn().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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?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[?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: omega8_lift0.diffn().r() == (-C.y/C.x).diffn()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0.diffn().r() == (-C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l(((C.x)^(-1)).teichmuller()*C.yteichmuller().diffn() + C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l== (-C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lsage: (((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r() == (-C.y/C.x).diffn()

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r() == (-C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)).teichmuler() * C.x.teichmuler().difn().r() = (-C.y/C.x).difn()[?7h[?12l[?25h[?25l[?7l2)).teichmuler() * C.x.teichmuler().difn().r() = (-C.y/C.x).difn()[?7h[?12l[?25h[?25l[?7lsage: (((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-2)).teichmuller()) * C.x.teichmuller().diffn()).r() == (-C.y/C.x).diffn()

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-2)).teichmuller()) * C.x.teichmuller().diffn()).r() == (-C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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)^(-1).teichmuler()*C.y.teichmuler().difn() + C.y.teichmuler()*(C.x^(-2).teichmuler() * C.x.teichmuler().difn()).r() = (-C.y/C.x).difn()
[?7h[?12l[?25h[?25l[?7lsage: -(((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-2)).teichmuller()) * C.x.teichmuller().diffn()).r() == (-C.y/C.x).diffn()


+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-(((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-2)).teichmuller()) * C.x.teichmuller().diffn()).r() == (-C.y/C.x).diffn()
[?7h[?12l[?25h[?25l[?7l
([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-2)).teichmuller()) * C.x.teichmuller().diffn()).r()

+[?7h[?12l[?25h[?2004l[?7h((-x)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lsage: (-C.y/C.x).diffn()

+[?7h[?12l[?25h[?2004l[?7h((x^2 + 1)/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-C.y/C.x).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[?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[?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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?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[?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[?7l2[?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: (-C.y/C.x).diffn() == -(C.x)^(-1)*C.y.diffn() + C.y*(C.x)^(-2)*C.dx

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-(C.x)^(-1)*C.y.diffn() + C.y*(C.x)^(-2)*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().*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lt*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7le*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7li*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lc*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lh*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lm*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lu*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7ll*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7ll*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7le*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lr*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l(*C.y.difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l()*C.y.difn() + C.y*(C.x)^(-2)*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((C.x)^(-1).teichmuler()*C.y.difn() + C.y*(C.x)^(-2)*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(()).teichmuler()*C.y.difn() + C.y*(C.x)^(-2)*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[?7ltdifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7ledifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lidifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lcdifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lhdifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lmdifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7ludifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lldifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lldifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7ledifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lrdifn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l(difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l()difn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l().difn() + C.y*(C.x)^(-2)*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.*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lt*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7le*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7li*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lc*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lh*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lm*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lu*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7ll*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7ll*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7le*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lr*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l(*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l()*(C.x)^(-2)*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((C.x)^(-2)*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().*C.dx[?7h[?12l[?25h[?25l[?7lt*C.dx[?7h[?12l[?25h[?25l[?7le*C.dx[?7h[?12l[?25h[?25l[?7li*C.dx[?7h[?12l[?25h[?25l[?7lc*C.dx[?7h[?12l[?25h[?25l[?7lh*C.dx[?7h[?12l[?25h[?25l[?7lm*C.dx[?7h[?12l[?25h[?25l[?7lu*C.dx[?7h[?12l[?25h[?25l[?7ll*C.dx[?7h[?12l[?25h[?25l[?7ll*C.dx[?7h[?12l[?25h[?25l[?7le*C.dx[?7h[?12l[?25h[?25l[?7lr*C.dx[?7h[?12l[?25h[?25l[?7l(*C.dx[?7h[?12l[?25h[?25l[?7l()*C.dx[?7h[?12l[?25h[?25l[?7l(())*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[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?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()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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-(C.x)^(-1).teichmuler()*C.y.teichmuler().difn() + C.y.teichmuler()*(C.x)^(-2).teichmuler()*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l -(C.x)^(-1).teichmuler()*C.y.teichmuler().difn() + C.y.teichmuler()*(C.x)^(-2).teichmuler()*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l=-(C.x)^(-1).teichmuler()*C.y.teichmuler().difn() + C.y.teichmuler()*(C.x)^(-2).teichmuler()*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l -(C.x)^(-1).teichmuler()*C.y.teichmuler().difn() + C.y.teichmuler()*(C.x)^(-2).teichmuler()*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lsage: a = -((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x)^(-2).teichmuller())*C.x.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [48], in <cell line: 1>()
+----> 1 a = -((C.x)**(-Integer(1))).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x)**(-Integer(2)).teichmuller())*C.x.teichmuller().diffn()
+
+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 = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.integer.Integer' object has no attribute 'teichmuller'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = -((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x)^(-2).teichmuller())*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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()).teichmuler()*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l((C.x)^(-2).teichmuler()*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lsage: a = -((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*(((C.x)^(-2)).teichmuller())*C.x.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = -((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*(((C.x)^(-2)).teichmuller())*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-(C.x)^(-1)*C.y.diffn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lsage: a.r() == -(C.x)^(-1)*C.y.diffn() + C.y*(C.x)^(-2)*C.dx

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.r() == -(C.x)^(-1)*C.y.diffn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l = -((C.x)^(-1)).teichmuller()*C.y.teichmuller(.diffn() + C.y.teichmuller()*(((C.x)^(-2)).teichmuller())*C.x.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lC.x)^(-2).teichmuller())*C.xteichmuller().diffn()[?7h[?12l[?25h[?25l[?7l(-C.y/C.x).diffn() == -(C.x)^-1)*Cy.diffn() + Cy*(C.x^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-(((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-2)).teichmuller()) * C.x.teichmuller().diffn()).r()[?7h[?12l[?25h[?25l[?7l() == (-C.y/C.x).diffn()
[?7h[?12l[?25h[?25l[?7l
(C.x)^(-1).teichmuler()*C.y.teichmuler().difn() + C.y.teichmuler()*(C.x^(-2).teichmuler() * C.x.teichmuler().difn().r() = (-C.y/C.x).difn()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lomega8_lift0.diffn().r() == (-Cy/C.x).diffn()[?7h[?12l[?25h[?25l[?7l(((C.x)^(-1)).teichmuller()*C.yteichmuller().diffn() + C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r()[?7h[?12l[?25h[?25l[?7lomega8_lift0.diffn().r() == (-Cy/C.x).diffn()[?7h[?12l[?25h[?25l[?7l(((C.x)^(-1)).teichmuller()*C.yteichmuller().diffn() + C.y.teichmuller()*((C.x^(-1)).teichmuller()) * C.x.teichmuller().diffn()).r()[?7h[?12l[?25h[?25l[?7lomega8_lift0[?7h[?12l[?25h[?25l[?7l.diffn().r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - omega8_lift[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - omega8_lift[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0 - a

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [51], in <cell line: 1>()
+----> 1 omega8_lift0 - a
+
+File <string>:35, in __sub__(self, other)
+
+File <string>:29, in __add__(self, other)
+
+AttributeError: 'superelliptic_drw_form' object has no attribute 't'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0 - a[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0 - a[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0

+[?7h[?12l[?25h[?2004l[?7h[2/x*y]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0[?7h[?12l[?25h[?25l[?7l - a[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l. - a[?7h[?12l[?25h[?25l[?7ld - a[?7h[?12l[?25h[?25l[?7li - a[?7h[?12l[?25h[?25l[?7lf - a[?7h[?12l[?25h[?25l[?7lf - a[?7h[?12l[?25h[?25l[?7ln - a[?7h[?12l[?25h[?25l[?7l( - a[?7h[?12l[?25h[?25l[?7l() - a[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0.diffn() - a

+[?7h[?12l[?25h[?2004l[?7h0
+[?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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
+ 
+ [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
+ 
+ 0 
+ 
+
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcompare[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpare[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: compare

+[?7h[?12l[?25h[?2004l[?7h[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcompare[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: compare.r()

+[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcompare.r()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?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: compare.frobenius()

+[?7h[?12l[?25h[?2004l[?7h((-x^2 + 1)/(x^6*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcompare.frobenius()[?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: compare.frobenius().expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t^8 + 2*t^16 + O(t^18)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0.diffn() - a[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: omega0_lift0

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [59], in <cell line: 1>()
+----> 1 omega0_lift0
+
+NameError: name 'omega0_lift0' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega0_lift0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_lift0[?7h[?12l[?25h[?25l[?7l8_lift0[?7h[?12l[?25h[?25l[?7l.diffn() - a[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0[?7h[?12l[?25h[?25l[?7l - a[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: omega8_lift0 - compare

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [61], in <cell line: 1>()
+----> 1 omega8_lift0 - compare
+
+File <string>:39, in __sub__(self, other)
+
+AttributeError: 'superelliptic_drw_form' object has no attribute 'omega0'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0 - compare[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l. - compare[?7h[?12l[?25h[?25l[?7lo - compare[?7h[?12l[?25h[?25l[?7lm - compare[?7h[?12l[?25h[?25l[?7le - compare[?7h[?12l[?25h[?25l[?7lg - compare[?7h[?12l[?25h[?25l[?7la - compare[?7h[?12l[?25h[?25l[?7l8 - compare[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: omega8_lift0.omega8 - compare

+[?7h[?12l[?25h[?2004l[?7hdV([((2*x^4 + 2*x^2 + 2)/x^6)*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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [63], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:22, in <module>
+
+File <string>:30, in de_rham_witt_lift(cech_class, prec)
+
+File <string>:74, in __sub__(self, other)
+
+File <string>:81, in __add__(self, other)
+
+AttributeError: 'superelliptic_form' object has no attribute 'h1'
+[?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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+test: False
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]) 
+ 
+ [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y]) 
+ 
+ 0 
+ 
+
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+test: False
+test 2: dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+test0: True
+test: False
+test 2: dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+test: True
+test 2: dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+test: True
+test 1: True
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+test: True
+test 1: True
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [69], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:22, in <module>
+
+File <string>:33, in de_rham_witt_lift(cech_class, prec)
+
+File <string>:29, in __add__(self, other)
+
+AttributeError: 'superelliptic_drw_form' object has no attribute 't'
+[?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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+test: True
+test 1: True
+test 2: False
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*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
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+test: True
+test 1: True
+test 2: True
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+[?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('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+test: True
+test 1: True
+test 2: True
+test 3: False False True
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [73], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:22, in <module>
+
+File <string>:28, in de_rham_witt_lift(cech_class, prec)
+
+File <string>:29, in __add__(self, other)
+
+AttributeError: 'superelliptic_drw_form' object has no attribute 't'
+[?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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+test: True
+test 1: True
+test 2: True
+test 3: True True True
+[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+[?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$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+test: True
+test 1: True
+test 2: True
+test 3: True True True
+---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [1], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:24, in <module>
+
+NameError: name 'aux' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.r() == -(C.x)^(-1)*C.y.diffn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7lux.r()[?7h[?12l[?25h[?25l[?7ltometa2).coordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7leta2lift[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2lift[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbautom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7l autom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7l autom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7lautom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7l=autom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7l autom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b = autom(eta2lift) - eta2lift

+[?7h[?12l[?25h[?2004l([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])) drw cech
+[(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]) drw form
+((x^4 + x^2 - 1)/(x^2*y - y)) dx form
+(1/(x^2 + 2))*y function
+(1/(x^2 + 2))*y function
+[2/x*y] witt
+2/x*y function
+0 function
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = autom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7lsage: b

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((-x^4)/(x^3*y - x^2*y - x*y + y)) dx) + dV([((x^2 + 1)/(x^3 + 2*x^2 + 2*x + 1))*y]), [(1/(x^2 + x))*y] + V(((x + 2)/(x^2 + x))*y), [(1/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 - x^7 + x^2 - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((x^3 + 2*x^2 + 2*x + 2)/(x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b.r()

+[?7h[?12l[?25h[?2004l[?7h((1/y) dx, (1/(x^2 + x))*y, (1/(x^2*y + x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.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[?7lb.r()[?7h[?12l[?25h[?25l[?7l = autom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: b - eta1

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [6], in <cell line: 1>()
+----> 1 b - eta1
+
+NameError: name 'eta1' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1.r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lam_witt_lift[?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[?7le[?7h[?12l[?25h[?25l[?7lsage: eta1 = de_rham_witt_lift(C.de

+ C.de_rham_basis                     C.degrees_de_rham1                 

+ C.degrees_de_rham0                  C.degrees_holomorphic_differentials

+

+

+ [?7h[?12l[?25h[?25l[?7l_rham_basis

+ C.de_rham_basis                    

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l[

+

+

+[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: eta1 = de_rham_witt_lift(C.de_rham_basis[0])

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [7], in <cell line: 1>()
+----> 1 eta1 = de_rham_witt_lift(C.de_rham_basis[Integer(0)])
+
+TypeError: 'method' object is not subscriptable
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1 = de_rham_witt_lift(C.de_rham_basis[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([0])[?7h[?12l[?25h[?25l[?7l)[0])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: eta1 = de_rham_witt_lift(C.de_rham_basis()[0])

+[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1 = de_rham_witt_lift(C.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l - aux[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1 = de_rham_witt_lift(C.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l[0])[?7h[?12l[?25h[?25l[?7lb - eta1[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = autom(eta2lift) - eta2lift[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: b = autom(eta2lift) - eta2lift - eta1

+[?7h[?12l[?25h[?2004l([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])) drw cech
+[(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]) drw form
+((x^4 + x^2 - 1)/(x^2*y - y)) dx form
+(1/(x^2 + 2))*y function
+(1/(x^2 + 2))*y function
+[2/x*y] witt
+2/x*y function
+0 function
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = autom(eta2lift) - eta2lift - eta1[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?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: b.omega0.frobenius()

+[?7h[?12l[?25h[?2004l[?7h(1/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.omega0.frobenius()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.frobenius()[?7h[?12l[?25h[?25l[?7l8.frobenius()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b.omega8.frobenius()

+[?7h[?12l[?25h[?2004l[?7h((-x^3 + x^2 - 1)/(x^4*y - x^3*y + x^2*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.omega8.frobenius()[?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[?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[?7lsage: b.omega8.frobenius().expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t^2 + t^10 + O(t^12)
+[?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[?2004lomega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2lift[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laeta2lift[?7h[?12l[?25h[?25l[?7lueta2lift[?7h[?12l[?25h[?25l[?7lteta2lift[?7h[?12l[?25h[?25l[?7loeta2lift[?7h[?12l[?25h[?25l[?7lmeta2lift[?7h[?12l[?25h[?25l[?7l(eta2lift[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(eta2lift).coordinates()

+[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [14], in <cell line: 1>()
+----> 1 autom(eta2lift).coordinates()
+
+File <string>:63, in coordinates(self, basis)
+
+File <string>:81, in coordinates(self)
+
+File <string>:87, in coordinates(self)
+
+File <string>:87, in coordinates(self)
+
+    [... skipping similar frames: coordinates at line 87 (686 times)]
+
+File <string>:87, in coordinates(self)
+
+File <string>:52, in coordinates(self)
+
+File <string>:102, in degrees_de_rham0(self)
+
+File <string>:76, in basis_de_rham_degrees(self)
+
+File <string>:60, in holomorphic_differentials_basis(self)
+
+File <string>:52, in basis_holomorphic_differentials_degree(self)
+
+File <string>:7, in __init__(self, C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    704 x0, y0 = x, y
+    705 try:
+--> 706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+    708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
+    709                     x0, y0, self))
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:688, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
+    686 yd = y.denominator()
+    687 try:
+--> 688     return (xn * yd, yn * xd)
+    689 except (AttributeError, TypeError, ValueError):
+    690     pass
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
+   1514     return (<Element>left)._mul_(right)
+   1515 if BOTH_ARE_ELEMENT(cl):
+-> 1516     return coercion_model.bin_op(left, right, mul)
+   1517 
+   1518 cdef long value
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
+   1198 # Now coerce to a common parent and do the operation there
+   1199 try:
+-> 1200     xy = self.canonical_coercion(x, y)
+   1201 except TypeError:
+   1202     self._record_exception()
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion()
+   1313     x_elt = x
+   1314 if y_map is not None:
+-> 1315     y_elt = (<Map>y_map)._call_(y)
+   1316 else:
+   1317     y_elt = y
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
+    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
+    286 cdef Map m
+--> 287 cdef Element e = method(C)
+    288 if e is None:
+    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
+    196 var = R.variable_name()
+    197 if var in self._parent.variable_names():
+--> 198     return R(self.polynomial(self._parent(var)))
+    199 else:
+    200     return R([self])
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:426, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
+    424         v.append(B(w))
+    425         z *= var
+--> 426     return ring(v)
+    427 
+    428 cpdef dict _mpoly_dict_recursive(self, tuple vars=None, base_ring=None):
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:416, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
+    414 C = self.element_class
+    415 if isinstance(x, (list, tuple)):
+--> 416     return C(self, x, check=check, is_gen=False, construct=construct)
+    417 if isinstance(x, range):
+    418     return C(self, list(x), check=check, is_gen=False,
+    419              construct=construct)
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(eta2lift).coordinates()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm(eta2lift).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[?7lsage: autom(eta2lift)

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2*x))*y] d[x] + V(((x^4 - x^3 - x^2 + x + 1)/(x^2*y + x*y + y)) dx) + dV([(x/(x^2 + x + 1))*y]), [(2/(x + 1))*y], [(2/(x^4 + x^3 + 2*x^2 + 2*x))*y] d[x] + V(((-x^7 - x^6 + x^4 - x^3 - x^2 + 1)/(x^6*y - x^5*y - x^4*y - x^3*y - x^2*y - x*y + y)) dx) + dV([((2*x^4 + 2*x^3 + 2*x^2 + x)/(x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(eta2lift)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbautom(eta2lift)[?7h[?12l[?25h[?25l[?7l autom(eta2lift)[?7h[?12l[?25h[?25l[?7l=autom(eta2lift)[?7h[?12l[?25h[?25l[?7l autom(eta2lift)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l) - eta2lift - eta1[?7h[?12l[?25h[?25l[?7l() - eta2lift - eta1[?7h[?12l[?25h[?25l[?7lsage: b = autom(eta2lift) - eta2lift - eta1

+[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [16], in <cell line: 1>()
+----> 1 b = autom(eta2lift) - eta2lift - eta1
+
+File <string>:23, in autom(self)
+
+File <string>:20, in autom(self)
+
+File <string>:99, in diffn(self, dy_w)
+
+File <string>:99, in diffn(self, dy_w)
+
+File <string>:73, in diffn(self, dy_w)
+
+File <string>:177, in dy_w(C)
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
+   2412         return x
+   2413 
+-> 2414     return coercion_model.bin_op(left, right, operator.mul)
+   2415 
+   2416 cpdef _mul_(self, right):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:48, in __rmul__(self, other)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
+   1526     if not err:
+   1527         return (<Element>right)._mul_long(value)
+-> 1528     return coercion_model.bin_op(left, right, mul)
+   1529 except TypeError:
+   1530     return NotImplemented
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:43, in __rmul__(self, other)
+
+File <string>:31, in __add__(self, other)
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
+   2412         return x
+   2413 
+-> 2414     return coercion_model.bin_op(left, right, operator.mul)
+   2415 
+   2416 cpdef _mul_(self, right):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:70, in __rmul__(self, constant)
+
+File <string>:14, in __init__(self, C, g)
+
+File <string>:223, in reduction(C, g)
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = autom(eta2lift) - eta2lift - eta1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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) - eta2lift - eta1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b = autom(eta2lift)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = autom(eta2lift)[?7h[?12l[?25h[?25l[?7l.omega8.frobenus().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b.coordinates()

+[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [18], in <cell line: 1>()
+----> 1 b.coordinates()
+
+File <string>:63, in coordinates(self, basis)
+
+File <string>:81, in coordinates(self)
+
+File <string>:87, in coordinates(self)
+
+File <string>:87, in coordinates(self)
+
+    [... skipping similar frames: coordinates at line 87 (328 times)]
+
+File <string>:87, in coordinates(self)
+
+File <string>:86, in coordinates(self)
+
+File <string>:52, in __sub__(self, other)
+
+File <string>:14, in __init__(self, C, g)
+
+File <string>:216, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    704 x0, y0 = x, y
+    705 try:
+--> 706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+    708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
+    709                     x0, y0, self))
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.coordinates()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b.r()

+[?7h[?12l[?25h[?2004l[?7h(((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.r()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b.r().coordinates()

+[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [20], in <cell line: 1>()
+----> 1 b.r().coordinates()
+
+File <string>:81, in coordinates(self)
+
+File <string>:87, in coordinates(self)
+
+File <string>:87, in coordinates(self)
+
+    [... skipping similar frames: coordinates at line 87 (295 times)]
+
+File <string>:87, in coordinates(self)
+
+File <string>:56, in coordinates(self)
+
+File <string>:98, in de_rham_basis(self)
+
+File <string>:76, in basis_de_rham_degrees(self)
+
+File <string>:60, in holomorphic_differentials_basis(self)
+
+File <string>:52, in basis_holomorphic_differentials_degree(self)
+
+File <string>:7, in __init__(self, C, g)
+
+File <string>:256, in reduction_form(C, g)
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?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---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [21], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:26, in <module>
+
+TypeError: 'method' object is not subscriptable
+[?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---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [22], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:26, in <module>
+
+AttributeError: 'NoneType' object has no attribute 'coordinates'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[1]

+[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(eta2lift)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: autom(C.de_rham_basis()[1])

+[?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('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [25], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:26, in <module>
+
+File <string>:16, in autom(self)
+
+TypeError: superelliptic_cech.__init__() missing 1 required positional argument: 'fct'
+[?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[?2004lself (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
+self ((1/y) dx, (1/(x^2 + x))*y, (1/(x^2*y + x*y)) dx)
+self ((1/y) dx, (2/(x^3 + x^2))*y, ((x^2 + x + 1)/(x^2*y + x*y)) dx)
+self ((1/y) dx, (1/(x^4 + x^3))*y, ((x^4 + x^3 + x^2 - x - 1)/(x^4*y + x^3*y)) dx)
+self ((1/y) dx, (2/(x^5 + x^4))*y, ((x^5 + x^4 + x^2 + x - 1)/(x^5*y + x^4*y)) dx)
+self ((1/y) dx, (1/(x^6 + x^5))*y, ((x^5 + x^4 - 1)/(x^5*y + x^4*y)) dx)
+self ((1/y) dx, (2/(x^7 + x^6))*y, ((x^7 + x^6 - x^2 + x + 1)/(x^7*y + x^6*y)) dx)
+self ((1/y) dx, (1/(x^8 + x^7))*y, ((x^8 + x^7 - x^2 - x + 1)/(x^8*y + x^7*y)) dx)
+self ((1/y) dx, (2/(x^9 + x^8))*y, ((x^8 + x^7 + 1)/(x^8*y + x^7*y)) dx)
+self ((1/y) dx, (1/(x^10 + x^9))*y, ((x^10 + x^9 + x^2 - x - 1)/(x^10*y + x^9*y)) dx)
+self ((1/y) dx, (2/(x^11 + x^10))*y, ((x^11 + x^10 + x^2 + x - 1)/(x^11*y + x^10*y)) dx)
+self ((1/y) dx, (1/(x^12 + x^11))*y, ((x^11 + x^10 - 1)/(x^11*y + x^10*y)) dx)
+self ((1/y) dx, (2/(x^13 + x^12))*y, ((x^13 + x^12 - x^2 + x + 1)/(x^13*y + x^12*y)) dx)
+self ((1/y) dx, (1/(x^14 + x^13))*y, ((x^14 + x^13 - x^2 - x + 1)/(x^14*y + x^13*y)) dx)
+self ((1/y) dx, (2/(x^15 + x^14))*y, ((x^14 + x^13 + 1)/(x^14*y + x^13*y)) dx)
+self ((1/y) dx, (1/(x^16 + x^15))*y, ((x^16 + x^15 + x^2 - x - 1)/(x^16*y + x^15*y)) dx)
+self ((1/y) dx, (2/(x^17 + x^16))*y, ((x^17 + x^16 + x^2 + x - 1)/(x^17*y + x^16*y)) dx)
+self ((1/y) dx, (1/(x^18 + x^17))*y, ((x^17 + x^16 - 1)/(x^17*y + x^16*y)) dx)
+self ((1/y) dx, (2/(x^19 + x^18))*y, ((x^19 + x^18 - x^2 + x + 1)/(x^19*y + x^18*y)) dx)
+self ((1/y) dx, (1/(x^20 + x^19))*y, ((x^20 + x^19 - x^2 - x + 1)/(x^20*y + x^19*y)) dx)
+self ((1/y) dx, (2/(x^21 + x^20))*y, ((x^20 + x^19 + 1)/(x^20*y + x^19*y)) dx)
+self ((1/y) dx, (1/(x^22 + x^21))*y, ((x^22 + x^21 + x^2 - x - 1)/(x^22*y + x^21*y)) dx)
+self ((1/y) dx, (2/(x^23 + x^22))*y, ((x^23 + x^22 + x^2 + x - 1)/(x^23*y + x^22*y)) dx)
+self ((1/y) dx, (1/(x^24 + x^23))*y, ((x^23 + x^22 - 1)/(x^23*y + x^22*y)) dx)
+self ((1/y) dx, (2/(x^25 + x^24))*y, ((x^25 + x^24 - x^2 + x + 1)/(x^25*y + x^24*y)) dx)
+self ((1/y) dx, (1/(x^26 + x^25))*y, ((x^26 + x^25 - x^2 - x + 1)/(x^26*y + x^25*y)) dx)
+self ((1/y) dx, (2/(x^27 + x^26))*y, ((x^26 + x^25 + 1)/(x^26*y + x^25*y)) dx)
+self ((1/y) dx, (1/(x^28 + x^27))*y, ((x^28 + x^27 + x^2 - x - 1)/(x^28*y + x^27*y)) dx)
+self ((1/y) dx, (2/(x^29 + x^28))*y, ((x^29 + x^28 + x^2 + x - 1)/(x^29*y + x^28*y)) dx)
+self ((1/y) dx, (1/(x^30 + x^29))*y, ((x^29 + x^28 - 1)/(x^29*y + x^28*y)) dx)
+self ((1/y) dx, (2/(x^31 + x^30))*y, ((x^31 + x^30 - x^2 + x + 1)/(x^31*y + x^30*y)) dx)
+self ((1/y) dx, (1/(x^32 + x^31))*y, ((x^32 + x^31 - x^2 - x + 1)/(x^32*y + x^31*y)) dx)
+self ((1/y) dx, (2/(x^33 + x^32))*y, ((x^32 + x^31 + 1)/(x^32*y + x^31*y)) dx)
+self ((1/y) dx, (1/(x^34 + x^33))*y, ((x^34 + x^33 + x^2 - x - 1)/(x^34*y + x^33*y)) dx)
+self ((1/y) dx, (2/(x^35 + x^34))*y, ((x^35 + x^34 + x^2 + x - 1)/(x^35*y + x^34*y)) dx)
+self ((1/y) dx, (1/(x^36 + x^35))*y, ((x^35 + x^34 - 1)/(x^35*y + x^34*y)) dx)
+self ((1/y) dx, (2/(x^37 + x^36))*y, ((x^37 + x^36 - x^2 + x + 1)/(x^37*y + x^36*y)) dx)
+self ((1/y) dx, (1/(x^38 + x^37))*y, ((x^38 + x^37 - x^2 - x + 1)/(x^38*y + x^37*y)) dx)
+self ((1/y) dx, (2/(x^39 + x^38))*y, ((x^38 + x^37 + 1)/(x^38*y + x^37*y)) dx)
+self ((1/y) dx, (1/(x^40 + x^39))*y, ((x^40 + x^39 + x^2 - x - 1)/(x^40*y + x^39*y)) dx)
+self ((1/y) dx, (2/(x^41 + x^40))*y, ((x^41 + x^40 + x^2 + x - 1)/(x^41*y + x^40*y)) dx)
+self ((1/y) dx, (1/(x^42 + x^41))*y, ((x^41 + x^40 - 1)/(x^41*y + x^40*y)) dx)
+self ((1/y) dx, (2/(x^43 + x^42))*y, ((x^43 + x^42 - x^2 + x + 1)/(x^43*y + x^42*y)) dx)
+self ((1/y) dx, (1/(x^44 + x^43))*y, ((x^44 + x^43 - x^2 - x + 1)/(x^44*y + x^43*y)) dx)
+self ((1/y) dx, (2/(x^45 + x^44))*y, ((x^44 + x^43 + 1)/(x^44*y + x^43*y)) dx)
+self ((1/y) dx, (1/(x^46 + x^45))*y, ((x^46 + x^45 + x^2 - x - 1)/(x^46*y + x^45*y)) dx)
+self ((1/y) dx, (2/(x^47 + x^46))*y, ((x^47 + x^46 + x^2 + x - 1)/(x^47*y + x^46*y)) dx)
+self ((1/y) dx, (1/(x^48 + x^47))*y, ((x^47 + x^46 - 1)/(x^47*y + x^46*y)) dx)
+self ((1/y) dx, (2/(x^49 + x^48))*y, ((x^49 + x^48 - x^2 + x + 1)/(x^49*y + x^48*y)) dx)
+self ((1/y) dx, (1/(x^50 + x^49))*y, ((x^50 + x^49 - x^2 - x + 1)/(x^50*y + x^49*y)) dx)
+self ((1/y) dx, (2/(x^51 + x^50))*y, ((x^50 + x^49 + 1)/(x^50*y + x^49*y)) dx)
+self ((1/y) dx, (1/(x^52 + x^51))*y, ((x^52 + x^51 + x^2 - x - 1)/(x^52*y + x^51*y)) dx)
+self ((1/y) dx, (2/(x^53 + x^52))*y, ((x^53 + x^52 + x^2 + x - 1)/(x^53*y + x^52*y)) dx)
+self ((1/y) dx, (1/(x^54 + x^53))*y, ((x^53 + x^52 - 1)/(x^53*y + x^52*y)) dx)
+self ((1/y) dx, (2/(x^55 + x^54))*y, ((x^55 + x^54 - x^2 + x + 1)/(x^55*y + x^54*y)) dx)
+self ((1/y) dx, (1/(x^56 + x^55))*y, ((x^56 + x^55 - x^2 - x + 1)/(x^56*y + x^55*y)) dx)
+self ((1/y) dx, (2/(x^57 + x^56))*y, ((x^56 + x^55 + 1)/(x^56*y + x^55*y)) dx)
+self ((1/y) dx, (1/(x^58 + x^57))*y, ((x^58 + x^57 + x^2 - x - 1)/(x^58*y + x^57*y)) dx)
+self ((1/y) dx, (2/(x^59 + x^58))*y, ((x^59 + x^58 + x^2 + x - 1)/(x^59*y + x^58*y)) dx)
+self ((1/y) dx, (1/(x^60 + x^59))*y, ((x^59 + x^58 - 1)/(x^59*y + x^58*y)) dx)
+self ((1/y) dx, (2/(x^61 + x^60))*y, ((x^61 + x^60 - x^2 + x + 1)/(x^61*y + x^60*y)) dx)
+self ((1/y) dx, (1/(x^62 + x^61))*y, ((x^62 + x^61 - x^2 - x + 1)/(x^62*y + x^61*y)) dx)
+self ((1/y) dx, (2/(x^63 + x^62))*y, ((x^62 + x^61 + 1)/(x^62*y + x^61*y)) dx)
+self ((1/y) dx, (1/(x^64 + x^63))*y, ((x^64 + x^63 + x^2 - x - 1)/(x^64*y + x^63*y)) dx)
+self ((1/y) dx, (2/(x^65 + x^64))*y, ((x^65 + x^64 + x^2 + x - 1)/(x^65*y + x^64*y)) dx)
+self ((1/y) dx, (1/(x^66 + x^65))*y, ((x^65 + x^64 - 1)/(x^65*y + x^64*y)) dx)
+self ((1/y) dx, (2/(x^67 + x^66))*y, ((x^67 + x^66 - x^2 + x + 1)/(x^67*y + x^66*y)) dx)
+self ((1/y) dx, (1/(x^68 + x^67))*y, ((x^68 + x^67 - x^2 - x + 1)/(x^68*y + x^67*y)) dx)
+self ((1/y) dx, (2/(x^69 + x^68))*y, ((x^68 + x^67 + 1)/(x^68*y + x^67*y)) dx)
+self ((1/y) dx, (1/(x^70 + x^69))*y, ((x^70 + x^69 + x^2 - x - 1)/(x^70*y + x^69*y)) dx)
+self ((1/y) dx, (2/(x^71 + x^70))*y, ((x^71 + x^70 + x^2 + x - 1)/(x^71*y + x^70*y)) dx)
+self ((1/y) dx, (1/(x^72 + x^71))*y, ((x^71 + x^70 - 1)/(x^71*y + x^70*y)) dx)
+self ((1/y) dx, (2/(x^73 + x^72))*y, ((x^73 + x^72 - x^2 + x + 1)/(x^73*y + x^72*y)) dx)
+self ((1/y) dx, (1/(x^74 + x^73))*y, ((x^74 + x^73 - x^2 - x + 1)/(x^74*y + x^73*y)) dx)
+self ((1/y) dx, (2/(x^75 + x^74))*y, ((x^74 + x^73 + 1)/(x^74*y + x^73*y)) dx)
+self ((1/y) dx, (1/(x^76 + x^75))*y, ((x^76 + x^75 + x^2 - x - 1)/(x^76*y + x^75*y)) dx)
+self ((1/y) dx, (2/(x^77 + x^76))*y, ((x^77 + x^76 + x^2 + x - 1)/(x^77*y + x^76*y)) dx)
+self ((1/y) dx, (1/(x^78 + x^77))*y, ((x^77 + x^76 - 1)/(x^77*y + x^76*y)) dx)
+self ((1/y) dx, (2/(x^79 + x^78))*y, ((x^79 + x^78 - x^2 + x + 1)/(x^79*y + x^78*y)) dx)
+self ((1/y) dx, (1/(x^80 + x^79))*y, ((x^80 + x^79 - x^2 - x + 1)/(x^80*y + x^79*y)) dx)
+self ((1/y) dx, (2/(x^81 + x^80))*y, ((x^80 + x^79 + 1)/(x^80*y + x^79*y)) dx)
+self ((1/y) dx, (1/(x^82 + x^81))*y, ((x^82 + x^81 + x^2 - x - 1)/(x^82*y + x^81*y)) dx)
+self ((1/y) dx, (2/(x^83 + x^82))*y, ((x^83 + x^82 + x^2 + x - 1)/(x^83*y + x^82*y)) dx)
+self ((1/y) dx, (1/(x^84 + x^83))*y, ((x^83 + x^82 - 1)/(x^83*y + x^82*y)) dx)
+self ((1/y) dx, (2/(x^85 + x^84))*y, ((x^85 + x^84 - x^2 + x + 1)/(x^85*y + x^84*y)) dx)
+self ((1/y) dx, (1/(x^86 + x^85))*y, ((x^86 + x^85 - x^2 - x + 1)/(x^86*y + x^85*y)) dx)
+self ((1/y) dx, (2/(x^87 + x^86))*y, ((x^86 + x^85 + 1)/(x^86*y + x^85*y)) dx)
+self ((1/y) dx, (1/(x^88 + x^87))*y, ((x^88 + x^87 + x^2 - x - 1)/(x^88*y + x^87*y)) dx)
+self ((1/y) dx, (2/(x^89 + x^88))*y, ((x^89 + x^88 + x^2 + x - 1)/(x^89*y + x^88*y)) dx)
+self ((1/y) dx, (1/(x^90 + x^89))*y, ((x^89 + x^88 - 1)/(x^89*y + x^88*y)) dx)
+self ((1/y) dx, (2/(x^91 + x^90))*y, ((x^91 + x^90 - x^2 + x + 1)/(x^91*y + x^90*y)) dx)
+self ((1/y) dx, (1/(x^92 + x^91))*y, ((x^92 + x^91 - x^2 - x + 1)/(x^92*y + x^91*y)) dx)
+self ((1/y) dx, (2/(x^93 + x^92))*y, ((x^92 + x^91 + 1)/(x^92*y + x^91*y)) dx)
+self ((1/y) dx, (1/(x^94 + x^93))*y, ((x^94 + x^93 + x^2 - x - 1)/(x^94*y + x^93*y)) dx)
+self ((1/y) dx, (2/(x^95 + x^94))*y, ((x^95 + x^94 + x^2 + x - 1)/(x^95*y + x^94*y)) dx)
+self ((1/y) dx, (1/(x^96 + x^95))*y, ((x^95 + x^94 - 1)/(x^95*y + x^94*y)) dx)
+self ((1/y) dx, (2/(x^97 + x^96))*y, ((x^97 + x^96 - x^2 + x + 1)/(x^97*y + x^96*y)) dx)
+self ((1/y) dx, (1/(x^98 + x^97))*y, ((x^98 + x^97 - x^2 - x + 1)/(x^98*y + x^97*y)) dx)
+self ((1/y) dx, (2/(x^99 + x^98))*y, ((x^98 + x^97 + 1)/(x^98*y + x^97*y)) dx)
+self ((1/y) dx, (1/(x^100 + x^99))*y, ((x^100 + x^99 + x^2 - x - 1)/(x^100*y + x^99*y)) dx)
+self ((1/y) dx, (2/(x^101 + x^100))*y, ((x^101 + x^100 + x^2 + x - 1)/(x^101*y + x^100*y)) dx)
+self ((1/y) dx, (1/(x^102 + x^101))*y, ((x^101 + x^100 - 1)/(x^101*y + x^100*y)) dx)
+self ((1/y) dx, (2/(x^103 + x^102))*y, ((x^103 + x^102 - x^2 + x + 1)/(x^103*y + x^102*y)) dx)
+self ((1/y) dx, (1/(x^104 + x^103))*y, ((x^104 + x^103 - x^2 - x + 1)/(x^104*y + x^103*y)) dx)
+self ((1/y) dx, (2/(x^105 + x^104))*y, ((x^104 + x^103 + 1)/(x^104*y + x^103*y)) dx)
+self ((1/y) dx, (1/(x^106 + x^105))*y, ((x^106 + x^105 + x^2 - x - 1)/(x^106*y + x^105*y)) dx)
+self ((1/y) dx, (2/(x^107 + x^106))*y, ((x^107 + x^106 + x^2 + x - 1)/(x^107*y + x^106*y)) dx)
+self ((1/y) dx, (1/(x^108 + x^107))*y, ((x^107 + x^106 - 1)/(x^107*y + x^106*y)) dx)
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [26], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:26, in <module>
+
+File <string>:82, in coordinates(self)
+
+File <string>:88, in coordinates(self)
+
+File <string>:88, in coordinates(self)
+
+    [... skipping similar frames: coordinates at line 88 (103 times)]
+
+File <string>:88, in coordinates(self)
+
+File <string>:53, in coordinates(self)
+
+File <string>:102, in degrees_de_rham0(self)
+
+File <string>:76, in basis_de_rham_degrees(self)
+
+File <string>:60, in holomorphic_differentials_basis(self)
+
+File <string>:52, in basis_holomorphic_differentials_degree(self)
+
+File <string>:7, in __init__(self, C, g)
+
+File <string>:259, in reduction_form(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:711, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
+    709                     x0, y0, self))
+    710 try:
+--> 711     return self._element_class(self, x, y, coerce=coerce)
+    712 except TypeError:
+    713     if parent(x) is parent(x0):
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:115, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
+    113 if coerce:
+    114     self.__numerator   = parent.ring()(numerator)
+--> 115     self.__denominator = parent.ring()(denominator)
+    116 else:
+    117     self.__numerator   = numerator
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+   1001 
+   1002         try:
+-> 1003             return self(str(element))
+   1004         except TypeError:
+   1005             pass
+
+File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
+    192 except AttributeError:
+    193     return super().__repr__()
+--> 194 result = reprfunc()
+    195 if isinstance(result, str):
+    196     return result
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
+   2688         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
+   2689     """
+-> 2690     return self._repr()
+   2691 
+   2692 def _latex_(self, name=None):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2667, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
+   2665         else:
+   2666             var = ""
+-> 2667         s += "%s%s"%(x,var)
+   2668 s = s.replace(" + -", " - ")
+   2669 s = re.sub(r' 1(\.0+)?\*',' ', s)
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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$ 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[?2004lself (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
+self ((1/y) dx, (1/(x^2 + x))*y, (1/(x^2*y + x*y)) dx)
+self ((1/y) dx, (2/(x^3 + x^2))*y, ((x^2 + x + 1)/(x^2*y + x*y)) dx)
+self ((1/y) dx, (1/(x^4 + x^3))*y, ((x^4 + x^3 + x^2 - x - 1)/(x^4*y + x^3*y)) dx)
+self ((1/y) dx, (2/(x^5 + x^4))*y, ((x^5 + x^4 + x^2 + x - 1)/(x^5*y + x^4*y)) dx)
+self ((1/y) dx, (1/(x^6 + x^5))*y, ((x^5 + x^4 - 1)/(x^5*y + x^4*y)) dx)
+self ((1/y) dx, (2/(x^7 + x^6))*y, ((x^7 + x^6 - x^2 + x + 1)/(x^7*y + x^6*y)) dx)
+self ((1/y) dx, (1/(x^8 + x^7))*y, ((x^8 + x^7 - x^2 - x + 1)/(x^8*y + x^7*y)) dx)
+self ((1/y) dx, (2/(x^9 + x^8))*y, ((x^8 + x^7 + 1)/(x^8*y + x^7*y)) dx)
+self ((1/y) dx, (1/(x^10 + x^9))*y, ((x^10 + x^9 + x^2 - x - 1)/(x^10*y + x^9*y)) dx)
+self ((1/y) dx, (2/(x^11 + x^10))*y, ((x^11 + x^10 + x^2 + x - 1)/(x^11*y + x^10*y)) dx)
+self ((1/y) dx, (1/(x^12 + x^11))*y, ((x^11 + x^10 - 1)/(x^11*y + x^10*y)) dx)
+self ((1/y) dx, (2/(x^13 + x^12))*y, ((x^13 + x^12 - x^2 + x + 1)/(x^13*y + x^12*y)) dx)
+self ((1/y) dx, (1/(x^14 + x^13))*y, ((x^14 + x^13 - x^2 - x + 1)/(x^14*y + x^13*y)) dx)
+self ((1/y) dx, (2/(x^15 + x^14))*y, ((x^14 + x^13 + 1)/(x^14*y + x^13*y)) dx)
+self ((1/y) dx, (1/(x^16 + x^15))*y, ((x^16 + x^15 + x^2 - x - 1)/(x^16*y + x^15*y)) dx)
+self ((1/y) dx, (2/(x^17 + x^16))*y, ((x^17 + x^16 + x^2 + x - 1)/(x^17*y + x^16*y)) dx)
+self ((1/y) dx, (1/(x^18 + x^17))*y, ((x^17 + x^16 - 1)/(x^17*y + x^16*y)) dx)
+self ((1/y) dx, (2/(x^19 + x^18))*y, ((x^19 + x^18 - x^2 + x + 1)/(x^19*y + x^18*y)) dx)
+self ((1/y) dx, (1/(x^20 + x^19))*y, ((x^20 + x^19 - x^2 - x + 1)/(x^20*y + x^19*y)) dx)
+self ((1/y) dx, (2/(x^21 + x^20))*y, ((x^20 + x^19 + 1)/(x^20*y + x^19*y)) dx)
+self ((1/y) dx, (1/(x^22 + x^21))*y, ((x^22 + x^21 + x^2 - x - 1)/(x^22*y + x^21*y)) dx)
+self ((1/y) dx, (2/(x^23 + x^22))*y, ((x^23 + x^22 + x^2 + x - 1)/(x^23*y + x^22*y)) dx)
+self ((1/y) dx, (1/(x^24 + x^23))*y, ((x^23 + x^22 - 1)/(x^23*y + x^22*y)) dx)
+self ((1/y) dx, (2/(x^25 + x^24))*y, ((x^25 + x^24 - x^2 + x + 1)/(x^25*y + x^24*y)) dx)
+self ((1/y) dx, (1/(x^26 + x^25))*y, ((x^26 + x^25 - x^2 - x + 1)/(x^26*y + x^25*y)) dx)
+self ((1/y) dx, (2/(x^27 + x^26))*y, ((x^26 + x^25 + 1)/(x^26*y + x^25*y)) dx)
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [1], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:26, in <module>
+
+File <string>:82, in coordinates(self)
+
+File <string>:88, in coordinates(self)
+
+File <string>:88, in coordinates(self)
+
+    [... skipping similar frames: coordinates at line 88 (22 times)]
+
+File <string>:88, in coordinates(self)
+
+File <string>:57, in coordinates(self)
+
+File <string>:98, in de_rham_basis(self)
+
+File <string>:91, in basis_de_rham_degrees(self)
+
+File <string>:5, in __init__(self, C, omega, fct)
+
+File <string>:93, in diffn(self)
+
+File /ext/sage/9.7/src/sage/categories/quotient_fields.py:610, in QuotientFields.ElementMethods.derivative(self, *args)
+    580 r"""
+    581 The derivative of this rational function, with respect to variables
+    582 supplied in args.
+   (...)
+    607     2/(x^3 + 3*x^2*y + 3*x*y^2 + y^3)
+    608 """
+    609 from sage.misc.derivative import multi_derivative
+--> 610 return multi_derivative(self, args)
+
+File /ext/sage/9.7/src/sage/misc/derivative.pyx:222, in sage.misc.derivative.multi_derivative()
+    220 
+    221     for arg in derivative_parse(args):
+--> 222         F = F._derivative(arg)
+    223     return F
+    224 
+
+File /ext/sage/9.7/src/sage/categories/quotient_fields.py:612, in QuotientFields.ElementMethods._derivative(self, var)
+    609     from sage.misc.derivative import multi_derivative
+    610     return multi_derivative(self, args)
+--> 612 def _derivative(self, var=None):
+    613     r"""
+    614     Returns the derivative of this rational function with respect to the
+    615     variable ``var``.
+   (...)
+    668         (-t + 1)/(t^3 + 3*t^2 + 3*t + 1)
+    669     """
+    670     R = self.parent()
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?7lprint(autom(C.de_rham_basis()[1]).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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7llomorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.

+  C.a_number                               C.cartier_matrix                         C.de_rham_basis                           

+  C.base_ring                              C.characteristic                         C.degrees_de_rham0                        

+  C.basis_de_rham_degrees                  C.cohomology_of_structure_sheaf_basis    C.degrees_de_rham1                       >

+  C.basis_holomorphic_differentials_degree C.crystalline_cohomology_basis           C.degrees_holomorphic_differentials       

+ [?7h[?12l[?25h[?25l[?7la_number

+ C.a_number                              

+

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7lcartier_matrix

+ C.a_number                               C.cartier_matrix                        [?7h[?12l[?25h[?25l[?7lharacteristc

+ C.cartier_matrix                        

+ C.characteristic                        [?7h[?12l[?25h[?25l[?7lohomology_of_structure_sheaf_basis

+

+ C.characteristic                        

+ C.cohomology_of_structure_sheaf_basis   [?7h[?12l[?25h[?25l[?7l(

+

+

+

+

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis()

+[?7h[?12l[?25h[?2004l[?7h[2/x*y]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?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[?7laC.cohomology_of_structure_sheaf_basis()[0][?7h[?12l[?25h[?25l[?7luC.cohomology_of_structure_sheaf_basis()[0][?7h[?12l[?25h[?25l[?7ltC.cohomology_of_structure_sheaf_basis()[0][?7h[?12l[?25h[?25l[?7loC.cohomology_of_structure_sheaf_basis()[0][?7h[?12l[?25h[?25l[?7lmC.cohomology_of_structure_sheaf_basis()[0][?7h[?12l[?25h[?25l[?7l(C.cohomology_of_structure_sheaf_basis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(C.cohomology_of_structure_sheaf_basis()[0]).coordinates()

+[?7h[?12l[?25h[?2004l[?7h[1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l = autm(b[0])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsperelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lerelliptic(x^3 + 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[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + 1, 2)[?7h[?12l[?25h[?25l[?7l7 + 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[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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^7 + 1, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^7 + 1, 2)[?7h[?12l[?25h[?25l[?7l.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lde_rham_basis()[1][?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

+[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx),
+ ((x/y) dx, 0, (x/y) dx),
+ ((x^2/y) dx, 0, (x^2/y) dx),
+ (((-x^5)/y) dx, 2/x*y, ((-1)/(x^2*y)) dx),
+ (0 dx, 2/x^2*y, (1/(x^3*y)) dx),
+ ((x^3/y) dx, 2/x^3*y, 0 dx)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lhomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis()

+[?7h[?12l[?25h[?2004l[?7h[2/x*y, 2/x^2*y, 2/x^3*y]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^7 + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?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: C = superelliptic(x^7 + 1, 5)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7l.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis()

+[?7h[?12l[?25h[?2004l[?7h[2/x*y,
+ 2/x*y^2,
+ 2/x^2*y^2,
+ 2/x*y^3,
+ 2/x^2*y^3,
+ 2/x^3*y^3,
+ 2/x^4*y^3,
+ 2/x*y^4,
+ 2/x^2*y^4,
+ 2/x^3*y^4,
+ 2/x^4*y^4,
+ 2/x^5*y^4]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^7 + 1, 5)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7l.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7l.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

+[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx),
+ ((1/y^2) dx, 0, (1/y^2) dx),
+ ((x/y^2) dx, 0, (x/y^2) dx),
+ ((1/y^3) dx, 0, (1/y^3) dx),
+ ((x/y^3) dx, 0, (x/y^3) dx),
+ ((x^2/y^3) dx, 0, (x^2/y^3) dx),
+ ((x^3/y^3) dx, 0, (x^3/y^3) dx),
+ ((1/y^4) dx, 0, (1/y^4) dx),
+ ((x/y^4) dx, 0, (x/y^4) dx),
+ ((x^2/y^4) dx, 0, (x^2/y^4) dx),
+ ((x^3/y^4) dx, 0, (x^3/y^4) dx),
+ ((x^4/y^4) dx, 0, (x^4/y^4) dx),
+ (((-x^5)/y) dx, 2/x*y^4, ((-1)/(x^2*y)) dx),
+ (0 dx, 2/x^2*y^4, (1/(x^3*y)) dx),
+ ((x^3/y) dx, 2/x^3*y^4, 0 dx),
+ (((-x^2)/y) dx, 2/x^4*y^4, ((-1)/(x^5*y)) dx),
+ (0 dx, 2/x^5*y^4, (1/(x^6*y)) dx),
+ ((x^5/y^2) dx, 2/x*y^3, ((-1)/(x^2*y^2)) dx),
+ (((-x^4)/y^2) dx, 2/x^2*y^3, (1/(x^3*y^2)) dx),
+ (0 dx, 2/x^3*y^3, 0 dx),
+ ((x^2/y^2) dx, 2/x^4*y^3, ((-1)/(x^5*y^2)) dx),
+ (0 dx, 2/x*y^2, ((-1)/(x^2*y^3)) dx),
+ ((x^4/y^3) dx, 2/x^2*y^2, (1/(x^3*y^3)) dx),
+ (((-x^5)/y^4) dx, 2/x*y, ((-1)/(x^2*y^4)) 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[?7lC.de_rham_basis([?7h[?12l[?25h[?25l[?7l = superelliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^7 + 1, 5)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^7 + 1, 5)[?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^7 + 1, 5)[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

+[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx),
+ ((1/y^2) dx, 0, (1/y^2) dx),
+ ((x/y^2) dx, 0, (x/y^2) dx),
+ ((1/y^3) dx, 0, (1/y^3) dx),
+ ((x/y^3) dx, 0, (x/y^3) dx),
+ ((x^2/y^3) dx, 0, (x^2/y^3) dx),
+ ((x^3/y^3) dx, 0, (x^3/y^3) dx),
+ ((1/y^4) dx, 0, (1/y^4) dx),
+ ((x/y^4) dx, 0, (x/y^4) dx),
+ ((x^2/y^4) dx, 0, (x^2/y^4) dx),
+ ((x^3/y^4) dx, 0, (x^3/y^4) dx),
+ ((x^4/y^4) dx, 0, (x^4/y^4) dx),
+ (((-x^5)/y) dx, 2/x*y^4, ((-1)/(x^2*y)) dx),
+ (0 dx, 2/x^2*y^4, (1/(x^3*y)) dx),
+ ((x^3/y) dx, 2/x^3*y^4, 0 dx),
+ (((-x^2)/y) dx, 2/x^4*y^4, ((-1)/(x^5*y)) dx),
+ (0 dx, 2/x^5*y^4, (1/(x^6*y)) dx),
+ ((x^5/y^2) dx, 2/x*y^3, ((-1)/(x^2*y^2)) dx),
+ (((-x^4)/y^2) dx, 2/x^2*y^3, (1/(x^3*y^2)) dx),
+ (0 dx, 2/x^3*y^3, 0 dx),
+ ((x^2/y^2) dx, 2/x^4*y^3, ((-1)/(x^5*y^2)) dx),
+ (0 dx, 2/x*y^2, ((-1)/(x^2*y^3)) dx),
+ ((x^4/y^3) dx, 2/x^2*y^2, (1/(x^3*y^3)) dx),
+ (((-x^5)/y^4) dx, 2/x*y, ((-1)/(x^2*y^4)) dx)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lhomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: C.cohomology_of_structure_sheaf_basis()

+[?7h[?12l[?25h[?2004l[?7h[2/x*y^4,
+ 2/x^2*y^4,
+ 2/x^3*y^4,
+ 2/x^4*y^4,
+ 2/x^5*y^4,
+ 2/x*y^3,
+ 2/x^2*y^3,
+ 2/x^3*y^3,
+ 2/x^4*y^3,
+ 2/x*y^2,
+ 2/x^2*y^2,
+ 2/x*y]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.cohomology_of_structure_sheaf_basis()[0]).coordinates()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ltom(C.cohomology_of_structure_sheaf_basis()[0]).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[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).coordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).coordinates()[?7h[?12l[?25h[?25l[?7l[0]).coordinates()[?7h[?12l[?25h[?25l[?7l[0]).coordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7l[0]).cordinates()[?7h[?12l[?25h[?25l[?7ld[0]).cordinates()[?7h[?12l[?25h[?25l[?7le[0]).cordinates()[?7h[?12l[?25h[?25l[?7l_[0]).cordinates()[?7h[?12l[?25h[?25l[?7lrh[0]).coordinates()[?7h[?12l[?25h[?25l[?7la[0]).cordinates()[?7h[?12l[?25h[?25l[?7lm[0]).cordinates()[?7h[?12l[?25h[?25l[?7l_[0]).cordinates()[?7h[?12l[?25h[?25l[?7lb[0]).cordinates()[?7h[?12l[?25h[?25l[?7la[0]).cordinates()[?7h[?12l[?25h[?25l[?7ls[0]).cordinates()[?7h[?12l[?25h[?25l[?7li[0]).cordinates()[?7h[?12l[?25h[?25l[?7ls[0]).cordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.de_rham_basis[0]).coordinates()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [17], in <cell line: 1>()
+----> 1 autom(C.de_rham_basis[Integer(0)]).coordinates()
+
+TypeError: 'method' object is not subscriptable
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.de_rham_basis[0]).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([0]).cordinates()[?7h[?12l[?25h[?25l[?7l)[0]).cordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.de_rham_basis()[0]).coordinates()

+[?7h[?12l[?25h[?2004lself ((1/y) dx, 0, (1/y) dx)
+[?7h[1, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.de_rham_basis()[0]).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]).cordinates()[?7h[?12l[?25h[?25l[?7l1]).cordinates()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: autom(C.de_rham_basis()[1]).coordinates()

+[?7h[?12l[?25h[?2004lself (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [19], in <cell line: 1>()
+----> 1 autom(C.de_rham_basis()[Integer(1)]).coordinates()
+
+File <string>:71, in coordinates(self)
+
+AttributeError: 'superelliptic_cech' object has no attribute 'coorinates'
+[?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[?7lautom(C.de_rham_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.de_rham_basis()[1]).coordinates()

+[?7h[?12l[?25h[?2004lself (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
+self ((1/y) dx, 0, (1/y) dx)
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [21], in <cell line: 1>()
+----> 1 autom(C.de_rham_basis()[Integer(1)]).coordinates()
+
+File <string>:71, in coordinates(self)
+
+File <string>:56, in coordinates(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 = <object>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[?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(C.de_rham_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.de_rham_basis()[1]).coordinates()

+[?7h[?12l[?25h[?2004lself (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
+self ((1/y) dx, 0, (1/y) dx)
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [23], in <cell line: 1>()
+----> 1 autom(C.de_rham_basis()[Integer(1)]).coordinates()
+
+File <string>:71, in coordinates(self)
+
+TypeError: unsupported operand type(s) for +: 'sage.modules.vector_modn_dense.Vector_modn_dense' and 'list'
+[?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[?7lautom(C.de_rham_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.de_rham_basis()[1]).coordinates()

+[?7h[?12l[?25h[?2004lself (((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
+self ((1/y) dx, 0, (1/y) dx)
+[?7h(1, 1)
+[?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(C.de_rham_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.de_rham_basis()[1]).coordinates()

+[?7h[?12l[?25h[?2004l[?7h(1, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+(1, 1)
+omega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+aux before reduce (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V((1/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [1], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:26, in <module>
+
+File <string>:74, in coordinates(self, basis)
+
+TypeError: unsupported operand type(s) for /: 'superelliptic_form' and 'superelliptic_function'
+[?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[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+(1, 1)
+omega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+aux before reduce (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V((1/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [2], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:26, in <module>
+
+File <string>:75, in coordinates(self, basis)
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?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[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+(1, 1)
+omega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+aux before reduce (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V((1/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [3], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:26, in <module>
+
+File <string>:79, in coordinates(self, basis)
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly.teichmuller().diffn().frobeniu()[?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[?7l2[?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[?7lsage: C.y/(C.x^2+C.x)

+[?7h[?12l[?25h[?2004l[?7h(1/(x^2 + x))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+C.x)[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2+C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?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[?7lsage: (C.y/(C.x^2+C.x)).expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht + 2*t^3 + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+C.x)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.teichmuler().f[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.teichmuller().f

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller().f[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: C.x.teichmuller().t

+[?7h[?12l[?25h[?2004l[?7hx
+[?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[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+(1, 1)
+omega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+aux_f_t_0 0
+aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), V((1/(x^2 + x))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [8], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:26, in <module>
+
+File <string>:82, in coordinates(self, basis)
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller().t[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis[?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.x.teichmuller().t[?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+(1, 1)
+omega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+aux_f_t_0 0
+aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), V((1/(x^4 + 2*x^3 + 2*x^2 + x))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [9], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:26, in <module>
+
+File <string>:82, in coordinates(self, basis)
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?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[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+(1, 1)
+omega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [10], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:26, in <module>
+
+File <string>:84, in coordinates(self, basis)
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?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[?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[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+(1, 1)
+omega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [1], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:26, in <module>
+
+File <string>:84, in coordinates(self, basis)
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2+C.x)).expansion_at_infty()[?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[?7l()[?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[?7lsage: (0*C.x).pth_root()

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 + x)/(x^2*y + x*y + y)[?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[?7ld[?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[?7lCy)*C.dx[?7h[?12l[?25h[?25l[?7l.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[?7lC*y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l*y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.y + 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[?7lCx*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.x*C.y + 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[?7lCx^2*y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.x^2*y + C.x*C.y + 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[?7lCy + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.y + C.x*C.y + 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[?7lCx)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l/x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7lx)/(C.x^2*C.y + C.x*C.y + 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[?7lCx^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + 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[?7lCx^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7lsage: ((-C.

+....: x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7lx^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + 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[?7lsage: ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx

+....: 

+....: )

+[?7h[?12l[?25h[?2004l[?7h((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + 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(-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7la(-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l=(-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7lsage: a = (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7la = (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.r() == -(C.x)^(-1)*C.y.diffn() + C.y*()^(-2)*dx[?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[?7l[?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[?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: a.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t^-2 + 2 + 2*t^4 + t^6 + O(t^8)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lsage: a.is_regular_on_U

+ a.is_regular_on_U0    

+ a.is_regular_on_Uinfty

+

+

+ [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0

+ a.is_regular_on_U0    

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l

+

+

+[?7h[?12l[?25h[?25l[?7lsage: a.is_regular_on_U0

+[?7h[?12l[?25h[?2004l[?7h<bound method superelliptic_form.is_regular_on_U0 of ((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7l((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + 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[?7la.is_regular_on_U0[?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.is_regular_on_U0()

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7la.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7l = (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)*C.dx[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: a = C.de_rham_basis()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7lb = C.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b = C.de_rham_basis()[1]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = 4*b[0][?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[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7ltalline_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A = C.crystalline_cohomology_basis()[0]

+[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lC = C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l = C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lB = C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()[1]

+[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lutom(C.de_rham_bais()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[0]).coordinates()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(b)

+[?7h[?12l[?25h[?2004l[?7h(((x + 1)/y) dx, (2/(x + 1))*y, ((-1)/(x*y + y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(b).coordinates()

+[?7h[?12l[?25h[?2004l[?7h(1, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b).coordinates()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lsage: autom(B) - B - A

+[?7h[?12l[?25h[?2004l[?7h(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V((1/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller().t[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly/(C.x^2+C.x)[?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(x^2+C.x)[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2+C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().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().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (C.y/(C.x^2+C.x)).expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht + 2*t^3 + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2+C.x)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lautomB) - B - A[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lDautom(B) - B - A[?7h[?12l[?25h[?25l[?7l autom(B) - B - A[?7h[?12l[?25h[?25l[?7l=autom(B) - B - A[?7h[?12l[?25h[?25l[?7l autom(B) - B - A[?7h[?12l[?25h[?25l[?7lsage: D = autom(B) - B - A

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD = autom(B) - B - A[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: D.r()

+[?7h[?12l[?25h[?2004l[?7h(0 dx, (1/(x^2 + x))*y, ((-x^2 - x + 1)/(x^2*y + x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.r()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.[?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[?7lD[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?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[?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[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-D.r().f.difn()[?7h[?12l[?25h[?25l[?7lsage: D.r().omega8 == -D.r().f.diffn()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.r().omega8 == -D.r().f.diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.r().omega8 == -D.r().f.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?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(C.y/(C.x^2+C.x))[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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= (C.y/(C.x^2+C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: D.f -= (C.y/(C.x^2+C.x)).teichmuller()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.f -= (C.y/(C.x^2+C.x)).teichmuller()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: D.omega8 = D.omega0 - D.f.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.omega8 = D.omega0 - D.f.diffn()[?7h[?12l[?25h[?25l[?7lsage: D

+[?7h[?12l[?25h[?2004l[?7h(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), V((1/(x^2 + x))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.omega8 = D.omega0 - D.f.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[?7lD[?7h[?12l[?25h[?25l[?7l.omega8 = D.omega0 - D.f.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[?7lD[?7h[?12l[?25h[?25l[?7l.omega8 = D.omega0 - D.f.diffn()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?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: D.omega0.h2 = 0*C.x

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.omega0.h2 = 0*C.x[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf -= (C.y/(C.x^2+C.x)).teichmuller()[?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[?7ly[?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[?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[?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[?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[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2 + C.x + C.one).verschiebung()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: D.f -= (C.y/(C.x^2 + C.x + C.one)).verschiebung()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.f -= (C.y/(C.x^2 + C.x + C.one)).verschiebung()[?7h[?12l[?25h[?25l[?7lomega0.h2 = 0*C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.omega8 = D.omega0 - D.f.diffn()[?7h[?12l[?25h[?25l[?7lf -= (C.y/(C.x^2+C.x)).techmuller()[?7h[?12l[?25h[?25l[?7lomega8 = D.omega0 - D.f.dffn()[?7h[?12l[?25h[?25l[?7lsage: D.omega8 = D.omega0 - D.f.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.omega8 = D.omega0 - D.f.diffn()[?7h[?12l[?25h[?25l[?7lsage: D

+[?7h[?12l[?25h[?2004l[?7h(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), V((1/(x^4 + 2*x^3 + 2*x^2 + x))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.omega8 = D.omega0 - D.f.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[?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[?7lD[?7h[?12l[?25h[?25l[?7l.omega8 = D.omega0 - D.f.diffn()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l3[?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[?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: D.omega8.h2 = 0*C.x

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.omega8.h2 = 0*C.x[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf -= (C.y/(C.x^2 + C.x + C.one)).verschiebung()[?7h[?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/(x^4 + 2*x^3 + 2*x^2 + x))*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy[?7h[?12l[?25h[?25l[?7l.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*/(x^4 + 2*x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7lC/(x^4 + 2*x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7l./(x^4 + 2*x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7lo/(x^4 + 2*x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7ln/(x^4 + 2*x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7le/(x^4 + 2*x^3 + 2*x^2 + x)*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[?7lCx^4 + 2*x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7l/x^4 + 2*x^3 + 2*x^2 + x)*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[?7lx^4 + 2*x^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7l.x^4 + 2*x^3 + 2*x^2 + x)*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[?7lCx^3 + 2*x^2 + x)*C.y[?7h[?12l[?25h[?25l[?7l.x^3 + 2*x^2 + x)*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[?7lCx^2 + x)*C.y[?7h[?12l[?25h[?25l[?7l.x^2 + x)*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[?7lCx)*C.y[?7h[?12l[?25h[?25l[?7l.x)*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((2*C.one/(C.x^4 + 2*C.x^3 + 2*C.x^2 + C.x))*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[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: D.f += ((2*C.one/(C.x^4 + 2*C.x^3 + 2*C.x^2 + C.x))*C.y).verschiebung()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.f += ((2*C.one/(C.x^4 + 2*C.x^3 + 2*C.x^2 + C.x))*C.y).verschiebung()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega8.h2 = 0*C.x[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: D.omega0 - D.f.diffn() == D.omega8

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lD.omega0 - D.f.diffn() == D.omega8[?7h[?12l[?25h[?25l[?7lsage: D

+[?7h[?12l[?25h[?2004l[?7h(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-x^3 + x^2 + x)/(x^2*y + x*y + y)) 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[?7lC^3 + x^2 + x)/(x^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l^3 + x^2 + x)/(x^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l/^3 + x^2 + x)/(x^2*y + x*y + y) 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^3 + x^2 + x)/(x^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^3 + x^2 + x)/(x^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l.x^3 + x^2 + x)/(x^2*y + x*y + y) 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[?7lCx^2 + x)/(x^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l.x^2 + x)/(x^2*y + x*y + y) 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[?7lCx)/(x^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l.x)/(x^2*y + x*y + y) 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[?7lCx^2*y + x*y + y) dx[?7h[?12l[?25h[?25l[?7l.x^2*y + x*y + y) 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[?7lCy + x*y + y) dx[?7h[?12l[?25h[?25l[?7l.y + x*y + y) 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[?7lCx*y + y) dx[?7h[?12l[?25h[?25l[?7l.x*y + y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy + y) dx[?7h[?12l[?25h[?25l[?7l.y + y) 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[?7lCy) dx[?7h[?12l[?25h[?25l[?7l.y) 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[?7lCdx[?7h[?12l[?25h[?25l[?7l.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* 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[?7la(-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7la(-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l=(-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7lsage: aa = (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx

+[?7h[?12l[?25h[?2004l  Input In [30]
+    aa = (-C.x**Integer(3) + C.x**Integer(2) + C.x)/(C.x**Integer(2)*C.y + C.x*C.y + C.y))* C.dx
+                                                                                         ^
+SyntaxError: unmatched ')'
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laa = (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + 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()* 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[?7lsage: aa = (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laa = (-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7la[?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[?7lsage: aa.is_regular_on_U

+ aa.is_regular_on_U0    

+ aa.is_regular_on_Uinfty

+

+

+ [?7h[?12l[?25h[?25l[?7l0

+ aa.is_regular_on_U0    

+

+ <unknown> [?7h[?12l[?25h[?25l[?7linfty

+ aa.is_regular_on_U0    

+ aa.is_regular_on_Uinfty[?7h[?12l[?25h[?25l[?7l(

+

+

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aa.is_regular_on_Uinfty()

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7laa.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l0()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aa.is_regular_on_U0()

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: B

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B.r()

+[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB.r()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: B0 = B.omega0

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 = B.omega0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: B0

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B0.r()

+[?7h[?12l[?25h[?2004l[?7h(x/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0.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[?7lB0.r()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l = B.omega0[?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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.*C.y.difn()[?7h[?12l[?25h[?25l[?7lt*C.y.difn()[?7h[?12l[?25h[?25l[?7le*C.y.difn()[?7h[?12l[?25h[?25l[?7li*C.y.difn()[?7h[?12l[?25h[?25l[?7lc*C.y.difn()[?7h[?12l[?25h[?25l[?7lh*C.y.difn()[?7h[?12l[?25h[?25l[?7lm*C.y.difn()[?7h[?12l[?25h[?25l[?7lu*C.y.difn()[?7h[?12l[?25h[?25l[?7lk*C.y.difn()[?7h[?12l[?25h[?25l[?7lk*C.y.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn()[?7h[?12l[?25h[?25l[?7l*C.y.difn()[?7h[?12l[?25h[?25l[?7ll*C.y.difn()[?7h[?12l[?25h[?25l[?7ll*C.y.difn()[?7h[?12l[?25h[?25l[?7le*C.y.difn()[?7h[?12l[?25h[?25l[?7lr*C.y.difn()[?7h[?12l[?25h[?25l[?7l(*C.y.difn()[?7h[?12l[?25h[?25l[?7l()*C.y.difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7lt.difn()[?7h[?12l[?25h[?25l[?7le.difn()[?7h[?12l[?25h[?25l[?7li.difn()[?7h[?12l[?25h[?25l[?7lc.difn()[?7h[?12l[?25h[?25l[?7lh.difn()[?7h[?12l[?25h[?25l[?7lm.difn()[?7h[?12l[?25h[?25l[?7lu.difn()[?7h[?12l[?25h[?25l[?7ll.difn()[?7h[?12l[?25h[?25l[?7ll.difn()[?7h[?12l[?25h[?25l[?7le.difn()[?7h[?12l[?25h[?25l[?7lr.difn()[?7h[?12l[?25h[?25l[?7l(.difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lsage: B0 - C.x.teichmuller()*C.y.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7hV(((x^8 - x^6 + 1)/y) dx) + dV([(2*x^4 + 2*x^2 + 2)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 - C.x.teichmuller()*C.y.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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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.teichmuler()*C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B0 -= C.x.teichmuller()*C.y.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 -= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: B0

+[?7h[?12l[?25h[?2004l[?7hV(((x^8 - x^6 + 1)/y) dx) + dV([(2*x^4 + 2*x^2 + 2)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller().t[?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[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x*C.y.diffn() == B.r()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [42], in <cell line: 1>()
+----> 1 C.x*C.y.diffn() == B.r()
+
+File <string>:12, in __eq__(self, other)
+
+AttributeError: 'superelliptic_cech' object has no attribute 'reduce'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x*C.y.diffn() == B.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[?7lor()[?7h[?12l[?25h[?25l[?7lomr()[?7h[?12l[?25h[?25l[?7ler()[?7h[?12l[?25h[?25l[?7lgr()[?7h[?12l[?25h[?25l[?7lar()[?7h[?12l[?25h[?25l[?7l0r()[?7h[?12l[?25h[?25l[?7l.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[?7lsage: C.x*C.y.diffn() == B.omega0.r()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0[?7h[?12l[?25h[?25l[?7lsage: B

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+(1, 1)
+omega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [45], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:26, in <module>
+
+File <string>:84, in coordinates(self, basis)
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()[1]

+[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: B

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l -= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l= B.omega0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB.omega0[?7h[?12l[?25h[?25l[?7lsage: B0 = B.omega0

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 = B.omega0[?7h[?12l[?25h[?25l[?7l = C.crystlline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0 = B.omega0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: B0 -= C.x.teichmuller()*C.y.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 -= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: B0

+[?7h[?12l[?25h[?2004l[?7hV(((x^8 - x^6 + 1)/y) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: B8 = B.omega8

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8 = B.omega8[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B.r()

+[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB.r()[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: B.r().omega8

+[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB.r().omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsB.r().omega8[?7h[?12l[?25h[?25l[?7leB.r().omega8[?7h[?12l[?25h[?25l[?7lcB.r().omega8[?7h[?12l[?25h[?25l[?7loB.r().omega8[?7h[?12l[?25h[?25l[?7lnB.r().omega8[?7h[?12l[?25h[?25l[?7ldB.r().omega8[?7h[?12l[?25h[?25l[?7l(B.r().omega8[?7h[?12l[?25h[?25l[?7lB.r().omega8[?7h[?12l[?25h[?25l[?7l_B.r().omega8[?7h[?12l[?25h[?25l[?7lpB.r().omega8[?7h[?12l[?25h[?25l[?7laB.r().omega8[?7h[?12l[?25h[?25l[?7ltB.r().omega8[?7h[?12l[?25h[?25l[?7lcB.r().omega8[?7h[?12l[?25h[?25l[?7lhB.r().omega8[?7h[?12l[?25h[?25l[?7ljB.r().omega8[?7h[?12l[?25h[?25l[?7l(B.r().omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(B.r().omega8)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: second_patch(B.r().omega8)

+[?7h[?12l[?25h[?2004l[?7h(x/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?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[?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[?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[?7lsage: u = C.one

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu = C.one[?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: u = C.one/C.x

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv1[?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[?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[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB.r().omega8[?7h[?12l[?25h[?25l[?7l8 = B.omega8[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?7lv[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?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[?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: B8 -= u.teichmuller()*v.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8 -= u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: B8

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^4 + 2*x^2))*y] d[x] + V(((x^8 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^6 + 2)/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8[?7h[?12l[?25h[?25l[?7l -= u.teichmuller()*v.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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l+= u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lsage: B8 += u.teichmuller()*v.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8 += u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B8 += u.teichmuller()*v.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8 += u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: B8

+[?7h[?12l[?25h[?2004l[?7hV(((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8[?7h[?12l[?25h[?25l[?7l.r().omega8[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B.r()

+[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* 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[?7lCy)* C.dx[?7h[?12l[?25h[?25l[?7l/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[?7ly)* C.dx[?7h[?12l[?25h[?25l[?7l.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[?7lCx^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^8*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[?7lCy - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.y - C.x^8*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[?7lCx^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^10*C.y - C.x^8*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)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7lC)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7lo)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7ln)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7le)/(C.x^10*C.y - C.x^8*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[?7lCx^2 - C.one)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^2 - C.one)/(C.x^10*C.y - C.x^8*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[?7lCx^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*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[?7lCx^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y)* C.dx[?7h[?12l[?25h[?25l[?7lsage: ((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx

+[?7h[?12l[?25h[?2004l[?7h((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*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[?7la((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7l ((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7l=((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7l ((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7lsage: a = ((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = ((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7l.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls_regular_on_U0()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?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[?7lsage: a.is_regular_on_Uinfty()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l((2*x^6 + 2)/(x^8 + 2*x^6))*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[?7lb = C.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((2*x^6 + 2)/(x^8 + 2*x^6))*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.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[?7lCx^6)*C.y[?7h[?12l[?25h[?25l[?7l.x^6)*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[?7lCx^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7l.x^8 + 2*C.x^6)*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*)/(C.x^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7lC)/(C.x^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7l.)/(C.x^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7lo)/(C.x^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7ln)/(C.x^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7le)/(C.x^8 + 2*C.x^6)*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[?7lCx^6 + 2*C.one)/(C.x^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7l.x^6 + 2*C.one)/(C.x^8 + 2*C.x^6)*C.y[?7h[?12l[?25h[?25l[?7lsage: b = ((2*C.x^6 + 2*C.one)/(C.x^8 + 2*C.x^6))*C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = ((2*C.x^6 + 2*C.one)/(C.x^8 + 2*C.x^6))*C.y[?7h[?12l[?25h[?25l[?7l.r().coordinates()[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?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[?7lb = ((2*C.x^6 + 2*C.one)/(C.x^8 + 2*C.x^6))*C.y[?7h[?12l[?25h[?25l[?7l.r().coordinates()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: b.expansion

+ b.expansion         

+ b.expansion_at_infty

+

+

+ [?7h[?12l[?25h[?25l[?7l

+ b.expansion         

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

+ b.expansion         

+ b.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(

+

+

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t + 2*t^5 + t^9 + t^17 + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lb.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = ((2*C.x^6 + 2*C.one)/(C.x^8 + 2*C.x^6))*C.y[?7h[?12l[?25h[?25l[?7la.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l = ((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7l((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7lB.r()[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l += u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l -= u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7luone/C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7lB.r().omega8[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l8 = B.omega8[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l -= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l= B.omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0 = B.omega0[?7h[?12l[?25h[?25l[?7l-= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l8 = B.omega8[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7l().omega8[?7h[?12l[?25h[?25l[?7lsecond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7lu = C.one[?7h[?12l[?25h[?25l[?7l/C.x[?7h[?12l[?25h[?25l[?7lvy/(C.x)^2[?7h[?12l[?25h[?25l[?7lB8 -= u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l += u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7l((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7la = ((C.x^8 - C.x^4 - C.x^2 - C.one)/(C.x^10*C.y - C.x^8*C.y))* C.dx[?7h[?12l[?25h[?25l[?7l.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lb = ((2*C.x^6 + 2*C.one)/(C.x^8 + 2*C.x^6))*C.y[?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[?7lB.r()[?7h[?12l[?25h[?25l[?7lsage: B

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B.r()

+[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x*C.y.diffn() == B.omega0.r()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7l()[1][?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[1]

+[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB.r()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()[0]

+[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l -= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l= B.omega0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB.omega0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega0[?7h[?12l[?25h[?25l[?7lsage: B0 = B.omega0

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 = B.omega0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-= C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l C.x.teichmuler()*C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?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: B0 - C.y.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7hV(((x^5 + x^3)/y) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 - C.y.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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l8 - C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laB8 - C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7laB8 - C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lsage: aaB8 - C.y.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [75], in <cell line: 1>()
+----> 1 aaB8 - C.y.teichmuller().diffn()
+
+NameError: name 'aaB8' is not defined
+[?2004h[?25l[?7lsage: [?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[?7lsage: v = C.y/(C.x)^2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7laaB8 - C.yteichmuller().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8 - C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lB8 - C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l+ C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lv.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B8 + C.v.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [77], in <cell line: 1>()
+----> 1 B8 + C.v.teichmuller().diffn()
+
+AttributeError: 'superelliptic' object has no attribute 'v'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8 + C.v.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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lv.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B8 + v.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((x^8 + x^6 - x^5 + x^4 + x^3 + x^2 + x - 1)/(x^9*y - x^8*y)) dx) + dV([((2*x^6 + x^3 + 1)/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8 + v.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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l- v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lsage: B8 - v.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7h[(2/(x^3 + 2*x))*y] d[x] + V(((-x^8 - x^6 - x^5 - x^4 + x^3 - x^2 + x + 1)/(x^9*y + x^8*y)) dx) + dV([((2*x^6 + 2*x^3 + 1)/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB8 - v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B.r()

+[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB.r()[?7h[?12l[?25h[?25l[?7l().omega8[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsB.r().omega8[?7h[?12l[?25h[?25l[?7leB.r().omega8[?7h[?12l[?25h[?25l[?7lcB.r().omega8[?7h[?12l[?25h[?25l[?7loB.r().omega8[?7h[?12l[?25h[?25l[?7lnB.r().omega8[?7h[?12l[?25h[?25l[?7ldB.r().omega8[?7h[?12l[?25h[?25l[?7l_B.r().omega8[?7h[?12l[?25h[?25l[?7lpB.r().omega8[?7h[?12l[?25h[?25l[?7laB.r().omega8[?7h[?12l[?25h[?25l[?7ltB.r().omega8[?7h[?12l[?25h[?25l[?7lcB.r().omega8[?7h[?12l[?25h[?25l[?7lhB.r().omega8[?7h[?12l[?25h[?25l[?7l(B.r().omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: second_patch(B.r().omega8)

+[?7h[?12l[?25h[?2004l[?7h((-1)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7lB.r()[?7h[?12l[?25h[?25l[?7l8 - v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lCv.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lvteichmuller().diffn()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lsecond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.de_rham_basis()[1][?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[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7lsecod_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7lB.r()[?7h[?12l[?25h[?25l[?7l8 - v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lCv.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lvteichmuller().diffn()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lsecond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7lC.geus()[?7h[?12l[?25h[?25l[?7l[?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[?7lsage: lo

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [83], in <cell line: 1>()
+----> 1 lo
+
+NameError: name 'lo' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+omega8_lift [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+(1, 1)
+omega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+omega8_lift [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [84], in <cell line: 1>()
+----> 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 <string>:31, in <module>
+
+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 <string>:26, in <module>
+
+File <string>:84, in coordinates(self, basis)
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?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.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7llline_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+omega8_lift - 0
+omega8_lift + [(2/(x^3 + 2*x))*y] d[x] + V(((-x^2 - 1)/(x^5*y)) dx) + dV([(2/(x^5 + 2*x^3))*y])
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+omega8_lift [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+omega8_lift - [(2/(x^3 + 2*x^2))*y] d[x] + V(((-x^7 + x^6 - x^5 - x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((2*x^2 + x + 2)/(x^7 + 2*x^6))*y])
+omega8_lift + [(1/(x^3 + x^2))*y] d[x] + V(((x^7 + x^6 + x^5 + x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((x^2 + x + 1)/(x^7 + x^6))*y])
+[?7h[([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])),
+ ([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l.crystalline_cohomology_basis()[?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[?7laC.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lsage: a = C.crystalline_cohomology_basis()[0]

+[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+omega8_lift - 0
+omega8_lift + [(2/(x^3 + 2*x))*y] d[x] + V(((-x^2 - 1)/(x^5*y)) dx) + dV([(2/(x^5 + 2*x^3))*y])
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+omega8_lift [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+omega8_lift - [(2/(x^3 + 2*x^2))*y] d[x] + V(((-x^7 + x^6 - x^5 - x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((2*x^2 + x + 2)/(x^7 + 2*x^6))*y])
+omega8_lift + [(1/(x^3 + x^2))*y] d[x] + V(((x^7 + x^6 + x^5 + x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((x^2 + x + 1)/(x^7 + x^6))*y])
+[?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[?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.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcrystalline_cohomology_basis()[?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[?7l[?7h[?12l[?25h[?25l[?7laC.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lC.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lsage: a = C.crystalline_cohomology_basis()[0]

+[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+omega8_lift - 0
+omega8_lift + [(2/(x^3 + 2*x))*y] d[x] + V(((-x^2 - 1)/(x^5*y)) dx) + dV([(2/(x^5 + 2*x^3))*y])
+omega0_regular (0, x)
+omega8 ((-1)/(x*y)) dx second_patch(omega8) (x/y) dx
+omega8_regular 1 (0, 2*x)
+omega8_regular 2 (0, 2/x)
+omega8_lift [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+omega8_lift - [(2/(x^3 + 2*x^2))*y] d[x] + V(((-x^7 + x^6 - x^5 - x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((2*x^2 + x + 2)/(x^7 + 2*x^6))*y])
+omega8_lift + [(1/(x^3 + x^2))*y] d[x] + V(((x^7 + x^6 + x^5 + x^3 + x^2 - 1)/(x^8*y)) dx) + dV([((x^2 + x + 1)/(x^7 + x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: a.omega8

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = 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[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l(C.x)^2[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?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[?7ly[?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 [?7h[?12l[?25h[?25l[?7lC.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[?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[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?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[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: v^2 - u - u^3

+[?7h[?12l[?25h[?2004l[?7h1/x^3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv^2 - u - u^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 u^3[?7h[?12l[?25h[?25l[?7l+ u^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[?7lsage: v^2 - u + u^3

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv^2 - u + u^3[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lu =C.one/C.x[?7h[?12l[?25h[?25l[?7lvy/(C.x)^2[?7h[?12l[?25h[?25l[?7la.omega8[?7h[?12l[?25h[?25l[?7lsage: a.omega8

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?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[?7l)[?7h[?12l[?25h[?25l[?7l()[?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.omega8 + v.diffn()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [9], in <cell line: 1>()
+----> 1 a.omega8 + v.diffn()
+
+File <string>:81, in __add__(self, other)
+
+AttributeError: 'superelliptic_form' object has no attribute 'h1'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega8 + v.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[?7ltdifn()[?7h[?12l[?25h[?25l[?7ledifn()[?7h[?12l[?25h[?25l[?7lidifn()[?7h[?12l[?25h[?25l[?7lcdifn()[?7h[?12l[?25h[?25l[?7lhdifn()[?7h[?12l[?25h[?25l[?7lmdifn()[?7h[?12l[?25h[?25l[?7ludifn()[?7h[?12l[?25h[?25l[?7lldifn()[?7h[?12l[?25h[?25l[?7lldifn()[?7h[?12l[?25h[?25l[?7ledifn()[?7h[?12l[?25h[?25l[?7lrdifn()[?7h[?12l[?25h[?25l[?7l(difn()[?7h[?12l[?25h[?25l[?7l()difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l/difn()[?7h[?12l[?25h[?25l[?7ldifn()[?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.omega8 + v.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7h[(2/(x^3 + 2*x))*y] d[x] + V(((x^2 + 1)/(x^5*y)) dx) + dV([((x^2 + 1)/(x^5 + 2*x^3))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega8 + v.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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l- v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lsage: a.omega8 - v.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7hV(((-x^2 - 1)/(x^5*y)) dx) + dV([1/x^3*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega8 - v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: a

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.omega8 - v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lr() ==(Cx)^(-1)*C.y.diffn() + C.y*(C.x)^(-2)*C.dx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.r()

+[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv^2 - u + u^3[?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: v.diffn()

+[?7h[?12l[?25h[?2004l[?7h(1/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv.diffn()[?7h[?12l[?25h[?25l[?7lar()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.omega8 - v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: a.omega8 - v.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7hV(((-x^2 - 1)/(x^5*y)) dx) + dV([1/x^3*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega8 - v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega8 - v.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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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.omega8 - v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?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[?7lla[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lU[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (a.omega8 - v.teichmuller().diffn()).omega.is_regular_on_U0()

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a.omega8 - v.teichmuller().diffn()).omega.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?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[?7lsage: (a.omega8 - v.teichmuller().diffn()).omega.is_regular_on_Uinfty()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a.omega8 - v.teichmuller().diffn()).omega.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?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[?7lh[?7h[?12l[?25h[?25l[?7l2[?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[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lU[?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: (a.omega8 - v.teichmuller().diffn()).h2.is_regular_on_Uinfty()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [18], in <cell line: 1>()
+----> 1 (a.omega8 - v.teichmuller().diffn()).h2.is_regular_on_Uinfty()
+
+AttributeError: 'superelliptic_function' object has no attribute 'is_regular_on_Uinfty'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a.omega8 - v.teichmuller().diffn()).h2.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7li[?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[?7l()[?7h[?12l[?25h[?25l[?7lsage: (a.omega8 - v.teichmuller().diffn()).h2.expansion()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [19], in <cell line: 1>()
+----> 1 (a.omega8 - v.teichmuller().diffn()).h2.expansion()
+
+TypeError: superelliptic_function.expansion() missing 1 required positional argument: 'pt'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a.omega8 - v.teichmuller().diffn()).h2.expansion()[?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[?7lsage: (a.omega8 - v.teichmuller().diffn()).h2.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^3 + 2*t^7 + 2*t^11 + t^15 + 2*t^19 + O(t^23)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a.omega8 - v.teichmuller().diffn()).h2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lis_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lomega.is_regularon_Uinfty()[?7h[?12l[?25h[?25l[?7lh2.is_regular_onUinfty()[?7h[?12l[?25h[?25l[?7lexpansion()[?7h[?12l[?25h[?25l[?7l_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[?7la.omega8 - v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: a

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
+[?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$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lresult.factor()[?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[?7lsage: regula

+ regular_form

+ regulator   

+

+

+ [?7h[?12l[?25h[?25l[?7lr_form

+ regular_form

+

+ <unknown> [?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[?7l()[?7h[?12l[?25h[?25l[?7lsage: regular_form(C.dx)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+

+

+

+ [?7h[?12l[?25h[?25l[?7lregular_form(C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form(C.dx)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm_witt_lift[?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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lam_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(C.de_rham_basis()[0])

+[?7h[?12l[?25h[?2004lomega0_regular (0, 1)
+omega8 (1/y) dx second_patch(omega8) ((-1)/y) dx
+omega8_regular 1 (0, 1)
+omega8_regular 2 (0, 1)
+omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+omega8_lift - 0
+omega8_lift + [(2/(x^3 + 2*x))*y] d[x] + V(((-x^2 - 1)/(x^5*y)) dx) + dV([(2/(x^5 + 2*x^3))*y])
+[?7h([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
+[?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.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rhm_basis()[1][?7h[?12l[?25h[?25l[?7lx.expansion(pt=(-1, 0))[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.dx.regular_form()

+[?7h[?12l[?25h[?2004l[?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[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.dx.regular_form()[?7h[?12l[?25h[?25l[?7lsage: C.dx.regular_form()

+[?7h[?12l[?25h[?2004l[?7h<repr(<__main__.superelliptic_regular_form at 0x7f293c63c4f0>) failed: NameError: name 'A' is not defined>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.dx.regular_form()[?7h[?12l[?25h[?25l[?7lsage: C.dx.regular_form()

+[?7h[?12l[?25h[?2004l[?7h1 dx + 0 dy
+[?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[?2004lTraceback (most recent call last):
+
+  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input In [11] in <cell line: 1>
+    load('init.sage')
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:18 in <module>
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:8
+    if self.dx.form = _sage_const_0 :
+       ^
+SyntaxError: cannot assign to attribute here. Maybe you meant '==' instead of '='?
+
+[?2004h[?25l[?7lsage: [?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[?7lk[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lift.r()[?7h[?12l[?25h[?25l[?7l[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.dx.regular_form()[?7h[?12l[?25h[?25l[?7lsage: C.dx.regular_form()

+[?7h[?12l[?25h[?2004l[?7h<repr(<__main__.superelliptic_regular_form at 0x7f293c5f6ec0>) failed: AttributeError: 'superelliptic_function' object has no attribute 'form'>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.dx.regular_form()[?7h[?12l[?25h[?25l[?7lsage: C.dx.regular_form()

+[?7h[?12l[?25h[?2004l[?7h1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.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).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(C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l(C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l()C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l.)C.dx).regular_form()[?7h[?12l[?25h[?25l[?7ly)C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l(C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l-C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l1C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l()C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l()*C.dx).regular_form()[?7h[?12l[?25h[?25l[?7lsage: ((C.y)^(-1)*C.dx).regular_form()

+[?7h[?12l[?25h[?2004l[?7h1 dy
+[?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[?7l((C.y)^(-1)*C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA((C.y)^(-1)*C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l ((C.y)^(-1)*C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l=((C.y)^(-1)*C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l ((C.y)^(-1)*C.dx).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[?7lsage: A = ((C.y)^(-1)*C.dx).regular_form()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = ((C.y)^(-1)*C.dx).regular_form()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A

+[?7h[?12l[?25h[?2004l[?7h1 dy
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?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[?7lsage: A.form

+[?7h[?12l[?25h[?2004l[?7h<bound method superelliptic_regular_form.form of 1 dy>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.form[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.form()

+[?7h[?12l[?25h[?2004l[?7h(1/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[?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.dx.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[?7lC.dx.regular_form()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcrystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lstalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [23], in <cell line: 1>()
+----> 1 C.crystalline_cohomology_basis()
+
+File <string>:39, in crystalline_cohomology_basis(self, prec)
+
+File <string>:15, in de_rham_witt_lift(cech_class, prec)
+
+AttributeError: 'tuple' object has no attribute '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[?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[?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[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [26], in <cell line: 1>()
+----> 1 C.crystalline_cohomology_basis()
+
+File <string>:39, in crystalline_cohomology_basis(self, prec)
+
+File <string>:15, in de_rham_witt_lift(cech_class, prec)
+
+AttributeError: 'tuple' object has no attribute 'dx'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form(C.dx)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_form(C.dx)[?7h[?12l[?25h[?25l[?7lsage: regular_form(C.dx)

+[?7h[?12l[?25h[?2004l[?7h1 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[?7lregular_form(C.dx)[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l[?7h[([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])),
+ ([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[0].omega0.regular_form()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [31], in <cell line: 1>()
+----> 1 B[Integer(0)].omega0.regular_form()
+
+AttributeError: 'superelliptic_drw_form' object has no attribute 'regular_form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF = GF(4, 'a')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[0].omega0.regular_form()[?7h[?12l[?25h[?25l[?7l0 - C.y.teichmler().diffn()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsage: B01 = super

+ super                          superelliptic_cech             superelliptic_drw_form         superelliptic_regular_drw_form supersingular_D               

+ superelliptic                  superelliptic_drw/             superelliptic_form             superelliptic_regular_form     supersingular_j               

+ superelliptic/                 superelliptic_drw_cech         superelliptic_function         superelliptic_witt                                           

+

+ [?7h[?12l[?25h[?25l[?7lsupere

+

+

+[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?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[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: B01 = B[0].omega0

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+

+ [?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l

+ B01.curve     B01.h2       

+ B01.frobenius B01.omega    

+ B01.h1        B01.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[?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[?7l[?7h[?12l[?25h[?25l[?7l'init.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/automorphism.sage')[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l(relliptic_drw/automorphism.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.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7lre.sage')[?7h[?12l[?25h[?25l[?7lg.sage')[?7h[?12l[?25h[?25l[?7lu.sage')[?7h[?12l[?25h[?25l[?7ll.sage')[?7h[?12l[?25h[?25l[?7la.sage')[?7h[?12l[?25h[?25l[?7lr.sage')[?7h[?12l[?25h[?25l[?7l_.sage')[?7h[?12l[?25h[?25l[?7lf.sage')[?7h[?12l[?25h[?25l[?7lo.sage')[?7h[?12l[?25h[?25l[?7lr.sage')[?7h[?12l[?25h[?25l[?7lm.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/regular_form.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+

+ [?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7l[0].omega0.rular_form()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohmology_basis()[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomlgy_basis()[?7h[?12l[?25h[?25l[?7lB = C.crystalline_chmology_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7l

+

+

+ 

+

+

+

+

+

+

+

+

+

+

+

+

+

+ [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7lsage: B01 = B[0].omega0

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+ [?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7l =C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l01= B[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l

+ B01.curve        B01.h2           B01.regular_form

+ B01.frobenius    B01.omega                        

+ B01.h1           B01.r                            [?7h[?12l[?25h[?25l[?7lcurve

+ B01.curve       

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7lh2

+ B01.curve        B01.h2          [?7h[?12l[?25h[?25l[?7lregular_form

+ B01.h2           B01.regular_form[?7h[?12l[?25h[?25l[?7l

+

+

+

+[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B01.regular_form()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [36], in <cell line: 1>()
+----> 1 B01.regular_form()
+
+File <string>:37, in regular_drw_form(omega)
+
+TypeError: 'superelliptic' object is not callable
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+

+

+

+

+ [?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/regular_form.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+

+

+

+ [?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.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[?7l(nit.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[?7lsuperelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/regular_form.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+

+ [?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l =C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l =C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l01= B[0].omega0[?7h[?12l[?25h[?25l[?7lsage: B01 = B[0].omega0

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+

+ [?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7legular_form()[?7h[?12l[?25h[?25l[?7lsage: B01.regular_form()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [42], in <cell line: 1>()
+----> 1 B01.regular_form()
+
+File <string>:41, in regular_drw_form(omega)
+
+TypeError: superelliptic_drw_form.__init__() takes 4 positional arguments but 5 were given
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/regular_form.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l =C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7linit.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[?7lsuperelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l =C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7lsage: B01 = B[0].omega0

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01 = B[0].omega0[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7lsage: B01.regular_form()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [47], in <cell line: 1>()
+----> 1 B01.regular_form()
+
+AttributeError: 'superelliptic_drw_form' object has no attribute 'regular_form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l =C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lsage: load('superelliptic_drw/regular_form.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l =C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l01.regular_form()[?7h[?12l[?25h[?25l[?7l1.regular_form()[?7h[?12l[?25h[?25l[?7lsage: B01.regular_form()

+[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [1] d[y] + V(((x^5 + x^3)/y) dx) + dV(0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('superelliptic_drw/regular_form.sage')[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: B01 = B[0].omega8

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01 = B[0].omega8[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lnd_patch[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B01 = second_patch(B01)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01 = second_patch(B01)[?7h[?12l[?25h[?25l[?7lB[0].omega8[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: B01.regular_form()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [53], in <cell line: 1>()
+----> 1 B01.regular_form()
+
+AttributeError: 'NoneType' object has no attribute 'regular_form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB01.regular_form()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: B01

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?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$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ qsage -i parsivelib galois Representations
+make build/make/Makefile --stop
+make[1]: Entering directory '/ext/sage/9.7'
+make[1]: 'build/make/Makefile' is up to date.
+make[1]: Leaving directory '/ext/sage/9.7'
+build/bin/sage-logger \
+	"cd build/make && ./install 'all-toolchain'" logs/install.log
+tee: logs/install.log: Read-only file system
+make[1]: Entering directory '/ext/sage/9.7/build/make'
+make[1]: Leaving directory '/ext/sage/9.7/build/make'
+*** ALL ENVIRONMENT VARIABLES BEFORE BUILD: ***
+ANACONDA2019=/ext/anaconda-2019.03
+ANACONDA2020=/ext/anaconda2020.02
+ANACONDA2021=/ext/anaconda2021.11
+ANACONDA2022=/ext/anaconda2022.05
+ANACONDA3=/ext/anaconda3
+ANACONDA5=/ext/anaconda5
+BROWSER_PORT=6001
+COCALC_CODE_PORT=6004
+COCALC_EXTRA_ENV=e30=
+COCALC_JUPYTERLAB_PORT=6002
+COCALC_JUPYTER_PORT=6003
+COCALC_NODE=kucalc-prod3-node-pbpa
+COCALC_PLUTO_PORT=6005
+COCALC_PROJECT_CONFIG=eyJxdW90YSI6eyJuZXR3b3JrIjp0cnVlLCJtZW1iZXJfaG9zdCI6dHJ1ZSwicHJpdmlsZWdlZCI6ZmFsc2UsIm1lbW9yeV9yZXF1ZXN0IjozMDAsImNwdV9yZXF1ZXN0IjowLjA1LCJkaXNrX3F1b3RhIjo4MDAwLCJtZW1vcnlfbGltaXQiOjEyMDAwLCJjcHVfbGltaXQiOjIsImlkbGVfdGltZW91dCI6MTgwMCwiYWx3YXlzX3J1bm5pbmciOmZhbHNlLCJkZWRpY2F0ZWRfdm0iOmZhbHNlLCJkZWRpY2F0ZWRfZGlza3MiOltdfX0=
+COCALC_PROJECT_DATASTORE=false
+COCALC_PROJECT_ID=6b7177d7-4a24-4810-937c-d1fa861bd29e
+COCALC_PROJECT_IMAGE_NAME=ubuntu2004
+COCALC_SECRET_TOKEN=/secrets/secret-token/token
+COCALC_SSH_PORT=2222
+COCALC_TERMINAL_FILENAME=.run.term-0.term
+COCALC_ULIMIT_OPEN_FILES=10000
+COCALC_USERNAME=user
+DEBUG=project:*,cocalc:*
+DEBUG_HIDE_DATE=yes
+ELAN_HOME=/ext/lean
+EXT=/ext
+HISTCONTROL=ignoredups
+HOME=/home/user
+HOSTNAME=project-6b7177d7-4a24-4810-937c-d1fa861bd29e
+HUB_PORT=6000
+ISOCHRONES=/ext/data/isochrones
+JULIA_DEPOT_PATH=/home/user/.julia:/ext/julia/depot/
+JUPYTER_PATH=/ext/jupyter
+LANG=en_US.UTF-8
+LANGUAGE=en_US:en
+LC_ALL=C.UTF-8
+LESSCLOSE=/usr/bin/lesspipe %s %s
+LESSOPEN=| /usr/bin/lesspipe %s
+LESS_TERMCAP_se=
+LESS_TERMCAP_so=
+LS_COLORS=rs=0:di=01;34:ln=01;36:mh=00:pi=40;33:so=01;35:do=01;35:bd=40;33;01:cd=40;33;01:or=40;31;01:mi=00:su=37;41:sg=30;43:ca=30;41:tw=30;42:ow=34;42:st=37;44:ex=01;32:*.tar=01;31:*.tgz=01;31:*.arc=01;31:*.arj=01;31:*.taz=01;31:*.lha=01;31:*.lz4=01;31:*.lzh=01;31:*.lzma=01;31:*.tlz=01;31:*.txz=01;31:*.tzo=01;31:*.t7z=01;31:*.zip=01;31:*.z=01;31:*.dz=01;31:*.gz=01;31:*.lrz=01;31:*.lz=01;31:*.lzo=01;31:*.xz=01;31:*.zst=01;31:*.tzst=01;31:*.bz2=01;31:*.bz=01;31:*.tbz=01;31:*.tbz2=01;31:*.tz=01;31:*.deb=01;31:*.rpm=01;31:*.jar=01;31:*.war=01;31:*.ear=01;31:*.sar=01;31:*.rar=01;31:*.alz=01;31:*.ace=01;31:*.zoo=01;31:*.cpio=01;31:*.7z=01;31:*.rz=01;31:*.cab=01;31:*.wim=01;31:*.swm=01;31:*.dwm=01;31:*.esd=01;31:*.jpg=01;35:*.jpeg=01;35:*.mjpg=01;35:*.mjpeg=01;35:*.gif=01;35:*.bmp=01;35:*.pbm=01;35:*.pgm=01;35:*.ppm=01;35:*.tga=01;35:*.xbm=01;35:*.xpm=01;35:*.tif=01;35:*.tiff=01;35:*.png=01;35:*.svg=01;35:*.svgz=01;35:*.mng=01;35:*.pcx=01;35:*.mov=01;35:*.mpg=01;35:*.mpeg=01;35:*.m2v=01;35:*.mkv=01;35:*.webm=01;35:*.ogm=01;35:*.mp4=01;35:*.m4v=01;35:*.mp4v=01;35:*.vob=01;35:*.qt=01;35:*.nuv=01;35:*.wmv=01;35:*.asf=01;35:*.rm=01;35:*.rmvb=01;35:*.flc=01;35:*.avi=01;35:*.fli=01;35:*.flv=01;35:*.gl=01;35:*.dl=01;35:*.xcf=01;35:*.xwd=01;35:*.yuv=01;35:*.cgm=01;35:*.emf=01;35:*.ogv=01;35:*.ogx=01;35:*.aac=00;36:*.au=00;36:*.flac=00;36:*.m4a=00;36:*.mid=00;36:*.midi=00;36:*.mka=00;36:*.mp3=00;36:*.mpc=00;36:*.ogg=00;36:*.ra=00;36:*.wav=00;36:*.oga=00;36:*.opus=00;36:*.spx=00;36:*.xspf=00;36:
+MAKE=make
+MAKEFLAGS= V=1
+MAKELEVEL=1
+MAKE_TERMERR=/dev/pts/0
+MAKE_TERMOUT=/dev/pts/0
+MFLAGS=
+MKL_THREADING_LAYER=GNU
+MPLBACKEND=Agg
+NLTK_DATA=/ext/data/nltk_data
+NVM_INC=/cocalc/nvm/versions/node/v16.19.1/include/node
+OLDPWD=/ext/sage/9.7
+PATH=/ext/sage/9.7/build/bin:/ext/sage/9.7/src/bin:/ext/sage/9.7/local/bin:/cocalc/bin:/cocalc/src/smc-project/bin:/home/user/bin:/home/user/.local/bin:/ext/bin:/usr/lib/xpra:/opt/ghc/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/ext/data/homer/bin:/ext/data/weblogo:/usr/lib/postgresql/10/bin
+PGHOST=localhost
+PROMPT_COMMAND=history -a
+PWD=/ext/sage/9.7/build/make
+PYTHONPATH=/ext/sage/9.7/local
+PYTHONUSERBASE=/home/user/.local
+QT_QPA_PLATFORM=xcb
+SAGE_ATLAS_LIB=/usr/lib/
+SAGE_ENV_CONFIG_SOURCED=1
+SAGE_LOCAL=/ext/sage/9.7/local
+SAGE_LOGFILE=logs/install.log
+SAGE_LOGS=/ext/sage/9.7/logs/pkgs
+SAGE_NUM_THREADS=1
+SAGE_NUM_THREADS_PARALLEL=4
+SAGE_ORIG_PATH=/cocalc/bin:/cocalc/src/smc-project/bin:/home/user/bin:/home/user/.local/bin:/ext/bin:/usr/lib/xpra:/opt/ghc/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/ext/data/homer/bin:/ext/data/weblogo:/usr/lib/postgresql/10/bin
+SAGE_ORIG_PATH_SET=True
+SAGE_PKGCONFIG=/ext/sage/9.7/local/lib/pkgconfig
+SAGE_ROOT=/ext/sage/9.7
+SAGE_SHARE=/ext/sage/9.7/local/share
+SAGE_SRC=/ext/sage/9.7/src
+SAGE_VENV=/ext/sage/9.7/local/var/lib/sage/venv-python3.10.5
+SCREENDIR=/tmp/screen
+SHELL=/bin/bash
+SHLVL=3
+SMC=/tmp/.cocalc
+TERM=xterm-256color
+TZ=Etc/UTC
+USER=user
+XDG_RUNTIME_DIR=/tmp/xdg-runtime-user
+_=/usr/bin/env
+_JAVA_OPTIONS=-Xms64m
+***********************************************
+make[1]: Entering directory '/ext/sage/9.7/build/make'
+make --no-print-directory toolchain
+make[2]: Nothing to be done for 'toolchain'.
+make --no-print-directory toolchain-deps
+make --no-print-directory /ext/sage/9.7/local/var/lib/sage/installed/.dummy
+make[3]: '/ext/sage/9.7/local/var/lib/sage/installed/.dummy' is up to date.
+make --no-print-directory /ext/sage/9.7/local/var/lib/sage/installed/.dummy
+make[3]: '/ext/sage/9.7/local/var/lib/sage/installed/.dummy' is up to date.
+make --no-print-directory /ext/sage/9.7/local/var/lib/sage/installed/.dummy
+make[3]: '/ext/sage/9.7/local/var/lib/sage/installed/.dummy' is up to date.
+make --no-print-directory /ext/sage/9.7/local/var/lib/sage/installed/.dummy
+make[3]: '/ext/sage/9.7/local/var/lib/sage/installed/.dummy' is up to date.
+make[1]: Leaving directory '/ext/sage/9.7/build/make'
+
+real	0m0.278s
+user	0m0.238s
+sys	0m0.020s
+Sage build/upgrade complete!
+
+Error: package 'parsivelib' not found
+Note: if it is an old-style package, installing these is no longer supported
+]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[?7lload('superelliptic_drw/regular_form.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[?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[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcrystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[0].omega0.regular_frm()[?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[?7lB[0][?7h[?12l[?25h[?25l[?7l0B[0][?7h[?12l[?25h[?25l[?7l B[0][?7h[?12l[?25h[?25l[?7l=B[0][?7h[?12l[?25h[?25l[?7l B[0][?7h[?12l[?25h[?25l[?7lsage: B0 = B[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 = B[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = B[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega8_lift0.omega8 - compare[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = AS.holomrphic_differentials_basis()[-1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: om = B[0].omega8

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = B[0].omega8[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage -i parsivelib galois Representations[?7h[?12l[?25h[?25l[?7lecond_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lnd_patch(B.r().omega8)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?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[?7lsage: second_patch(om)

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(2*x/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(om)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: second_patch(om).r()

+[?7h[?12l[?25h[?2004l[?7h((-1)/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.expansion(pt = (-1, 0))[?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[?7lsom.r()[?7h[?12l[?25h[?25l[?7leom.r()[?7h[?12l[?25h[?25l[?7lcom.r()[?7h[?12l[?25h[?25l[?7lom.r()[?7h[?12l[?25h[?25l[?7lnom.r()[?7h[?12l[?25h[?25l[?7ldom.r()[?7h[?12l[?25h[?25l[?7l_om.r()[?7h[?12l[?25h[?25l[?7lpom.r()[?7h[?12l[?25h[?25l[?7laom.r()[?7h[?12l[?25h[?25l[?7ltom.r()[?7h[?12l[?25h[?25l[?7lcom.r()[?7h[?12l[?25h[?25l[?7lhom.r()[?7h[?12l[?25h[?25l[?7l(om.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[?7lsage: second_patch(om.r())

+[?7h[?12l[?25h[?2004l[?7h((-1)/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[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsom[?7h[?12l[?25h[?25l[?7leom[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = B[0].omega8[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?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_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?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: om = second_patch(om)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = second_patch(om)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.expansion(p = (-1, 0))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lgular_form[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form()

+[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [1] d[y] + V(((x^5 + x^3)/y) dx) + dV(x*y)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7l = second_patch(om)[?7h[?12l[?25h[?25l[?7lsecond_patch(om.r())[?7h[?12l[?25h[?25l[?7l().r([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7l = B[0].omega8[?7h[?12l[?25h[?25l[?7lB0[][?7h[?12l[?25h[?25l[?7lom[].omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l].omega8[?7h[?12l[?25h[?25l[?7l1].omega8[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = B[1].omega8

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = B[1].omega8[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7l = B[1].omega8[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7l = second_patch(om)[?7h[?12l[?25h[?25l[?7lsecond_patch(om.r())[?7h[?12l[?25h[?25l[?7lom = second_patch(om)[?7h[?12l[?25h[?25l[?7lsage: om = second_patch(om)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = second_patch(om)[?7h[?12l[?25h[?25l[?7lB[1].omega8[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form()

+[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [2*x] d[y] + V(((-x^10 - x^8 - x^6 + x^2)/(x^2*y - y)) dx) + dV((2*x^4 + 2*x^2 + 2)*y)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx.<x> = PolynomialRing(R)[?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[?7l[?7h[?12l[?25h[?25l[?7l-x^10 - x^8 - x^6 + x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-x^10 - x^8 - x^6 + x^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?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[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?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[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (-x^10 - x^8 - x^6 + x^2).quo_rem(x^2 - 1)

+[?7h[?12l[?25h[?2004l[?7h(2*x^8 + x^6 + 1, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 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[?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[?7leta1 = de_rham_witt_lift(C.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: eta2

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(1/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta2.r()

+[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.r()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega8.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0omega.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.omega.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[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta2.omega0.regular_form()

+[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [x] d[y] + V(0 dx) + dV((2*x^4 + 2*x^2 + 2)*y)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega0.regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7l8.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[?7lseta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7leta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7lceta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7loeta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7lneta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7ldeta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7l_eta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7lpeta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7laeta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7lteta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7lceta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7lheta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7l(eta2.omega8.regular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().regular_form()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: second_patch(eta2.omega8).regular_form()

+[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [2*x] d[y] + V(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV((2*x^4 + 2*x^2 + 2)*y)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)[?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[?7lx[?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[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1).quo_rem(x^10 - x^8)

+[?7h[?12l[?25h[?2004l[?7h(2*x^8 + x^6 + 2, x^8 + 2*x^4 + 2*x^2 + 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lstalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()[1]

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega0.regular_form()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?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[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lEC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lTC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lAC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l2C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ETA2 = C.crystalline_cohomology_basis()[1]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: ETA2 - eta2

+[?7h[?12l[?25h[?2004l[?7h(V(((x^8 - x^6 + 1)/y) dx) + dV([(x^4 + x^2 + 1)*y]), V((x^4 + x^2 + 1)*y), V(((x^8 - x^6 + 1)/y) dx))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^8 - x^6 + 1)/y) 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[?7lCx^8 - x^6 + 1)/y) dx[?7h[?12l[?25h[?25l[?7l.x^8 - x^6 + 1)/y) 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[?7lCx^6 + 1)/y) dx[?7h[?12l[?25h[?25l[?7l.x^6 + 1)/y) 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)/y) dx[?7h[?12l[?25h[?25l[?7lC)/y) dx[?7h[?12l[?25h[?25l[?7l.)/y) dx[?7h[?12l[?25h[?25l[?7lo)/y) dx[?7h[?12l[?25h[?25l[?7ln)/y) dx[?7h[?12l[?25h[?25l[?7le)/y) dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy) dx[?7h[?12l[?25h[?25l[?7l.y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.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[?7lsage: (C.x^8 - C.x^6 + C.one)/C.y)*C.dx

+[?7h[?12l[?25h[?2004l  Input In [11]
+    (C.x**Integer(8) - C.x**Integer(6) + C.one)/C.y)*C.dx
+                                                   ^
+SyntaxError: unmatched ')'
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^8 - C.x^6 + C.one)/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*C.dx[?7h[?12l[?25h[?25l[?7lsage: (C.x^8 - C.x^6 + C.one)/C.y*C.dx

+[?7h[?12l[?25h[?2004l[?7h((x^8 - x^6 + 1)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^8 - C.x^6 + C.one)/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((C.x^8 - C.x^6 + C.one)/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[?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.x^8 - C.x^6 + C.one)/C.y*C.dx).expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^-16 + t^-8 + O(t^-6)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega0.regular_form()[?7h[?12l[?25h[?25l[?7lt[?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[?7loeta[?7h[?12l[?25h[?25l[?7lmeta[?7h[?12l[?25h[?25l[?7l eta[?7h[?12l[?25h[?25l[?7l eta[?7h[?12l[?25h[?25l[?7leta[?7h[?12l[?25h[?25l[?7l=eta[?7h[?12l[?25h[?25l[?7l eta[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: om = eta.omega8

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [14], in <cell line: 1>()
+----> 1 om = eta.omega8
+
+AttributeError: 'function' object has no attribute 'omega8'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = eta.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = eta2.omega8

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = eta2.omega8[?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.regular_form()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.r()

+[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.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[?7lsom.r()[?7h[?12l[?25h[?25l[?7leom.r()[?7h[?12l[?25h[?25l[?7lcom.r()[?7h[?12l[?25h[?25l[?7lom.r()[?7h[?12l[?25h[?25l[?7lnom.r()[?7h[?12l[?25h[?25l[?7ldom.r()[?7h[?12l[?25h[?25l[?7l_om.r()[?7h[?12l[?25h[?25l[?7lpom.r()[?7h[?12l[?25h[?25l[?7laom.r()[?7h[?12l[?25h[?25l[?7ltom.r()[?7h[?12l[?25h[?25l[?7lcom.r()[?7h[?12l[?25h[?25l[?7lhom.r()[?7h[?12l[?25h[?25l[?7l(om.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[?7lsage: second_patch(om.r())

+[?7h[?12l[?25h[?2004l[?7h(x/y) dx
+[?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 [?7h[?12l[?25h[?25l[?7lC.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[?7l[?7h[?12l[?25h[?25l[?7lv.diffn()[?7h[?12l[?25h[?25l[?7l = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.y/(C.x)^2[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7lom.r()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = eta2.omega8[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?7lv[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?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 - u.teichmuller()*v.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^4 + 2*x^2))*y] d[x] + V(((-x^18 - x^16 - x^14 - x^10 - x^8 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^6 + 2)/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom - u.teichmuller()*v.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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l+ u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om + u.teichmuller()*v.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7hV(((-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1.frobnius()[?7h[?12l[?25h[?25l[?7l = C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*(C.y).diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 + u.teichmuller()*v.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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lmom + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l1om + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l om + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l=om + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l om + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = om + u.teichmuller()*v.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = om + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.frbenis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?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: om1.omega.expansion

+ om1.omega.expansion         

+ om1.omega.expansion_at_infty

+

+

+ [?7h[?12l[?25h[?25l[?7l

+ om1.omega.expansion         

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

+ om1.omega.expansion         

+ om1.omega.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(

+

+

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.omega.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t^-16 + 2*t^-8 + O(t^-6)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lom1.omega.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[?7la.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.omega.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lfrobenius()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?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: om1.frobenius()

+[?7h[?12l[?25h[?2004l[?7h((-x^6 + x^4 + x^2 - 1)/(x^6*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7lom1.frobenius()[?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[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.frobenius().expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2 + 2*t^4 + t^8 + O(t^10)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?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[?7lsage: om1.h2.expansion

+ om1.h2.expansion         

+ om1.h2.expansion_at_infty

+

+

+ [?7h[?12l[?25h[?25l[?7l

+ om1.h2.expansion         

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

+ om1.h2.expansion         

+ om1.h2.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(

+

+

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.h2.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t + 2*t^5 + t^9 + 2*t^13 + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+ [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7ltalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()[1]

+[?7h[?12l[?25h[?2004lresult.omega8 == compare False
+result.omega8 == compare False
+[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()[1]

+[?7h[?12l[?25h[?2004lresult.omega8 == compare False
+result.omega8 - compare dV([((x^2 + 1)/x^3)*y])
+result.omega8 == compare False
+result.omega8 - compare dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+ [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lEC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lTC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lAC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l2C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: ETA2 = C.crystalline_cohomology_basis()[1]

+[?7h[?12l[?25h[?2004lresult.omega8 == compare False
+result.omega8 - compare dV([((x^2 + 1)/x^3)*y])
+result.omega8 == compare False
+result.omega8 - compare dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+

+

+

+

+

+

+

+

+

+ [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+

+

+

+

+

+

+

+

+ [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: ETA2 = C.crystalline_cohomology_basis()[1]

+[?7h[?12l[?25h[?2004lresult.omega8 == compare False
+result.omega8 - compare dV([((2*x^2 + 1)/x^3)*y])
+result.omega8 == compare False
+result.omega8 - compare dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+

+

+

+ [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+

+

+ [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: ETA2 = C.crystalline_cohomology_basis()[1]

+[?7h[?12l[?25h[?2004lresult.omega8 == compare False
+result.omega8 - compare dV([1/x^3*y])
+result.omega8 == compare False
+result.omega8 - compare dV([((2*x^4 + 2*x^2 + 2)/x^6)*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[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: ETA2 = C.crystalline_cohomology_basis()[1]

+[?7h[?12l[?25h[?2004lresult.omega8 == compare True
+result.omega8 - compare 0
+result.omega8 == compare True
+result.omega8 - compare 0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loETA2[?7h[?12l[?25h[?25l[?7lmETA2[?7h[?12l[?25h[?25l[?7l ETA2[?7h[?12l[?25h[?25l[?7l=ETA2[?7h[?12l[?25h[?25l[?7l ETA2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: om = ETA2.omega8

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l\[?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(om.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_[?7h[?12l[?25h[?25l[?7lpatch(om.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[?7lsage: second_patch(om)

+[?7h[?12l[?25h[?2004l[?7h[(2/(x^2 + 2))*y] d[x] + V(((-x^2)/y) dx) + dV([(1/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(om)[?7h[?12l[?25h[?25l[?7lom = ETA2.omega8[?7h[?12l[?25h[?25l[?7lETA2= C.crystlline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lom =ETA2.omeg8[?7h[?12l[?25h[?25l[?7lsecond_patch(om)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(om)[?7h[?12l[?25h[?25l[?7lom = ETA2.omega8[?7h[?12l[?25h[?25l[?7lETA2= C.crystlline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom1.h2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lfrobeniu().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lomega.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = om + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7luone/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[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7lsecond_patch(om)[?7h[?12l[?25h[?25l[?7lom = ETA2.omega8[?7h[?12l[?25h[?25l[?7lETA2= C.crystlline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom1.h2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lfrobeniu().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lomega.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = om + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7luone/C.x[?7h[?12l[?25h[?25l[?7lsecond_patch(om.r())[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7lsecond_patch(om.r())[?7h[?12l[?25h[?25l[?7lom.r()[?7h[?12l[?25h[?25l[?7l = eta2.omega8[?7h[?12l[?25h[?25l[?7l.omega8[?7h[?12l[?25h[?25l[?7l((C.x^8 - C.x^6 + C.one)/C.y*C.dx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lC.x^8 - C.x^6 + C.one)/C.y*C.dx[?7h[?12l[?25h[?25l[?7l)*C.dx[?7h[?12l[?25h[?25l[?7lETA2 -eta2[?7h[?12l[?25h[?25l[?7l=C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1).quo_rem(x^10 - x^8)[?7h[?12l[?25h[?25l[?7lsecond_patch(eta2.omega8).regular_form()[?7h[?12l[?25h[?25l[?7leta2.omega0.rgular_form()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llod('init.sage')[?7h[?12l[?25h[?25l[?7l(-x^10 - x^8 - x^6 + x^2).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7l = second_patch(om)[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7l(-x^10 - x^8 - x^6 + x^2).quo_rem(x^2 - 1)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7let2[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lomega0.regular_form()[?7h[?12l[?25h[?25l[?7lsecond_patch(ta2.omega8).regular_form()[?7h[?12l[?25h[?25l[?7l(-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1).quo_rem(x^10 - x^8)[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l-eta2[?7h[?12l[?25h[?25l[?7l(C.x^8- C.x^6 + C.one)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7l*C.dx[?7h[?12l[?25h[?25l[?7l(C.x^8 - C.x^6 + C.one)/C.y*C.dx).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lom = eta.omega8[?7h[?12l[?25h[?25l[?7l2.omega8[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lsecond_patch(om.r())[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7lvy/(C.x)^2[?7h[?12l[?25h[?25l[?7lom - u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1 = om + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.omega.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lfrobenius()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lh2.expanion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lom =ETA2.omeg8[?7h[?12l[?25h[?25l[?7lsecond_patch(om)[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7l = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = ETA2.omega8[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: om - u.teichmuller()*v.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^4 + 2*x^2))*y] d[x] + V(((x^8 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^6 + 2)/(x^8 + 2*x^6))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom - u.teichmuller()*v.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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l+ u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 + u.teichmuller()*v.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7hV(((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom + u.teichmuller()*v.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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAom + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l om + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l=om + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l om + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = om + u.teichmuller()*v.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = om + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.for()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?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[?7lsage: A.omega.expansion

+ A.omega.expansion         

+ A.omega.expansion_at_infty

+

+

+ [?7h[?12l[?25h[?25l[?7l

+ A.omega.expansion         

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

+ A.omega.expansion         

+ A.omega.expansion_at_infty[?7h[?12l[?25h[?25l[?7l

+

+

+[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.omega.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^4 + t^8 + 2*t^12 + O(t^14)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lA.omega.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.omega.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?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[?7lnsion

+ A.h2.expansion         

+ A.h2.expansion_at_infty

+ 

+

+ [?7h[?12l[?25h[?25l[?7l

+ A.h2.expansion         

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

+ A.h2.expansion         

+ A.h2.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(

+

+

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.h2.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t + 2*t^5 + t^9 + 2*t^13 + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lutom(B) - B - A[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7leta2lift)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(ETA2).coordinates()

+[?7h[?12l[?25h[?2004l(1, 1)
+result.omega8 == compare True
+result.omega8 - compare 0
+result.omega8 == compare True
+result.omega8 - compare 0
+aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [47], in <cell line: 1>()
+----> 1 autom(ETA2).coordinates()
+
+File <string>:84, in coordinates(self, basis)
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-eta2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l1 = C.crystaline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: ETA1 = C.crystalline_cohomology_basis()[0]

+[?7h[?12l[?25h[?2004lresult.omega8 == compare True
+result.omega8 - compare 0
+result.omega8 == compare True
+result.omega8 - compare 0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA1 = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l21[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-eta2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lE[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laETA2 - ETA1[?7h[?12l[?25h[?25l[?7luETA2 - ETA1[?7h[?12l[?25h[?25l[?7ltETA2 - ETA1[?7h[?12l[?25h[?25l[?7loETA2 - ETA1[?7h[?12l[?25h[?25l[?7lmETA2 - ETA1[?7h[?12l[?25h[?25l[?7l(ETA2 - ETA1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() - ETA1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7luautom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7lxautom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7l autom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7l=autom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7l autom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: aux = autom(ETA2) - ETA1 - ETA2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = autom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux

+[?7h[?12l[?25h[?2004l[?7h(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1 = C.x.teichmuller()*(C.y.teichmuller().diffn()) - (2*(C.x)^(-1)).teichmuller()*(C.y/C.x^2).teichmuller().diffn() + (C.y/C.x).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l [?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: aux1 = aux

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1 = aux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly/(C.x^2+C.x)[?7h[?12l[?25h[?25l[?7l/(C.x^2+C.x)[?7h[?12l[?25h[?25l[?7lsage: C.y/(C.x^2+C.x)

+[?7h[?12l[?25h[?2004l[?7h(1/(x^2 + x))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+C.x)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?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[?7ln[?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[?7lsage: C.y/(C.x^2+C.x).expansion_at_infty()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [53], in <cell line: 1>()
+----> 1 C.y/(C.x**Integer(2)+C.x).expansion_at_infty()
+
+File <string>:75, in __truediv__(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 = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.laurent_series_ring_element.LaurentSeries' object has no attribute 'function'
+[?2004h[?25l[?7lsage: [?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.y/(C.x^2+C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?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()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2+C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.y/(C.x^2+C.x)).expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht + 2*t^3 + t^5 + 2*t^9 + 2*t^13 + t^17 + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2+C.x)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7laux1 = aux[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = autom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7lETA1 = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lautom(ETA2).coordates()[?7h[?12l[?25h[?25l[?7lA.h2.expansion_at_infty[?7h[?12l[?25h[?25l[?7lomega.expansionat_infty()[?7h[?12l[?25h[?25l[?7l = om + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.omega.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lh2.expansion_atinfty()[?7h[?12l[?25h[?25l[?7lautom(ETA2).coordinates[?7h[?12l[?25h[?25l[?7lETA1 = C.crystalle_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7laux = autom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1 = aux[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+C.x)[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2+C.x)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/(C.x^2+C.x)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7laux1 = aux[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = autom(ETA2) - ETA1 - ETA2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1 = aux[?7h[?12l[?25h[?25l[?7l = aux[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: aux1

+[?7h[?12l[?25h[?2004l[?7h(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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: aux1.f.t = 0*C.x

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1.f.t = 0*C.x[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?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[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux1.omega0.h2 = 0*Cx

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [57], in <cell line: 1>()
+----> 1 aux1.omega0.h2 = Integer(0)*Cx
+
+NameError: name 'Cx' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1.omega0.h2 = 0*Cx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux1.omega0.h2 = 0*C.x

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1.omega0.h2 = 0*C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = 0*C.x[?7h[?12l[?25h[?25l[?7l = 0*C.x[?7h[?12l[?25h[?25l[?7lf = 0*C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-= 0*C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.f -= aux.omega0[?7h[?12l[?25h[?25l[?7l.f -= aux.omega0[?7h[?12l[?25h[?25l[?7l.f -= aux.omega0[?7h[?12l[?25h[?25l[?7l.f -= aux.omega0[?7h[?12l[?25h[?25l[?7l.f -= aux.omega0[?7h[?12l[?25h[?25l[?7l.f -= aux.omega0[?7h[?12l[?25h[?25l[?7lf -= aux.omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux1.f -= aux.omega0.h2.verschiebung()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1.f -= aux.omega0.h2.verschiebung()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: aux1

+[?7h[?12l[?25h[?2004l[?7h(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.f -= aux.omega0.h2.verschiebung()[?7h[?12l[?25h[?25l[?7lomega0.h2 = 0*Cx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?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[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux1.omega8 = aux1.omega0 - aux1.f.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1.omega8 = aux1.omega0 - aux1.f.diffn()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: aux1

+[?7h[?12l[?25h[?2004l[?7h(V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((2*x^5 + 2*x^4 + x^3 + 2*x^2 + x + 2)/(x^2 + x))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.omega8 = aux1.omega0 - aux1.f.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[?7laux1[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(aux1[?7h[?12l[?25h[?25l[?7l()aux1[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)aux1[?7h[?12l[?25h[?25l[?7l.)aux1[?7h[?12l[?25h[?25l[?7lx)aux1[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^aux1[?7h[?12l[?25h[?25l[?7l(aux1[?7h[?12l[?25h[?25l[?7l()aux1[?7h[?12l[?25h[?25l[?7l()paux1[?7h[?12l[?25h[?25l[?7l-aux1[?7h[?12l[?25h[?25l[?7l1aux1[?7h[?12l[?25h[?25l[?7laux1[?7h[?12l[?25h[?25l[?7laux1[?7h[?12l[?25h[?25l[?7l()aux1[?7h[?12l[?25h[?25l[?7l(aux1[?7h[?12l[?25h[?25l[?7l-aux1[?7h[?12l[?25h[?25l[?7lpaux1[?7h[?12l[?25h[?25l[?7l+aux1[?7h[?12l[?25h[?25l[?7l1aux1[?7h[?12l[?25h[?25l[?7l()aux1[?7h[?12l[?25h[?25l[?7l()*aux1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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(C.x)^(-p+1)*aux1.omega0.[?7h[?12l[?25h[?25l[?7le(C.x)^(-p+1)*aux1.omega0.[?7h[?12l[?25h[?25l[?7ls(C.x)^(-p+1)*aux1.omega0.[?7h[?12l[?25h[?25l[?7lt(C.x)^(-p+1)*aux1.omega0.[?7h[?12l[?25h[?25l[?7l (C.x)^(-p+1)*aux1.omega0.[?7h[?12l[?25h[?25l[?7l=(C.x)^(-p+1)*aux1.omega0.[?7h[?12l[?25h[?25l[?7l (C.x)^(-p+1)*aux1.omega0.[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: test = (C.x)^(-p+1)*aux1.omega0.omega

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltest = (C.x)^(-p+1)*aux1.omega0.omega[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: test

+[?7h[?12l[?25h[?2004l[?7h((-x^2 + x + 1)/(x^3*y + x^2*y + x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltest[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lftest[?7h[?12l[?25h[?25l[?7lctest[?7h[?12l[?25h[?25l[?7ltest[?7h[?12l[?25h[?25l[?7l test[?7h[?12l[?25h[?25l[?7l test[?7h[?12l[?25h[?25l[?7ltest[?7h[?12l[?25h[?25l[?7l=test[?7h[?12l[?25h[?25l[?7l test[?7h[?12l[?25h[?25l[?7lstest[?7h[?12l[?25h[?25l[?7lutest[?7h[?12l[?25h[?25l[?7lptest[?7h[?12l[?25h[?25l[?7letest[?7h[?12l[?25h[?25l[?7lrtest[?7h[?12l[?25h[?25l[?7letest[?7h[?12l[?25h[?25l[?7lltest[?7h[?12l[?25h[?25l[?7lltest[?7h[?12l[?25h[?25l[?7lltest[?7h[?12l[?25h[?25l[?7litest[?7h[?12l[?25h[?25l[?7lptest[?7h[?12l[?25h[?25l[?7ltest[?7h[?12l[?25h[?25l[?7litest[?7h[?12l[?25h[?25l[?7lctest[?7h[?12l[?25h[?25l[?7l_test[?7h[?12l[?25h[?25l[?7lftest[?7h[?12l[?25h[?25l[?7lutest[?7h[?12l[?25h[?25l[?7lntest[?7h[?12l[?25h[?25l[?7lctest[?7h[?12l[?25h[?25l[?7ltest[?7h[?12l[?25h[?25l[?7litest[?7h[?12l[?25h[?25l[?7lotest[?7h[?12l[?25h[?25l[?7lntest[?7h[?12l[?25h[?25l[?7l(test[?7h[?12l[?25h[?25l[?7lCtest[?7h[?12l[?25h[?25l[?7l,test[?7h[?12l[?25h[?25l[?7l test[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: fct = superellliptic_function(C, test.form)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [65], in <cell line: 1>()
+----> 1 fct = superellliptic_function(C, test.form)
+
+NameError: name 'superellliptic_function' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = superellliptic_function(C, test.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[?7liptic_function(C, test.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[?7lsage: fct = superelliptic_function(C, test.form)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = superelliptic_function(C, test.form)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?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: fct.pth_root()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [67], in <cell line: 1>()
+----> 1 fct.pth_root()
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx*C.y.diffn( == B.omega0.r()[?7h[?12l[?25h[?25l[?7l.teichmuller().t[?7h[?12l[?25h[?25l[?7lteichmuller().t[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (3*C.x.teichmuller()).diffn()

+[?7h[?12l[?25h[?2004l[?7hdV([x^3])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*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[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: (2*C.x.teichmuller()).diffn()

+[?7h[?12l[?25h[?2004l[?7h[2] d[x]dV([x^3])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA1 = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: ETA1

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), V(((x^2 + 1)/x)*y), [(1/(x^3 + 2*x))*y] d[x] + V((x/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA1[?7h[?12l[?25h[?25l[?7l(2*C.x.teichmuller()).diffn()[?7h[?12l[?25h[?25l[?7lsage: (2*C.x.teichmuller()).diffn()

+[?7h[?12l[?25h[?2004l[?7h[2] d[x]dV([x^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[?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[?7l(2*C.x.teichmuller()).diffn()[?7h[?12l[?25h[?25l[?7lsage: (2*C.x.teichmuller()).diffn()

+[?7h[?12l[?25h[?2004l[?7h[2] d[x] + dV([x^3])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*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[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lC.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2(C.x.teichmuler()).difn()[?7h[?12l[?25h[?25l[?7l*(C.x.teichmuler()).difn()[?7h[?12l[?25h[?25l[?7l((C.x.teichmuler()).difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: 2*((C.x.teichmuller()).diffn())

+[?7h[?12l[?25h[?2004l[?7h[2] d[x] + V((x^2) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*((C.x.teichmuller()).diffn())[?7h[?12l[?25h[?25l[?7l(2*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*((C.x.teichmuller()).diffn())[?7h[?12l[?25h[?25l[?7lsage: (2*C.x.teichmuller()).diffn() == 2*((C.x.teichmuller()).diffn())

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*C.x.teichmuller()).diffn() == 2*((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[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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.teichmuler().difn() = 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load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(2*C.x.teichmuller()).diffn() == 2*((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[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?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*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l 2*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()2*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l(), 2*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (2*C.x.teichmuller()).diffn(), 2*((C.x.teichmuller()).diffn())

+[?7h[?12l[?25h[?2004l[?7h([2] d[x] + dV([x^3]), [2] d[x] + V((x^2) dx))
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+[?7h[?12l[?25h[?2004l[?7h([2] d[x] + dV([x^3]), [2] d[x] + V((x^2) dx))
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+[?7h[?12l[?25h[?2004l[?7h([2] d[x] + dV([x^3]), [2] d[x] + dV([x^3]))
+[?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[?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[?7lA.h2.expansion_at_infty()[?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[?7l(2*(C.x.teichmuller())).diffn(), (C.x.teichmuller()+C.x.teichmuller()).diffn()[?7h[?12l[?25h[?25l[?7lsage: (2*(C.x.teichmuller())).diffn(), (C.x.teichmuller()+C.x.teichmuller()).diffn()

+[?7h[?12l[?25h[?2004l[?7h([2] d[x] + dV([x^3]), [2] d[x] + dV([x^3]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*(C.x.teichmuller())).diffn(), (C.x.teichmuller()+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[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7l(2*(C.x.teichmuller())).diffn(), (C.x.teichmuller()+C.x.teichmuller()).diffn()[?7h[?12l[?25h[?25l[?7l2*((C.x.teichmuller())diffn())[?7h[?12l[?25h[?25l[?7lC.x.teichmuler().diffn(), 2*((C.xteichmuller()).diffn())[?7h[?12l[?25h[?25l[?7lsage: (2*C.x.teichmuller()).diffn(), 2*((C.x.teichmuller()).diffn())

+[?7h[?12l[?25h[?2004l[?7h([2] d[x] + dV([x^3]), [2] d[x] + V((x^2) dx))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*C.x.teichmuller()).diffn(), 2*((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[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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.teichmuler().difn(), 2*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l(C.x.teichmuler().difn(), 2*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l(C.x.teichmuler().difn(), 2*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()).difn(), 2*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (2*(C.x.teichmuller())).diffn(), 2*((C.x.teichmuller()).diffn())

+[?7h[?12l[?25h[?2004l[?7h([2] d[x] + dV([x^3]), [2] d[x] + V((x^2) dx))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*b[0][?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[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?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[?7lsage: 3*(C.x.teichmuller().diffn())

+[?7h[?12l[?25h[?2004l[?7h + V((x^2) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*(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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()

+[?7h[?12l[?25h[?2004l[?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[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()

+[?7h[?12l[?25h[?2004lTrue False
+[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?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[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()

+[?7h[?12l[?25h[?2004l(self.omega - other.omega).cartier() - H.diffn() (-1) dx
+[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?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[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()

+[?7h[?12l[?25h[?2004lH 2*x
+(self.omega - other.omega).cartier() - H.diffn() (-1) dx
+[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l()[?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[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()

+[?7h[?12l[?25h[?2004lH 2*x
+(self.omega - other.omega).cartier() 1 dx
+[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: 3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct.pth_root()[?7h[?12l[?25h[?25l[?7lor i in range(10):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lac[0].coordinates():[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lrange[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l0[?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[?7lsage: for a in range(0, 9):

+....: [?7h[?12l[?25h[?25l[?7lp = 3[?7h[?12l[?25h[?25l[?7lrint(type(a))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l3*(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[?7l3*(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[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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.teichmuler().difn() = 3*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7la*(C.x.teichmuler().difn() = 3*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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.teichmuler().difn()))[?7h[?12l[?25h[?25l[?7l(C.x.teichmuler().difn()))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7laC.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la*C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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*(C.x.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l....:     print(a*(C.x.teichmuller().diffn()) == a*(C.x.teichmuller()).diffn())

+....: [?7h[?12l[?25h[?25l[?7lsage: for a in range(0, 9):

+....:     print(a*(C.x.teichmuller().diffn()) == a*(C.x.teichmuller()).diffn())

+....: 

+[?7h[?12l[?25h[?2004lTrue
+True
+True
+True
+True
+True
+True
+True
+True
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+C.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.teichmuller().diffn().frobenius()[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lteichmuller().diffn().frobenius()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lichmuller().diffn().frobenius()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega0.regular_form()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l - aux[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA1[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: ETA2 = C.crystalline_cohomology_basis()[1]

+[?7h[?12l[?25h[?2004lresult.omega8 == compare True
+result.omega8 - compare 0
+result.omega8 == compare True
+result.omega8 - compare 0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lsage: ETA1 = C.crystalline_cohomology_basis()[0]

+[?7h[?12l[?25h[?2004lresult.omega8 == compare True
+result.omega8 - compare 0
+result.omega8 == compare True
+result.omega8 - compare 0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA1 = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l21[?7h[?12l[?25h[?25l[?7lsage: ETA2

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?7lETA2[?7h[?12l[?25h[?25l[?7l1 = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7l21[?7h[?12l[?25h[?25l[?7lsage: ETA2 = C.crystalline_cohomology_basis()[1]

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldx.regular_form()[?7h[?12l[?25h[?25l[?7le_ham_basis()[1][?7h[?12l[?25h[?25l[?7l_rham_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[1]

+[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[?2004h[?25l[?7lsage: [?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[?7l[?7h[?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*(C.x.teichmuller())).diffn(), 2*((C.x.teichmuller()).diffn())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l/)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()%[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lsage: (3/2)%9

+[?7h[?12l[?25h[?2004l[?7h6
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly.teichmuller.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lteichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3/2)%9[?7h[?12l[?25h[?25l[?7l-x^18 - x^16 - x^14 - x^10 - x^8 - x^4 - x^2 - 1).quo_rem(x^10 - x^8)[?7h[?12l[?25h[?25l[?7l1/2)*C..teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()%9[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lsage: (-1/2)%9

+[?7h[?12l[?25h[?2004l[?7h4
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*(C.x.teichmuller().diffn()) == (C.x^3).verschiebung().diffn()[?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[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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: 3*C.x.teichmuller()

+[?7h[?12l[?25h[?2004l[?7hV(x^3)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*C.x.teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 3*C.x.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7hV((x^2) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lffn()[?7h[?12l[?25h[?25l[?7lsage: C.y.diffn()

+[?7h[?12l[?25h[?2004l[?7h(1/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^7 + x^3 + x)/(x^2*y - 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[?7lCx^7 + x^3 + x)/(x^2*y - y)[?7h[?12l[?25h[?25l[?7l/x^7 + x^3 + x)/(x^2*y - 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[?7lx^7 + x^3 + x)/(x^2*y - y)[?7h[?12l[?25h[?25l[?7l.x^7 + x^3 + x)/(x^2*y - 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[?7lCx^3 + x)/(x^2*y - y)[?7h[?12l[?25h[?25l[?7l.x^3 + x)/(x^2*y - 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[?7lCx)/(x^2*y - y)[?7h[?12l[?25h[?25l[?7l.x)/(x^2*y - 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[?7lCx^2*y - y)[?7h[?12l[?25h[?25l[?7l.x^2*y - 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[?7lCy - y)[?7h[?12l[?25h[?25l[?7l.y - 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[?7lCy)[?7h[?12l[?25h[?25l[?7l.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[?7lC[?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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?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(C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l()C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l()*C.x^2*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)*C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l.)*C.x^2*C.dx[?7h[?12l[?25h[?25l[?7ly)*C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^*C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l(*C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l()*C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-)*C.x^2*C.dx[?7h[?12l[?25h[?25l[?7l3)*C.x^2*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[?7l2[?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[?7l8[?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[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()+[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l7)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?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[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ((-C.x^7 + C.x^3 + C.x)/(C.x^2*C.y - C.y)) == (C.y)^(-3)*C.x^2*C.dx+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [31], in <cell line: 1>()
+----> 1 ((-C.x**Integer(7) + C.x**Integer(3) + C.x)/(C.x**Integer(2)*C.y - C.y)) == (C.y)**(-Integer(3))*C.x**Integer(2)*C.dx+ Integer(2)*C.x**Integer(8)*(C.y)**(-Integer(3))+(C.x**Integer(5) - C.x**Integer(7))/(Integer(2)*C.y**Integer(5))
+
+File <string>:19, in __add__(self, other)
+
+AttributeError: 'superelliptic_function' object has no attribute 'form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-C.x^7 + C.x^3 + C.x)/(C.x^2*C.y - C.y)) == (C.y)^(-3)*C.x^2*C.dx+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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^7 + C.x^3 + C.x)/(C.x^2*C.y - C.y)) == (C.y)^(-3)*C.x^2+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-C.x^7 + C.x^3 + C.x)/(C.x^2*C.y - C.y)) == (C.y)^(-3)*C.x^2+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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^7 + C.x^3 + C.x)/(C.x^2*C.y - C.y)) == (C.y)^(-3)*C.x^2+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l*C.dx+ 2*C.x^8*(C.y^-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7lC.y.diffn()[?7h[?12l[?25h[?25l[?7l3*Cx.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lC.ydiffn()[?7h[?12l[?25h[?25l[?7l((-C.x^7 + C.x^3 + C.x)/(C.x^2*C.y - C.y)) == (C.y)^(-3)*C.x^2*C.dx+ 2*C.x^8*(C.y)^(-3)+(C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l+ 2*C.x^8*(C.y)^(-3+C.x^5 - C.x^7)/(2*C.y^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.y.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[1][?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[1]

+[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7lmC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l=C.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: om = C.de_rham_basis()[1].omega8

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.de_rham_basis()[1].omega8[?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[?7lsom[?7h[?12l[?25h[?25l[?7leom[?7h[?12l[?25h[?25l[?7lcom[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lnom[?7h[?12l[?25h[?25l[?7ldom[?7h[?12l[?25h[?25l[?7l_om[?7h[?12l[?25h[?25l[?7lpom[?7h[?12l[?25h[?25l[?7laom[?7h[?12l[?25h[?25l[?7ltom[?7h[?12l[?25h[?25l[?7lcom[?7h[?12l[?25h[?25l[?7lhom[?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[?7l[?7h[?12l[?25h[?25l[?7lsage: second_patch(om)

+[?7h[?12l[?25h[?2004l[?7h(x/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(om)[?7h[?12l[?25h[?25l[?7l().r()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: second_patch(om).regular_form()

+[?7h[?12l[?25h[?2004l[?7h2*x dy
+[?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.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcrystlline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()[1]

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [38], in <cell line: 1>()
+----> 1 C.crystalline_cohomology_basis()[Integer(1)]
+
+File <string>:52, in crystalline_cohomology_basis(self, prec)
+
+File <string>:23, in de_rham_witt_lift(cech_class, prec)
+
+NameError: name 'omega' 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[?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[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()[1]

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [40], in <cell line: 1>()
+----> 1 C.crystalline_cohomology_basis()[Integer(1)]
+
+File <string>:52, in crystalline_cohomology_basis(self, prec)
+
+File <string>:24, in de_rham_witt_lift(cech_class, prec)
+
+File <string>:13, in de_rham_witt_lift_form8(omega)
+
+NameError: name 'g' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?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[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()[1]

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx*C.y.diffn() == B.mega0.r()[?7h[?12l[?25h[?25l[?7l.teichmuller().t[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lhm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: C.x.teichmuller()*C.y.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller()*C.y.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[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAC.x.teichmuler()*C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l C.x.teichmuler()*C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l=C.x.teichmuler()*C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l C.x.teichmuler()*C.y.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lsage: A = C.x.teichmuller()*C.y.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB0 = B[0][?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.crystalline_cohomology_basis()[?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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?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[?7lde_rham_witt_lift_form0C.x/C.y*C.dx[?7h[?12l[?25h[?25l[?7l(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[?7lsage: B = de_rham_witt_lift_form0(C.x/C.y*C.dx)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C.x.teichmuller()*C.y.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[?7lB[?7h[?12l[?25h[?25l[?7lsage: A == B

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega0.regular_form()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1 = de_rham_wittliftC.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7lsage: eta1 = de_rham_witt_lift(C.de_rham_basis()[0])

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+ [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
[?7h[?12l[?25h[?25l[?7l
sage: eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())


+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+

+

+

+

+

+

+

+

+

+

+

+ [?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l10[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lsage: ETA1 = C.crystalline_cohomology_basis()[0]

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+

+

+ [?7h[?12l[?25h[?25l[?7leta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: eta1 - ETA1

+[?7h[?12l[?25h[?2004l[?7h( + V(((-x^3)/y) dx) + dV([2*x*y]), V(2*x*y), V(((-x^3)/y) dx))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7leta1 - ETA1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta1 - ETA1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().re[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (eta1 - ETA1).reduce()

+[?7h[?12l[?25h[?2004l[?7h(V(((-x^3)/y) dx), [0], V(((-x^3)/y) dx))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7leta1 - ETA1[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: eta1

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: eta1.omega0

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1.omega0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta1.omega0.regular_form()

+[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [1] d[y] + V((x^5/y) dx) + dV(2*x*y)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1.omega0.regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lseta1.omega8[?7h[?12l[?25h[?25l[?7leta1.omega8[?7h[?12l[?25h[?25l[?7lceta1.omega8[?7h[?12l[?25h[?25l[?7loneta1.omega8[?7h[?12l[?25h[?25l[?7ldeta1.omega8[?7h[?12l[?25h[?25l[?7l_eta1.omega8[?7h[?12l[?25h[?25l[?7lpeta1.omega8[?7h[?12l[?25h[?25l[?7laeta1.omega8[?7h[?12l[?25h[?25l[?7lteta1.omega8[?7h[?12l[?25h[?25l[?7lceta1.omega8[?7h[?12l[?25h[?25l[?7lheta1.omega8[?7h[?12l[?25h[?25l[?7l(eta1.omega8[?7h[?12l[?25h[?25l[?7leta1.omega8[?7h[?12l[?25h[?25l[?7l(eta1.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: second_patch(eta1.omega8).regular_form()

+[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [1] d[y] + V(((x^8 + x^6 + 1)/(x^3*y)) dx) + dV(x*y)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(eta1.omega8).regular_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1.omega8).regular_form()[?7h[?12l[?25h[?25l[?7l1.omega8).regular_form()[?7h[?12l[?25h[?25l[?7l1.omega8).regular_form()[?7h[?12l[?25h[?25l[?7lE1.omega8).regular_form()[?7h[?12l[?25h[?25l[?7lT1.omega8).regular_form()[?7h[?12l[?25h[?25l[?7lA1.omega8).regular_form()[?7h[?12l[?25h[?25l[?7lsage: second_patch(ETA1.omega8).regular_form()

+[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [1] d[y] + V(((x^5 + x^3)/y) dx) + dV(x*y)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.expansion_at_infty()[?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[?7lsage: v = C.y/(C.x)^2

+[?7h[?12l[?25h[?2004l[?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[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?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[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy/x)^3[?7h[?12l[?25h[?25l[?7l/y/x)^3[?7h[?12l[?25h[?25l[?7ly/x)^3[?7h[?12l[?25h[?25l[?7l.y/x)^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx)^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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy - v - (C.y/C.x)^3[?7h[?12l[?25h[?25l[?7l.y - v - (C.y/C.x)^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCv - (C.y/C.x)^3[?7h[?12l[?25h[?25l[?7l.v - (C.y/C.x)^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.y - C.v - (C.y/C.x)^3

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [57], in <cell line: 1>()
+----> 1 C.y - C.v - (C.y/C.x)**Integer(3)
+
+AttributeError: 'superelliptic' object has no attribute 'v'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y - C.v - (C.y/C.x)^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 - (C.y/C.x)^3[?7h[?12l[?25h[?25l[?7lv - (C.y/C.x)^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 - v - (C.y/C.x)^3

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ;1R;1R;1R;1R;1R1R;1R;1R;1R;1R;1R 
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;1R
+bash: syntax error near unexpected token `;'
+]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[?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[?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[?7lsage: v = C.y/(C.x)^2

+[?7h[?12l[?25h[?2004l[?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[?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[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?7lv[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?7lCy.teichmuler() - v.teichmuler()[?7h[?12l[?25h[?25l[?7l.y.teichmuler() - v.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()+[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l ()[?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[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?7lv()[?7h[?12l[?25h[?25l[?7le()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7ls()[?7h[?12l[?25h[?25l[?7lc()[?7h[?12l[?25h[?25l[?7lh()[?7h[?12l[?25h[?25l[?7li()[?7h[?12l[?25h[?25l[?7le()[?7h[?12l[?25h[?25l[?7lb()[?7h[?12l[?25h[?25l[?7lu()[?7h[?12l[?25h[?25l[?7ln()[?7h[?12l[?25h[?25l[?7lg()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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).verschiebung()[?7h[?12l[?25h[?25l[?7l.).verschiebung()[?7h[?12l[?25h[?25l[?7ly).verschiebung()[?7h[?12l[?25h[?25l[?7l*).verschiebung()[?7h[?12l[?25h[?25l[?7lv).verschiebung()[?7h[?12l[?25h[?25l[?7l^).verschiebung()[?7h[?12l[?25h[?25l[?7l2).verschiebung()[?7h[?12l[?25h[?25l[?7l ).verschiebung()[?7h[?12l[?25h[?25l[?7l-).verschiebung()[?7h[?12l[?25h[?25l[?7l ).verschiebung()[?7h[?12l[?25h[?25l[?7lC).verschiebung()[?7h[?12l[?25h[?25l[?7l.).verschiebung()[?7h[?12l[?25h[?25l[?7ly).verschiebung()[?7h[?12l[?25h[?25l[?7l^).verschiebung()[?7h[?12l[?25h[?25l[?7l2).verschiebung()[?7h[?12l[?25h[?25l[?7l*).verschiebung()[?7h[?12l[?25h[?25l[?7lv).verschiebung()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=
[?7h[?12l[?25h[?25l[?7l
sage: C.y.teichmuller() - v.teichmuller()+ (C.y*v^2 - C.y^2*v).verschiebung() =
=

+....: [?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[?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[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l3.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?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[?7l3).teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.teichmuller() - v.teichmuller()+ (C.y*v^2 - C.y^2*v).verschiebung() =
=

+....: ( (C.y/C.x)^3).teichmuller()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller() - v.teichmuller()+ (C.y*v^2 - C.y^2*v).verschiebung() =
=

+....: ( (C.y/C.x)^3).teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l
[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

+()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(

+ (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l
(

+)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(). 
=

+( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7ld


+=( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l
i

+ =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7lf =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7lf =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7ln =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l( =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?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*v^2 - C.y^2*v).verschiebung().
d

+ifn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7ld+ (C.y*v^2 - C.y^2*v).verschiebung()
.

+difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7li+ (C.y*v^2 - C.y^2*v).verschiebung(
)

+.difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7lf+ (C.y*v^2 - C.y^2*v).verschiebung
(

+).difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7lf+ (C.y*v^2 - C.y^2*v).verschiebun
g

+().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7ln+ (C.y*v^2 - C.y^2*v).verschiebu
n

+g().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l(+ (C.y*v^2 - C.y^2*v).verschieb
u

+ng().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l()+ (C.y*v^2 - C.y^2*v).verschie
b

+ung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(). - v.teichmuler().difn()+ (C.y*v^2 - C.y^2*v).verschi
e

+bung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7ld - v.teichmuler().difn()+ (C.y*v^2 - C.y^2*v).versch
i

+ebung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7li - v.teichmuler().difn()+ (C.y*v^2 - C.y^2*v).versc
h

+iebung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7lf - v.teichmuler().difn()+ (C.y*v^2 - C.y^2*v).vers
c

+hiebung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7lf - v.teichmuler().difn()+ (C.y*v^2 - C.y^2*v).ver
s

+chiebung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7ln - v.teichmuler().difn()+ (C.y*v^2 - C.y^2*v).ve
r

+schiebung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l( - v.teichmuler().difn()+ (C.y*v^2 - C.y^2*v).v
e

+rschiebung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l() - v.teichmuler().difn()+ (C.y*v^2 - C.y^2*v).
v

+erschiebung().difn() =( (C.y/C.x)^3).teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l

+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn() - v.teichmuller().diffn()+ (C.y*v^2 - C.y^2*v).
v

+....: erschiebung().diffn() =( (C.y/C.x)^3).teichmuller().diffn()

+[?7h[?12l[?25h[?2004l  Input In [4]
+    C.y.teichmuller().diffn() - v.teichmuller().diffn()+ (C.y*v**Integer(2) - C.y**Integer(2)*v).verschiebung().diffn() =( (C.y/C.x)**Integer(3)).teichmuller().diffn()
+    ^
+SyntaxError: cannot assign to expression here. Maybe you meant '==' instead of '='?
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn() - v.teichmuller().diffn()+ (C.y*v^2 - C.y^2*v).
v

+....: erschiebung().diffn() =( (C.y/C.x)^3).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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()= =( (C.y/C.x)^3).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=( (C.y/C.x)^3).teichmuler().difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.teichmuller().diffn() - v.teichmuller().diffn()+ (C.y*v^2 - C.y^2*v).
v

+....: erschiebung().diffn()==( (C.y/C.x)^3).teichmuller().diffn()

+[?7h[?12l[?25h[?2004l
+[?7hTrue
+[?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[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta1 - ETA1).reduce()[?7h[?12l[?25h[?25l[?7lC.y/(C.x^2+Cx)).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?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[?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/C.x)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)[?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[?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[?7lf[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x)^2*(C.y/C.x).diffn()

+[?7h[?12l[?25h[?2004l[?7h((-x^4 + 1)/(x^2*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1.omega0.regular_form()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l - ETA1[?7h[?12l[?25h[?25l[?7lsage: eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).ver
s

+....: chiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).versch
i

+....: ebung())[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).ver
s

+chiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).versch
i

+ebung())[?7h[?12l[?25h[?25l[?7lsage: eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).ver
s

+....: chiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).versch
i

+....: ebung())

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA1 = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lsage: ETA1 = C.crystalline_cohomology_basis()[0]

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7lsage: v

+[?7h[?12l[?25h[?2004l[?7h1/x^2*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7lETA1 = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lsage: eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).ver
s

+....: chiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).versch
i

+....: ebung())[?7h[?12l[?25h[?25l[?7l(C.y/C.x)^2*(C.y/C.x).diffn()

+ 

+ [?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn() - v.teichmuller().diffn()+ (C.y*v^2 - C.y^2*v).
v

+....: erschiebung().diffn()==( (C.y/C.x)^3).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l(C.y/C.x)^2*(C.y/C.x).diffn()

+ [?7h[?12l[?25h[?25l[?7lsage: (C.y/C.x)^2*(C.y/C.x).diffn()

+[?7h[?12l[?25h[?2004l[?7h((-x^4 + 1)/(x^2*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y/C.x)^2*(C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lv[?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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y*v^2 - C.y^2*v)

+[?7h[?12l[?25h[?2004l[?7h((2*x^4 + 2*x^2 + 2)/x^3)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y*v^2 - C.y^2*v)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y*v^2 - C.y^2*v).coordinates()

+[?7h[?12l[?25h[?2004l[?7h[1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).ver
s

+....: chiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).versch
i

+....: ebung())[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: eta1

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(x/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((-x^5 + x^3 + x)/(x^2*y - y)) dx) + dV([(1/(x^3 + 2*x))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.de_rham_basis()[1].omega8[?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[?7lom = C.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1.h2expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = om + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?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[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lby[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(().mult_by_p()[?7h[?12l[?25h[?25l[?7l(()).mult_by_p()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lC)).mult_by_p()[?7h[?12l[?25h[?25l[?7l.)).mult_by_p()[?7h[?12l[?25h[?25l[?7lx)).mult_by_p()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l^).mult_by_p()[?7h[?12l[?25h[?25l[?7l(().mult_by_p()[?7h[?12l[?25h[?25l[?7l(()).mult_by_p()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l-)).mult_by_p()[?7h[?12l[?25h[?25l[?7l2)).mult_by_p()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l*).mult_by_p()[?7h[?12l[?25h[?25l[?7l(().mult_by_p()[?7h[?12l[?25h[?25l[?7l(()).mult_by_p()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lC)).mult_by_p()[?7h[?12l[?25h[?25l[?7l.)).mult_by_p()[?7h[?12l[?25h[?25l[?7ly)).mult_by_p()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l^).mult_by_p()[?7h[?12l[?25h[?25l[?7l(().mult_by_p()[?7h[?12l[?25h[?25l[?7l(()).mult_by_p()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l0)).mult_by_p()[?7h[?12l[?25h[?25l[?7l)).mult_by_p()[?7h[?12l[?25h[?25l[?7l-)).mult_by_p()[?7h[?12l[?25h[?25l[?7l1)).mult_by_p()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l*).mult_by_p()[?7h[?12l[?25h[?25l[?7lC).mult_by_p()[?7h[?12l[?25h[?25l[?7l.).mult_by_p()[?7h[?12l[?25h[?25l[?7ld).mult_by_p()[?7h[?12l[?25h[?25l[?7lx).mult_by_p()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l
sage: om1 = v.teichmuller().diffn() + ((C.x)^(-2)*(C.y)^(-1)*C.dx).mult_by_p() 
+

+....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

+ [?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[?7ly)[?7h[?12l[?25h[?25l[?7l/)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1 = v.teichmuller().diffn() + ((C.x)^(-2)*(C.y)^(-1)*C.dx).mult_by_p() 
+

+....: (C.y/C.x^3).verschiebung().diffn()

+[?7h[?12l[?25h[?2004l
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [14], in <cell line: 1>()
+----> 1 om1 = v.teichmuller().diffn() + ((C.x)**(-Integer(2))*(C.y)**(-Integer(1))*C.dx).mult_by_p() +(C.y/C.x**Integer(3)).verschiebung().diffn()
+
+AttributeError: 'superelliptic_form' object has no attribute 'mult_by_p'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA == B[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l C.x.teichmuller()*C.y.teichmuller().diffn()[?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: A = C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C.dx[?7h[?12l[?25h[?25l[?7l.h2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: A.h2.expansion_at_infty()

+  A.cartier               A.expansion_at_infty    A.jth_component         
 

+  A.coordinates           A.form                  A.reduce                
 

+  A.curve                 A.is_regular_on_U0      A.reduce2               
>

+  A.expansion             A.is_regular_on_Uinfty  A.regular_form          
 

+ [?7h[?12l[?25h[?25l[?7lcartier

+ A.cartier              

+

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7lexpansion_at_infty

+ A.cartier               A.expansion_at_infty   [?7h[?12l[?25h[?25l[?7ljth_component

+ A.expansion_at_infty    A.jth_component        [?7h[?12l[?25h[?25l[?7lresidue

+ expansion_at_inftyjth_component     residue       

+ frm       reducesrre_duality_pairing 

+<is_rgular_on_U0reduce2         vrshiebung 

+ is_regular_on_Uinftyregular_form                                 
[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ljth_component

+ A.jth_component         A.residue              [?7h[?12l[?25h[?25l[?7lexpansion_at_infty

+ A.expansion_at_infty    A.jth_component        [?7h[?12l[?25h[?25l[?7lcartier

+ cartier           expansion_at_inftyjth_component 

+ cordinatesform  rduce                

+ curv           is_regular_on_U0rdue2     >

+ expansion           is_regular_on_Uinfty A.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[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lby[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(A)

+[?7h[?12l[?25h[?2004l[?7hV((x^2) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(A)[?7h[?12l[?25h[?25l[?7lA = C.dx[?7h[?12l[?25h[?25l[?7lsage: om1 = v.teichmuller().diffn() + ((C.x)^(-2)*(C.y)^(-1)*C.dx).mult_by_p() 
+

+....: (C.y/C.x^3).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l
()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l( +
(

+C.y/C.x^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l +(
C

+.y/C.x^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l +(C
.

+y/C.x^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l +(C.
y

+/C.x^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l +(C.y
/

+C.x^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l +(C.y/
C

+.x^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l +(C.y/C
.

+x^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l +(C.y/C.
x

+^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l +(C.y/C.x
^

+3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l +(C.y/C.x^
3

+).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l +(C.y/C.x^3
)

+.verschiebung().difn()[?7h[?12l[?25h[?25l[?7l() +(C.y/C.x^3)
.

+verschiebung().difn()[?7h[?12l[?25h[?25l[?7l()) +(C.y/C.x^3
)

+.verschiebung().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() +(C.y/C.x^3)
.

+verschiebung().difn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lm((C.x)^(-2)*(C.y)^(-1)*C.dx) +(C.y/C.x^3
)

+.verschiebung().difn()[?7h[?12l[?25h[?25l[?7lu((C.x)^(-2)*(C.y)^(-1)*C.dx) +(C.y/C.x^
3

+).verschiebung().difn()[?7h[?12l[?25h[?25l[?7ll((C.x)^(-2)*(C.y)^(-1)*C.dx) +(C.y/C.x
^

+3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7lt((C.x)^(-2)*(C.y)^(-1)*C.dx) +(C.y/C.
x

+^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l_((C.x)^(-2)*(C.y)^(-1)*C.dx) +(C.y/C
.

+x^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7lb((C.x)^(-2)*(C.y)^(-1)*C.dx) +(C.y/
C

+.x^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7ly((C.x)^(-2)*(C.y)^(-1)*C.dx) +(C.y
/

+C.x^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l_((C.x)^(-2)*(C.y)^(-1)*C.dx) +(C.
y

+/C.x^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7lp((C.x)^(-2)*(C.y)^(-1)*C.dx) +(C
.

+y/C.x^3).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(

+)[?7h[?12l[?25h[?25l[?7l(

+)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(

+)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(

+)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = v.teichmuller().diffn() + mult_by_p((C.x)^(-2)*(C.y)^(-1)*C.dx) +(C
.

+....: y/C.x^3).verschiebung().diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lta1[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.omega0.regular_form()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?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[?7l1[?7h[?12l[?25h[?25l[?7lsage: eta1.omega8 == om1

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1.omega8 == om1[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).ver
s

+....: chiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).versch
i

+....: ebung())[?7h[?12l[?25h[?25l[?7l-ETA1

+ 

+ [?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lE[?7h[?12l[?25h[?25l[?7lTA1[?7h[?12l[?25h[?25l[?7lsage: eta1 - ETA1

+[?7h[?12l[?25h[?2004l[?7h( + V(((-x^3)/y) dx) + dV([2*x*y]), V(2*x*y), V(((-x^3)/y) dx))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1 - ETA1[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(eta1 - ETA1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).reduce()[?7h[?12l[?25h[?25l[?7l().reduce()[?7h[?12l[?25h[?25l[?7lsage: (eta1 - ETA1).reduce()

+[?7h[?12l[?25h[?2004l[?7h(V(((-x^3)/y) dx), [0], V(((-x^3)/y) dx))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(ETA1.omega8).regular_form()[?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_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC.y)[?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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lff[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: second_patch(C.x^3*C.y.diffn())

+[?7h[?12l[?25h[?2004l[?7h((-1)/(x^3*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.x^3*C.y.diffn())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l+_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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^3*C.y.diffn()).expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^-6 + 2*t^-2 + O(t^4)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x^3*C.y.diffn()).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[?7lsage: (C.x^3*C.y.diffn()).expansion_at_infty(prec = 30)

+[?7h[?12l[?25h[?2004l[?7ht^-6 + 2*t^-2 + t^10 + t^18 + O(t^24)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1 - ETA1[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2.omega0.regular_form()[?7h[?12l[?25h[?25l[?7l - aux[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA1 = C.crystalline_cohomology_basis()[0][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l21[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lsage: ETA2 = C.crystalline_cohomology_basis()[1]

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA2 = C.crystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-eta2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lta2[?7h[?12l[?25h[?25l[?7lsage: ETA2 - eta2

+[?7h[?12l[?25h[?2004l[?7h( + V(((x^8 - x^6 + 1)/y) dx) + dV([(x^4 + x^2 + 1)*y]), V((x^4 + x^2 + 1)*y), V(((x^8 - x^6 + 1)/y) dx))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lETA2 - eta2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(ETA2 - eta2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (ETA2 - eta2).reduce()

+[?7h[?12l[?25h[?2004l[?7h(V(((x^8 - x^6 + 1)/y) dx), [0], V(((x^8 - x^6 + 1)/y) dx))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(ETA2 - eta2).reduce()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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(ETA2 - eta2).reduce()[?7h[?12l[?25h[?25l[?7l (ETA2 - eta2).reduce()[?7h[?12l[?25h[?25l[?7l=(ETA2 - eta2).reduce()[?7h[?12l[?25h[?25l[?7l (ETA2 - eta2).reduce()[?7h[?12l[?25h[?25l[?7lsage: A = (ETA2 - eta2).reduce()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = (ETA2 - eta2).reduce()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= (ETA2 - eta2).reduce()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: A = A.omega8.omega

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = A.omega8.omega[?7h[?12l[?25h[?25l[?7l.h2.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[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lsage: A.expansion

+ A.expansion         

+ A.expansion_at_infty

+

+

+ [?7h[?12l[?25h[?25l[?7l

+ A.expansion         

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

+ A.expansion         

+ A.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(

+

+

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^-16 + t^-8 + O(t^-6)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lA.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: A.expansion_at_infty(prec = 30)

+[?7h[?12l[?25h[?2004l[?7ht^-16 + t^-8 + t^-4 + 1 + 2*t^4 + 2*t^12 + O(t^14)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7lA.expansion_at_infty(prec = 30)[?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[?7le[?7h[?12l[?25h[?25l[?7li[?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[?7lir()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.cartier().expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^-6 + 2*t^-2 + O(t^4)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn() - v.teichmuller().diffn()+ (C.y*v^2 - C.y^2*v).verschiebung().diffn()==( (C.y/C.x)^3).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis[1][?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[1][?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()[1]

+[?7h[?12l[?25h[?2004l[?7h((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7leC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lcC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7loC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lnC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7ldC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7l_C.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lpC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7laC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7ltC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lcC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7lhC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7l(C.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: second_patch(C.de_rham_basis()[1].omega8)

+[?7h[?12l[?25h[?2004l[?7h(x/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7lsage: u

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [34], in <cell line: 1>()
+----> 1 u
+
+NameError: name 'u' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l = C.one/C.x[?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[?7l-(((C.x)^(-1)).teichmuller()*C.y.teichmuller().diffn() + C.y.teichmuller()*((C.x^(-2)).teichmuller()) * C.x.teichmuller().diffn()).r()[?7h[?12l[?25h[?25l[?7lu[?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: -u*v.diffn()

+[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux1[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ltom(ETA2).coordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l(ETA2).coordinates()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(ETA2).coordinates()

+[?7h[?12l[?25h[?2004l(1, 1)
+omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [37], in <cell line: 1>()
+----> 1 autom(ETA2).coordinates()
+
+File <string>:84, in coordinates(self, basis)
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = A.omega8.omega[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* 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[?7lCy)* C.dx[?7h[?12l[?25h[?25l[?7l.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[?7lCx*y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l/x*y + 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[?7lx*y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x*y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.y + 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[?7lCy + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.y + C.x*C.y + 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[?7lCx^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l/x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7lx^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^2*C.y + C.x*C.y + 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[?7lCx)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x)/(C.x^2*C.y + C.x*C.y + 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[?7lCx^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + 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[?7lCx^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + 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[?7lsage: A = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lcartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: A.cartier().expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h1 + 2*t^2 + t^4 + t^6 + 2*t^8 + O(t^10)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.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[?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.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[?7lexpansion_at_infty()[?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[?7l3)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: A.expansion_at_infty(prec = 30)

+[?7h[?12l[?25h[?2004l[?7h2*t^-2 + 2 + 2*t^4 + t^6 + t^12 + t^16 + t^18 + 2*t^22 + O(t^28)
+[?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.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcrystlline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lrystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[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[?7lBC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lc = C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lr = C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lys= C.crystalline_chmlogy_bais()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: Bcrys = C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBcrys = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(ETA2).coordinates()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB) - B - A[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[p[?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[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lb)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lB)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(Bcrys[1]).coordinates(basis = Bcrys)

+[?7h[?12l[?25h[?2004l(1, 1)
+aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [43], in <cell line: 1>()
+----> 1 autom(Bcrys[Integer(1)]).coordinates(basis = Bcrys)
+
+File <string>:85, in coordinates(self, basis)
+
+File <string>:56, in coordinates(self)
+
+File <string>:93, in coordinates(self, basis)
+
+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/categories/map.pyx:788, in sage.categories.map.Map._call_()
+    786     return self._call_with_args(x, args, kwds)
+    787 
+--> 788 cpdef Element _call_(self, x):
+    789     """
+    790     Call method with a single argument, not implemented in the base class.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
+   1249     return num
+   1250 if check and not den.is_unit():
+   1251     # This should probably be a ValueError.
+   1252     # However, too much existing code is expecting this to throw a
+   1253     # TypeError, so we decided to keep it for the time being.
+-> 1254     raise TypeError("fraction must have unit denominator")
+   1255 return num * den.inverse_of_unit()
+
+TypeError: fraction must have unit denominator
+[?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[?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[?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[?7lautom(Bcrys[1]).coordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7lBcrys = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: Bcrys = C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBcrys = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(Bcrys[1]).coordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7lsage: autom(Bcrys[1]).coordinates(basis = Bcrys)

+[?7h[?12l[?25h[?2004lcoordinates of form self (1/y) dx
+(1, 1)
+aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
+aux_divided_by_p (((x + 1)/(x*y - y)) dx, 0, ((x + 1)/(x*y - y)) dx)
+aux_divided_by_p.omega8 == aux.omega8.omega.cartier() True
+coordinates of form self ((x + 1)/(x*y - y)) dx
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [47], in <cell line: 1>()
+----> 1 autom(Bcrys[Integer(1)]).coordinates(basis = Bcrys)
+
+File <string>:87, in coordinates(self, basis)
+
+File <string>:56, in coordinates(self)
+
+File <string>:94, in coordinates(self, basis)
+
+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/categories/map.pyx:788, in sage.categories.map.Map._call_()
+    786     return self._call_with_args(x, args, kwds)
+    787 
+--> 788 cpdef Element _call_(self, x):
+    789     """
+    790     Call method with a single argument, not implemented in the base class.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
+   1249     return num
+   1250 if check and not den.is_unit():
+   1251     # This should probably be a ValueError.
+   1252     # However, too much existing code is expecting this to throw a
+   1253     # TypeError, so we decided to keep it for the time being.
+-> 1254     raise TypeError("fraction must have unit denominator")
+   1255 return num * den.inverse_of_unit()
+
+TypeError: fraction must have unit denominator
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(Bcrys[1]).coordinates(basis = Bcrys)[?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(Bcrys[1]).coordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7lBcrys = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: Bcrys = C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBcrys = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(Bcrys[1]).coordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAautom(Bcrys[1]).cordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7lAautom(Bcrys[1]).cordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7l autom(Bcrys[1]).cordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7l=autom(Bcrys[1]).cordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7l autom(Bcrys[1]).cordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7lsage: AA = autom(Bcrys[1]).coordinates(basis = Bcrys)

+[?7h[?12l[?25h[?2004lcoordinates of form self (1/y) dx
+(1, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAA = autom(Bcrys[1]).coordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lsage: AA

+[?7h[?12l[?25h[?2004l[?7h( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAA[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AA.reduce()

+[?7h[?12l[?25h[?2004l[?7h( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [0],  + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAA.reduce()[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lsage: AA

+[?7h[?12l[?25h[?2004l[?7h( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]), [0],  + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(1/(x^2 + x + 1))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAA[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.reduce()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loA.omega0.omega[?7h[?12l[?25h[?25l[?7lmA.omega0.omega[?7h[?12l[?25h[?25l[?7l A.omega0.omega[?7h[?12l[?25h[?25l[?7l-A.omega0.omega[?7h[?12l[?25h[?25l[?7l=A.omega0.omega[?7h[?12l[?25h[?25l[?7l A.omega0.omega[?7h[?12l[?25h[?25l[?7lA.omega0.omega[?7h[?12l[?25h[?25l[?7lA.omega0.omega[?7h[?12l[?25h[?25l[?7lA.omega0.omega[?7h[?12l[?25h[?25l[?7l=A.omega0.omega[?7h[?12l[?25h[?25l[?7l A.omega0.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = AA.omega0.omega

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = AA.omega0.omega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.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[?7lom = AA.omega0.omega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om

+[?7h[?12l[?25h[?2004l[?7h((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx
+[?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.r()[?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 + 1)/(x*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.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[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?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[?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().expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h1 + 2*t^2 + t^4 + t^6 + 2*t^8 + O(t^10)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(Bcrys[1]).coordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l(Bcrys[1]).coordinates(basis = Bcrys)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: autom(Bcrys[1])

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2*x))*y] d[x] + V(((x^4 - x^3 - x^2 + x + 1)/(x^2*y + x*y + y)) dx) + dV([((x^6 + 2*x^5 + 2*x^3 + x^2 + x)/(x^2 + x + 1))*y]), [(2/(x + 1))*y] + V((x^4 + x^3 + x^2)*y), [(2/(x^4 + x^3 + 2*x^2 + 2*x))*y] d[x] + V(((-x^7 - x^6 + x^4 - x^3 - x^2 + 1)/(x^6*y - x^5*y - x^4*y - x^3*y - x^2*y - x*y + y)) dx) + dV([((2*x^4 + 2*x^3 + 2*x^2 + x)/(x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(Bcrys[1])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: autom(Bcrys[1]) - Bcrys[0] - Bcrys[1]

+[?7h[?12l[?25h[?2004l[?7h( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(Bcrys[1]) - Bcrys[0] - Bcrys[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrautom(Bcrys[1]) - Bcrys[0] - Bcrys[1][?7h[?12l[?25h[?25l[?7lrautom(Bcrys[1]) - Bcrys[0] - Bcrys[1][?7h[?12l[?25h[?25l[?7l autom(Bcrys[1]) - Bcrys[0] - Bcrys[1][?7h[?12l[?25h[?25l[?7l=autom(Bcrys[1]) - Bcrys[0] - Bcrys[1][?7h[?12l[?25h[?25l[?7l autom(Bcrys[1]) - Bcrys[0] - Bcrys[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[?7lsage: rr = autom(Bcrys[1]) - Bcrys[0] - Bcrys[1]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBcrys = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lcr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: Bcrys[1]

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBcrys[1][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loBcrys[1].omega0[?7h[?12l[?25h[?25l[?7lmBcrys[1].omega0[?7h[?12l[?25h[?25l[?7l Bcrys[1].omega0[?7h[?12l[?25h[?25l[?7l=Bcrys[1].omega0[?7h[?12l[?25h[?25l[?7l Bcrys[1].omega0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?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 = Bcrys[1].omega0

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = Bcrys[1].omega0[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?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[?7lautom(Bcrys[1]) - Bcrys[0] - Bcrys[1][?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lom1).frobenius()[?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[?7lom[?7h[?12l[?25h[?25l[?7l = Bcrys[1].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = Bcrys[1].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?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 = Bcrys[1].omega0

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = Bcrys[1].omega0[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: om0 = Bcrys[0].omega0

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom0 = Bcrys[0].omega0[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0 = Bcrys[0].omega0[?7h[?12l[?25h[?25l[?7l = Bcrys[0].omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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(Bcrys[1]) - Bcrys[0] - Bcrys[1][?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lto[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lom1).frobenius()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(om1)

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^2 + 2*x))*y] d[x] + V(((x^4 - x^3 - x^2 + x + 1)/(x^2*y + x*y + y)) dx) + dV([((x^6 + 2*x^5 + 2*x^3 + x^2 + x)/(x^2 + x + 1))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(om1)[?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[?7l1[?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[?7l0[?7h[?12l[?25h[?25l[?7lsage: autom(om1) - om1 - om0

+[?7h[?12l[?25h[?2004l[?7h + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom0 = Bcrys[0].omega0[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l11[?7h[?12l[?25h[?25l[?7lsage: om1

+[?7h[?12l[?25h[?2004l[?7h[(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.h2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lomega.expansionat_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: om1.omega

+[?7h[?12l[?25h[?2004l[?7h((x^4 + x^2 - 1)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.omega[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.omega.regular_form()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBcrys[1][?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[1][?7h[?12l[?25h[?25l[?7lsage: Bcrys[1]

+[?7h[?12l[?25h[?2004l[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^4 + x^2 - 1)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]), [2/x*y] + V((x^4 + x^2 + 1)*y), [(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.omega.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = Bcrys[1].omega0[?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[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?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[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?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: om1 - C.x.teichmuller()*C.y().teichmuller().diffn()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [72], in <cell line: 1>()
+----> 1 om1 - C.x.teichmuller()*C.y().teichmuller().diffn()
+
+TypeError: 'superelliptic_function' object is not callable
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 - C.x.teichmuller()*C.y().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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 - C.x.teichmuller()*C.y.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7hV(((x^8 - x^6 + 1)/y) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC.de_rha_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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[?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[?7lsage: autom(C.x.teichmuller().diffn())

+[?7h[?12l[?25h[?2004l[?7h[1] d[x]dV([x^2 + x])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x.teichmuller().diffn())[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lom1) - om1 - om0[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1) - om1 - om0[?7h[?12l[?25h[?25l[?7lsage: autom(om1) - om1 - om0

+[?7h[?12l[?25h[?2004l[?7h + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 - C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.omegargular_fom()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1.regular_form()

+[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [x] d[y] + V(((x^8 - x^6 + 1)/y) dx) + dV(0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0 = Bcrys[0].omega0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om0.regular_form()

+[?7h[?12l[?25h[?2004l[?7h[0] d[x] + [1] d[y] + V(((x^5 + x^3)/y) dx) + dV(0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(ETA2 - eta2).reduce()[?7h[?12l[?25h[?25l[?7lx^8 - x^6).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8 - x^6).quo_rem(x^3 - x)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x^8 - x^6)[?7h[?12l[?25h[?25l[?7l (x^8 - x^6)[?7h[?12l[?25h[?25l[?7l=(x^8 - x^6)[?7h[?12l[?25h[?25l[?7l (x^8 - x^6)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = (x^8 - x^6)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = (x^8 - x^6)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: g(x+1) - g

+[?7h[?12l[?25h[?2004l[?7h2*x^7 + x^6 + 2*x^5 + x^4 + x^2 + 2*x
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = (x^8- x^6)[?7h[?12l[?25h[?25l[?7lom0.regular_form()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lautom(om1) - m1 - om0[?7h[?12l[?25h[?25l[?7lom1.regular_frm()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lg = (x^8 - x^6)[?7h[?12l[?25h[?25l[?7l(x+1) -g[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = (x^8- x^6)[?7h[?12l[?25h[?25l[?7lom0.regular_form()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lautom(om1) - m1 - om0[?7h[?12l[?25h[?25l[?7l(C.x.teichmuller().diffn())[?7h[?12l[?25h[?25l[?7l(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAautom(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7l autom(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7l=autom(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7l autom(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = autom(om1) - om1 - om0

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = autom(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBcrys[1][?7h[?12l[?25h[?25l[?7l = de_rham_witt_lift_form0(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[?7lC)[?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[?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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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^2 + C.x)*C.y^2*C.y.difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lbu[?7h[?12l[?25h[?25l[?7l[?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[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?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[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leschiebung()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrschiebung()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(().verschiebung()[?7h[?12l[?25h[?25l[?7l(()).verschiebung()[?7h[?12l[?25h[?25l[?7l*).verschiebung()[?7h[?12l[?25h[?25l[?7lC).verschiebung()[?7h[?12l[?25h[?25l[?7l.).verschiebung()[?7h[?12l[?25h[?25l[?7ly).verschiebung()[?7h[?12l[?25h[?25l[?7l.).verschiebung()[?7h[?12l[?25h[?25l[?7ld).verschiebung()[?7h[?12l[?25h[?25l[?7li).verschiebung()[?7h[?12l[?25h[?25l[?7lf).verschiebung()[?7h[?12l[?25h[?25l[?7lf).verschiebung()[?7h[?12l[?25h[?25l[?7ln).verschiebung()[?7h[?12l[?25h[?25l[?7l(().verschiebung()[?7h[?12l[?25h[?25l[?7l(()).verschiebung()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l*)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lC)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l.)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lx)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l^)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l7)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l )*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l+)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l )*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lC)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l.)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lx)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l^)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l6)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l )*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l+)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l )*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lC)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l.)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lx)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l^)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l5)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l )*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l+)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l )*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lC)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l.)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lx)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l^)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l4)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l )*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l+)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l )*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l2)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l*)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lC)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l.)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lx)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l^)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l3)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l+)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lC)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l.)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lx)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l^)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l2)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l+)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l2)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l*)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lC)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l.)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7lx)*C.y.difn().verschiebung()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = ((C.x^2 + C.x)*C.y^2*C.y.diffn()).verschiebung() + ((2*C.x^7 + C.x^6 + C.x^5 + C.x^4 + 2*C.x^3+C.x^2+2*C.x)*C.y.diffn()).verschiebung()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = autom(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = autom(om1) - om1 - om0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l= B[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lsage: A == B

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA == B[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(prec = 30)[?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: A.cartier()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [83], in <cell line: 1>()
+----> 1 A.cartier()
+
+AttributeError: 'superelliptic_drw_form' object has no attribute 'cartier'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.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[?7locartier()[?7h[?12l[?25h[?25l[?7lmcartier()[?7h[?12l[?25h[?25l[?7lecartier()[?7h[?12l[?25h[?25l[?7lgcartier()[?7h[?12l[?25h[?25l[?7lacartier()[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7lsage: A.omega.cartier()

+[?7h[?12l[?25h[?2004l[?7h((x + 1)/(x*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.omega.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[?7lA.omega.cartier()[?7h[?12l[?25h[?25l[?7lsage: A

+[?7h[?12l[?25h[?2004l[?7h + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^5 + x^4 + x^2 + x)/(x^2 + x + 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(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7l.(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7lq(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7lu(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7lo(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7l_(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7lr(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7le(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7lm(x^2 + x + 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[?7lsage: (x^5 + x^4 + x^2 + x).quo_rem(x^2 + x + 1)

+[?7h[?12l[?25h[?2004l[?7h(x^3 + 2*x + 2, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7lsage: u

+[?7h[?12l[?25h[?2004l[?7h1/x
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?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[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: u.expansion

+ u.expansion         

+ u.expansion_at_infty

+

+

+ [?7h[?12l[?25h[?25l[?7l

+ u.expansion         

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

+ u.expansion         

+ u.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(

+

+

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: u.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^2 + 2*t^6 + 2*t^10 + t^14 + 2*t^18 + O(t^22)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lu.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.expansion_at_infty()[?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[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lsage: A

+[?7h[?12l[?25h[?2004l[?7h + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.omega.cartier()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7lsage: A.omega.cartier()

+[?7h[?12l[?25h[?2004l[?7h((x + 1)/(x*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.omega.cartier()[?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: A.omega.cartier().cartier()

+[?7h[?12l[?25h[?2004l[?7h((-1)/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[?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.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx.egular_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(C.dx[?7h[?12l[?25h[?25l[?7l()C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC)C.dx[?7h[?12l[?25h[?25l[?7l.)C.dx[?7h[?12l[?25h[?25l[?7ly)C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^C.dx[?7h[?12l[?25h[?25l[?7l(C.dx[?7h[?12l[?25h[?25l[?7l-C.dx[?7h[?12l[?25h[?25l[?7l1C.dx[?7h[?12l[?25h[?25l[?7l()C.dx[?7h[?12l[?25h[?25l[?7l()*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[?7lo(C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lm(C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l (C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l=(C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l (C.y)^(-1)*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[?7lsage: om = (C.y)^(-1)*C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7limport itertools.product as product[?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[?7lrtier[?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[?7lsage: inv_cartier(om)

+[?7h[?12l[?25h[?2004l[?7h((x^3 - x)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7linv_cartier(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[?7linv_cartier(om)[?7h[?12l[?25h[?25l[?7lninv_cartier(om)[?7h[?12l[?25h[?25l[?7lvinv_cartier(om)[?7h[?12l[?25h[?25l[?7l_inv_cartier(om)[?7h[?12l[?25h[?25l[?7lcinv_cartier(om)[?7h[?12l[?25h[?25l[?7lainv_cartier(om)[?7h[?12l[?25h[?25l[?7lrinv_cartier(om)[?7h[?12l[?25h[?25l[?7ltinv_cartier(om)[?7h[?12l[?25h[?25l[?7linv_cartier(om)[?7h[?12l[?25h[?25l[?7leinv_cartier(om)[?7h[?12l[?25h[?25l[?7lrinv_cartier(om)[?7h[?12l[?25h[?25l[?7l(inv_cartier(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[?7lsage: inv_cartier(inv_cartier(om))

+[?7h[?12l[?25h[?2004l[?7h((x^12 - x^10 - x^6 + x^4)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7linv_cartier(inv_cartier(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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7linv_cartier(inv_cartier(om)[?7h[?12l[?25h[?25l[?7linv_cartier(inv_cartier(om)[?7h[?12l[?25h[?25l[?7l inv_cartier(inv_cartier(om)[?7h[?12l[?25h[?25l[?7l=inv_cartier(inv_cartier(om)[?7h[?12l[?25h[?25l[?7l inv_cartier(inv_cartier(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[?7lsage: ii = inv_cartier(inv_cartier(om))

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l/dx[?7h[?12l[?25h[?25l[?7ldx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy) C.dx[?7h[?12l[?25h[?25l[?7l.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[?7lCy + C.y) C.dx[?7h[?12l[?25h[?25l[?7l.y + 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[?7lCx*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l.x*C.y + 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[?7lCy + C.x*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l.y + C.x*C.y + 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[?7lCx^2*C.y + C.x*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l.x^2*C.y + C.x*C.y + 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[?7lCx)/(C.x^2*C.y + C.x*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l.x)/(C.x^2*C.y + C.x*C.y + 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[?7lC x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l. x^2 + C.x)/(C.x^2*C.y + C.x*C.y + 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[?7lx^2 + C.x)/(C.x^2*C.y + C.x*C.y + 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[?7lCx^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y) C.dx[?7h[?12l[?25h[?25l[?7l.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + 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()* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.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[?7li[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: ((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx - ii

+[?7h[?12l[?25h[?2004l[?7h((-x^14 - x^13 + x^11 + x^10 + x^8 + x^7 - x^5 - x^4 - x^3 + x^2 + x)/(x^2*y + x*y + y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lii = inv_cartier(inv_cartier(om))[?7h[?12l[?25h[?25l[?7li[?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[?7lsage: ii.is_regular_on_U

+ ii.is_regular_on_U0    

+ ii.is_regular_on_Uinfty

+

+

+ [?7h[?12l[?25h[?25l[?7l0

+ ii.is_regular_on_U0    

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l(

+

+

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ii.is_regular_on_U0()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lii.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7l((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx - ii[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx - i).cartier()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx - ii).cartier()

+[?7h[?12l[?25h[?2004l[?7h((-x^4 + x^3 + x^2 + 1)/(x*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7l(((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx - ii).cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx - ii).cartier().cartier()

+[?7h[?12l[?25h[?2004l[?7h(1/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx - ii).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 i).cartier()[?7h[?12l[?25h[?25l[?7l+ i).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[?7lsage: (((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx + ii).cartier()

+[?7h[?12l[?25h[?2004l[?7h((x^4 - x^3 - x^2 - x + 1)/(x*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx + ii).cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx + ii).cartier().cartier()

+[?7h[?12l[?25h[?2004l[?7h0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx + ii).cartier().cartier()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-().cartier()[?7h[?12l[?25h[?25l[?7l+()[?7h[?12l[?25h[?25l[?7l().cartier()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().cartier()[?7h[?12l[?25h[?25l[?7lsage: (((-C.x^3 +C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx + ii).cartier().cartier()

+[?7h[?12l[?25h[?2004l[?7h0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.is_regular()[?7h[?12l[?25h[?25l[?7lsage: x

+[?7h[?12l[?25h[?2004l[?7hx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in range(0, 9):[?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[?7h[?12l[?25h[?25l[?7l=[?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[?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.[?7h[?12l[?25h[?25l[?7lsage: G.

+  G.abs                         G.all_roots_in_interval       G.base_ring                   G.change_variable_name        G.compose_trunc                

+  G.adams_operator              G.any_root                    G.cartesian_product           G.coefficients                G.composed_op                  

+  G.add_bigoh                   G.args                        G.category                    G.complex_roots               G.constant_coefficient        >

+  G.additive_order              G.base_extend                 G.change_ring                 G.compose_power               G.content_ideal                

+ [?7h[?12l[?25h[?25l[?7labs

+ G.abs                        

+

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7lll_roots_in_interval

+ G.abs                         G.all_roots_in_interval      [?7h[?12l[?25h[?25l[?7lbase_ring

+ G.all_roots_in_interval       G.base_ring                  [?7h[?12l[?25h[?25l[?7lchange_variable_name

+ G.base_ring                   G.change_variable_name       [?7h[?12l[?25h[?25l[?7lompose_tunc

+ G.change_variable_name        G.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[?7lhammingweight

+ G.hamming_weight              G.inverse_mod                [?7h[?12l[?25h[?25l[?7ls_cyclotomic_factor

+ G.hamming_weight             

+ G.has_cyclotomic_factor      [?7h[?12l[?25h[?25l[?7lomogenize

+

+ G.has_cyclotomic_factor      

+ G.homogenize                 [?7h[?12l[?25h[?25l[?7linteral

+

+

+ G.homogenize                 

+ G.integral                   [?7h[?12l[?25h[?25l[?7l(

+

+

+

+

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: G.integral()

+[?7h[?12l[?25h[?2004l[?7hx^4 + 2*x^2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lG.integral()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lG.integral()[?7h[?12l[?25h[?25l[?7l = x^3 + x[?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[?7l2[?7h[?12l[?25h[?25l[?7lsage: G = x^3 + x + x^2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+

+ [?7h[?12l[?25h[?25l[?7lG = x^3 + x + x^2[?7h[?12l[?25h[?25l[?7l.integral()[?7h[?12l[?25h[?25l[?7lsage: G.integral()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ZeroDivisionError                         Traceback (most recent call last)
+Input In [109], in <cell line: 1>()
+----> 1 G.integral()
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral()
+   3992 cdef Py_ssize_t n
+   3993 zero = Q.zero()
+-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv)
+   3995               if self.get_unsafe(n) else zero for n in range(self.degree() + 1)]
+   3996 return S(p)
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
+   1202     self._record_exception()
+   1203 else:
+-> 1204     return PyObject_CallObject(op, xy)
+   1205 
+   1206 if op is mul:
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
+   1735 cdef int cl = classify_elements(left, right)
+   1736 if HAVE_SAME_PARENT(cl):
+-> 1737     return (<Element>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[(<IntegerMod_int>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 * (<IntegerMod_int>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[?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[?7lom = (C.y)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1].omega8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?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(C.y/C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?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 = (C.y/C.x).diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()[?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[?2004l[?7h((x^5 + 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[?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[?7lom.int()[?7h[?12l[?25h[?25l[?7lsage: om.int()

+[?7h[?12l[?25h[?2004l[?7h((x^5 + x)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.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(C.y/C.x)[?7h[?12l[?25h[?25l[?7lsage: om.int() - (C.y/C.x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [115], in <cell line: 1>()
+----> 1 om.int() - (C.y/C.x)
+
+File <string>:26, in __sub__(self, other)
+
+AttributeError: 'superelliptic_function' object has no attribute 'form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?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[?7lom.int() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lsage: om = (C.y/C.x).diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7lsage: om.int() - (C.y/C.x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [118], in <cell line: 1>()
+----> 1 om.int() - (C.y/C.x)
+
+File <string>:199, in int(self)
+
+File <string>:19, in __add__(self, other)
+
+AttributeError: 'superelliptic_function' object has no attribute 'form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int() - (C.y/C.x)[?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[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [119], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:199, in int(self)
+
+File <string>:19, in __add__(self, other)
+
+AttributeError: 'superelliptic_function' object has no attribute 'form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7l = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lsage: om = (C.y/C.x).diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lcartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?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.carier()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [122], in <cell line: 1>()
+----> 1 om.carier()
+
+AttributeError: 'superelliptic_form' object has no attribute 'carier'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.carier()[?7h[?12l[?25h[?25l[?7l)[?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()[?7h[?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[?7lsage: om.cartier().expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h0
+[?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[?7lsage: om.cartier()

+[?7h[?12l[?25h[?2004l[?7h0 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[?7lier()[?7h[?12l[?25h[?25l[?7l = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l.carier()[?7h[?12l[?25h[?25l[?7ltier().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[?7lom.cartier()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lier()[?7h[?12l[?25h[?25l[?7l = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l.carier()[?7h[?12l[?25h[?25l[?7ltier().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[?7lom.cartier()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lier()[?7h[?12l[?25h[?25l[?7l = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7lsage: om.int() - (C.y/C.x)

+[?7h[?12l[?25h[?2004l[?7h((x^5 + 2*x^2 + x + 1)/(x^3 + 2*x))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(om.int() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?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: (om.int() - (C.y/C.x)).pth_root()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [126], in <cell line: 1>()
+----> 1 (om.int() - (C.y/C.x)).pth_root()
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7l = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.de_rham_basis[1].omega8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: om = C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7linn[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

+[?7h[?12l[?25h[?2004l[?7hx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = 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[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = C.y.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.y.diffn()[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lsage: om.int()

+[?7h[?12l[?25h[?2004l[?7h((x^3 + x)/(x^2 + 2))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l() - (C.y/C.x)[?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[?7lsage: om.int() - C.y

+[?7h[?12l[?25h[?2004l[?7h((x^3 + 2*x^2 + x + 1)/(x^2 + 2))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int() - 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(om.int() - 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[?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: (om.int() - C.y).pth_root()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [132], in <cell line: 1>()
+----> 1 (om.int() - C.y).pth_root()
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int() - C.y[?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[?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.int().diffn()

+[?7h[?12l[?25h[?2004l[?7h(x^5/(x^2*y - 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[?7lom.int().diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = C.y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l C.y.diffn()[?7h[?12l[?25h[?25l[?7lsage: om = C.y.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.y.diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int().diffn()[?7h[?12l[?25h[?25l[?7lsage: om.int().diffn()

+[?7h[?12l[?25h[?2004l[?7h(1/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int().diffn()[?7h[?12l[?25h[?25l[?7l = C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int().diffn()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int().diffn()[?7h[?12l[?25h[?25l[?7l(om.int() - C.y).pth_root()[?7h[?12l[?25h[?25l[?7lom.int() - C.y[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l = C.y.diffn()[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l = C.dx[?7h[?12l[?25h[?25l[?7l(om.int() - (C.y/C.x)).pth_root()[?7h[?12l[?25h[?25l[?7lom.int() - (C.y/C.x)[?7h[?12l[?25h[?25l[?7lcartier()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lier()[?7h[?12l[?25h[?25l[?7l = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lsage: om = (C.y/C.x).diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int().diffn()[?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().diffn()[?7h[?12l[?25h[?25l[?7lsage: om.int().diffn()

+[?7h[?12l[?25h[?2004l[?7h((-x^2 - 1)/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int().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[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om.int().diffn() == om

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int().diffn() == om[?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[?2004l[?7h((x^4 + 1)/(x^5 + x^3 + x))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = (C.y/C.x).diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.y.diffn()[?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[?7lsage: om = C.x*C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = C.x*C.y[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?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[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.difn()[?7h[?12l[?25h[?25l[?7lmom.difn()[?7h[?12l[?25h[?25l[?7l om.difn()[?7h[?12l[?25h[?25l[?7l=om.difn()[?7h[?12l[?25h[?25l[?7l om.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = om.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.diffn()[?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[?2004l[?7h((x^5 + x^3)/(x^4 + x^2 + 1))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l().diffn() == om[?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[?2004l[?7h(x^3/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(C.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_g8(aux)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7losition_g0_g8(aux)[1].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[?7lo)[?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: decomposition_g0_g8(om.int())

+[?7h[?12l[?25h[?2004l[?7h(((x^5 + x^3)/(x^4 + x^2 + 1))*y, 0, 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+

+

+

+

+

+

+

+

+ [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

+[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lTraceback (most recent call last):
+
+  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input In [1] in <cell line: 1>
+    load('init.sage')
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:21 in <module>
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:22
+    if self.dx = _sage_const_0 *C.x and self.y = _sage_const_0 *C.x:
+       ^
+SyntaxError: cannot assign to attribute here. Maybe you meant '==' instead of '='?
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg(x+1) - g[?7h[?12l[?25h[?25l[?7l = (x^8- x^6)[?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[?7l7[?7h[?12l[?25h[?25l[?7l[?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[?7ly[?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[?7l2[?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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?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.[?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[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7log.difn()[?7h[?12l[?25h[?25l[?7lmg.difn()[?7h[?12l[?25h[?25l[?7l g.difn()[?7h[?12l[?25h[?25l[?7l=g.difn()[?7h[?12l[?25h[?25l[?7l g.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int().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 = g.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.difn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int().diffn()[?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[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [6], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:21, in int(self)
+
+AttributeError: 'superelliptic_regular_form' object has no attribute 'fct_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[?7lom.int()[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7lg.diffn()[?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[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [9], in <cell line: 1>()
+----> 1 om = om.regular_form()
+
+AttributeError: 'superelliptic_regular_form' object has no attribute 'regular_form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7lg.diffn()[?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[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = g.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?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[?2004l---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [12], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:28, in int(self)
+
+ValueError: not enough values to unpack (expected 2, got 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lself.fct_field = Fxy, Rxy, x, 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[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lselfFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, 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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ld[?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[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(om.int() - C.y).pth_root()[?7h[?12l[?25h[?25l[?7lx^5 + x^4 + x^2 + x).quo_rem(x^2 + x + 1)[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?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[?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[?7lsage: (x^6*y^7).exponents()

+[?7h[?12l[?25h[?2004l[?7h[(6, 7)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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(x^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7l,(x^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7l (x^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7lj(x^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7l (x^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7l=(x^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7l (x^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: i, j = (x^6*y^7).exponents()[0]

+[?7h[?12l[?25h[?2004l[?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[?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[?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[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ZeroDivisionError                         Traceback (most recent call last)
+Input In [20], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:30, in int(self)
+
+File <string>:30, in int(self)
+
+    [... skipping similar frames: int at line 30 (3 times)]
+
+File <string>:30, in int(self)
+
+File <string>:29, in int(self)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1739, in sage.structure.element.Element.__truediv__()
+   1737     return (<Element>left)._div_(right)
+   1738 if BOTH_ARE_ELEMENT(cl):
+-> 1739     return coercion_model.bin_op(left, right, truediv)
+   1740 
+   1741 try:
+
+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 (<Element>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[(<IntegerMod_int>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 * (<IntegerMod_int>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[?7lom.int()[?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)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2 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[?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[?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[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.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)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
+[?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.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[?2004l---------------------------------------------------------------------------
+ZeroDivisionError                         Traceback (most recent call last)
+Input In [27], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:30, in int(self)
+
+File <string>:30, in int(self)
+
+    [... skipping similar frames: int at line 30 (3 times)]
+
+File <string>:30, in int(self)
+
+File <string>:29, in int(self)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1739, in sage.structure.element.Element.__truediv__()
+   1737     return (<Element>left)._div_(right)
+   1738 if BOTH_ARE_ELEMENT(cl):
+-> 1739     return coercion_model.bin_op(left, right, truediv)
+   1740 
+   1741 try:
+
+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 (<Element>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[(<IntegerMod_int>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 * (<IntegerMod_int>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[?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[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7lg.diffn()[?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[?7lload('init.sage')[?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[?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[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?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[?7lom = om.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)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
+[?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.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)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
+m dx x^18*y
+int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19) dy
+m dx x^16*y
+int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17) dy
+m dx x^12*y
+int(self) ((2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13) dy
+m dx x^10*y
+int(self) (2*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^6
+int(self) (2*y + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^4
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+---------------------------------------------------------------------------
+ZeroDivisionError                         Traceback (most recent call last)
+Input In [33], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:32, in int(self)
+
+File <string>:32, in int(self)
+
+    [... skipping similar frames: int at line 32 (3 times)]
+
+File <string>:32, in int(self)
+
+File <string>:31, in int(self)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1739, in sage.structure.element.Element.__truediv__()
+   1737     return (<Element>left)._div_(right)
+   1738 if BOTH_ARE_ELEMENT(cl):
+-> 1739     return coercion_model.bin_op(left, right, truediv)
+   1740 
+   1741 try:
+
+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 (<Element>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[(<IntegerMod_int>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 * (<IntegerMod_int>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[?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[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = C.x^7 * C.y^8

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.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 om.regular_form()[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

+[?7h[?12l[?25h[?2004l[?7h(x^18 + x^16 - x^12 - x^10) dx
+[?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.int()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lsage: om.int()

+[?7h[?12l[?25h[?2004l[?7hx^19 + 2*x^17 + 2*x^13 + x^11
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7lsage: g = 2*C.x*C.y^3

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in range(0, 9):[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.diffn()

+[?7h[?12l[?25h[?2004l[?7h((-x^6 - x^4 - x^2)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l()o[?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[?7log.difn()[?7h[?12l[?25h[?25l[?7lmg.difn()[?7h[?12l[?25h[?25l[?7l g.difn()[?7h[?12l[?25h[?25l[?7l=g.difn()[?7h[?12l[?25h[?25l[?7l g.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?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[?2004l[?7h(2*x^4 + x^2)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l = 2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l- C.x - 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- C.y[?7h[?12l[?25h[?25l[?7l- C.y[?7h[?12l[?25h[?25l[?7l- C.y[?7h[?12l[?25h[?25l[?7l- C.y[?7h[?12l[?25h[?25l[?7l- C.y[?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[?7lsage: g = - C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lnm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm.int()[?7h[?12l[?25h[?25l[?7l = g.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lint()[?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 = g.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpip install -U sage[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

+[?7h[?12l[?25h[?2004l[?7h(2) dy
+[?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.int()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lsage: om.int()

+[?7h[?12l[?25h[?2004lint(self) (2) dy
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [46], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:23, in int(self)
+
+AttributeError: 'superelliptic_regular_form' object has no attribute '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[?7lg = - 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 C.y[?7h[?12l[?25h[?25l[?7lsage: g = - C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = - 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[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?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[?2004l[?7h((2*x^2 + 2)/(x^4 + x^2 + 1))*y
+[?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[?7lr()[?7h[?12l[?25h[?25l[?7legular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = g.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?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) (2) dy
+---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [52], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:36, in int(self)
+
+NameError: name 'dy' 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('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.y[?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[?7lsage: g = - C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?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) (2) dy
+m dx 1
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [57], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:38, in int(self)
+
+ValueError: not enough values to unpack (expected 2, got 1)
+[?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[?7lg = - C.y[?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[?7lsage: g = - C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?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) (2) dy
+m dx 1
+int(self) ((1/(x^2 + 2))*y + 2) dy
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+   1008 # now try calling the base ring's __call__ methods
+-> 1009 element = self.base_ring()(element)
+   1010 _p = p_NSet(sa2si(element,_ring), _ring)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    896 if no_extra_args:
+--> 897     return mor._call_(x)
+    898 else:
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
+   1691 for f in self.__list:
+-> 1692     x = f._call_(x)
+   1693 return x
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12066, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_()
+  12065 """
+> 12066 cpdef Element _call_(self, x):
+  12067     """
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12091, in sage.rings.polynomial.polynomial_element.ConstantPolynomialSection._call_()
+  12090 else:
+> 12091     raise TypeError("not a constant polynomial")
+  12092 
+
+TypeError: not a constant polynomial
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [62], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:40, in int(self)
+
+File <string>:35, 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/multi_polynomial_libsingular.pyx:1013, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+   1011         return new_MP(self,_p)
+   1012     except (TypeError, ValueError):
+-> 1013         raise TypeError("Could not find a mapping of the passed element to this ring.")
+   1014 
+   1015 def _repr_(self):
+
+TypeError: Could not find a mapping of the passed element to this ring.
+[?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.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l - C.y[?7h[?12l[?25h[?25l[?7lsage: g = - C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?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) (2) dy
+m dy 1
+int(self) (0) dy
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [67], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:40, in int(self)
+
+File <string>: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 = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'function'
+[?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 = om.regular_form()[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7lg = - C.y[?7h[?12l[?25h[?25l[?7lsage: g = - C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lsage: om.int()

+[?7h[?12l[?25h[?2004lint(self) (2) dy
+m dy 1
+int(self) (0) dy
+[?7h2*y
+[?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[?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[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7lsage: om = om.regular_form()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = om.regular_form()[?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)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
+m dx x^18*y
+int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19) dy
+m dx x^16*y
+int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17) dy
+m dx x^12*y
+int(self) ((2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13) dy
+m dx x^10*y
+int(self) (2*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^6
+int(self) (2*y + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^4
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+---------------------------------------------------------------------------
+ZeroDivisionError                         Traceback (most recent call last)
+Input In [76], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:32, in int(self)
+
+File <string>:32, in int(self)
+
+    [... skipping similar frames: int at line 32 (3 times)]
+
+File <string>:32, in int(self)
+
+File <string>:31, in int(self)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1739, in sage.structure.element.Element.__truediv__()
+   1737     return (<Element>left)._div_(right)
+   1738 if BOTH_ARE_ELEMENT(cl):
+-> 1739     return coercion_model.bin_op(left, right, truediv)
+   1740 
+   1741 try:
+
+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 (<Element>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[(<IntegerMod_int>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 * (<IntegerMod_int>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[?7lom.int()[?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)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
+[?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[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3 - C.x - 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[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l.2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l.2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: g = 2*C.x*C.y^3

+[?7h[?12l[?25h[?2004l[?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 = om.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= om.regular_form()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?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[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 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(2*x^6 + 2*x^4 + 2*x^2) dy
+[?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[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?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[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?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[?7l[?7h[?12l[?25h[?25l[?7l[?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 = 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[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l-uteichmullr()*v.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 = 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[?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)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
+m dx x^18*y
+int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19) dy
+m dx x^16*y
+int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17) dy
+m dx x^12*y
+int(self) ((2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13) dy
+m dx x^10*y
+int(self) (2*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^6
+int(self) (2*y + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^4
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dx y
+int(self) (2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dx 1
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
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+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [84], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:33, in int(self)
+
+File <string>:33, in int(self)
+
+    [... skipping similar frames: int at line 33 (6 times)]
+
+File <string>:42, in int(self)
+
+    [... skipping similar frames: int at line 33 (1 times)]
+
+File <string>:42, in int(self)
+
+    [... skipping similar frames: int at line 33 (159 times), int at line 42 (159 times)]
+
+File <string>:33, in int(self)
+
+File <string>:42, in int(self)
+
+File <string>:27, 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:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+   1001 
+   1002         try:
+-> 1003             return self(str(element))
+   1004         except TypeError:
+   1005             pass
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:991, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+    989     else:
+    990         element = element.replace("^","**")
+--> 991         element = eval(element, d, {})
+    992 except (SyntaxError, NameError):
+    993     raise TypeError("Could not find a mapping of the passed element to this ring.")
+
+File <string>:1, in <module>
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?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 = 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[?7l C.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[?7ldiffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.int()[?7h[?12l[?25h[?25l[?7lm[?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[?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)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
+m dx x^12*y
+int(self) ((x^18 + x^16 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (x^13) dy
+m dx x^4
+int(self) ((x^18 + x^16 + 2*x^10 + 2)*y + 2*x^6 + 2*x^2 + 2) dx + (x^13) dy
+m dx x^18*y
+int(self) ((x^16 + 2*x^10 + 2)*y + 2*x^6 + 2*x^2 + 2) dx + (2*x^19 + x^13) dy
+m dx y
+int(self) ((x^16 + 2*x^10)*y + 2*x^6 + 2*x^2 + 2) dx + (2*x^19 + x^13 + x) dy
+m dx x^16*y
+int(self) (2*x^10*y + 2*x^6 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + x) dy
+m dx x^6
+int(self) (2*x^10*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + x) dy
+m dx x^10*y
+int(self) (2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^17
+int(self) (x^16*y + 2*x^2 + 2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
+m dx x^16*y
+int(self) (2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx 1
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
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+m dx x^2
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+m dx x^12*y
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+int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx
+m dx y
+int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x) dy
+m dx x^10*y
+int(self) ((x^18 + x^16 + 2*x^12)*y + 2*x^2) dx + (2*x^11 + x) dy
+m dx x^2
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+m dx y
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+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^17
+int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
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+int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
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+int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
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+int(self) ((x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x) dy
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+int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
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+int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
+m dx y
+int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
+m dx x^16*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^13
+int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
+m dx x^12*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
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+int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
+m dx x^18*y
+int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
+m dx x^2
+m dy x^17
+int(self) ((x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^13) dy
+m dx x^10*y
+int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + x^16 + 2)*y + 2*x^2) dx + (x^13 + 2*x^11) dy
+m dx x^16*y
+int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^11
+int(self) ((2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + x^13) dy
+m dx y
+int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
+m dx x^2
+m dy x^13
+int(self) ((2*x^12 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^17 + x) dy
+m dx x^10*y
+int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
+m dx x^12*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^13
+int(self) ((x^18 + 2*x^12)*y + 2*x^2) dx + (x^17 + 2*x^11 + x) dy
+m dx x^12*y
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^17
+int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
+m dx x^16*y
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x
+int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx y
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^11
+int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
+m dx x^10*y
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x
+int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^13
+int(self) ((2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11) dy
+m dx x^12*y
+int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^11
+int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
+m dx x^2
+m dy x
+int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
+m dx y
+int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
+m dx x^2
+m dy x
+int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
+m dx x^2
+m dy x^13
+int(self) ((x^18 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17) dy
+m dx x^2
+m dy x^17
+int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx
+m dx x^10*y
+int(self) ((x^18 + x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^11) dy
+m dx x^18*y
+int(self) ((x^16 + 2*x^12 + 2)*y + 2*x^2) dx + (2*x^19 + 2*x^11) dy
+m dx x^12*y
+int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
+m dx x^16*y
+int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^17
+int(self) ((x^16 + 2)*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + x^16 + 2)*y + 2*x^2) dx + (x^13 + 2*x^11) dy
+m dx x^2
+m dy x^11
+int(self) ((x^18 + x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (x^13) dy
+m dx x^18*y
+int(self) ((x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (2*x^19 + x^13) dy
+m dx y
+int(self) ((x^16 + 2*x^10)*y + 2*x^2) dx + (2*x^19 + x^13 + x) dy
+m dx x^16*y
+int(self) (2*x^10*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + x) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
+m dx x^2
+m dy x
+int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
+m dx y
+int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
+m dx x^2
+m dy x^17
+int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
+m dx x^2
+m dy x
+int(self) ((x^18 + x^16 + 2*x^10 + 2)*y + 2*x^2) dx + (x^13) dy
+m dx x^2
+m dy x^13
+int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^2) dx
+m dx y
+int(self) ((x^18 + x^16 + 2*x^12 + 2*x^10)*y + 2*x^2) dx + (x) dy
+m dx x^12*y
+int(self) ((x^18 + x^16 + 2*x^10)*y + 2*x^2) dx + (x^13 + x) dy
+m dx x^10*y
+int(self) ((x^18 + x^16)*y + 2*x^2) dx + (x^13 + 2*x^11 + x) dy
+m dx x^16*y
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x
+int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+int(self) (2*y + 2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^11
+int(self) ((x^18 + 2*x^10 + 2)*y + 2*x^2) dx + (x^17 + x^13) dy
+m dx x^10*y
+int(self) ((x^18 + 2)*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx y
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^11
+int(self) ((x^18 + 2*x^10)*y + 2*x^2) dx + (x^17 + x^13 + x) dy
+m dx x^10*y
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^17
+int(self) (x^16*y + 2*x^2) dx + (2*x^19 + x^13 + 2*x^11 + x) dy
+m dx x^16*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^13
+int(self) (2*x^12*y + 2*x^2) dx + (2*x^19 + x^17 + 2*x^11 + x) dy
+m dx x^2
+m dy x
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [88], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:34, in int(self)
+
+File <string>:34, in int(self)
+
+    [... skipping similar frames: int at line 34 (5 times)]
+
+File <string>:43, in int(self)
+
+    [... skipping similar frames: int at line 34 (2 times)]
+
+File <string>:43, in int(self)
+
+    [... skipping similar frames: int at line 34 (229 times), int at line 43 (229 times)]
+
+File <string>:34, in int(self)
+
+File <string>:43, in int(self)
+
+File <string>:42, in int(self)
+
+File <string>:51, in __sub__(self, other)
+
+File <string>:224, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
+   1514     return (<Element>left)._mul_(right)
+   1515 if BOTH_ARE_ELEMENT(cl):
+-> 1516     return coercion_model.bin_op(left, right, mul)
+   1517 
+   1518 cdef long value
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
+   1198 # Now coerce to a common parent and do the operation there
+   1199 try:
+-> 1200     xy = self.canonical_coercion(x, y)
+   1201 except TypeError:
+   1202     self._record_exception()
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion()
+   1309 x_map, y_map = coercions
+   1310 if x_map is not None:
+-> 1311     x_elt = (<Map>x_map)._call_(x)
+   1312 else:
+   1313     x_elt = x
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
+    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
+    286 cdef Map m
+--> 287 cdef Element e = method(C)
+    288 if e is None:
+    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
+    196 var = R.variable_name()
+    197 if var in self._parent.variable_names():
+--> 198     return R(self.polynomial(self._parent(var)))
+    199 else:
+    200     return R([self])
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:419, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
+    417 w = {remove_from_tuple(e, ind): val
+    418      for e, val in self.dict().iteritems() if not e[ind]}
+--> 419 v = [B(w)]  # coefficients that don't involve var
+    420 z = var
+    421 for i in range(1,d+1):
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:462, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
+    460     if x.type() != 't_POL':
+    461         x = x.Polrev()
+--> 462 elif isinstance(x, FiniteRingElement):
+    463     try:
+    464         return self(x.polynomial())
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?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[?7lom.int()[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form()[?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[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = g.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[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lnt()[?7h[?12l[?25h[?25l[?7lsage: om.int()

+[?7h[?12l[?25h[?2004lint(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
+---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [92], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:26, in int(self)
+
+NameError: name 'random_choice' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form()[?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[?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[?7lom.int()[?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[?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^[[A[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?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[?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[?7lload('init.sage')[?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[?7lom.int()[?7h[?12l[?25h[?25l[?7l = g.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[?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)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
+---------------------------------------------------------------------------
+IndexError                                Traceback (most recent call last)
+Input In [97], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:38, in int(self)
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/random.py:378, in Random.choice(self, seq)
+    376 """Choose a random element from a non-empty sequence."""
+    377 # raises IndexError if seq is empty
+--> 378 return seq[self._randbelow(len(seq))]
+
+IndexError: list index out of range
+[?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 = g.diffn().regular_form()[?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[?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[?7l = g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l= g.diffn().regular_form()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?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 = g.diffn().regular_form().int()

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+int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dy x^19
+int(self) ((x^18 + 2)*y + 2*x^2 + 2) dx + (x^17 + x^13 + 2*x^11) dy
+m dx x^18*y
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+File <string>:60, in __mul__(self, other)
+
+File <string>:14, in __init__(self, C, g)
+
+File <string>:220, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:632, in PolynomialRing(base_ring, *args, **kwds)
+    630         raise TypeError("you must specify the names of the variables")
+--> 632 names = normalize_names(n, names)
+    634 # At this point, we have only handled the "names" keyword if it was
+    635 # needed. Since we know the variable names, it would logically be
+    636 # an error to specify an additional "names" keyword. However,
+   (...)
+    639 # and we allow this for historical reasons. However, the names
+    640 # must be consistent!
+
+File /ext/sage/9.7/src/sage/structure/category_object.pyx:900, in sage.structure.category_object.normalize_names()
+    899 
+--> 900 cpdef normalize_names(Py_ssize_t ngens, names):
+    901     r"""
+
+File /ext/sage/9.7/src/sage/structure/category_object.pyx:993, in sage.structure.category_object.normalize_names()
+    992     # Convert names to strings and strip whitespace
+--> 993     names = [str(x).strip() for x in names]
+    994 else:
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+
+During handling of the above exception, another exception occurred:
+
+AttributeError                            Traceback (most recent call last)
+Input In [100], in <cell line: 1>()
+----> 1 om = g.diffn().regular_form().int()
+
+File <string>:35, in int(self)
+
+File <string>:35, in int(self)
+
+    [... skipping similar frames: int at line 35 (4 times)]
+
+File <string>:44, in int(self)
+
+    [... skipping similar frames: int at line 35 (1 times)]
+
+File <string>:44, in int(self)
+
+    [... skipping similar frames: int at line 35 (219 times), int at line 44 (219 times)]
+
+File <string>:35, in int(self)
+
+File <string>:44, in int(self)
+
+File <string>:34, in int(self)
+
+File <string>:63, in __mul__(self, other)
+
+AttributeError: 'superelliptic_function' object has no attribute 'form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lTraceback (most recent call last):
+
+  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input In [101] in <cell line: 1>
+    load('init.sage')
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:21 in <module>
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:30
+    print('m dx', m)
+    ^
+IndentationError: expected an indented block after 'for' statement on line 29
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form().int()[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [102], in <cell line: 1>()
+----> 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 <string>:30, in <module>
+
+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 <string>:21, in <module>
+
+File <string>:73, in diffn(self, dy_w)
+
+File <string>:177, in dy_w(C)
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
+   2412         return x
+   2413 
+-> 2414     return coercion_model.bin_op(left, right, operator.mul)
+   2415 
+   2416 cpdef _mul_(self, right):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:48, in __rmul__(self, other)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
+   1526     if not err:
+   1527         return (<Element>right)._mul_long(value)
+-> 1528     return coercion_model.bin_op(left, right, mul)
+   1529 except TypeError:
+   1530     return NotImplemented
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:43, in __rmul__(self, other)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
+   1526     if not err:
+   1527         return (<Element>right)._mul_long(value)
+-> 1528     return coercion_model.bin_op(left, right, mul)
+   1529 except TypeError:
+   1530     return NotImplemented
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:43, in __rmul__(self, other)
+
+    [... skipping similar frames: sage.structure.coerce.CoercionModel.bin_op at line 1242 (3 times), sage.structure.element.Element.__mul__ at line 1528 (3 times), __rmul__ at line 43 (2 times)]
+
+File <string>:43, in __rmul__(self, other)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
+   1526     if not err:
+   1527         return (<Element>right)._mul_long(value)
+-> 1528     return coercion_model.bin_op(left, right, mul)
+   1529 except TypeError:
+   1530     return NotImplemented
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:41, in __rmul__(self, other)
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
+   1962         return y
+   1963 
+-> 1964     return coercion_model.bin_op(left, right, operator.mul)
+   1965 
+   1966 cpdef _mul_(self, right):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:70, in __rmul__(self, constant)
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?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 = g.diffn().regular_form().int()[?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[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form().int()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form().int()

+[?7h[?12l[?25h[?2004lint(self) ((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
+m dx x^18*y
+int(self) ((x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19) dy
+m dx x^16*y
+int(self) ((2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17) dy
+m dx x^12*y
+int(self) ((2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13) dy
+m dx x^10*y
+int(self) (2*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^6
+int(self) (2*y + 2*x^4 + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^4
+int(self) (2*y + 2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11) dy
+m dx x^2
+m dx y
+int(self) (2*x^2 + 2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dx 1
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
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+m dx x^18*y
+int(self) (2*x^2) dx + (2*x^19 + x^17 + x^13 + 2*x^11 + x) dy
+m dx x^2
+m dy x^19
+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
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+m dx x^2
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+int(self) (x^18*y + 2*x^2) dx + (x^17 + x^13 + 2*x^11 + x) dy
+m dx x^18*y
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [105], in <cell line: 1>()
+----> 1 om = g.diffn().regular_form().int()
+
+File <string>:35, in int(self)
+
+File <string>:35, in int(self)
+
+    [... skipping similar frames: int at line 35 (6 times)]
+
+File <string>:44, in int(self)
+
+    [... skipping similar frames: int at line 35 (1 times)]
+
+File <string>:44, in int(self)
+
+    [... skipping similar frames: int at line 35 (70 times), int at line 44 (70 times)]
+
+File <string>:35, in int(self)
+
+File <string>:44, in int(self)
+
+File <string>:34, in int(self)
+
+File <string>:82, in __pow__(self, exp)
+
+File <string>:7, in __init__(self, C, g)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:632, in PolynomialRing(base_ring, *args, **kwds)
+    629     except KeyError:
+    630         raise TypeError("you must specify the names of the variables")
+--> 632 names = normalize_names(n, names)
+    634 # At this point, we have only handled the "names" keyword if it was
+    635 # needed. Since we know the variable names, it would logically be
+    636 # an error to specify an additional "names" keyword. However,
+   (...)
+    639 # and we allow this for historical reasons. However, the names
+    640 # must be consistent!
+    641 if "names" in kwds:
+
+File /ext/sage/9.7/src/sage/structure/category_object.pyx:900, in sage.structure.category_object.normalize_names()
+    898         return dir_with_other_class(self, self.category().parent_class)
+    899 
+--> 900 cpdef normalize_names(Py_ssize_t ngens, names):
+    901     r"""
+    902     Return a tuple of strings of variable names of length ngens given
+
+File /ext/sage/9.7/src/sage/structure/category_object.pyx:993, in sage.structure.category_object.normalize_names()
+    991 if isinstance(names, (tuple, list)):
+    992     # Convert names to strings and strip whitespace
+--> 993     names = [str(x).strip() for x in names]
+    994 else:
+    995     # Interpret names as string and convert to tuple of strings
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?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[?7l[?7h[?12l[?25h[?25l[?7lg[?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().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.diffn().regular_form()

+[?7h[?12l[?25h[?2004l[?7h((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l.2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l.2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = 2*C.x*C.y^3

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form().int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn().regular_form().int()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?7lsage: om

+[?7h[?12l[?25h[?2004l[?7h(2*x^6 + 2*x^4 + 2*x^2) dy
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?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[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = C.x^7 * C.y^8

+[?7h[?12l[?25h[?2004l[?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 = 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[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form(); om

+[?7h[?12l[?25h[?2004l[?7h(x^18 + x^16 + 2*x^12 + 2*x^10) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8[?7h[?12l[?25h[?25l[?7lsage: g

+[?7h[?12l[?25h[?2004l[?7hx^19 + 2*x^17 + 2*x^13 + x^11
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form(); om[?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) dx
+m dx x^18
+int(self) (x^16 + 2*x^12 + 2*x^10) dx
+m dx x^16
+int(self) (2*x^12 + 2*x^10) dx
+m dx x^12
+int(self) (2*x^10) dx
+m dx x^10
+int(self) (0) dy
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [115], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:35, in int(self)
+
+File <string>:35, in int(self)
+
+    [... skipping similar frames: int at line 35 (1 times)]
+
+File <string>:35, in int(self)
+
+File <string>: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 = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'function'
+[?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[?7lg[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8[?7h[?12l[?25h[?25l[?7lsage: g = C.x^7 * C.y^8

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form(); om

+[?7h[?12l[?25h[?2004l[?7h(x^18 + x^16 + 2*x^12 + 2*x^10) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form(); om[?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) dx
+m dx x^18
+int(self) (x^16 + 2*x^12 + 2*x^10) dx
+m dx x^16
+int(self) (2*x^12 + 2*x^10) dx
+m dx x^12
+int(self) (2*x^10) dx
+m dx x^10
+int(self) (0) dy
+[?7hx^19 + 2*x^17 + 2*x^13 + x^11
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C.x^7 * C.y^8[?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[?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: g - om.int()

+[?7h[?12l[?25h[?2004lint(self) (x^18 + x^16 + 2*x^12 + 2*x^10) dx
+m dx x^18
+int(self) (x^16 + 2*x^12 + 2*x^10) dx
+m dx x^16
+int(self) (2*x^12 + 2*x^10) dx
+m dx x^12
+int(self) (2*x^10) dx
+m dx x^10
+int(self) (0) dy
+[?7h0
+[?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[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l.2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l.2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = 2*C.x*C.y^3

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lnm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm.int()[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l g.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn().regular_form(); om

+[?7h[?12l[?25h[?2004l[?7h(2*x^6 + 2*x^4 + 2*x^2) dy
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn().regular_form(); om[?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()

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+m dy x^6
+int(self) (2*x^4 + 2*x^2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2) dy
+m dx x^3*y
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+m dx x^3*y
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+int(self) (x^3*y) dx + (2*x^2) dy
+m dx x^3*y
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+m dx x^3*y
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+m dx x^3*y
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+int(self) (x^3*y) dx + (2*x^2) dy
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+int(self) (x^3*y) dx + (2*x^2) dy
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+int(self) (x^3*y) dx + (2*x^2) dy
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+int(self) (2*x^4 + 2*x^2) dy
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+int(self) (x^3*y) dx + (2*x^2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2) dy
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+int(self) (x^3*y) dx + (2*x^2) dy
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+int(self) (x^3*y) dx + (2*x^2) dy
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+int(self) (x^3*y) dx + (2*x^2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2) dy
+m dy x^4
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [123], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:44, in int(self)
+
+File <string>:44, in int(self)
+
+File <string>:35, in int(self)
+
+    [... skipping similar frames: int at line 44 (1 times)]
+
+File <string>:35, in int(self)
+
+    [... skipping similar frames: int at line 44 (84 times), int at line 35 (84 times)]
+
+File <string>:44, in int(self)
+
+File <string>:35, in int(self)
+
+File <string>:43, in int(self)
+
+File <string>:52, in __sub__(self, other)
+
+File <string>:14, in __init__(self, C, g)
+
+File <string>:223, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
+    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
+    286 cdef Map m
+--> 287 cdef Element e = method(C)
+    288 if e is None:
+    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
+    196 var = R.variable_name()
+    197 if var in self._parent.variable_names():
+--> 198     return R(self.polynomial(self._parent(var)))
+    199 else:
+    200     return R([self])
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:411, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
+    409 # Make polynomial ring over all variables except var.
+    410 S = R.base_ring()[tuple(Z)]
+--> 411 ring = S[var]
+    412 if not self:
+    413     return ring(0)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
+   1273         except AttributeError:
+   1274             return self.list()[n]
+-> 1275     return meth(n)
+   1276 
+   1277 #########################################################################
+
+File /ext/sage/9.7/src/sage/categories/rings.py:1176, in Rings.ParentMethods.__getitem__(self, arg)
+   1173 # 2. Otherwise, try to return a polynomial ring
+   1175 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
+-> 1176 return PolynomialRing(self, elts)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:561, in PolynomialRing(base_ring, *args, **kwds)
+    557 names = None  # Unknown variable names
+    559 # Use a single-variate ring by default unless the "singular"
+    560 # implementation is asked.
+--> 561 multivariate = kwds.get("implementation") == "singular"
+    563 # Check specifically for None because it is an easy mistake to
+    564 # make and Integer(None) returns 0, so we wouldn't catch this
+    565 # otherwise.
+    566 if any(arg is None for arg in args):
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = g.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7lg = 2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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^6*y^7).exponents()[?7h[?12l[?25h[?25l[?7l2*(C.x.teichmuller)).diffn(), 2*((C.x.teichmuller()).diffn())[?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[?7l4[?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[?7l^[?7h[?12l[?25h[?25l[?7l2[?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[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (2*x^4 + 2*x^2).quo_rem(x^3 - x)

+[?7h[?12l[?25h[?2004l[?7h(2*x, x^2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(2*x^4 + 2*x^2) dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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*x^4 + 2*x^2) dy[?7h[?12l[?25h[?25l[?7l[?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^4 + 2*x^2) dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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(2*Cx^4 + 2*x^2) dy[?7h[?12l[?25h[?25l[?7lm(2*Cx^4 + 2*x^2) dy[?7h[?12l[?25h[?25l[?7l (2*Cx^4 + 2*x^2) dy[?7h[?12l[?25h[?25l[?7l=(2*Cx^4 + 2*x^2) dy[?7h[?12l[?25h[?25l[?7l (2*Cx^4 + 2*x^2) dy[?7h[?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^4 + 2*x^2) dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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^2) dy[?7h[?12l[?25h[?25l[?7l.x^2) dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()* dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldy[?7h[?12l[?25h[?25l[?7lCdy[?7h[?12l[?25h[?25l[?7l.dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?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 = (2*C.x^4 + 2*C.x^2)*C.y.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (2*C.x^4 + 2*C.x^2)*C.y.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?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[?7h0 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.[?7h[?12l[?25h[?25l[?7lint()[?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[?2004l[?7h((x^6 + x^2)/(x^4 + x^2 + 1))*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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[1][?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly.teichmuller.diffn() - v.teichmuller().diffn()+ (C.y*v^2 - C.y^2*v).verschiebung().diffn()==( (C.y/C.x)^3).teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y*C.y.diffn()

+[?7h[?12l[?25h[?2004l[?7h1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = (2*C.x^4 + 2*C.x^2)*C.y.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[?7lg = 2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7lsage: g = 2*C.x*C.y^3

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = (2*C.x^4 + 2*C.x^2)*C.y.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn().regular_form(); om[?7h[?12l[?25h[?25l[?7l.diffn().regular_form(); 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[?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[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1.regular_form()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l=Bcrys[1].omega0[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1 = om.regular_form()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = om.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7lfrobenius().expansion_at_infty()[?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[?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[?7lsage: om1.form() == om

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.form() == om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1

+[?7h[?12l[?25h[?2004l[?7h(2*x^6 + 2*x^4 + 2*x^2) dy
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

+[?7h[?12l[?25h[?2004l[?7h((-x^6 - x^4 - x^2)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = 2*C.x*C.y^3[?7h[?12l[?25h[?25l[?7lsage: g

+[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2)*y
+[?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[?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[?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[?7lC))[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l2))[?7h[?12l[?25h[?25l[?7l*))[?7h[?12l[?25h[?25l[?7lC))[?7h[?12l[?25h[?25l[?7l.))[?7h[?12l[?25h[?25l[?7lx))[?7h[?12l[?25h[?25l[?7l^))[?7h[?12l[?25h[?25l[?7l3))[?7h[?12l[?25h[?25l[?7l ))[?7h[?12l[?25h[?25l[?7l+))[?7h[?12l[?25h[?25l[?7l ))[?7h[?12l[?25h[?25l[?7l2))[?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[?7l2)[?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[?7l4)[?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[?7lC)[?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[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om2 = (C.y*(2*C.x^3 + 2*C.x)+(2*C.x^4 - 2*C.x^2))*C.y.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = (C.y*(2*C.x^3 + 2*C.x)+(2*C.x^4 - 2*C.x^2))*C.y.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2 = (C.y*(2*C.x^3 + 2*C.x)+(2*C.x^4 - 2*C.x^2))*C.y.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[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om2 == om1

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [138], in <cell line: 1>()
+----> 1 om2 == om1
+
+File <string>:12, in __eq__(self, other)
+
+AttributeError: 'superelliptic_regular_form' object has no attribute 'reduce'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 == om1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om2 == om

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 == 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 om[?7h[?12l[?25h[?25l[?7l om[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om2 - om

+[?7h[?12l[?25h[?2004l[?7h((x^6 - x^3*y - x^2 - x*y)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 - 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(om2 - 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[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (om2 - om).regular_form()

+[?7h[?12l[?25h[?2004l[?7h((2*x^3 + 2*x)*y + x^6 + 2*x^2) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: g

+[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.diffn().regular_form()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lffn().regular_form()[?7h[?12l[?25h[?25l[?7lsage: g.diffn().regular_form()

+[?7h[?12l[?25h[?2004l[?7h(2*x^6 + 2*x^4 + 2*x^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.diffn().regular_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[?7lsage: g.diffn()

+[?7h[?12l[?25h[?2004l[?7h((-x^6 - x^4 - x^2)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: g.regular_form()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [145], in <cell line: 1>()
+----> 1 g.regular_form()
+
+AttributeError: 'superelliptic_function' object has no attribute 'regular_form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.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[?7ldregular_form()[?7h[?12l[?25h[?25l[?7liregular_form()[?7h[?12l[?25h[?25l[?7lfregular_form()[?7h[?12l[?25h[?25l[?7lfregular_form()[?7h[?12l[?25h[?25l[?7lnregular_form()[?7h[?12l[?25h[?25l[?7l(regular_form()[?7h[?12l[?25h[?25l[?7l()regular_form()[?7h[?12l[?25h[?25l[?7l().regular_form()[?7h[?12l[?25h[?25l[?7lsage: g.diffn().regular_form()

+[?7h[?12l[?25h[?2004l[?7h(2*x^6 + 2*x^4 + 2*x^2) dy
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn().regular_form()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.diffn()

+[?7h[?12l[?25h[?2004l[?7h((-x^6 - x^4 - x^2)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l().regular_form()[?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: g.diffn().int()

+[?7h[?12l[?25h[?2004l[?7h(2*x^4 + x^2)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.diffn().int()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().regular_form()[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7ldiffn().regular_form()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().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[?7lg = C.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[?7lom2 - om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = g.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?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[?2004l[?7h((2*x^8 + 2)/(x^4 + x^2 + 1))*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[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om

+[?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[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7legular_form()[?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()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form()

+[?7h[?12l[?25h[?2004l[?7h((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form()[?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.regular_form().form()

+[?7h[?12l[?25h[?2004l[?7h((x^21 - x^17 - x^15 + x^11 - x^6*y - x^4*y - x^3 - x^2*y + x - y)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?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.regular_form().form().int()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ZeroDivisionError                         Traceback (most recent call last)
+Input In [155], in <cell line: 1>()
+----> 1 om.regular_form().form().int()
+
+File <string>:199, in int(self)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral()
+   3992 cdef Py_ssize_t n
+   3993 zero = Q.zero()
+-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv)
+   3995               if self.get_unsafe(n) else zero for n in range(self.degree() + 1)]
+   3996 return S(p)
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
+   1202     self._record_exception()
+   1203 else:
+-> 1204     return PyObject_CallObject(op, xy)
+   1205 
+   1206 if op is mul:
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
+   1735 cdef int cl = classify_elements(left, right)
+   1736 if HAVE_SAME_PARENT(cl):
+-> 1737     return (<Element>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[(<IntegerMod_int>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 * (<IntegerMod_int>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[?7lom.regular_form().form().int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form().int()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?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[?7lsage: om.regular_form().form() == om

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l = g.diffn()[?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().int()[?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[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.regular_form()[?7h[?12l[?25h[?25l[?7l().form()[?7h[?12l[?25h[?25l[?7l().int()[?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[?7l[?7h[?12l[?25h[?25l[?7l[?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.regular_form().form() == om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om

+[?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[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.regular_form().form() == om[?7h[?12l[?25h[?25l[?7lregular_form().form() == om[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form() == om

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

+[?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[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7l.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l om[?7h[?12l[?25h[?25l[?7l om[?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[?7l[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form() - om

+[?7h[?12l[?25h[?2004l[?7h((x^21 - x^18*y - x^17 - x^16*y - x^15 + x^12*y + x^11 + x^10*y - x^6*y + x^6 - x^4*y + x^4 - x^3 - x^2*y + x^2 + x + 1)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form() - om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lregular_form().form() - 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[?7lsage: om.regular_form().form()

+[?7h[?12l[?25h[?2004l[?7h((x^21 - x^17 - x^15 + x^11 - x^6*y - x^4*y - x^3 - x^2*y + x - y)/y) dx
+[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lsage: lo

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [1], in <cell line: 1>()
+----> 1 lo
+
+NameError: name 'lo' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?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 = 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[?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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: g = C.x*C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lfn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.reular_form().form()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lar_form().form()[?7h[?12l[?25h[?25l[?7l() - om[?7h[?12l[?25h[?25l[?7l== om[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form() == om

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7lg = C.x*C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7l() - om[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l = g.diffn()[?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[?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[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?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[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form() == om

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

+[?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[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.regular_form().form() == om[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form()

+[?7h[?12l[?25h[?2004l[?7h((x^18 + x^16 + 2*x^12 + 2*x^10 + 2)*y + 2*x^6 + 2*x^4 + 2*x^2 + 2) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form()[?7h[?12l[?25h[?25l[?7l().form() == om[?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.regular_form().form()

+[?7h[?12l[?25h[?2004l[?7h((x^21 - x^17 - x^15 + x^11 - x^6*y - x^4*y - x^3 - x^2*y + x - y)/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.regular_form().form()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l = .diffn()[?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[?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.regular_form().form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form()

+[?7h[?12l[?25h[?2004lif fct.denominator() == y:
+if fct.denominator() == 1:
+[?7h((x^21 - x^17 - x^15 + x^11 - x^6*y - x^4*y - x^3 - x^2*y + x - y)/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.regular_form().form()[?7h[?12l[?25h[?25l[?7l = .diffn()[?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[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form()

+[?7h[?12l[?25h[?2004lif fct.denominator() == y:
+fct, fct.numerator() x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1 x^18*y + x^16*y - x^12*y - x^10*y - x^6 - x^4 - x^2 - y - 1
+if fct.denominator() == 1:
+[?7h((x^21 - x^17 - x^15 + x^11 - x^6*y - x^4*y - x^3 - x^2*y + x - y)/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.regular_form().form()[?7h[?12l[?25h[?25l[?7l = .diffn()[?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[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form()[?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[?7lm[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form() == om

+[?7h[?12l[?25h[?2004lif fct.denominator() == y:
+[?7hTrue
+[?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.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l = .diffn()[?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[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form() == om

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == 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[?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().form() == om[?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.regular_form().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
+m dx x^18
+int(self) (x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
+m dx x^16
+int(self) (2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
+m dx x^12
+int(self) (2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
+m dx x^10
+int(self) (2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
+m dx 1
+int(self) (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
+m dy x^6
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
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+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
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+m dx x^3*y
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+m dx x^3*y
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+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
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+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
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+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
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+m dx x^3*y
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+int(self) (x^3*y) dx + (2*x^2 + 2) dy
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+m dx x^3*y
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+m dx x^3*y
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+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
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+m dx x^3*y
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+m dx x^3*y
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+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
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+int(self) (x^3*y) dx + (2*x^2 + 2) dy
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+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
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+int(self) (x^3*y) dx + (2*x^2 + 2) dy
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+int(self) (2*x^4 + 2*x^2 + 2) dy
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+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
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+m dx x^3*y
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+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
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+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+File <string>:59, in __mul__(self, other)
+
+File <string>:222, in reduction(C, g)
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+
+During handling of the above exception, another exception occurred:
+
+AttributeError                            Traceback (most recent call last)
+Input In [28], in <cell line: 1>()
+----> 1 om.regular_form().int()
+
+File <string>:35, in int(self)
+
+File <string>:35, in int(self)
+
+    [... skipping similar frames: int at line 35 (3 times)]
+
+File <string>:44, in int(self)
+
+File <string>:44, in int(self)
+
+    [... skipping similar frames: int at line 35 (124 times), int at line 44 (124 times)]
+
+File <string>:35, in int(self)
+
+File <string>:44, in int(self)
+
+File <string>:34, in int(self)
+
+File <string>:63, in __mul__(self, other)
+
+AttributeError: 'superelliptic_function' object has no attribute 'form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(C.de_rham_basis()[1].omega8)[?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[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l 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[?7lFxy, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lom.regular_form().int()[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7l[?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.regular_form().int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = .diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsecond_patch(om)[?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[?7lsage: om = superelliptic

+ superelliptic                  superelliptic_drw/             superelliptic_form             superelliptic_regular_form    

+ superelliptic/                 superelliptic_drw_cech         superelliptic_function         superelliptic_witt            

+ superelliptic_cech             superelliptic_drw_form         superelliptic_regular_drw_form                               

+

+ [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

+ superelliptic                 

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l_drw/

+ superelliptic                  superelliptic_drw/            [?7h[?12l[?25h[?25l[?7lform

+ superelliptic_drw/             superelliptic_form            [?7h[?12l[?25h[?25l[?7lregular_form

+ superelliptic_form             superelliptic_regular_form    [?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[?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[?7l3[?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[?7lC[?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[?7l2[?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[?7l)[?7h[?12l[?25h[?25l[?7lsage: om = superelliptic_regular_form(0*C.x, C.x^3 + 2*C.x^2 + 2*C.one)

+[?7h[?12l[?25h[?2004l
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [30], in <cell line: 1>()
+----> 1 om = superelliptic_regular_form(Integer(0)*C.x, C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.one)
+
+File <string>:39, in __add__(self, other)
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = superelliptic_regular_form(0*C.x, C.x^3 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lsage: om = superelliptic_regular_form(0*C.x, C.x^3 + 2*C.x^2 + 2*C.one)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = superelliptic_regular_form(0*C.x, C.x^3 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

+[?7h[?12l[?25h[?2004l[?7h(x^3 + 2*x^2 + 2) dy
+[?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.regular_form().int()[?7h[?12l[?25h[?25l[?7lint()[?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^3 + 2*x^2 + 2) dy
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+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [33], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:44, in int(self)
+
+File <string>:44, in int(self)
+
+File <string>:35, in int(self)
+
+    [... skipping similar frames: int at line 44 (1 times)]
+
+File <string>:35, in int(self)
+
+    [... skipping similar frames: int at line 44 (108 times), int at line 35 (108 times)]
+
+File <string>:44, in int(self)
+
+File <string>:35, in int(self)
+
+File <string>:43, in int(self)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
+   1526     if not err:
+   1527         return (<Element>right)._mul_long(value)
+-> 1528     return coercion_model.bin_op(left, right, mul)
+   1529 except TypeError:
+   1530     return NotImplemented
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:70, in __rmul__(self, constant)
+
+File <string>:14, in __init__(self, C, g)
+
+File <string>:223, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
+    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
+    286 cdef Map m
+--> 287 cdef Element e = method(C)
+    288 if e is None:
+    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
+    196 var = R.variable_name()
+    197 if var in self._parent.variable_names():
+--> 198     return R(self.polynomial(self._parent(var)))
+    199 else:
+    200     return R([self])
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:410, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
+    408 
+    409         # Make polynomial ring over all variables except var.
+--> 410         S = R.base_ring()[tuple(Z)]
+    411         ring = S[var]
+    412         if not self:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
+   1273         except AttributeError:
+   1274             return self.list()[n]
+-> 1275     return meth(n)
+   1276 
+   1277 #########################################################################
+
+File /ext/sage/9.7/src/sage/categories/rings.py:1176, in Rings.ParentMethods.__getitem__(self, arg)
+   1173 # 2. Otherwise, try to return a polynomial ring
+   1175 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
+-> 1176 return PolynomialRing(self, elts)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:51, in PolynomialRing(base_ring, *args, **kwds)
+     45 _cache = sage.misc.weak_dict.WeakValueDictionary()
+     48 # The signature for this function is too complicated to express sensibly
+     49 # in any other way besides *args and **kwds (in Python 3 or Cython, we
+     50 # could probably do better thanks to PEP 3102).
+---> 51 def PolynomialRing(base_ring, *args, **kwds):
+     52     r"""
+     53     Return the globally unique univariate or multivariate polynomial
+     54     ring with given properties and variable name or names.
+   (...)
+    551         TypeError: unable to convert 'x' to an integer
+    552     """
+    553     if not ring.is_Ring(base_ring):
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic_regular_form(0*C.x, C.x^3 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7ly + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l^ + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l2 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l+ + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lC + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l. + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lx + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = superelliptic_regular_form(0*C.x, C.y^2 + C.x + 2*C.x^2 + 2*C.one)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = superelliptic_regular_form(0*C.x, C.y^2 + C.x + 2*C.x^2 + 2*C.one)[?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[?7lsage: om.int()

+[?7h[?12l[?25h[?2004lint(self) (x^3 + 2*x^2 + 2) dy
+m dy x^3
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+int(self) (2*x*y) dx + (2) dy
+m dx x*y
+int(self) (2*x^2 + 2) dy
+m dy x^2
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [35], in <cell line: 1>()
+----> 1 om.int()
+
+File <string>:44, in int(self)
+
+File <string>:44, in int(self)
+
+File <string>:35, in int(self)
+
+    [... skipping similar frames: int at line 44 (1 times)]
+
+File <string>:35, in int(self)
+
+    [... skipping similar frames: int at line 44 (58 times), int at line 35 (58 times)]
+
+File <string>:44, in int(self)
+
+File <string>:35, in int(self)
+
+File <string>:43, in int(self)
+
+File <string>:51, in __sub__(self, other)
+
+File <string>:216, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    636 ring_one = self.ring().one()
+    637 try:
+--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
+    639 except (TypeError, ValueError):
+    640     pass
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:115, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
+    113 if coerce:
+    114     self.__numerator   = parent.ring()(numerator)
+--> 115     self.__denominator = parent.ring()(denominator)
+    116 else:
+    117     self.__numerator   = numerator
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:506, in FractionField_generic.ring(self)
+    503     s = 'FieldOfFractions(%s)' % self.ring()._magma_init_(magma)
+    504     return magma._with_names(s, self.variable_names())
+--> 506 def ring(self):
+    507     """
+    508     Return the ring that this is the fraction field of.
+    509 
+   (...)
+    516         Multivariate Polynomial Ring in x, y over Rational Field
+    517     """
+    518     return self._R
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.int()[?7h[?12l[?25h[?25l[?7l = superelliptic_regular_form(0*C.x, C.y^2 + C.x + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l = superelliptic_regular_form(0*C.x, C.y^2 + C.x + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l.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[?7lom.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lregular_form().int()[?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[?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.form().int()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ZeroDivisionError                         Traceback (most recent call last)
+Input In [36], in <cell line: 1>()
+----> 1 om.form().int()
+
+File <string>:199, in int(self)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral()
+   3992 cdef Py_ssize_t n
+   3993 zero = Q.zero()
+-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv)
+   3995               if self.get_unsafe(n) else zero for n in range(self.degree() + 1)]
+   3996 return S(p)
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
+   1202     self._record_exception()
+   1203 else:
+-> 1204     return PyObject_CallObject(op, xy)
+   1205 
+   1206 if op is mul:
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
+   1735 cdef int cl = classify_elements(left, right)
+   1736 if HAVE_SAME_PARENT(cl):
+-> 1737     return (<Element>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[(<IntegerMod_int>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 * (<IntegerMod_int>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[?7lom.form().int()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7l = superelliptic_regular_form(0*C.x, C.y^2 + C.x + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic_regular_form(0*C.x, C.x^3 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lFxy,Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lom =superelliptic_regular_form(0*C.x, C.x^3 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lFxy,Rxy, x, y=C.fct_field[?7h[?12l[?25h[?25l[?7lom.regular_form().int()[?7h[?12l[?25h[?25l[?7lform() == om[?7h[?12l[?25h[?25l[?7l = .diffn()[?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[?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[?7lom.form().int()[?7h[?12l[?25h[?25l[?7lsage: om.form().int()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ZeroDivisionError                         Traceback (most recent call last)
+Input In [38], in <cell line: 1>()
+----> 1 om.form().int()
+
+File <string>:199, in int(self)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:3994, in sage.rings.polynomial.polynomial_element.Polynomial.integral()
+   3992 cdef Py_ssize_t n
+   3993 zero = Q.zero()
+-> 3994 p = [zero] + [cm.bin_op(Q(self.get_unsafe(n)), n + 1, operator.truediv)
+   3995               if self.get_unsafe(n) else zero for n in range(self.degree() + 1)]
+   3996 return S(p)
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
+   1202     self._record_exception()
+   1203 else:
+-> 1204     return PyObject_CallObject(op, xy)
+   1205 
+   1206 if op is mul:
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1737, in sage.structure.element.Element.__truediv__()
+   1735 cdef int cl = classify_elements(left, right)
+   1736 if HAVE_SAME_PARENT(cl):
+-> 1737     return (<Element>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[(<IntegerMod_int>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 * (<IntegerMod_int>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[?7lom.form().int()[?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[?7lom.form().int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.form().int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = superelliptic_regular_form(0*C.x, C.y^2 + C.x + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.form().int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = superelliptic_regular_form(0*C.x, C.y^2 + C.x + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7l=[?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.[?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[?7lsage: om == g.diffn()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [39], in <cell line: 1>()
+----> 1 om == g.diffn()
+
+File <string>:12, in __eq__(self, other)
+
+AttributeError: 'superelliptic_regular_form' object has no attribute 'reduce'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom == g.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l. = g.difn()[?7h[?12l[?25h[?25l[?7lf = g.difn()[?7h[?12l[?25h[?25l[?7lo = g.difn()[?7h[?12l[?25h[?25l[?7lfor = g.difn()[?7h[?12l[?25h[?25l[?7lform = g.difn()[?7h[?12l[?25h[?25l[?7l( = g.difn()[?7h[?12l[?25h[?25l[?7l() = g.difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om.form() == g.diffn()

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.form() == g.diffn()[?7h[?12l[?25h[?25l[?7l == g.diffn()[?7h[?12l[?25h[?25l[?7l.form().int[?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[?7lom.form().int()[?7h[?12l[?25h[?25l[?7lint()[?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[?7lg = C.x^7 * C.y^8 + 2*C.x*C.y^3 - C.x - C.y[?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[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.form() == g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega8_lift0.omega8 - compare[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?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.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l superelliptic_regular_form(0*C.x, C.y^2 + C.x + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lg.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?7h[?12l[?25h[?25l[?7lsage: om = g.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = g.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.form() == g.diffn()[?7h[?12l[?25h[?25l[?7lregular_form().it()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lform() == om[?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[?7l() [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l om[?7h[?12l[?25h[?25l[?7lsage: om.regular_form().form() == om

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().form() == om[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7lint[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.int()

+[?7h[?12l[?25h[?2004l[?7h((2*x^8 + 2)/(x^4 + x^2 + 1))*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)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?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[?7lregular_form().form() == om[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lform().form() == 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[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint()[?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.regular_form().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
+m dx x^18
+int(self) (x^16 + 2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
+m dx x^16
+int(self) (2*x^12 + 2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
+m dx x^12
+int(self) (2*x^10 + 2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
+m dx x^10
+int(self) (2) dx + (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
+m dx 1
+int(self) (2*x^6 + 2*x^4 + 2*x^2 + 2) dy
+m dy x^6
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
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+m dx x^3*y
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+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
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+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
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+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
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+m dx x^3*y
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+m dy x^4
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+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
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+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
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+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
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+m dx x^3*y
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+m dx x^3*y
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+m dy x^4
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+m dx x^3*y
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+m dx x^3*y
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+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
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+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
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+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
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+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+^Cint(self) (2*x^4 + 2*x^2 + 2) dy
+---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [45], in <cell line: 1>()
+----> 1 om.regular_form().int()
+
+File <string>:35, in int(self)
+
+File <string>:35, in int(self)
+
+    [... skipping similar frames: int at line 35 (3 times)]
+
+File <string>:44, in int(self)
+
+File <string>:44, in int(self)
+
+    [... skipping similar frames: int at line 35 (70 times), int at line 44 (69 times)]
+
+File <string>:44, in int(self)
+
+File <string>:35, in int(self)
+
+File <string>:21, in int(self)
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.regular_form().int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = om.regular_form()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l(2*x^4 + 2*x^2 + 2) dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldy[?7h[?12l[?25h[?25l[?7lCdy[?7h[?12l[?25h[?25l[?7l.dy[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l*)*C.y.difn()[?7h[?12l[?25h[?25l[?7lC)*C.y.difn()[?7h[?12l[?25h[?25l[?7l.)*C.y.difn()[?7h[?12l[?25h[?25l[?7lo)*C.y.difn()[?7h[?12l[?25h[?25l[?7ln)*C.y.difn()[?7h[?12l[?25h[?25l[?7le)*C.y.difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^2 + 2*C.one)*C.y.difn()[?7h[?12l[?25h[?25l[?7l.x^2 + 2*C.one)*C.y.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^4 + 2*C.x^2 + 2*C.one)*C.y.difn()[?7h[?12l[?25h[?25l[?7l.x^4 + 2*C.x^2 + 2*C.one)*C.y.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = (2*C.x^4 + 2*C.x^2 + 2*C.one)*C.y.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = (2*C.x^4 + 2*C.x^2 + 2*C.one)*C.y.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.form() == om[?7h[?12l[?25h[?25l[?7lis_regular()[?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: om1.int()

+[?7h[?12l[?25h[?2004l[?7h(x^2 + 2)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?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[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lom1.int()[?7h[?12l[?25h[?25l[?7l = (2*C.x^4 + 2*C.x^2 + 2*C.one)*C.y.diffn()[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr_form()[?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: om1.regular_form().int()

+[?7h[?12l[?25h[?2004lint(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
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+m dx x^3*y
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+m dx x^3*y
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+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
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+m dx x^3*y
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+int(self) (x^3*y) dx + (2*x^2 + 2) dy
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+int(self) (x^3*y) dx + (2*x^2 + 2) dy
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+int(self) (2*x^4 + 2*x^2 + 2) dy
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+m dx x^3*y
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+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+m dx x^3*y
+int(self) (2*x^4 + 2*x^2 + 2) dy
+m dy x^4
+int(self) (x^3*y) dx + (2*x^2 + 2) dy
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [49], in <cell line: 1>()
+----> 1 om1.regular_form().int()
+
+File <string>:44, in int(self)
+
+File <string>:35, in int(self)
+
+File <string>:44, in int(self)
+
+File <string>:35, in int(self)
+
+    [... skipping similar frames: int at line 44 (68 times), int at line 35 (67 times)]
+
+File <string>:35, in int(self)
+
+File <string>:44, in int(self)
+
+File <string>:24, in int(self)
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
+   1962         return y
+   1963 
+-> 1964     return coercion_model.bin_op(left, right, operator.mul)
+   1965 
+   1966 cpdef _mul_(self, right):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:70, in __rmul__(self, constant)
+
+File <string>:14, in __init__(self, C, g)
+
+File <string>:214, in reduction(C, g)
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.regular_form().int()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lom1.int()[?7h[?12l[?25h[?25l[?7l = (2*C.x^4 + 2*C.x^2 + 2*C.one)*C.y.diffn()[?7h[?12l[?25h[?25l[?7l.regular_form().int()[?7h[?12l[?25h[?25l[?7l1 = (2*C.x^4 + 2*C.x^2 + 2*C.one)*C.y.diffn()[?7h[?12l[?25h[?25l[?7l.regular_form().int()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lregular_form().int()[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7lsage: om.int()

+[?7h[?12l[?25h[?2004l[?7h((2*x^8 + 2)/(x^4 + x^2 + 1))*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[?7lm[?7h[?12l[?25h[?25l[?7l1.regular_form().int()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lint()[?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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1.int()

+[?7h[?12l[?25h[?2004l[?7h(x^2 + 2)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.int()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1

+[?7h[?12l[?25h[?2004l[?7h((-x^4 - x^2 - 1)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1

+[?7h[?12l[?25h[?2004l[?7h((-x^4 - x^2 - 1)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lint()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?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[?7lsage: om1.int().diffn() == om1

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.int().diffn() == om1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.int().diffn()

+[?7h[?12l[?25h[?2004l[?7h((-x^4 - x^2 - 1)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y*C.y.diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: C.polynomial

+[?7h[?12l[?25h[?2004l[?7hx^3 + 2*x
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.polynomial[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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.polynomial)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?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[?7lsage: (C.polynomial)^2

+[?7h[?12l[?25h[?2004l[?7hx^6 + x^4 + x^2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.polynomial[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcrystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lstalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7luC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7ltC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7loC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lmC.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l(C.crystaline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(C.crystalline_cohomology_basis()[1]).coordinates()

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+coordinates of form self (1/y) dx
+(1, 1)
+omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+[?7h( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*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[?2004lTraceback (most recent call last):
+
+  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input In [59] in <cell line: 1>
+    load('init.sage')
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:3 in <module>
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:203
+    "If omega is regular, return form eta such that Cartier(eta) = omega"
+    ^
+IndentationError: expected an indented block after function definition on line 202
+
+[?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(C.crystalline_cohomology_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.crystalline_cohomology_basis()[1]).coordinates()

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+coordinates of form self (1/y) dx
+(1, 1)
+omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [61], in <cell line: 1>()
+----> 1 autom(C.crystalline_cohomology_basis()[Integer(1)]).coordinates()
+
+File <string>:78, in coordinates(self, basis)
+
+File <string>:207, in inv_cartier(omega)
+
+AttributeError: 'NoneType' object has no attribute 'dx'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?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[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.crystalline_cohomology_basis()[1]).coordinates()

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+coordinates of form self (1/y) dx
+(1, 1)
+omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega, omega_regular ((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx None
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [63], in <cell line: 1>()
+----> 1 autom(C.crystalline_cohomology_basis()[Integer(1)]).coordinates()
+
+File <string>:78, in coordinates(self, basis)
+
+File <string>:208, in inv_cartier(omega)
+
+AttributeError: 'NoneType' object has no attribute 'dx'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?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[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.crystalline_cohomology_basis()[1]).coordinates()

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+coordinates of form self (1/y) dx
+(1, 1)
+omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega, omega_regular ((-1)/y) dx (2) dy
+omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
+fct ((x^2 + 2*x + 1)/(x + 2))*y
+aux (V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx), [0], V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
+aux_divided_by_p (((x + 1)/(x*y - y)) dx, 0, ((x + 1)/(x*y - y)) dx)
+aux_divided_by_p.omega8 == aux.omega8.omega.cartier() True
+coordinates of form self ((x + 1)/(x*y - y)) dx
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [65], in <cell line: 1>()
+----> 1 autom(C.crystalline_cohomology_basis()[Integer(1)]).coordinates()
+
+File <string>:92, in coordinates(self, basis)
+
+File <string>:56, in coordinates(self)
+
+File <string>:94, in coordinates(self, basis)
+
+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/categories/map.pyx:788, in sage.categories.map.Map._call_()
+    786     return self._call_with_args(x, args, kwds)
+    787 
+--> 788 cpdef Element _call_(self, x):
+    789     """
+    790     Call method with a single argument, not implemented in the base class.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
+   1249     return num
+   1250 if check and not den.is_unit():
+   1251     # This should probably be a ValueError.
+   1252     # However, too much existing code is expecting this to throw a
+   1253     # TypeError, so we decided to keep it for the time being.
+-> 1254     raise TypeError("fraction must have unit denominator")
+   1255 return num * den.inverse_of_unit()
+
+TypeError: fraction must have unit denominator
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.int().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in range(0, 9):[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((x^2 + 2*x + 1)/(x + 2))*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[?7lCx^2 + 2*x + 1)/(x + 2)*y[?7h[?12l[?25h[?25l[?7l.x^2 + 2*x + 1)/(x + 2)*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[?7lCx + 1)/(x + 2)*y[?7h[?12l[?25h[?25l[?7l.x + 1)/(x + 2)*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)/(x + 2)*y[?7h[?12l[?25h[?25l[?7lC)/(x + 2)*y[?7h[?12l[?25h[?25l[?7l.)/(x + 2)*y[?7h[?12l[?25h[?25l[?7lo)/(x + 2)*y[?7h[?12l[?25h[?25l[?7ln)/(x + 2)*y[?7h[?12l[?25h[?25l[?7le)/(x + 2)*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[?7lCx + 2)*y[?7h[?12l[?25h[?25l[?7l.x + 2)*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*))*y[?7h[?12l[?25h[?25l[?7lC))*y[?7h[?12l[?25h[?25l[?7lo))*y[?7h[?12l[?25h[?25l[?7ln))*y[?7h[?12l[?25h[?25l[?7l))*y[?7h[?12l[?25h[?25l[?7l))*y[?7h[?12l[?25h[?25l[?7l))*y[?7h[?12l[?25h[?25l[?7lC))*y[?7h[?12l[?25h[?25l[?7l.))*y[?7h[?12l[?25h[?25l[?7lo))*y[?7h[?12l[?25h[?25l[?7ln))*y[?7h[?12l[?25h[?25l[?7le))*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[?7lCy[?7h[?12l[?25h[?25l[?7l.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = ((C.x^2 + 2*C.x + C.one)/(C.x + 2*C.one))*C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = ((C.x^2 + 2*C.x + C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff.diffn()

+[?7h[?12l[?25h[?2004l[?7h((x^4 - x^3 - x^2 - x + 1)/(x*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.diffn()[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = ((C.x^2 + 2*C.x + C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautomC.crystalline_cohomlogy_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lff = (C.x^2 + 2*C.x + C.ne)/(C.x + 2*C.one))*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[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.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[?7lmf.difn()[?7h[?12l[?25h[?25l[?7lf.difn()[?7h[?12l[?25h[?25l[?7lof.difn()[?7h[?12l[?25h[?25l[?7lmf.difn()[?7h[?12l[?25h[?25l[?7l f.difn()[?7h[?12l[?25h[?25l[?7l=f.difn()[?7h[?12l[?25h[?25l[?7l f.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om = ff.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = ff.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.int()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lsage: om.is_regular_on_U

+ om.is_regular_on_U0    

+ om.is_regular_on_Uinfty

+

+

+ [?7h[?12l[?25h[?25l[?7l0

+ om.is_regular_on_U0    

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l(

+

+

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.is_regular_on_U0()

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+ [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7l = ff.diffn()[?7h[?12l[?25h[?25l[?7lff.din()[?7h[?12l[?25h[?25l[?7l = ((C.x^2 + 2*C.x + C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lautomC.crystalline_cohomlogy_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lsage: autom(C.crystalline_cohomology_basis()[1]).coordinates()

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+coordinates of form self (1/y) dx
+(1, 1)
+omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega, omega_regular ((-1)/y) dx (2) dy
+omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
+aux.omega0.omega ((-x^12 + x^10 + x^6 - x^4)/y) dx
+aux.omega0.h2 (x^6 + 2*x^4 + x^3 + 2*x)*y
+aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
+aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
+aux_divided_by_p.omega8 == aux.omega8.omega.cartier() True
+sage/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'
+  """
+---------------------------------------------------------------------------
+RecursionError                            Traceback (most recent call last)
+Input In [71], in <cell line: 1>()
+----> 1 autom(C.crystalline_cohomology_basis()[Integer(1)]).coordinates()
+
+File <string>:95, in coordinates(self, basis)
+
+File <string>:70, in coordinates(self)
+
+File <string>:70, in coordinates(self)
+
+    [... skipping similar frames: coordinates at line 70 (2941 times)]
+
+File <string>:70, in coordinates(self)
+
+File <string>:50, in coordinates(self)
+
+File <string>:98, in de_rham_basis(self)
+
+File <string>:91, in basis_de_rham_degrees(self)
+
+File <string>:5, in __init__(self, C, omega, fct)
+
+File <string>:95, in diffn(self)
+
+File <string>:7, in __init__(self, C, g)
+
+File <string>:259, in reduction_form(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx: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:638, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    636 ring_one = self.ring().one()
+    637 try:
+--> 638     return self._element_class(self, x, ring_one, coerce=coerce)
+    639 except (TypeError, ValueError):
+    640     pass
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
+    112 FieldElement.__init__(self, parent)
+    113 if coerce:
+--> 114     self.__numerator   = parent.ring()(numerator)
+    115     self.__denominator = parent.ring()(denominator)
+    116 else:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx: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/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+   1007 try:
+   1008     # now try calling the base ring's __call__ methods
+-> 1009     element = self.base_ring()(element)
+   1010     _p = p_NSet(sa2si(element,_ring), _ring)
+   1011     return new_MP(self,_p)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx: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:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
+    378 else:
+    379     try:
+--> 380         z = integer_ring.Z(value)
+    381     except (TypeError, ValueError):
+    382         from sage.structure.element import Expression
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
+    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
+    286 cdef Map m
+--> 287 cdef Element e = method(C)
+    288 if e is None:
+    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:831, in sage.rings.fraction_field_element.FractionFieldElement._conversion()
+    829     return R(self.__numerator)
+    830 else:
+--> 831     self.reduce()
+    832     num = R(self.__numerator)
+    833     inv_den = R(self.__denominator).inverse_of_unit()
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:1239, in sage.rings.fraction_field_element.FractionFieldElement_1poly_field.reduce()
+   1237 if self._is_reduced:
+   1238     return
+-> 1239 super(self.__class__, self).reduce()
+   1240 self.normalize_leading_coefficients()
+   1241 
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:164, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
+    162     return codomain.coerce(nnum/nden)
+    163 
+--> 164 cpdef reduce(self):
+    165     """
+    166     Reduce this fraction.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:197, in sage.rings.fraction_field_element.FractionFieldElement.reduce()
+    195     return
+    196 try:
+--> 197     g = self.__numerator.gcd(self.__denominator)
+    198     if not g.is_unit():
+    199         self.__numerator //= g
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
+   4492 def new_method(self, other, *args, **kwargs):
+   4493     if have_same_parent(self, other):
+-> 4494         return method(self, other, *args, **kwargs)
+   4495     else:
+   4496         a, b = coercion_model.canonical_coercion(self, other)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4913, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
+   4911         raise NotImplementedError("%s does not provide a gcd implementation for univariate polynomials"%self._parent._base)
+   4912     else:
+-> 4913         return doit(self, other)
+   4914 
+   4915 @coerce_binop
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:946, in FractionField_generic._gcd_univariate_polynomial(self, f, g)
+    944 f1 = Num(f.numerator())
+    945 g1 = Num(g.numerator())
+--> 946 return Pol(f1.gcd(g1)).monic()
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:4494, in sage.structure.element.coerce_binop.new_method()
+   4492 def new_method(self, other, *args, **kwargs):
+   4493     if have_same_parent(self, other):
+-> 4494         return method(self, other, *args, **kwargs)
+   4495     else:
+   4496         a, b = coercion_model.canonical_coercion(self, other)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:4907, in sage.rings.polynomial.polynomial_element.Polynomial.gcd()
+   4905 if tgt.ngens() > 1 and tgt._has_singular:
+   4906     g = flatten(self).gcd(flatten(other))
+-> 4907     return flatten.section()(g)
+   4908 try:
+   4909     doit = self._parent._base._gcd_univariate_polynomial
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:769, in sage.categories.map.Map.__call__()
+    767 if P is D: # we certainly want to call _call_/with_args
+    768     if not args and not kwds:
+--> 769         return self._call_(x)
+    770     return self._call_with_args(x, args, kwds)
+    771 # Is there coercion?
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
+    786     return self._call_with_args(x, args, kwds)
+    787 
+--> 788 cpdef Element _call_(self, x):
+    789     """
+    790     Call method with a single argument, not implemented in the base class.
+
+File /ext/sage/9.7/src/sage/rings/polynomial/flatten.py:397, in UnflatteningMorphism._call_(self, p)
+    395     newpol[l - 1] = {}
+    396 if (i == len(expo) - 1 or expo[i + 1][idx:] != cur_exp[idx:]):
+--> 397     newpol[l] = R(newpol[l], check=False)
+    398 else:
+    399     break
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:899, in sage.structure.parent.Parent.__call__()
+    897         return mor._call_(x)
+    898     else:
+--> 899         return mor._call_with_args(x, args, kwds)
+    900 
+    901 raise TypeError(_LazyString("No conversion defined from %s to %s", (R, self), {}))
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:180, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args()
+    178     print(type(C), C)
+    179     print(type(C._element_constructor), C._element_constructor)
+--> 180 raise
+    181 
+    182 
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:170, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args()
+    168         return C._element_constructor(x)
+    169     else:
+--> 170         return C._element_constructor(x, **kwds)
+    171 else:
+    172     if len(kwds) == 0:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:469, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
+    467 elif isinstance(x, sage.rings.power_series_ring_element.PowerSeries):
+    468     x = x.truncate()
+--> 469 return C(self, x, check, is_gen, construct=construct, **kwds)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:129, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__()
+    127         except AttributeError:
+    128             pass
+--> 129     Polynomial_template.__init__(self, parent, x, check, is_gen, construct)
+    130 
+    131 cdef Polynomial_template _new(self):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_template.pxi:158, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template.__init__()
+    156 for deg, coef in x.iteritems():
+    157     celement_pow(monomial, gen, deg, NULL, (<Polynomial_template>self)._cparent)
+--> 158     celement_mul(monomial, &(<Polynomial_template>self.__class__(parent, coef)).x, monomial, (<Polynomial_template>self)._cparent)
+    159     celement_add(&self.x, &self.x, monomial, (<Polynomial_template>self)._cparent)
+    160 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:129, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__()
+    127         except AttributeError:
+    128             pass
+--> 129     Polynomial_template.__init__(self, parent, x, check, is_gen, construct)
+    130 
+    131 cdef Polynomial_template _new(self):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_template.pxi:107, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template.__init__()
+    105 cdef Py_ssize_t deg
+    106 
+--> 107 Polynomial.__init__(self, parent, is_gen=is_gen)
+    108 
+    109 (<Polynomial_template>self)._cparent = get_cparent(self._parent)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:233, in sage.rings.polynomial.polynomial_element.Polynomial.__init__()
+    231     True
+    232 """
+--> 233 CommutativeAlgebraElement.__init__(self, parent)
+    234 self._is_gen = is_gen
+    235 
+
+RecursionError: maximum recursion depth exceeded while calling a Python object
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?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[?7lB = ((C.x^2 + C.x)*C.y^2*C.y.diffn()).verschiebung() + ((2*C.x^7 + C.x^6 + C.x^5 + C.x^4 + 2*C.x^3+C.x^2+2*C.x)*C.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomolog_basis[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lrystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.crystalline_cohomology_basis()[1]).coordinates()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lBcrys[1]) - Bcrys[0] - Bcry[1][?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?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[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(B[1]).coordinates(basis = B)

+[?7h[?12l[?25h[?2004lcoordinates of form self (1/y) dx
+(1, 1)
+omega, omega_regular ((-1)/y) dx (2) dy
+omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
+aux.omega0.omega ((-x^12 + x^10 + x^6 - x^4)/y) dx
+aux.omega0.h2 (x^6 + 2*x^4 + x^3 + 2*x)*y
+aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [74], in <cell line: 1>()
+----> 1 autom(B[Integer(1)]).coordinates(basis = B)
+
+File <string>:100, in coordinates(self, basis)
+
+File <string>:70, in coordinates(self)
+
+File <string>:70, in coordinates(self)
+
+    [... skipping similar frames: coordinates at line 70 (940 times)]
+
+File <string>:70, in coordinates(self)
+
+File <string>:60, in coordinates(self)
+
+File <string>:107, in coordinates(self, basis, basis_holo, prec)
+
+File <string>:79, in serre_duality_pairing(self, fct, prec)
+
+File <string>:143, in expansion_at_infty(self, place, prec)
+
+File <string>:135, in expansion_at_infty(self, place, prec)
+
+File <string>:18, in naive_hensel(fct, F, start, prec)
+
+File /ext/sage/9.7/src/sage/rings/big_oh.py:141, in O(*x, **kwds)
+    138     return x.parent().completion(x.parent().gen())(0, x.degree(), **kwds)
+    140 elif isinstance(x, laurent_series_ring_element.LaurentSeries):
+--> 141     return laurent_series_ring_element.LaurentSeries(x.parent(), 0).\
+    142         add_bigoh(x.valuation(), **kwds)
+    144 elif isinstance(x, PuiseuxSeries):
+    145     return x.add_bigoh(x.valuation(), **kwds)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:148, in sage.rings.laurent_series_ring_element.LaurentSeries.__init__()
+    146     f = parent._power_series_ring(f)
+    147 elif not isinstance(f, PowerSeries):
+--> 148     f = parent._power_series_ring(f)
+    149 ## now this is a power series, over a different ring ...
+    150 ## requires that power series rings with same vars over the
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/power_series_ring.py:823, in PowerSeriesRing_generic._element_constructor_(self, f, prec, check)
+    821         else:
+    822             raise TypeError("Can only convert series into ring with same variable name.")
+--> 823 return self.element_class(self, f, prec, check=check)
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
+     42     ValueError: series has negative valuation
+     43 """
+---> 44 R = parent._poly_ring()
+     45 if isinstance(f, Element):
+     46     if (<Element>f)._parent is R:
+
+File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
+    958         pass
+    959     return False
+--> 961 def _poly_ring(self):
+    962     """
+    963     Return the underlying polynomial ring used to represent elements of
+    964     this power series ring.
+   (...)
+    970         Univariate Polynomial Ring in t over Integer Ring
+    971     """
+    972     return self.__poly_ring
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*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[?7lg((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y[?7h[?12l[?25h[?25l[?7lg((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y[?7h[?12l[?25h[?25l[?7l ((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y[?7h[?12l[?25h[?25l[?7l=((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y[?7h[?12l[?25h[?25l[?7l ((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*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[?7lCx^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l.x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1)*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[?7lCx^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l.x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1)*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[?7lCx^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l.x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1)*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[?7lCx^4 + 2*x^2 + 2*x)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l.x^4 + 2*x^2 + 2*x)/(x^2 + x + 1)*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[?7lCx^2 + 2*x)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l.x^2 + 2*x)/(x^2 + x + 1)*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[?7lCx)/(x^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l.x)/(x^2 + x + 1)*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[?7lCx^2 + x + 1)*y[?7h[?12l[?25h[?25l[?7l.x^2 + x + 1)*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[?7lCx + 1)*y[?7h[?12l[?25h[?25l[?7l.x + 1)*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))*y[?7h[?12l[?25h[?25l[?7lC))*y[?7h[?12l[?25h[?25l[?7l.))*y[?7h[?12l[?25h[?25l[?7lo))*y[?7h[?12l[?25h[?25l[?7ln))*y[?7h[?12l[?25h[?25l[?7le))*y[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy[?7h[?12l[?25h[?25l[?7l.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gg = ((2*C.x^8 + 2*C.x^7 + C.x^5 + C.x^4 + 2*C.x^2 + 2*C.x)/(C.x^2 + C.x + C.one))*C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = ((2*C.x^8 + 2*C.x^7 + C.x^5 + C.x^4 + 2*C.x^2 + 2*C.x)/(C.x^2 + C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lroot[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: gg.pth_root()

+[?7h[?12l[?25h[?2004l[?7h((2*x^2 + x + 2)/(x + 2))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^12 + x^10 + x^6 - x^4)/y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.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[?7lp((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7lm((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7lm((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l1((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l.((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l ((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l=((-x^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l ((-x^12 + x^10 + x^6 - x^4)/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[?7lCx^12 + x^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l.x^12 + x^10 + x^6 - x^4)/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 = (-C.x^12 + x^10 + x^6 - x^4)/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[?7lCx^10 + x^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l.x^10 + x^6 - x^4)/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[?7lCx^6 - x^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l.x^6 - x^4)/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[?7lCx^4)/y) C.dx[?7h[?12l[?25h[?25l[?7l.x^4)/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[?7lCy) C.dx[?7h[?12l[?25h[?25l[?7l.y) C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()* 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[?7lsage: om1 = ((-C.x^12 + C.x^10 + C.x^6 - C.x^4)/C.y)* C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = ((-C.x^12 + C.x^10 + C.x^6 - C.x^4)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2-om[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l== om[?7h[?12l[?25h[?25l[?7l (C.y*(2*C.x^3 + 2*C.x)+(2*C.x^4 - 2*C.x^2))*C.y.diffn()[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.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[?7lCx^3 + x^2 + x)/(x^2*y + x*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^3 + x^2 + x)/(x^2*y + x*y + 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[?7lCx^2 + x)/(x^2*y + x*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^2 + x)/(x^2*y + x*y + 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[?7lCx)/(x^2*y + x*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l.x)/(x^2*y + x*y + 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[?7lCx^2*y + x*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^2*y + x*y + 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[?7lCy + x*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l.y + x*y + 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[?7lCx*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l.x*y + y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy + y)* C.dx[?7h[?12l[?25h[?25l[?7l.y + 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[?7lCy)* C.dx[?7h[?12l[?25h[?25l[?7l.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[?7lsage: om2 = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + 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[?7h[?12l[?25h[?25l[?7lcompare.frobenius().expansion_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[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRcartier(om1) -[?7h[?12l[?25h[?25l[?7l cartier(om1) -[?7h[?12l[?25h[?25l[?7l=cartier(om1) -[?7h[?12l[?25h[?25l[?7l cartier(om1) -[?7h[?12l[?25h[?25l[?7l()[?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[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7l1[?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[?7lo[?7h[?12l[?25h[?25l[?7lm[?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[?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: R = om1.cartier() - om2.cartier()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR = om1.cartier() - om2.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[?7lg[?7h[?12l[?25h[?25l[?7lg[?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: R == gg.pth_root()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [80], in <cell line: 1>()
+----> 1 R == gg.pth_root()
+
+File <string>:12, in __eq__(self, other)
+
+AttributeError: 'superelliptic_function' object has no attribute 'reduce'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR == gg.pth_root()[?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: R == gg.pth_root().diffn()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?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[?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[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lth[?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[?7l(())[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_cech(C, om1.cartier(), gg.pth_root())

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(C, om1.cartier(), gg.pth_root())[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

+[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [83], in <cell line: 1>()
+----> 1 xi.coordinates()
+
+File <string>:70, in coordinates(self)
+
+File <string>:70, in coordinates(self)
+
+    [... skipping similar frames: coordinates at line 70 (91 times)]
+
+File <string>:70, in coordinates(self)
+
+File <string>:66, in coordinates(self)
+
+File <string>:7, in decomposition_g0_g8(fct, prec)
+
+File <string>:107, in coordinates(self, basis, basis_holo, prec)
+
+File <string>:79, in serre_duality_pairing(self, fct, prec)
+
+File <string>:142, in expansion_at_infty(self, place, prec)
+
+File <string>:137, in expansion_at_infty(self, place, prec)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
+   1512 cdef int cl = classify_elements(left, right)
+   1513 if HAVE_SAME_PARENT(cl):
+-> 1514     return (<Element>left)._mul_(right)
+   1515 if BOTH_ARE_ELEMENT(cl):
+   1516     return coercion_model.bin_op(left, right, mul)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_()
+    911 cdef LaurentSeries right = <LaurentSeries>right_r
+    912 return type(self)(self._parent,
+--> 913                   self.__u * right.__u,
+    914                   self.__n + right.__n)
+    915 
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
+   1512 cdef int cl = classify_elements(left, right)
+   1513 if HAVE_SAME_PARENT(cl):
+-> 1514     return (<Element>left)._mul_(right)
+   1515 if BOTH_ARE_ELEMENT(cl):
+   1516     return coercion_model.bin_op(left, right, mul)
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_()
+    538 """
+    539 prec = self._mul_prec(right_r)
+--> 540 return PowerSeries_poly(self._parent,
+    541                         self.__f * (<PowerSeries_poly>right_r).__f,
+    542                         prec=prec,
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
+     42     ValueError: series has negative valuation
+     43 """
+---> 44 R = parent._poly_ring()
+     45 if isinstance(f, Element):
+     46     if (<Element>f)._parent is R:
+
+File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
+    958         pass
+    959     return False
+--> 961 def _poly_ring(self):
+    962     """
+    963     Return the underlying polynomial ring used to represent elements of
+    964     this power series ring.
+   (...)
+    970         Univariate Polynomial Ring in t over Integer Ring
+    971     """
+    972     return self.__poly_ring
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: xi1

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [84], in <cell line: 1>()
+----> 1 xi1
+
+NameError: name 'xi1' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi1[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi

+[?7h[?12l[?25h[?2004l[?7h(((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi

+[?7h[?12l[?25h[?2004l[?7h(((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7loordinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

+[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [87], in <cell line: 1>()
+----> 1 xi.coordinates()
+
+File <string>:50, in coordinates(self)
+
+File <string>:98, in de_rham_basis(self)
+
+File <string>:76, in basis_de_rham_degrees(self)
+
+File <string>:60, in holomorphic_differentials_basis(self)
+
+File <string>:52, in basis_holomorphic_differentials_degree(self)
+
+File <string>:7, in __init__(self, C, g)
+
+File <string>:259, in reduction_form(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:711, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
+    709                     x0, y0, self))
+    710 try:
+--> 711     return self._element_class(self, x, y, coerce=coerce)
+    712 except TypeError:
+    713     if parent(x) is parent(x0):
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:115, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
+    113 if coerce:
+    114     self.__numerator   = parent.ring()(numerator)
+--> 115     self.__denominator = parent.ring()(denominator)
+    116 else:
+    117     self.__numerator   = numerator
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+   1001 
+   1002         try:
+-> 1003             return self(str(element))
+   1004         except TypeError:
+   1005             pass
+
+File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
+    192 except AttributeError:
+    193     return super().__repr__()
+--> 194 result = reprfunc()
+    195 if isinstance(result, str):
+    196     return result
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
+   2688         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
+   2689     """
+-> 2690     return self._repr()
+   2691 
+   2692 def _latex_(self, name=None):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
+   2654 if n != m-1:
+   2655     s += " + "
+-> 2656 x = y = repr(x)
+   2657 if y.find("-") == 0:
+   2658     y = y[1:]
+
+File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
+    192 except AttributeError:
+    193     return super().__repr__()
+--> 194 result = reprfunc()
+    195 if isinstance(result, str):
+    196     return result
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:338, in sage.rings.fraction_field_FpT.FpTElement._repr_()
+    336 """
+    337 if nmod_poly_degree(self._denom) == 0 and nmod_poly_get_coeff_ui(self._denom, 0) == 1:
+--> 338     return repr(self.numer())
+    339 else:
+    340     numer_s = repr(self.numer())
+
+File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
+    192 except AttributeError:
+    193     return super().__repr__()
+--> 194 result = reprfunc()
+    195 if isinstance(result, str):
+    196     return result
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
+   2688         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
+   2689     """
+-> 2690     return self._repr()
+   2691 
+   2692 def _latex_(self, name=None):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
+   2654 if n != m-1:
+   2655     s += " + "
+-> 2656 x = y = repr(x)
+   2657 if y.find("-") == 0:
+   2658     y = y[1:]
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1.cartier(), gg.pth_root())[?7h[?12l[?25h[?25l[?7lR =gg.pth_roo().diffn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l om1cartier() - om2.cartier()[?7h[?12l[?25h[?25l[?7lom2= ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7l112 + C.x^10+ C.x^6 - C.x^4)/C.y) C.dx[?7h[?12l[?25h[?25l[?7lgg.pth_root()[?7h[?12l[?25h[?25l[?7l = ((2*C.x^8 + 2*C.x^7 + C.x^5 + C.x^4 + 2*C.x^2 + 2*C.x)/(C.x^2 + C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7lautomB[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004lfomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lff.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[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ltom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: autom(B[1]).coordinates(basis = B)

+[?7h[?12l[?25h[?2004lcoordinates of form self (1/y) dx
+(1, 1)
+omega, omega_regular ((-1)/y) dx (2) dy
+omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
+aux.omega0.omega ((-x^12 + x^10 + x^6 - x^4)/y) dx
+aux.omega0.h2 (x^6 + 2*x^4 + x^3 + 2*x)*y
+aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^6 + x^5 + 2*x^2 + 2*x + 1)/(x^2 + x))*y),  + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [90], in <cell line: 1>()
+----> 1 autom(B[Integer(1)]).coordinates(basis = B)
+
+File <string>:99, in coordinates(self, basis)
+
+File <string>:85, in div_by_p(self)
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 + x)/(x^2*y + x*y + y)) 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[?7lx[?7h[?12l[?25h[?25l[?7lsage: ((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx

+[?7h[?12l[?25h[?2004l  Input In [91]
+    ((-x**Integer(3) + x**Integer(2) + x)/(x**Integer(2)*y + x*y + y)) dx
+                                                                       ^
+SyntaxError: invalid syntax
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7lsage: om2 = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: om2

+[?7h[?12l[?25h[?2004l[?7h((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?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[?7lsage: om2.expansion

+ om2.expansion         

+ om2.expansion_at_infty

+

+

+ [?7h[?12l[?25h[?25l[?7l

+ om2.expansion         

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

+ om2.expansion         

+ om2.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(

+

+

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om2.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t^-2 + 2 + 2*t^4 + t^6 + O(t^8)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+ [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 +x)/(*y+ *y + y)) dx[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 +x)/(*y+ *y + y)) dx[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: autom(B[1]).coordinates(basis = B)

+[?7h[?12l[?25h[?2004lcoordinates of form self (1/y) dx
+(1, 1)
+aux 0 ( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y),  + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
+omega, omega_regular ((-1)/y) dx (2) dy
+omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
+aux.omega0.omega ((-x^12 + x^10 + x^6 - x^4)/y) dx
+aux.omega0.h2 (x^6 + 2*x^4 + x^3 + 2*x)*y
+aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^6 + x^5 + 2*x^2 + 2*x + 1)/(x^2 + x))*y),  + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [97], in <cell line: 1>()
+----> 1 autom(B[Integer(1)]).coordinates(basis = B)
+
+File <string>:100, in coordinates(self, basis)
+
+File <string>:86, in div_by_p(self)
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?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[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?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[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+^C---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/categories/rings.py:1129, in Rings.ParentMethods.__getitem__(self, arg)
+   1128 try:
+-> 1129     minpolys = [a.minpoly() for a in elts]
+   1130 except (AttributeError, NotImplementedError, ValueError, TypeError):
+
+File /ext/sage/9.7/src/sage/categories/rings.py:1129, in <listcomp>(.0)
+   1128 try:
+-> 1129     minpolys = [a.minpoly() for a in elts]
+   1130 except (AttributeError, NotImplementedError, ValueError, TypeError):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    493 """
+--> 494 return self.getattr_from_category(name)
+    495 
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    506     cls = P._abstract_element_class
+--> 507 return getattr_from_other_class(self, cls, name)
+    508 
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+
+AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular' object has no attribute 'minpoly'
+
+During handling of the above exception, another exception occurred:
+
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [99], in <cell line: 1>()
+----> 1 B = C.crystalline_cohomology_basis(); autom(B[Integer(1)]).coordinates(basis = B)
+
+File <string>:53, in crystalline_cohomology_basis(self, prec)
+
+File <string>:24, in de_rham_witt_lift(cech_class, prec)
+
+File <string>:6, in de_rham_witt_lift_form0(omega)
+
+File <string>:99, in diffn(self, dy_w)
+
+File <string>:73, in diffn(self, dy_w)
+
+File <string>:177, in dy_w(C)
+
+File <string>:149, in auxilliary_derivative(P)
+
+File <string>:55, in __rmul__(self, other)
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
+   1962         return y
+   1963 
+-> 1964     return coercion_model.bin_op(left, right, operator.mul)
+   1965 
+   1966 cpdef _mul_(self, right):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:55, in __rmul__(self, other)
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
+   1962         return y
+   1963 
+-> 1964     return coercion_model.bin_op(left, right, operator.mul)
+   1965 
+   1966 cpdef _mul_(self, right):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:55, in __rmul__(self, other)
+
+File <string>:84, in __add__(self, other)
+
+File <string>:31, in __add__(self, other)
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
+   2412         return x
+   2413 
+-> 2414     return coercion_model.bin_op(left, right, operator.mul)
+   2415 
+   2416 cpdef _mul_(self, right):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:70, in __rmul__(self, constant)
+
+File <string>:14, in __init__(self, C, g)
+
+File <string>:223, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
+    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
+    286 cdef Map m
+--> 287 cdef Element e = method(C)
+    288 if e is None:
+    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
+    196 var = R.variable_name()
+    197 if var in self._parent.variable_names():
+--> 198     return R(self.polynomial(self._parent(var)))
+    199 else:
+    200     return R([self])
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:411, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
+    409 # Make polynomial ring over all variables except var.
+    410 S = R.base_ring()[tuple(Z)]
+--> 411 ring = S[var]
+    412 if not self:
+    413     return ring(0)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
+   1273         except AttributeError:
+   1274             return self.list()[n]
+-> 1275     return meth(n)
+   1276 
+   1277 #########################################################################
+
+File /ext/sage/9.7/src/sage/categories/rings.py:1129, in Rings.ParentMethods.__getitem__(self, arg)
+   1126 elts = normalize_arg(arg)
+   1128 try:
+-> 1129     minpolys = [a.minpoly() for a in elts]
+   1130 except (AttributeError, NotImplementedError, ValueError, TypeError):
+   1131     minpolys = None
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(); autom(B[1]).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[?7lautom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7luautom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7lxautom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7l autom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7l=autom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7l autom(B[1]).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[?7lsage: B = C.crystalline_cohomology_basis(); aux = autom(B[1]).coordinates(basis = B)

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+coordinates of form self (1/y) dx
+(1, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx1[?7h[?12l[?25h[?25l[?7lsage: aux

+[?7h[?12l[?25h[?2004l[?7h( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), [(1/(x^2 + x))*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y), [((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lomega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7loaux.omega8[?7h[?12l[?25h[?25l[?7lmaux.omega8[?7h[?12l[?25h[?25l[?7l aux.omega8[?7h[?12l[?25h[?25l[?7l=aux.omega8[?7h[?12l[?25h[?25l[?7l aux.omega8[?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 = aux.omega8

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = aux.omega8[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

+[?7h[?12l[?25h[?2004l[?7h[((2*x^2 + 2*x + 1)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^9 + x^7 + x^6 - x^5 + x^4 - x^2 - x - 1)/(x^8*y - x^7*y - x^6*y - x^5*y - x^4*y - x^3*y + x^2*y)) dx) + dV([((2*x^2 + x + 1)/(x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x))*y])
+[?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 = aux.omega8[?7h[?12l[?25h[?25l[?7l-u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?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[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?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()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7lt.difn()[?7h[?12l[?25h[?25l[?7le.difn()[?7h[?12l[?25h[?25l[?7li.difn()[?7h[?12l[?25h[?25l[?7lc.difn()[?7h[?12l[?25h[?25l[?7lh.difn()[?7h[?12l[?25h[?25l[?7lm.difn()[?7h[?12l[?25h[?25l[?7lu.difn()[?7h[?12l[?25h[?25l[?7ll.difn()[?7h[?12l[?25h[?25l[?7ll.difn()[?7h[?12l[?25h[?25l[?7le.difn()[?7h[?12l[?25h[?25l[?7lr.difn()[?7h[?12l[?25h[?25l[?7l).difn()[?7h[?12l[?25h[?25l[?7l(.difn()[?7h[?12l[?25h[?25l[?7l_.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l.difn()[?7h[?12l[?25h[?25l[?7l(.difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om - aux.f.t.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7h[((x^2 + x + 2)/(x^5 + x^4 + 2*x^3 + 2*x^2))*y] d[x] + V(((-x^8 - x^6 + x^4 - x^3 + x - 1)/(x^7*y - x^6*y - x^5*y - x^4*y - x^3*y - x^2*y + x*y)) dx) + dV([((x^2 + x + 2)/(x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom - aux.f.t.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom - aux.f.t.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[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 - aux.f.t.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lmom - aux.f.t.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l1om - aux.f.t.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l om - aux.f.t.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l=om - aux.f.t.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l om - aux.f.t.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l aux.f.t.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l+ aux.f.t.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om1 = om + aux.f.t.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = om + aux.f.t.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1

+[?7h[?12l[?25h[?2004l[?7h + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.int().diffn()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lform() == om[?7h[?12l[?25h[?25l[?7lrobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lni[?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: om1.frobenius()

+[?7h[?12l[?25h[?2004l[?7h(1/(x^2*y + x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.frobenius()[?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: om1.frobenius().expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^4 + 2*t^6 + t^8 + O(t^14)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l/[?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[?7ll[?7h[?12l[?25h[?25l[?7lar[?7h[?12l[?25h[?25l[?7l_[?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[?7lU[?7h[?12l[?25h[?25l[?7l8[?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: om1.omega.is_regular_on_Uinfty()

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.omega.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lsage: om1.omega.is_regular_on_Uinfty()

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.omega.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcis_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lais_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lris_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7ltis_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lis_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7leis_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lris_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l(is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l()is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l().is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.omega.cartier().is_regular_on_Uinfty()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1.omega.cartier().is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))* C.dx[?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[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: om2 = om1.omega

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = om1.omega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?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_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ltch[?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[?7lsage: om2 = second_patch(om1)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = second_patch(om1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = second_patch(om1)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom1.omeg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.omega[?7h[?12l[?25h[?25l[?7lsage: om2 = om1.omega

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = om1.omega[?7h[?12l[?25h[?25l[?7lsecond_ptch(om1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om2 = second_patch(om2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = second_patch(om2)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.expansion__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[?7lsage: om2.cartier()

+[?7h[?12l[?25h[?2004l[?7h((x + 1)/(x*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1omega.cartier().is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lsage: om1

+[?7h[?12l[?25h[?2004l[?7h + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y])
+[?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[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom1[?7h[?12l[?25h[?25l[?7l2.cartier()[?7h[?12l[?25h[?25l[?7l = second_patch(om2)[?7h[?12l[?25h[?25l[?7lom1.omeg[?7h[?12l[?25h[?25l[?7lsecond_ptch(om1)[?7h[?12l[?25h[?25l[?7lom1.omeg[?7h[?12l[?25h[?25l[?7l1.omegacartier().is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lis_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lfrobenus().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = om + aux.f.t.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l - aux.f.t.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = aux.omega8[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(); aux = autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7ltom(B[1]).coordinates(bsi = B)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lx = autom(B[1]).coordinte(basis = B)[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(); aux = autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7ltom(B[1]).coordinates(bsi = B)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: autom(B[1]).coordinates(basis = B)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [119], in <cell line: 1>()
+----> 1 autom(B[Integer(1)]).coordinates(basis = B)
+
+AttributeError: 'NoneType' object has no attribute 'coordinates'
+[?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[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lalline_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+coordinates of form self (1/y) dx
+(1, 1)
+aux 0 ( + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([((x^5 + x^4 + x^2 + x)/(x^2 + x + 1))*y]), V(((x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1)/(x^2 + x))*y),  + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
+omega, omega_regular ((-1)/y) dx (2) dy
+omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
+aux.omega0.omega ((-x^12 + x^10 + x^6 - x^4)/y) dx
+aux.omega0.h2 (x^6 + 2*x^4 + x^3 + 2*x)*y
+aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^6 + x^5 + 2*x^2 + 2*x + 1)/(x^2 + x))*y),  + V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx) + dV([(2/(x^4 + 2*x^3 + 2*x^2 + x))*y]))
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [120], in <cell line: 1>()
+----> 1 load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[Integer(1)]).coordinates(basis = B)
+
+File <string>:100, in coordinates(self, basis)
+
+File <string>:86, in div_by_p(self)
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* 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[?7lo((-x^3 + x^2 + x)/(x^2*y + x*y + y))* dx[?7h[?12l[?25h[?25l[?7lm((-x^3 + x^2 + x)/(x^2*y + x*y + y))* dx[?7h[?12l[?25h[?25l[?7l2((-x^3 + x^2 + x)/(x^2*y + x*y + y))* dx[?7h[?12l[?25h[?25l[?7l ((-x^3 + x^2 + x)/(x^2*y + x*y + y))* dx[?7h[?12l[?25h[?25l[?7l ((-x^3 + x^2 + x)/(x^2*y + x*y + y))* dx[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 + x)/(x^2*y + x*y + y))* dx[?7h[?12l[?25h[?25l[?7l=((-x^3 + x^2 + x)/(x^2*y + x*y + y))* dx[?7h[?12l[?25h[?25l[?7l ((-x^3 + x^2 + x)/(x^2*y + x*y + y))* dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCx^3 + x^2 + x)/(x^2*y + x*y + y)* dx[?7h[?12l[?25h[?25l[?7l/x^3 + x^2 + x)/(x^2*y + x*y + y)* dx[?7h[?12l[?25h[?25l[?7lx^3 + x^2 + x)/(x^2*y + x*y + y)* dx[?7h[?12l[?25h[?25l[?7l.x^3 + x^2 + x)/(x^2*y + x*y + y)* 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[?7lCx^2 + x)/(x^2*y + x*y + y)* dx[?7h[?12l[?25h[?25l[?7l.x^2 + x)/(x^2*y + x*y + y)* 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[?7lCx)/(x^2*y + x*y + y)* dx[?7h[?12l[?25h[?25l[?7l.x)/(x^2*y + x*y + y)* 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[?7lCx^2*y + x*y + y)* dx[?7h[?12l[?25h[?25l[?7l.x^2*y + x*y + y)* 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[?7lCy + x*y + y)* dx[?7h[?12l[?25h[?25l[?7l.y + x*y + y)* 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[?7lCx*y + y)* dx[?7h[?12l[?25h[?25l[?7l.x*y + y)* dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy + y)* dx[?7h[?12l[?25h[?25l[?7l.y + y)* 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[?7lCy)* dx[?7h[?12l[?25h[?25l[?7l.y)* 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 dx[?7h[?12l[?25h[?25l[?7l. dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: om2 = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpip install -U sage[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?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[?7lansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om2.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t^-2 + 2 + 2*t^4 + t^6 + O(t^8)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2.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[?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[?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[?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: om2.cartier().expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h1 + 2*t^2 + t^4 + t^6 + 2*t^8 + O(t^10)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+coordinates of form self (1/y) dx
+(1, 1)
+omega, omega_regular ((-1)/y) dx (2) dy
+omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
+aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
+aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
+aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [124], in <cell line: 1>()
+----> 1 load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[Integer(1)]).coordinates(basis = B)
+
+File <string>:101, in coordinates(self, basis)
+
+File <string>:70, in coordinates(self)
+
+File <string>:70, in coordinates(self)
+
+    [... skipping similar frames: coordinates at line 70 (234 times)]
+
+File <string>:70, in coordinates(self)
+
+File <string>:60, in coordinates(self)
+
+File <string>:107, in coordinates(self, basis, basis_holo, prec)
+
+File <string>:79, in serre_duality_pairing(self, fct, prec)
+
+File <string>:143, in expansion_at_infty(self, place, prec)
+
+File <string>:135, in expansion_at_infty(self, place, prec)
+
+File <string>:18, in naive_hensel(fct, F, start, prec)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:895, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
+    893     result = pol.get_unsafe(d)
+    894     for i in xrange(d - 1, -1, -1):
+--> 895         result = result * a + pol.get_unsafe(i)
+    896     return result
+    897 pol._compiled = CompiledPolynomialFunction(pol.list())
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
+   1512 cdef int cl = classify_elements(left, right)
+   1513 if HAVE_SAME_PARENT(cl):
+-> 1514     return (<Element>left)._mul_(right)
+   1515 if BOTH_ARE_ELEMENT(cl):
+   1516     return coercion_model.bin_op(left, right, mul)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_()
+    911 cdef LaurentSeries right = <LaurentSeries>right_r
+    912 return type(self)(self._parent,
+--> 913                   self.__u * right.__u,
+    914                   self.__n + right.__n)
+    915 
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
+   1512 cdef int cl = classify_elements(left, right)
+   1513 if HAVE_SAME_PARENT(cl):
+-> 1514     return (<Element>left)._mul_(right)
+   1515 if BOTH_ARE_ELEMENT(cl):
+   1516     return coercion_model.bin_op(left, right, mul)
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_()
+    538 """
+    539 prec = self._mul_prec(right_r)
+--> 540 return PowerSeries_poly(self._parent,
+    541                         self.__f * (<PowerSeries_poly>right_r).__f,
+    542                         prec=prec,
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
+     42     ValueError: series has negative valuation
+     43 """
+---> 44 R = parent._poly_ring()
+     45 if isinstance(f, Element):
+     46     if (<Element>f)._parent is R:
+
+File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
+    958         pass
+    959     return False
+--> 961 def _poly_ring(self):
+    962     """
+    963     Return the underlying polynomial ring used to represent elements of
+    964     this power series ring.
+   (...)
+    970         Univariate Polynomial Ring in t over Integer Ring
+    971     """
+    972     return self.__poly_ring
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+coordinates of form self (1/y) dx
+(1, 1)
+omega, omega_regular ((-1)/y) dx (2) dy
+omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
+aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
+aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [125], in <cell line: 1>()
+----> 1 load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[Integer(1)]).coordinates(basis = B)
+
+File <string>:100, in coordinates(self, basis)
+
+File <string>:86, in div_by_p(self)
+
+File <string>:26, in __sub__(self, other)
+
+AttributeError: 'superelliptic_function' object has no attribute 'form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+coordinates of form self (1/y) dx
+(1, 1)
+omega, omega_regular ((-1)/y) dx (2) dy
+omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
+aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
+aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
+aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
+aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
+^C---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:609, in PolynomialRing(base_ring, *args, **kwds)
+    608 try:
+--> 609     k = Integer(arg)
+    610 except TypeError:
+    611     # Interpret arg as names
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:717, in sage.rings.integer.Integer.__init__()
+    716 
+--> 717                 raise TypeError("unable to coerce %s to an integer" % type(x))
+    718 
+
+TypeError: unable to coerce <class 'tuple'> to an integer
+
+During handling of the above exception, another exception occurred:
+
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [126], in <cell line: 1>()
+----> 1 load('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[Integer(1)]).coordinates(basis = B)
+
+File <string>:102, in coordinates(self, basis)
+
+File <string>:70, in coordinates(self)
+
+File <string>:70, in coordinates(self)
+
+    [... skipping similar frames: coordinates at line 70 (133 times)]
+
+File <string>:70, in coordinates(self)
+
+File <string>:50, in coordinates(self)
+
+File <string>:98, in de_rham_basis(self)
+
+File <string>:91, in basis_de_rham_degrees(self)
+
+File <string>:7, in __init__(self, C, g)
+
+File <string>:259, in reduction_form(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    704 x0, y0 = x, y
+    705 try:
+--> 706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+    708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
+    709                     x0, y0, self))
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:688, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
+    686 yd = y.denominator()
+    687 try:
+--> 688     return (xn * yd, yn * xd)
+    689 except (AttributeError, TypeError, ValueError):
+    690     pass
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
+   1514     return (<Element>left)._mul_(right)
+   1515 if BOTH_ARE_ELEMENT(cl):
+-> 1516     return coercion_model.bin_op(left, right, mul)
+   1517 
+   1518 cdef long value
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
+   1198 # Now coerce to a common parent and do the operation there
+   1199 try:
+-> 1200     xy = self.canonical_coercion(x, y)
+   1201 except TypeError:
+   1202     self._record_exception()
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion()
+   1309 x_map, y_map = coercions
+   1310 if x_map is not None:
+-> 1311     x_elt = (<Map>x_map)._call_(x)
+   1312 else:
+   1313     x_elt = x
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
+    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
+    286 cdef Map m
+--> 287 cdef Element e = method(C)
+    288 if e is None:
+    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
+    196 var = R.variable_name()
+    197 if var in self._parent.variable_names():
+--> 198     return R(self.polynomial(self._parent(var)))
+    199 else:
+    200     return R([self])
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:410, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
+    408 
+    409         # Make polynomial ring over all variables except var.
+--> 410         S = R.base_ring()[tuple(Z)]
+    411         ring = S[var]
+    412         if not self:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
+   1273         except AttributeError:
+   1274             return self.list()[n]
+-> 1275     return meth(n)
+   1276 
+   1277 #########################################################################
+
+File /ext/sage/9.7/src/sage/categories/rings.py:1176, in Rings.ParentMethods.__getitem__(self, arg)
+   1173 # 2. Otherwise, try to return a polynomial ring
+   1175 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
+-> 1176 return PolynomialRing(self, elts)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:609, in PolynomialRing(base_ring, *args, **kwds)
+    607 for arg in args:
+    608     try:
+--> 609         k = Integer(arg)
+    610     except TypeError:
+    611         # Interpret arg as names
+    612         if names is not None:
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l = ((-C.x^3 + C.x^2 + C.x)/(C.x^2*C.y + C.x*C.y + C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((x + 1)/(x*y - y)) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l/dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldx[?7h[?12l[?25h[?25l[?7l.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[?7lCy)* C.dx[?7h[?12l[?25h[?25l[?7l.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[?7lCx*y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x*y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy - C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.y - 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[?7lCx + 1)/(C.x*C.y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x + 1)/(C.x*C.y - 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)/(C.x*C.y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7lC)/(C.x*C.y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.)/(C.x*C.y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7lo)/(C.x*C.y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7ln)/(C.x*C.y - C.y)* C.dx[?7h[?12l[?25h[?25l[?7le)/(C.x*C.y - 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[?7lsage: om2 = ((C.x + C.one)/(C.x*C.y - C.y))* C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.polynomial[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2 = ((C.x + C.one)/(C.x*C.y - C.y))* C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?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[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: om2.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h1 + 2*t^2 + t^4 + t^6 + 2*t^8 + O(t^10)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom2.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = om + aux.f.t.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((-x^3 + x)/y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy)*C.dx[?7h[?12l[?25h[?25l[?7l.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[?7lCx)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.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[?7lCx^3 + C.x)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.x^3 + 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[?7lsage: om1 = ((-C.x^3 + C.x)/C.y)*C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.diffn()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^3 + x)/y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()* dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l/dx[?7h[?12l[?25h[?25l[?7ldx[?7h[?12l[?25h[?25l[?7l.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[?7lCy)* C.dx[?7h[?12l[?25h[?25l[?7l.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[?7lCx)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.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[?7lCx^3 + C.x)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^3 + 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[?7lsage: f1 = ((-C.x^3 + C.x)/C.y)* C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = ((-C.x^3 + C.x)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l-C.x.teichmuller()*C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: om1 - f1.diffn() == om2

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [131], in <cell line: 1>()
+----> 1 om1 - f1.diffn() == om2
+
+AttributeError: 'superelliptic_form' object has no attribute 'diffn'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = ((-C.x^3 + C.x)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l((2*x^2 + x + 2)/(x + 2))*y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCy[?7h[?12l[?25h[?25l[?7l.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[?7lCx + 2)*C.y[?7h[?12l[?25h[?25l[?7l.x + 2)*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*))*C.y[?7h[?12l[?25h[?25l[?7lC))*C.y[?7h[?12l[?25h[?25l[?7l.))*C.y[?7h[?12l[?25h[?25l[?7lo))*C.y[?7h[?12l[?25h[?25l[?7ln))*C.y[?7h[?12l[?25h[?25l[?7le))*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*)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7lC)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7l.)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7lo)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7ln)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7le)/(C.x + 2*C.one)*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[?7lCx + 2*C.one)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7l>x + 2*C.one)/(C.x + 2*C.one)*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[?7lx + 2*C.one)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7l.x + 2*C.one)/(C.x + 2*C.one)*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[?7lCx^2 + C.x + 2*C.one)/(C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7l.x^2 + C.x + 2*C.one)/(C.x + 2*C.one)*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[?7lsage: f1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1 - f1.diffn()== om2[?7h[?12l[?25h[?25l[?7lsage: om1 - f1.diffn() == om2

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 - f1.diffn() == om2[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 +C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1 - f1.diffn()== om2[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 +C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1 - f1.diffn()== om2[?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[?7li[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1.cartier(), gg.pth_root())[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic_cech(C, om1.cartier(), gg.pth_root())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?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[?7l1)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_cech(C, om1, f1)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coordinates()[?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[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: xi.omega8 == omega2

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [135], in <cell line: 1>()
+----> 1 xi.omega8 == omega2
+
+NameError: name 'omega2' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega8 == omega2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi.omega8 == om2

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega8 == om2[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

+[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [137], in <cell line: 1>()
+----> 1 xi.coordinates()
+
+File <string>:70, in coordinates(self)
+
+File <string>:70, in coordinates(self)
+
+    [... skipping similar frames: coordinates at line 70 (516 times)]
+
+File <string>:70, in coordinates(self)
+
+File <string>:66, in coordinates(self)
+
+File <string>:7, in decomposition_g0_g8(fct, prec)
+
+File <string>:107, in coordinates(self, basis, basis_holo, prec)
+
+File <string>:79, in serre_duality_pairing(self, fct, prec)
+
+File <string>:143, in expansion_at_infty(self, place, prec)
+
+File <string>:135, in expansion_at_infty(self, place, prec)
+
+File <string>:18, in naive_hensel(fct, F, start, prec)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:881, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
+    879 d = pol.degree()
+    880 
+--> 881 if d <= 0 or (isinstance(a, Element) and R.is_exact() and a.is_zero()):
+    882     return cst # with the right parent thanks to the above coercion
+    883 elif pol._parent is R and a.is_gen():
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring.py:715, in LaurentSeriesRing.is_exact(self)
+    703     """
+    704     Get the precision to which exact elements are truncated when
+    705     necessary (most frequently when inverting).
+   (...)
+    711         5
+    712     """
+    713     return self._power_series_ring.default_prec()
+--> 715 def is_exact(self):
+    716     """
+    717     Laurent series rings are inexact.
+    718 
+   (...)
+    723         False
+    724     """
+    725     return False
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: f1

+[?7h[?12l[?25h[?2004l[?7h((2*x^2 + x + 2)/(x + 2))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f1.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7li[?7h[?12l[?25h[?25l[?7lsage: xi

+[?7h[?12l[?25h[?2004l[?7h(((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?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[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?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[?7lxi[?7h[?12l[?25h[?25l[?7lf1.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7lomega8 == om2[?7h[?12l[?25h[?25l[?7lega2[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7lom1 - f1.diffn() == om2[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 +C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1 - f1.diffn()== om2[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 +C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lsage: f1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lf1.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7lomega8 == om2[?7h[?12l[?25h[?25l[?7lega2[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7lom1 - f1.diffn() == om2[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 +C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1 - f1.diffn()== om2[?7h[?12l[?25h[?25l[?7lf1 = ((-C.x^3 + C.x)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7lom1 = (-C.x^3 + C.x)/C.y)*[?7h[?12l[?25h[?25l[?7lsage: om1 = ((-C.x^3 + C.x)/C.y)*C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7l= superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_cech(C, om1, f1)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi

+[?7h[?12l[?25h[?2004l[?7h(((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

+[?7h[?12l[?25h[?2004lcoordinates of (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+^R
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+coordinates of (0 dx, 0, 0 dx)
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [146], in <cell line: 1>()
+----> 1 xi.coordinates()
+
+File <string>:72, in coordinates(self)
+
+File <string>:72, in coordinates(self)
+
+    [... skipping similar frames: coordinates at line 72 (49 times)]
+
+File <string>:72, in coordinates(self)
+
+File <string>:67, in coordinates(self)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
+   1526     if not err:
+   1527         return (<Element>right)._mul_long(value)
+-> 1528     return coercion_model.bin_op(left, right, mul)
+   1529 except TypeError:
+   1530     return NotImplemented
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:23, in __rmul__(self, constant)
+
+File <string>:5, in __init__(self, C, omega, fct)
+
+File <string>:95, in diffn(self)
+
+File <string>:7, in __init__(self, C, g)
+
+File <string>:245, in reduction_form(C, g)
+
+File <string>:223, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
+    285     raise TypeError("Cannot coerce {} to {}".format(x, C))
+    286 cdef Map m
+--> 287 cdef Element e = method(C)
+    288 if e is None:
+    289     raise RuntimeError("BUG in coercion model: {} method of {} returned None".format(self.method_name, type(x)))
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
+    196 var = R.variable_name()
+    197 if var in self._parent.variable_names():
+--> 198     return R(self.polynomial(self._parent(var)))
+    199 else:
+    200     return R([self])
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:410, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
+    408 
+    409         # Make polynomial ring over all variables except var.
+--> 410         S = R.base_ring()[tuple(Z)]
+    411         ring = S[var]
+    412         if not self:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
+   1273         except AttributeError:
+   1274             return self.list()[n]
+-> 1275     return meth(n)
+   1276 
+   1277 #########################################################################
+
+File /ext/sage/9.7/src/sage/categories/rings.py:1103, in Rings.ParentMethods.__getitem__(self, arg)
+   1099         return (arg,)
+   1101 # 1. If arg is a list, try to return a power series ring.
+-> 1103 if isinstance(arg, list):
+   1104     if not arg:
+   1105         raise TypeError("power series rings must have at least one variable")
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?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[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7lom1 = ((-C.x^3 + C.x)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7lf1 = (2*2 + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lsage: f1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7lom1 = ((-C.x^3 + C.x)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7lsage: om1 = ((-C.x^3 + C.x)/C.y)*C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = ((-C.x^3 + C.x)/C.y)*C.dx[?7h[?12l[?25h[?25l[?7lf1 = (2*2 + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_cech(C, om1, f1)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

+[?7h[?12l[?25h[?2004lcoordinates of (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
+coordinates of (0 dx, 0, 0 dx)
+[?7h(0, 1)
+[?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[?7lB = C.crystalline_cohomology_basis(); aux = autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= C.crystalline_cohomology_basis(); aux = autom(B[1]).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[?7lautom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7lautom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7lautom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7lautom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7lautom(B[1]).cordinates(basis = B)[?7h[?12l[?25h[?25l[?7lutom(B[1]).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[?7lsage: B = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+coordinates of form self (1/y) dx
+(1, 1)
+omega, omega_regular ((-1)/y) dx (2) dy
+omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
+aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
+aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
+aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
+aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
+coord_aux_divided_by_p (0, 1)
+[?7h[1, 4]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: eta2 = superelliptic_drw_cech(C.x.teichmuller()*(C.y.teichmuller()).diffn() + ((2*C.x^4 + 2*C.x^2 + 2*C.one) * C.y).verschiebung().diffn(), - (C.y/C.x).teic
h

+....: muller())[?7h[?12l[?25h[?25l[?7lsage: eta2 = superelliptic_drw_cech(C.x.teichmuller()*(C.y.teichmuller()).diffn() + ((2*C.x^4 + 2*C.x^2 + 2*C.one) * C.y).verschiebung().diffn(), - (C.y/C.x).teic
h

+....: muller())

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: eta2 = superelliptic_drw_cech(C.x.teichmuller()*(C.y.teichmuller()).diffn() + ((2*C.x^4 + 2*C.x^2 + 2*C.one) * C.y).verschiebung().diffn(), - (C.y/C.x).teic
h

+....: muller())[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.omega0.regular_fom()

+ [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta2.coordinates(basis = B)

+[?7h[?12l[?25h[?2004l(0, 1)
+omega, omega_regular 0 dx (0) dy
+omega, omega_regular 0 dx (0) dy
+aux (0, V(((x^16 + x^10)/(x^10 + x^8 + x^6 + 2*x^4 + 2*x^2 + 2))*y), V(((-x^8 + x^6 - 1)/y) dx))
+aux_divided_by_p (0 dx, ((x^5 + x^3)/(x^4 + x^2 + 1))*y, ((-x^3)/y) dx)
+aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
+aux_divided_by_p (0 dx, ((x^5 + x^3)/(x^4 + x^2 + 1))*y, ((-x^3)/y) dx)
+coordinates of form self ((-x^3)/y) dx
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [155], in <cell line: 1>()
+----> 1 eta2.coordinates(basis = B)
+
+File <string>:102, in coordinates(self, basis)
+
+File <string>:73, in coordinates(self)
+
+File <string>:59, in coordinates(self)
+
+File <string>:94, in coordinates(self, basis)
+
+File <string>:16, in linear_representation_polynomials(polynomial, list_of_polynomials)
+
+File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:903, in sage.matrix.matrix2.Matrix.solve_right()
+    901 
+    902         if not self.is_square():
+--> 903             X = self._solve_right_general(C, check=check)
+    904         else:
+    905             try:
+
+File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:1026, in sage.matrix.matrix2.Matrix._solve_right_general()
+   1024     # Have to check that we actually solved the equation.
+   1025     if self*X != B:
+-> 1026         raise ValueError("matrix equation has no solutions")
+   1027 return X
+   1028 
+
+ValueError: matrix equation has no solutions
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-x^8 + x^6 - 1)/y) dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l* dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCdx[?7h[?12l[?25h[?25l[?7l.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[?7lCy)* C.dx[?7h[?12l[?25h[?25l[?7l.y)* C.dx[?7h[?12l[?25h[?25l[?7l/y)* C.dx[?7h[?12l[?25h[?25l[?7ly)* 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[?7lC1)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.1)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7lo)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7ln)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7le)/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[?7lCx^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^6 - C.one)/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[?7lCx^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l/x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7lx^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.x^8 + C.x^6 - C.one)/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[?7lo(-C.x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7lm(-C.x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7lm(-C.x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l (-C.x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l=(-C.x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l (-C.x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7lsage: omm = (-C.x^8 + C.x^6 - C.one)/C.y)* C.dx

+[?7h[?12l[?25h[?2004l  Input In [156]
+    omm = (-C.x**Integer(8) + C.x**Integer(6) - C.one)/C.y)* C.dx
+                                                          ^
+SyntaxError: unmatched ')'
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomm = (-C.x^8 + C.x^6 - C.one)/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* 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[?7lsage: omm = (-C.x^8 + C.x^6 - C.one)/C.y* C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomm = (-C.x^8 + C.x^6 - C.one)/C.y* C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omm.expansion

+ omm.expansion         

+ omm.expansion_at_infty

+

+

+ [?7h[?12l[?25h[?25l[?7l

+ omm.expansion         

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

+ omm.expansion         

+ omm.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(

+

+

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: omm.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t^-16 + 2*t^-8 + O(t^-6)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lomm.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?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[?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: omm.cartier().expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t^-6 + t^-2 + O(t^4)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7leta2.coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega0.regular_form()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: eta2.omega8

+[?7h[?12l[?25h[?2004l[?7h[(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8[?7h[?12l[?25h[?25l[?7l.frobenius().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta2.omega8.r()

+[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^8 + x^6 - 1)/y) 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[?7lo((-x^8 + x^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7lm((-x^8 + x^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7lm((-x^8 + x^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7l ((-x^8 + x^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7l=((-x^8 + x^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7l ((-x^8 + x^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCx^8 + x^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7l.x^8 + x^6 - 1)/y) 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[?7lCx^6 - 1)/y) dx)[?7h[?12l[?25h[?25l[?7l.x^6 - 1)/y) 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[?7lC1)/y) dx)[?7h[?12l[?25h[?25l[?7l.1)/y) dx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l.)/y) dx)[?7h[?12l[?25h[?25l[?7lo)/y) dx)[?7h[?12l[?25h[?25l[?7ln)/y) dx)[?7h[?12l[?25h[?25l[?7le)/y) dx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCy) dx)[?7h[?12l[?25h[?25l[?7l.y) dx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lCdx)[?7h[?12l[?25h[?25l[?7l.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[?7lsage: omm = ((-C.x^8 + C.x^6 - C.one)/C.y) C.dx)

+[?7h[?12l[?25h[?2004l  Input In [162]
+    omm = ((-C.x**Integer(8) + C.x**Integer(6) - C.one)/C.y) C.dx)
+                                                                 ^
+SyntaxError: unmatched ')'
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomm = ((-C.x^8 + C.x^6 - C.one)/C.y) C.dx)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: omm = ((-C.x^8 + C.x^6 - C.one)/C.y) C.dx

+[?7h[?12l[?25h[?2004l  Input In [163]
+    omm = ((-C.x**Integer(8) + C.x**Integer(6) - C.one)/C.y) C.dx
+                                                             ^
+SyntaxError: invalid syntax
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomm = ((-C.x^8 + C.x^6 - C.one)/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()* 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[?7lsage: omm = ((-C.x^8 + C.x^6 - C.one)/C.y)* C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomm = ((-C.x^8 + C.x^6 - C.one)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_ifty()[?7h[?12l[?25h[?25l[?7lexpansion_at_ifty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: omm.cartier().expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t^-6 + t^-2 + O(t^4)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8.r()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: eta2.omega8

+[?7h[?12l[?25h[?2004l[?7h[(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^10 + x^8 - x^2 + 1)/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2.omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
[?7h[?12l[?25h[?25l[?7l
sage: eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())


+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.omega8 == om1[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta1.coordinates()

+[?7h[?12l[?25h[?2004lcoordinates of form self (1/y) dx
+(1, 0)
+omega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega, omega_regular 0 dx (0) dy
+omega, omega_regular 0 dx (0) dy
+aux (0, [0], V(((-x^3)/y) dx))
+aux_divided_by_p (0 dx, 0, 0 dx)
+aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
+aux_divided_by_p (0 dx, 0, 0 dx)
+coord_aux_divided_by_p (0, 0)
+[?7h[1, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1.coordinates()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2omega8[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta1.coordinates()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2omega8[?7h[?12l[?25h[?25l[?7lsage: eta2 = superelliptic_drw_cech(C.x.teichmuller()*(C.y.teichmuller()).diffn() + ((2*C.x^4 + 2*C.x^2 + 2*C.one) * C.y).verschiebung().diffn(), - (C.y/C.x).teic
h

+....: muller())[?7h[?12l[?25h[?25l[?7l-ax

+ [?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: eta2 - B[1]

+[?7h[?12l[?25h[?2004l[?7h( + V(((-x^8 + x^6 - 1)/y) dx) + dV([(2*x^4 + 2*x^2 + 2)*y]), V((2*x^4 + 2*x^2 + 2)*y), V(((-x^8 + x^6 - 1)/y) dx))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2 - B[1][?7h[?12l[?25h[?25l[?7l1.coordinates()[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
[?7h[?12l[?25h[?25l[?7l
2.omega8[?7h[?12l[?25h[?25l[?7l1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
[?7h[?12l[?25h[?25l[?7l
.coordinates()[?7h[?12l[?25h[?25l[?7l2 - B[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[?7leta2 - B[1][?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?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[?7lB = C.crystalline_cohomology_basis(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7l[0].omega0.regular_frm()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: B[1].omega8

+[?7h[?12l[?25h[?2004l[?7h[(2/(x^4 + 2*x^2))*y] d[x] + V((1/(x^2*y)) dx) + dV([(2/(x^2 + 2))*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[1].omega8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta2 - B[1][?7h[?12l[?25h[?25l[?7l1.coordinates()[?7h[?12l[?25h[?25l[?7l2 - B[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[?7leta1.coordinates()[?7h[?12l[?25h[?25l[?7l = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
[?7h[?12l[?25h[?25l[?7l
2.omega8[?7h[?12l[?25h[?25l[?7lomm.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = ((-C.x^8 + C.x^6 - C.oe)/C.y)* C.dx[?7h[?12l[?25h[?25l[?7l.cartier().expansion_at_ifty()[?7h[?12l[?25h[?25l[?7leta2.omega8[?7h[?12l[?25h[?25l[?7l1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
[?7h[?12l[?25h[?25l[?7l
.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[?7lB[1].omega8[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].omega8[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B[1].omega8.r()

+[?7h[?12l[?25h[?2004l[?7h((-1)/(x*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lseB[1].omega8.r()[?7h[?12l[?25h[?25l[?7lcB[1].omega8.r()[?7h[?12l[?25h[?25l[?7loB[1].omega8.r()[?7h[?12l[?25h[?25l[?7lnB[1].omega8.r()[?7h[?12l[?25h[?25l[?7ldB[1].omega8.r()[?7h[?12l[?25h[?25l[?7l_B[1].omega8.r()[?7h[?12l[?25h[?25l[?7lpB[1].omega8.r()[?7h[?12l[?25h[?25l[?7laB[1].omega8.r()[?7h[?12l[?25h[?25l[?7ltB[1].omega8.r()[?7h[?12l[?25h[?25l[?7lcB[1].omega8.r()[?7h[?12l[?25h[?25l[?7lhB[1].omega8.r()[?7h[?12l[?25h[?25l[?7l(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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: second_patch(B[1].omega8.r())

+[?7h[?12l[?25h[?2004l[?7h(x/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsecond_patch(B[1].omega8.r())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = C.one/C.x[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.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[?7lv.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.y/(C.x)^2[?7h[?12l[?25h[?25l[?7lsage: v = C.y/(C.x)^2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7luone/C.x[?7h[?12l[?25h[?25l[?7lsecond_patch(B[1].omega8.r())[?7h[?12l[?25h[?25l[?7lB[1].omega8.r()[?7h[?12l[?25h[?25l[?7lsecond_patch(B[1].omega8.r())[?7h[?12l[?25h[?25l[?7lu = C.one/C.x[?7h[?12l[?25h[?25l[?7lvy/(C.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[?7lv = C.y/(C.x)^2[?7h[?12l[?25h[?25l[?7luone/C.x[?7h[?12l[?25h[?25l[?7lsecond_patch(B[1].omega8.r())[?7h[?12l[?25h[?25l[?7lB[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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?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[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.*v.difn()[?7h[?12l[?25h[?25l[?7lt*v.difn()[?7h[?12l[?25h[?25l[?7le*v.difn()[?7h[?12l[?25h[?25l[?7li*v.difn()[?7h[?12l[?25h[?25l[?7lc*v.difn()[?7h[?12l[?25h[?25l[?7lh*v.difn()[?7h[?12l[?25h[?25l[?7lm*v.difn()[?7h[?12l[?25h[?25l[?7lu*v.difn()[?7h[?12l[?25h[?25l[?7ll*v.difn()[?7h[?12l[?25h[?25l[?7ll*v.difn()[?7h[?12l[?25h[?25l[?7le*v.difn()[?7h[?12l[?25h[?25l[?7lr*v.difn()[?7h[?12l[?25h[?25l[?7l(*v.difn()[?7h[?12l[?25h[?25l[?7l()*v.difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltdifn()[?7h[?12l[?25h[?25l[?7ledifn()[?7h[?12l[?25h[?25l[?7lidifn()[?7h[?12l[?25h[?25l[?7lcdifn()[?7h[?12l[?25h[?25l[?7lhdifn()[?7h[?12l[?25h[?25l[?7lmdifn()[?7h[?12l[?25h[?25l[?7ludifn()[?7h[?12l[?25h[?25l[?7lldifn()[?7h[?12l[?25h[?25l[?7lldifn()[?7h[?12l[?25h[?25l[?7ledifn()[?7h[?12l[?25h[?25l[?7lrdifn()[?7h[?12l[?25h[?25l[?7l(difn()[?7h[?12l[?25h[?25l[?7l()difn()[?7h[?12l[?25h[?25l[?7l().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B[1].omega8 + u.teichmuller()*v.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?7h + V(((x^8 - x^4 - x^2 - 1)/(x^10*y - x^8*y)) dx) + dV([((2*x^4 + 2*x^2 + 2)/x^6)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[1].omega8 + u.teichmuller()*v.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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laB[1].omega8 + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7luB[1].omega8 + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7lxB[1].omega8 + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l=B[1].omega8 + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l B[1].omega8 + u.teichmuler()*v.teichmuler().difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: aux= B[1].omega8 + u.teichmuller()*v.teichmuller().diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux= B[1].omega8 + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?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: aux.h2.expansion

+ aux.h2.expansion         

+ aux.h2.expansion_at_infty

+

+

+ [?7h[?12l[?25h[?25l[?7l

+ aux.h2.expansion         

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

+ aux.h2.expansion         

+ aux.h2.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(

+

+

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.h2.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t + 2*t^5 + t^9 + 2*t^13 + O(t^21)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7laux.h2.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[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?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[?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[?7l()[?7h[?12l[?25h[?25l[?7l()[?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: aux.omega.cartier().expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t^6 + t^10 + O(t^16)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7leta2 - B[1][?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l- B[1][?7h[?12l[?25h[?25l[?7lsage: eta2 - B[1]

+[?7h[?12l[?25h[?2004l[?7h( + V(((-x^8 + x^6 - 1)/y) dx) + dV([(2*x^4 + 2*x^2 + 2)*y]), V((2*x^4 + 2*x^2 + 2)*y), V(((-x^8 + x^6 - 1)/y) dx))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((-x^3 + x^2 + x)/(x^2*y + x*y + y)) 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[?7laux.omega.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ltom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lB[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: autom(B[1]).coordinates(basis = B)

+[?7h[?12l[?25h[?2004lcoordinates of form self (1/y) dx
+(1, 1)
+omega, omega_regular ((-1)/y) dx (2) dy
+omega, omega_regular ((-x^3 + x)/y) dx (2*x^3 + x) dy
+aux (V(((-x^12 + x^10 + x^6 - x^4)/y) dx), V(((2*x^8 + 2*x^7 + x^5 + x^4 + 2*x^2 + 2*x)/(x^2 + x + 1))*y), V(((-x^3 + x^2 + x)/(x^2*y + x*y + y)) dx))
+aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
+aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
+aux_divided_by_p (((-x^3 + x)/y) dx, ((2*x^2 + x + 2)/(x + 2))*y, ((x + 1)/(x*y - y)) dx)
+coord_aux_divided_by_p (0, 1)
+[?7h[1, 4]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.polynomial[?7h[?12l[?25h[?25l[?7l = supereliptic(x^7 + 1, 5)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^7 + 1, 5)[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l(, 3)[?7h[?12l[?25h[?25l[?7l(, 3)[?7h[?12l[?25h[?25l[?7l(), 3)[?7h[?12l[?25h[?25l[?7l()x, 3)[?7h[?12l[?25h[?25l[?7l^, 3)[?7h[?12l[?25h[?25l[?7l3, 3)[?7h[?12l[?25h[?25l[?7l , 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l(), 3)[?7h[?12l[?25h[?25l[?7l(, 3)[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7l(, 3)[?7h[?12l[?25h[?25l[?7l(), 3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx), 3)[?7h[?12l[?25h[?25l[?7l^), 3)[?7h[?12l[?25h[?25l[?7l3), 3)[?7h[?12l[?25h[?25l[?7l ), 3)[?7h[?12l[?25h[?25l[?7l-), 3)[?7h[?12l[?25h[?25l[?7l ), 3)[?7h[?12l[?25h[?25l[?7lx), 3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^, 3)[?7h[?12l[?25h[?25l[?7l3, 3)[?7h[?12l[?25h[?25l[?7l , 3)[?7h[?12l[?25h[?25l[?7l+, 3)[?7h[?12l[?25h[?25l[?7l , 3)[?7h[?12l[?25h[?25l[?7l1, 3)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 3)[?7h[?12l[?25h[?25l[?7lx, 3)[?7h[?12l[?25h[?25l[?7l^, 3)[?7h[?12l[?25h[?25l[?7l3, 3)[?7h[?12l[?25h[?25l[?7l , 3)[?7h[?12l[?25h[?25l[?7l-, 3)[?7h[?12l[?25h[?25l[?7l , 3)[?7h[?12l[?25h[?25l[?7lx, 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: C = superelliptic((x^3 - x)^3 + x^3 - x, 3)

+[?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, 3)[?7h[?12l[?25h[?25l[?7l.polynomia[?7h[?12l[?25h[?25l[?7lcrystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7ltalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(; autom(B[1]).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(); autom(B[1]).coordinates(basis = B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ZeroDivisionError                         Traceback (most recent call last)
+Input In [182], in <cell line: 1>()
+----> 1 B = C.crystalline_cohomology_basis()
+
+File <string>:52, in crystalline_cohomology_basis(self, prec)
+
+File <string>:98, in de_rham_basis(self)
+
+File <string>:80, in basis_de_rham_degrees(self)
+
+File <string>:5, in __init__(self, C, omega, fct)
+
+File <string>:94, in diffn(self)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1739, in sage.structure.element.Element.__truediv__()
+   1737     return (<Element>left)._div_(right)
+   1738 if BOTH_ARE_ELEMENT(cl):
+-> 1739     return coercion_model.bin_op(left, right, truediv)
+   1740 
+   1741 try:
+
+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 (<Element>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/fraction_field_element.pyx:727, in sage.rings.fraction_field_element.FractionFieldElement._div_()
+    725 
+    726         if snum.is_zero():
+--> 727             raise ZeroDivisionError("fraction field element division by zero")
+    728 
+    729         rightinv = self.__class__(self._parent, sden, snum,
+
+ZeroDivisionError: fraction field element division by zero
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 3)[?7h[?12l[?25h[?25l[?7l.polynomia[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth()

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lCsuperelliptic((x^3 - x)^3 + x^3 - x, 3)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 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[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

+[?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])
+---------------------------------------------------------------------------
+IndexError                                Traceback (most recent call last)
+Input In [185], in <cell line: 1>()
+----> 1 B = C.crystalline_cohomology_basis()
+
+File <string>:53, in crystalline_cohomology_basis(self, prec)
+
+File <string>:31, in de_rham_witt_lift(cech_class, prec)
+
+File <string>:7, in decomposition_g0_g8(fct, prec)
+
+File <string>:107, in coordinates(self, basis, basis_holo, prec)
+
+File <string>:79, in serre_duality_pairing(self, fct, prec)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
+    542         return type(self)(self._parent, f, self.__n)
+    543 
+--> 544     return self.__u[i - self.__n]
+    545 
+    546 def __iter__(self):
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
+    451         return self.base_ring().zero()
+    452     else:
+--> 453         raise IndexError("coefficient not known")
+    454 return self.__f[n]
+    455 
+
+IndexError: coefficient not known
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?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: B = C.crystalline_cohomology_basis(prec = 100)

+[?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])
+---------------------------------------------------------------------------
+IndexError                                Traceback (most recent call last)
+Input In [186], in <cell line: 1>()
+----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100))
+
+File <string>:53, in crystalline_cohomology_basis(self, prec)
+
+File <string>:31, in de_rham_witt_lift(cech_class, prec)
+
+File <string>:7, in decomposition_g0_g8(fct, prec)
+
+File <string>:107, in coordinates(self, basis, basis_holo, prec)
+
+File <string>:79, in serre_duality_pairing(self, fct, prec)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
+    542         return type(self)(self._parent, f, self.__n)
+    543 
+--> 544     return self.__u[i - self.__n]
+    545 
+    546 def __iter__(self):
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
+    451         return self.base_ring().zero()
+    452     else:
+--> 453         raise IndexError("coefficient not known")
+    454 return self.__f[n]
+    455 
+
+IndexError: coefficient not known
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7l[?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.is_smooth()[?7h[?12l[?25h[?25l[?7lderham_basis()[1][?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

+[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx),
+ ((x/y) dx, 0, (x/y) dx),
+ ((x^2/y) dx, 0, (x^2/y) dx),
+ ((x^3/y) dx, 0, (x^3/y) dx),
+ ((x^7/y) dx, 2/x*y, ((-1)/(x*y)) dx),
+ (((-x^6)/y) dx, 2/x^2*y, 0 dx),
+ (0 dx, 2/x^3*y, (1/(x^3*y)) dx),
+ ((x^4/y) dx, 2/x^4*y, ((-1)/(x^4*y)) dx)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?7lC.de_rham_basis([?7h[?12l[?25h[?25l[?7lB = C.crystlline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lCsuperelliptic((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.de_rham_basis()[?7h[?12l[?25h[?25l[?7lcrystlline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lystalline_cohomology_basis()[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lBC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l=C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis()

+[?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])
+---------------------------------------------------------------------------
+IndexError                                Traceback (most recent call last)
+Input In [190], in <cell line: 1>()
+----> 1 B = C.crystalline_cohomology_basis()
+
+File <string>:53, in crystalline_cohomology_basis(self, prec)
+
+File <string>:31, in de_rham_witt_lift(cech_class, prec)
+
+File <string>:7, in decomposition_g0_g8(fct, prec)
+
+File <string>:107, in coordinates(self, basis, basis_holo, prec)
+
+File <string>:79, in serre_duality_pairing(self, fct, prec)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
+    542         return type(self)(self._parent, f, self.__n)
+    543 
+--> 544     return self.__u[i - self.__n]
+    545 
+    546 def __iter__(self):
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
+    451         return self.base_ring().zero()
+    452     else:
+--> 453         raise IndexError("coefficient not known")
+    454 return self.__f[n]
+    455 
+
+IndexError: coefficient not known
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lvc)[?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[?7l2)[?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: B = C.crystalline_cohomology_basis(prec = 200)

+[?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])
+---------------------------------------------------------------------------
+IndexError                                Traceback (most recent call last)
+Input In [191], in <cell line: 1>()
+----> 1 B = C.crystalline_cohomology_basis(prec = Integer(200))
+
+File <string>:53, in crystalline_cohomology_basis(self, prec)
+
+File <string>:34, in de_rham_witt_lift(cech_class, prec)
+
+File <string>:35, in decomposition_omega0_omega8(omega, prec)
+
+File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds)
+    583     return expression.sum(*args, **kwds)
+    584 elif max(len(args),len(kwds)) <= 1:
+--> 585     return sum(expression, *args, **kwds)
+    586 else:
+    587     from sage.symbolic.ring import SR
+
+File <string>:35, in <genexpr>(.0)
+
+File <string>:156, in residue(self, place, prec)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
+    542         return type(self)(self._parent, f, self.__n)
+    543 
+--> 544     return self.__u[i - self.__n]
+    545 
+    546 def __iter__(self):
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
+    451         return self.base_ring().zero()
+    452     else:
+--> 453         raise IndexError("coefficient not known")
+    454 return self.__f[n]
+    455 
+
+IndexError: coefficient not known
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?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[?7lB = C.crystalline_cohomology_basis(prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lCsuperelliptic((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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 200)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 200)

+[?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
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 200)[?7h[?12l[?25h[?25l[?7lsage: B

+[?7h[?12l[?25h[?2004l[?7h[([(1/(x^9 + 2*x))*y] d[x] + V(((-x)/(x^8*y - y)) dx) + dV([(x^9/(x^8 + 2))*y]), V(x*y), [(1/(x^9 + 2*x))*y] d[x] + V(((-x)/(x^8*y - y)) dx) + dV([(x/(x^8 + 2))*y])),
+ ([(1/(x^8 + 2))*y] d[x] + V(((-x^4)/(x^8*y - y)) dx) + dV([(x^12/(x^8 + 2))*y]), V(((x^8 + 1)/x^4)*y), [(1/(x^8 + 2))*y] d[x] + V(((-x^4)/(x^8*y - y)) dx) + dV([(1/(x^12 + 2*x^4))*y])),
+ ([(x/(x^8 + 2))*y] d[x] + V(((-x^7)/(x^8*y - y)) dx) + dV([(x^15/(x^8 + 2))*y]), V(((x^8 + 1)/x)*y), [(x/(x^8 + 2))*y] d[x] + V(((-x^7)/(x^8*y - y)) dx) + dV([(1/(x^9 + 2*x))*y])),
+ ([(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(x^18/(x^8 + 2))*y]), V((x^10 + x^2)*y), [(x^2/(x^8 + 2))*y] d[x] + V(((x^10 + x^2)/(x^8*y - y)) dx) + dV([(x^2/(x^8 + 2))*y])),
+ ([(x^6/(x^8 + 2))*y] d[x] + V(((x^14 + x^6)/(x^8*y - y)) dx) + dV([(x^30/(x^8 + 2))*y]), [2/x*y] + V(((x^24 + x^16 + x^8 + 2)/x^2)*y), [(2/(x^10 + 2*x^2))*y] d[x] + V(((-1)/(x^10*y - x^2*y)) dx) + dV([(2/(x^10 + 2*x^2))*y])),
+ ([(2*x^5/(x^8 + 2))*y] d[x] + V(((x^19 - x^11 + x^3)/(x^8*y - y)) dx) + dV([(2*x^27/(x^8 + 2))*y]), [2/x^2*y] + V((2*x^19 + 2*x^11 + 2*x^3)*y), V((1/(x^5*y)) dx)),
+ (V(((x^8 + 1)/y) dx), [2/x^3*y], [(1/(x^12 + 2*x^4))*y] d[x] + V(((-1)/(x^16*y - x^8*y)) dx) + dV([(1/(x^8 + 2))*y])),
+ ([(x^3/(x^8 + 2))*y] d[x] + V(((x^13 + x^5)/(x^8*y - y)) dx) + dV([(x^21/(x^8 + 2))*y]), [2/x^4*y] + V(((x^16 + x^8 + 1)/x^3)*y), [(2/(x^13 + 2*x^5))*y] d[x] + V(((-1)/(x^11*y - x^3*y)) dx) + dV([(2/(x^11 + 2*x^3))*y]))]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[1].omega8 + u.teichmuller()*v.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l00.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[?7laB[0][?7h[?12l[?25h[?25l[?7luB[0][?7h[?12l[?25h[?25l[?7ltB[0][?7h[?12l[?25h[?25l[?7loB[0][?7h[?12l[?25h[?25l[?7lmB[0][?7h[?12l[?25h[?25l[?7l(B[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[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(B[0]).coordinates(basis=B)

+[?7h[?12l[?25h[?2004l(1, 0, 0, 0, 0, 0, 0, 0)
+aux (0, V(((2*x^11 + 2*x^10 + 2*x^8 + 2*x^7)/(x^35 + x^34 + x^32 + x^31 + x^27 + 2*x^25 + x^24 + 2*x^22 + x^19 + 2*x^16 + x^13 + 2*x^11 + x^10 + 2*x^8 + 2*x^4 + 2*x^3 + 2*x + 2))*y), V(((x^8 + x^7 - x^6 + x^5 - x^4 + x^3 - 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_divided_by_p (0 dx, ((2*x^3 + 2*x^2)/(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, ((x^4 - x^3 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
+aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
+aux_divided_by_p (0 dx, ((2*x^3 + 2*x^2)/(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, ((x^4 - x^3 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
+coord_aux_divided_by_p (0, 0, 0, 0, 0, 0, 0, 0)
+[?7h[1, 0, 0, 0, 0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[0]).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]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l1]).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[?7lsage: autom(B[1]).coordinates(basis=B)

+[?7h[?12l[?25h[?2004l(1, 1, 0, 0, 0, 0, 0, 0)
+aux (0, V(((x^11 + x^10 + x^8 + x^7)/(x^32 + x^31 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^25 + x^24 + 2*x^23 + x^22 + 2*x^21 + 2*x^20 + 2*x^18 + 2*x^17 + x^16 + 2*x^15 + 2*x^14 + 2*x^12 + 2*x^11 + x^10 + 2*x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^4 + 2*x^3 + x + 1))*y), V(((x^10 + x^9 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - 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 (0 dx, ((x^3 + x^2)/(x^13 + 2*x^12 + 2*x^11 + x^10 + x^7 + 2*x^6 + 2*x^3 + x^2 + x + 2))*y, ((x^5 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
+aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
+aux_divided_by_p (0 dx, ((x^3 + x^2)/(x^13 + 2*x^12 + 2*x^11 + x^10 + x^7 + 2*x^6 + 2*x^3 + x^2 + x + 2))*y, ((x^5 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
+coord_aux_divided_by_p (0, 0, 0, 0, 0, 0, 0, 0)
+[?7h[1, 1, 0, 0, 0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[1]).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]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l2]).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[?7lsage: autom(B[2]).coordinates(basis=B)

+[?7h[?12l[?25h[?2004l(1, 2, 1, 0, 0, 0, 0, 0)
+aux (V(((x^54 - x^46 + x^45 - x^37 - x^30 + x^22 - x^21 + x^13)/y) dx), V(((x^65 + x^64 + x^62 + x^61 + 2*x^41 + 2*x^40 + 2*x^38 + 2*x^37 + 2*x^14 + 2*x^13 + x^11 + x^10 + 2*x^8 + 2*x^7)/(x^35 + x^34 + x^32 + x^31 + x^27 + 2*x^25 + x^24 + 2*x^22 + x^19 + 2*x^16 + x^13 + 2*x^11 + x^10 + 2*x^8 + 2*x^4 + 2*x^3 + 2*x + 2))*y), V(((x^13 - x^12 + x^11 - x^10 + x^9 - x^8 - x^2 + 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^15 + x^12 - x^7 - x^4)/y) dx, ((x^21 + x^20 + 2*x^13 + 2*x^12 + 2*x^4 + x^3 + 2*x^2)/(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, ((x^6 + x^5 + x^3 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
+aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
+aux_divided_by_p (((x^15 + x^12 - x^7 - x^4)/y) dx, ((x^21 + x^20 + 2*x^13 + 2*x^12 + 2*x^4 + x^3 + 2*x^2)/(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, ((x^6 + x^5 + x^3 + x^2)/(x^7*y - x^6*y + x^5*y - x^4*y + x^3*y - x^2*y + x*y - y)) dx)
+coord_aux_divided_by_p (0, 0, 0, 0, 2, 0, 0, 2)
+[?7h[1, 2, 1, 0, 6, 0, 0, 6]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(B[2]).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]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l3]).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[?7lsage: autom(B[3]).coordinates(basis=B)

+[?7h[?12l[?25h[?2004l(1, 0, 0, 1, 0, 0, 0, 0)
+aux (V(((x^63 - x^55 - x^39 - x^36 + x^31 + x^28 + x^12 - x^4)/y) dx), V(((x^76 + x^73 + x^70 + x^67 + x^64 + x^61 + x^58 + x^55 + 2*x^49 + 2*x^46 + 2*x^43 + 2*x^40 + 2*x^37 + 2*x^34 + 2*x^31 + 2*x^28 + x^25 + x^22 + x^19 + x^16 + 2*x^13 + 2*x^10 + 2*x^7 + 2*x^4 + 2*x)/(x^37 + x^34 + x^31 + x^29 + x^28 + x^26 + x^25 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^12 + x^11 + x^9 + x^8 + x^6 + x^3 + 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^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 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)
+aux.omega0.omega.cartier() - aux.f.f.pth_root().diffn() == aux.omega8.omega.cartier() True
+aux_divided_by_p (((x^18 - x^10 - x^9 + x)/y) dx, ((x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 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)
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [199], in <cell line: 1>()
+----> 1 autom(B[Integer(3)]).coordinates(basis=B)
+
+File <string>:102, in coordinates(self, basis)
+
+File <string>:73, in coordinates(self)
+
+File <string>:59, in coordinates(self)
+
+File <string>:93, in coordinates(self, basis)
+
+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/categories/map.pyx:788, in sage.categories.map.Map._call_()
+    786     return self._call_with_args(x, args, kwds)
+    787 
+--> 788 cpdef Element _call_(self, x):
+    789     """
+    790     Call method with a single argument, not implemented in the base class.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
+   1249     return num
+   1250 if check and not den.is_unit():
+   1251     # This should probably be a ValueError.
+   1252     # However, too much existing code is expecting this to throw a
+   1253     # TypeError, so we decided to keep it for the time being.
+-> 1254     raise TypeError("fraction must have unit denominator")
+   1255 return num * den.inverse_of_unit()
+
+TypeError: fraction must have unit denominator
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]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[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?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[?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[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis(prec = 200)[?7h[?12l[?25h[?25l[?7lCsuperelliptic((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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(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[?7lBautom(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[?7l autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lCautom(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[?7l[?7h[?12l[?25h[?25l[?7lc autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lr autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ly autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ls autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lt autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7la autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ll autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ll autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7li autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ln autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7le autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l_ autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lc autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lh autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lo autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lh autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lo autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lm autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lo autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ll autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lo autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lg autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ly autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l_ autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lb autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lv autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7la autom(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[?7la autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ls autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7li autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7ls autom(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[?7l(); 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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(); 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
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+File <string>:60, in __mul__(self, other)
+
+File <string>:14, in __init__(self, C, g)
+
+File <string>:224, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
+   1515 if BOTH_ARE_ELEMENT(cl):
+-> 1516     return coercion_model.bin_op(left, right, mul)
+   1517 
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
+   1199 try:
+-> 1200     xy = self.canonical_coercion(x, y)
+   1201 except TypeError:
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1311, in sage.structure.coerce.CoercionModel.canonical_coercion()
+   1310 if x_map is not None:
+-> 1311     x_elt = (<Map>x_map)._call_(x)
+   1312 else:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_()
+    286 cdef Map m
+--> 287 cdef Element e = method(C)
+    288 if e is None:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:198, in sage.rings.polynomial.multi_polynomial.MPolynomial._polynomial_()
+    197 if var in self._parent.variable_names():
+--> 198     return R(self.polynomial(self._parent(var)))
+    199 else:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial.pyx:411, in sage.rings.polynomial.multi_polynomial.MPolynomial.polynomial()
+    410 S = R.base_ring()[tuple(Z)]
+--> 411 ring = S[var]
+    412 if not self:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:1275, in sage.structure.parent.Parent.__getitem__()
+   1274         return self.list()[n]
+-> 1275 return meth(n)
+   1276 
+
+File /ext/sage/9.7/src/sage/categories/rings.py:1176, in Rings.ParentMethods.__getitem__(self, arg)
+   1175 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
+-> 1176 return PolynomialRing(self, elts)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:632, in PolynomialRing(base_ring, *args, **kwds)
+    630         raise TypeError("you must specify the names of the variables")
+--> 632 names = normalize_names(n, names)
+    634 # At this point, we have only handled the "names" keyword if it was
+    635 # needed. Since we know the variable names, it would logically be
+    636 # an error to specify an additional "names" keyword. However,
+   (...)
+    639 # and we allow this for historical reasons. However, the names
+    640 # must be consistent!
+
+File /ext/sage/9.7/src/sage/structure/category_object.pyx:900, in sage.structure.category_object.normalize_names()
+    899 
+--> 900 cpdef normalize_names(Py_ssize_t ngens, names):
+    901     r"""
+
+File /ext/sage/9.7/src/sage/structure/category_object.pyx:993, in sage.structure.category_object.normalize_names()
+    992     # Convert names to strings and strip whitespace
+--> 993     names = [str(x).strip() for x in names]
+    994 else:
+
+File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
+    193     return super().__repr__()
+--> 194 result = reprfunc()
+    195 if isinstance(result, str):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:2462, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular._repr_()
+   2461 cdef ring *_ring = self._parent_ring
+-> 2462 s = singular_polynomial_str(self._poly, _ring)
+   2463 return s
+
+File /ext/sage/9.7/src/sage/libs/singular/polynomial.pyx:442, in sage.libs.singular.polynomial.singular_polynomial_str()
+    441 s = plusminus_pattern.sub("\\1 \\2 ", s)
+--> 442 s = parenthvar_pattern.sub("\\1", s)
+    443 return s
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/re.py:324, in _subx(pattern, template)
+    322     return sre_parse.expand_template(template, match)
+--> 324 def _subx(pattern, template):
+    325     # internal: Pattern.sub/subn implementation helper
+    326     template = _compile_repl(template, pattern)
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+
+During handling of the above exception, another exception occurred:
+
+AttributeError                            Traceback (most recent call last)
+Input In [3], in <cell line: 1>()
+----> 1 B = C.crystalline_cohomology_basis(); autom(B[Integer(3)]).coordinates(basis=B)
+
+File <string>:53, in crystalline_cohomology_basis(self, prec)
+
+File <string>:24, in de_rham_witt_lift(cech_class, prec)
+
+File <string>:6, in de_rham_witt_lift_form0(omega)
+
+File <string>:73, in diffn(self, dy_w)
+
+File <string>:177, in dy_w(C)
+
+File /ext/sage/9.7/src/sage/rings/rational.pyx:2414, in sage.rings.rational.Rational.__mul__()
+   2412         return x
+   2413 
+-> 2414     return coercion_model.bin_op(left, right, operator.mul)
+   2415 
+   2416 cpdef _mul_(self, right):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:48, in __rmul__(self, other)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
+   1526     if not err:
+   1527         return (<Element>right)._mul_long(value)
+-> 1528     return coercion_model.bin_op(left, right, mul)
+   1529 except TypeError:
+   1530     return NotImplemented
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:43, in __rmul__(self, other)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
+   1526     if not err:
+   1527         return (<Element>right)._mul_long(value)
+-> 1528     return coercion_model.bin_op(left, right, mul)
+   1529 except TypeError:
+   1530     return NotImplemented
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:43, in __rmul__(self, other)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1528, in sage.structure.element.Element.__mul__()
+   1526     if not err:
+   1527         return (<Element>right)._mul_long(value)
+-> 1528     return coercion_model.bin_op(left, right, mul)
+   1529 except TypeError:
+   1530     return NotImplemented
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:43, in __rmul__(self, other)
+
+File <string>:31, in __add__(self, other)
+
+File <string>:63, in __mul__(self, other)
+
+AttributeError: 'superelliptic_function' object has no attribute 'form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(); 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[?7lp); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lr); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7le); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7lc); autom(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[?7l ); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l2); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l0); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l0); 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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?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); autom(B[3]).cordinates(basis=B)[?7h[?12l[?25h[?25l[?7l10); 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[?7lsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)

+[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [4], in <cell line: 1>()
+----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B)
+
+File <string>:52, in crystalline_cohomology_basis(self, prec)
+
+File <string>:98, in de_rham_basis(self)
+
+File <string>:80, in basis_de_rham_degrees(self)
+
+File <string>:5, in __init__(self, C, omega, fct)
+
+File <string>:28, in __sub__(self, other)
+
+File <string>:7, in __init__(self, C, g)
+
+File <string>:259, in reduction_form(C, g)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:711, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
+    709                     x0, y0, self))
+    710 try:
+--> 711     return self._element_class(self, x, y, coerce=coerce)
+    712 except TypeError:
+    713     if parent(x) is parent(x0):
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__()
+    112 FieldElement.__init__(self, parent)
+    113 if coerce:
+--> 114     self.__numerator   = parent.ring()(numerator)
+    115     self.__denominator = parent.ring()(denominator)
+    116 else:
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1003, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_()
+   1001 
+   1002         try:
+-> 1003             return self(str(element))
+   1004         except TypeError:
+   1005             pass
+
+File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
+    192 except AttributeError:
+    193     return super().__repr__()
+--> 194 result = reprfunc()
+    195 if isinstance(result, str):
+    196     return result
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
+   2688         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
+   2689     """
+-> 2690     return self._repr()
+   2691 
+   2692 def _latex_(self, name=None):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
+   2654 if n != m-1:
+   2655     s += " + "
+-> 2656 x = y = repr(x)
+   2657 if y.find("-") == 0:
+   2658     y = y[1:]
+
+File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
+    192 except AttributeError:
+    193     return super().__repr__()
+--> 194 result = reprfunc()
+    195 if isinstance(result, str):
+    196     return result
+
+File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:338, in sage.rings.fraction_field_FpT.FpTElement._repr_()
+    336 """
+    337 if nmod_poly_degree(self._denom) == 0 and nmod_poly_get_coeff_ui(self._denom, 0) == 1:
+--> 338     return repr(self.numer())
+    339 else:
+    340     numer_s = repr(self.numer())
+
+File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__()
+    192 except AttributeError:
+    193     return super().__repr__()
+--> 194 result = reprfunc()
+    195 if isinstance(result, str):
+    196     return result
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_()
+   2688         NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3
+   2689     """
+-> 2690     return self._repr()
+   2691 
+   2692 def _latex_(self, name=None):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2656, in sage.rings.polynomial.polynomial_element.Polynomial._repr()
+   2654 if n != m-1:
+   2655     s += " + "
+-> 2656 x = y = repr(x)
+   2657 if y.find("-") == 0:
+   2658     y = y[1:]
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: 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)
+aux (V(((x^63 - x^55 - x^39 - x^36 + x^31 + x^28 + x^12 - x^4)/y) dx), V(((x^76 + x^73 + x^70 + x^67 + x^64 + x^61 + x^58 + x^55 + 2*x^49 + 2*x^46 + 2*x^43 + 2*x^40 + 2*x^37 + 2*x^34 + 2*x^31 + 2*x^28 + x^25 + x^22 + x^19 + x^16 + 2*x^13 + 2*x^10 + 2*x^7 + 2*x^4 + 2*x)/(x^37 + x^34 + x^31 + x^29 + x^28 + x^26 + x^25 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^12 + x^11 + x^9 + x^8 + x^6 + x^3 + 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^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 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
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [5], in <cell line: 1>()
+----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B)
+
+File <string>:102, in coordinates(self, basis)
+
+File <string>:73, in coordinates(self)
+
+File <string>:59, in coordinates(self)
+
+File <string>:93, in coordinates(self, basis)
+
+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/categories/map.pyx:788, in sage.categories.map.Map._call_()
+    786     return self._call_with_args(x, args, kwds)
+    787 
+--> 788 cpdef Element _call_(self, x):
+    789     """
+    790     Call method with a single argument, not implemented in the base class.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
+   1249     return num
+   1250 if check and not den.is_unit():
+   1251     # This should probably be a ValueError.
+   1252     # However, too much existing code is expecting this to throw a
+   1253     # TypeError, so we decided to keep it for the time being.
+-> 1254     raise TypeError("fraction must have unit denominator")
+   1255 return num * den.inverse_of_unit()
+
+TypeError: fraction must have unit denominator
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomm.cartier().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l1 = ((-C.x^3 + 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((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx[?7h[?12l[?25h[?25l[?7lsage: om1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx

+[?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[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^9 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = ((2*C.x^2 + C.x + 2*C.one)/(C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.
x

+....: ^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2))*C.y[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.
x

+....: ^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2))*C.y

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [8], in <cell line: 1>()
+----> 1 f = ((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) + Integer(2)*C.x**Integer(16) + Integer(2)*C.x**Integer(15) + Integer(2)*C.x**Integer(14) + Integer(2)*C.x**Integer(13) + Integer(2)*C.x**Integer(12) + Integer(2)*C.x**Integer(11) + Integer(2)*C.x**Integer(10) + Integer(2)*C.x**Integer(9) + C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(6) + C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2))/(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(9) + C.x**Integer(8) + Integer(2)*C.x**Integer(7) + Integer(2)*C.x**Integer(6) + Integer(2)*C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2)))*C.y
+
+File <string>: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 = <object>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: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.
x

+....: ^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2))*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*))*C.y[?7h[?12l[?25h[?25l[?7lC))*C.y[?7h[?12l[?25h[?25l[?7l.))*C.y[?7h[?12l[?25h[?25l[?7lo))*C.y[?7h[?12l[?25h[?25l[?7ln))*C.y[?7h[?12l[?25h[?25l[?7le))*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[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.
x

+....: ^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [9], in <cell line: 1>()
+----> 1 f = ((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) + Integer(2)*C.x**Integer(16) + Integer(2)*C.x**Integer(15) + Integer(2)*C.x**Integer(14) + Integer(2)*C.x**Integer(13) + Integer(2)*C.x**Integer(12) + Integer(2)*C.x**Integer(11) + Integer(2)*C.x**Integer(10) + Integer(2)*C.x**Integer(9) + C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(6) + C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2))/(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(9) + C.x**Integer(8) + Integer(2)*C.x**Integer(7) + Integer(2)*C.x**Integer(6) + Integer(2)*C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2)*C.one))*C.y
+
+File <string>: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 = <object>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: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.
x

+....: ^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*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*)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^1 + C.x^10 + C.x^9 + C.x^8 + 2*C
.

+x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7lC)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^1 + C.x^10 + C.x^9 + C.x^8 + 2*
C

+.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7l.)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^1 + C.x^10 + C.x^9 + C.x^8 + 2
*

+C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7lo)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^1 + C.x^10 + C.x^9 + C.x^8 + 
2

+*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7ln)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^1 + C.x^10 + C.x^9 + C.x^8 +


+2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7le)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^1 + C.x^10 + C.x^9 + C.x^8 
+

+ 2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

+....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = ((C.x^18 - C.x^10 - C.x^9 + 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[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7luperelliptic_cech(C, om1, f1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_cech(C, om1, f)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7lomega8 == om2[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?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[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lU[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.omega0.is_regular_on_U0()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega0.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?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.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi.omega8.is_regular_on_Uinfty()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [14], in <cell line: 1>()
+----> 1 xi.coordinates()
+
+File <string>:73, in coordinates(self)
+
+File <string>:59, in coordinates(self)
+
+File <string>:93, in coordinates(self, basis)
+
+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/categories/map.pyx:788, in sage.categories.map.Map._call_()
+    786     return self._call_with_args(x, args, kwds)
+    787 
+--> 788 cpdef Element _call_(self, x):
+    789     """
+    790     Call method with a single argument, not implemented in the base class.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
+   1249     return num
+   1250 if check and not den.is_unit():
+   1251     # This should probably be a ValueError.
+   1252     # However, too much existing code is expecting this to throw a
+   1253     # TypeError, so we decided to keep it for the time being.
+-> 1254     raise TypeError("fraction must have unit denominator")
+   1255 return num * den.inverse_of_unit()
+
+TypeError: fraction must have unit denominator
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

+....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l.

+ 

+ [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lte[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2*C.x
^

+....: 9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.x^7 
+

+....:  2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2*C.x
^

+....: 9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.x^7 
+

+....:  2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [16], in <cell line: 1>()
+----> 1 ((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) + Integer(2)*C.x**Integer(16) + Integer(2)*C.x**Integer(15) + Integer(2)*C.x**Integer(14) + Integer(2)*C.x**Integer(13) + Integer(2)*C.x**Integer(12) + Integer(2)*C.x**Integer(11) + Integer(2)*C.x**Integer(10) + Integer(2)*C.x**Integer(9) + C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(6) + C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2))/(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(9) + C.x**Integer(8) + Integer(2)*C.x**Integer(7) + Integer(2)*C.x**Integer(6) + Integer(2)*C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x**Integer(2) + Integer(2)*C.x + Integer(2)*C.one))*C.y
+
+File <string>: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 = <object>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: ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2*C.x
^

+....: 9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.x^7 
+

+....:  2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lf.coordinates()

+ 

+ [?7h[?12l[?25h[?25l[?7lxi.cordinates()[?7h[?12l[?25h[?25l[?7lomega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l00()[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7lf = ((C.x^25 + C.x^24 + .x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

+....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(, om1, f)

+ 

+ [?7h[?12l[?25h[?25l[?7l.omega0.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7l8infty()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lf.cordinates()[?7h[?12l[?25h[?25l[?7l((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2*C.x
^

+....: 9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.x^7 
+

+....:  2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?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[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lordinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [17], in <cell line: 1>()
+----> 1 xi.coordinates()
+
+File <string>:73, in coordinates(self)
+
+File <string>:59, in coordinates(self)
+
+File <string>:93, in coordinates(self, basis)
+
+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/categories/map.pyx:788, in sage.categories.map.Map._call_()
+    786     return self._call_with_args(x, args, kwds)
+    787 
+--> 788 cpdef Element _call_(self, x):
+    789     """
+    790     Call method with a single argument, not implemented in the base class.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
+   1249     return num
+   1250 if check and not den.is_unit():
+   1251     # This should probably be a ValueError.
+   1252     # However, too much existing code is expecting this to throw a
+   1253     # TypeError, so we decided to keep it for the time being.
+-> 1254     raise TypeError("fraction must have unit denominator")
+   1255 return num * den.inverse_of_unit()
+
+TypeError: fraction must have unit denominator
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [18], in <cell line: 1>()
+----> 1 xi.coordinates()
+
+File <string>:73, in coordinates(self)
+
+File <string>:59, in coordinates(self)
+
+File <string>:93, in coordinates(self, basis)
+
+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/categories/map.pyx:788, in sage.categories.map.Map._call_()
+    786     return self._call_with_args(x, args, kwds)
+    787 
+--> 788 cpdef Element _call_(self, x):
+    789     """
+    790     Call method with a single argument, not implemented in the base class.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
+   1249     return num
+   1250 if check and not den.is_unit():
+   1251     # This should probably be a ValueError.
+   1252     # However, too much existing code is expecting this to throw a
+   1253     # TypeError, so we decided to keep it for the time being.
+-> 1254     raise TypeError("fraction must have unit denominator")
+   1255 return num * den.inverse_of_unit()
+
+TypeError: fraction must have unit denominator
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?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[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(om.int())[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_g8(om.int())[?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[?7lxi)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(xi.f)

+[?7h[?12l[?25h[?2004l[?7h(((x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11)/(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2))*y,
+ ((x^9 + 2*x^8 + x^7 + 2*x^5 + x^4 + 2*x^3 + 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,
+ 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg.pth_root()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = ((2*C.x^8 + 2*C.x^7 + C.x^5 + C.x^4 + 2*C.x^2 + 2*C.x)/(C.x^2 + C.x + C.one))*C.y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l(C.x^24 + C.x^22 + C.x^20 + C.x^18 + 2*C.x^15 + 2*C.x^13 + 2*C.x^11)/(C.x^14 + C.x^12 + C.x^10 + C.x^8 + 2*C.x^6 + 2*C.x^4 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lsage: gg = (C.x^24 + C.x^22 + C.x^20 + C.x^18 + 2*C.x^15 + 2*C.x^13 + 2*C.x^11)/(C.x^14 + C.x^12 + C.x^10 + C.x^8 + 2*C.x^6 + 2*C.x^4 + 2*C.x^2 + 2*C.one)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = (C.x^24 + C.x^22 + C.x^20 + C.x^18 + 2*C.x^15 + 2*C.x^13 + 2*C.x^11)/(C.x^14 + C.x^12 + C.x^10 + C.x^8 + 2*C.x^6 + 2*C.x^4 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lsage: gg

+[?7h[?12l[?25h[?2004l[?7h(x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11)/(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11)/(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7l.(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lq(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lu(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lo(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7l_(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lr(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7le(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lm(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: (x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11).quo_rem(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)

+[?7h[?12l[?25h[?2004l[?7h(x^10 + x^2 + 2*x, x^9 + x^8 + 2*x^7 + x^6 + 2*x^5 + x^4 + 2*x^3 + x^2 + 2*x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: xi.f

+[?7h[?12l[?25h[?2004l[?7h((x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.f[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.f.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.f.coordinates()[?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[?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[?7l[?7h[?12l[?25h[?25l[?7lsage: xi.f.coordinates(prec = 200)

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.f.coordinates(prec = 200)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l50)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: xi.f.coordinates(prec = 500)

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lsage: C.nb_of_pts_at_infty

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7l.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgC.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7lgC.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7l C.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7l=C.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7l C.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: gg = C.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgg = C.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11).quo_rem(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?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[?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[?7h[?12l[?25h[?25l[?7l, 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[?7l(x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11).quo_rem(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 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[?7lxi.f.coordinates(prec = 500)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?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[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxi.f.function[?7h[?12l[?25h[?25l[?7lxi.f.function[?7h[?12l[?25h[?25l[?7lyxi.f.function[?7h[?12l[?25h[?25l[?7l(xi.f.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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfFxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lfFxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lfFxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lfFxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lfFxy(xi.f.function)[?7h[?12l[?25h[?25l[?7l Fxy(xi.f.function)[?7h[?12l[?25h[?25l[?7l Fxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lFxy(xi.f.function)[?7h[?12l[?25h[?25l[?7l=Fxy(xi.f.function)[?7h[?12l[?25h[?25l[?7l Fxy(xi.f.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[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fffff = Fxy(xi.f.function)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfffff = Fxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: fffff

+[?7h[?12l[?25h[?2004l[?7h(x^25*y + x^24*y + x^23*y + x^22*y + x^21*y + x^20*y + x^19*y + x^18*y - 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 - y)/(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)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfffff[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lnum[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?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[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfffff.numerator()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ld()[?7h[?12l[?25h[?25l[?7le()[?7h[?12l[?25h[?25l[?7ln()[?7h[?12l[?25h[?25l[?7lo()[?7h[?12l[?25h[?25l[?7lm()[?7h[?12l[?25h[?25l[?7li()[?7h[?12l[?25h[?25l[?7ln()[?7h[?12l[?25h[?25l[?7la()[?7h[?12l[?25h[?25l[?7lt()[?7h[?12l[?25h[?25l[?7lo()[?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[?7lsage: fffff.numerator().quo_rem(fffff.denominator())

+[?7h[?12l[?25h[?2004l[?7h(x^10*y + x^2*y - x*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 - y)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.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.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[?7lfC.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.y[?7h[?12l[?25h[?25l[?7lfC.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.y[?7h[?12l[?25h[?25l[?7lfC.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.y[?7h[?12l[?25h[?25l[?7lfC.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.y[?7h[?12l[?25h[?25l[?7lfC.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.y[?7h[?12l[?25h[?25l[?7l 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.y[?7h[?12l[?25h[?25l[?7l=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.y[?7h[?12l[?25h[?25l[?7l 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.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[?7lsage: fffff = 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.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfffff = 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.y[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = 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.y[?7h[?12l[?25h[?25l[?7lsage: fffff = 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.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfffff = 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.y[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsage: fffff = (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.y))/(C.x^15 + C.x^14 + C.x^13 + C.x^12 
+

+....:  C.x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7lsage: fffff = (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.y))/(C.x^15 + C.x^14 + C.x^13 + C.x^12 
+

+....:  C.x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)

+[?7h[?12l[?25h[?2004l  Input In [35]
+    fffff = (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.y))/(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(9) + C.x**Integer(8) - C.x**Integer(7) - C.x**Integer(6) - C.x**Integer(5) - C.x**Integer(4) - C.x**Integer(3) - C.x**Integer(2) - C.x - Integer(1))
+                                                                                                                                                                                                           ^
+SyntaxError: unmatched ')'
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fffff = (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.y))/(C.x^15 + C.x^14 + C.x^13 + C.x^12 
+

+....:  C.x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l(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.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 +


+C.x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7lsage: fffff = (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.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 +

+....: C.x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [36], in <cell line: 1>()
+----> 1 fffff = (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.y)/(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(9) + C.x**Integer(8) - C.x**Integer(7) - C.x**Integer(6) - C.x**Integer(5) - C.x**Integer(4) - C.x**Integer(3) - C.x**Integer(2) - C.x - Integer(1))
+
+File <string>: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 = <object>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: fffff = (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.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 +
 

+....: C.x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l

+ [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(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.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + 
C

+....: .x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - C.one)[?7h[?12l[?25h[?25l[?7lsage: ffff = (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.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + 
C

+....: .x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - C.one)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ffff = (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.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + 
C

+....: .x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - C.one)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?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[?7lsion

+                     ffff.expansion         

+ ffff.expansion_at_infty

+

+

+ [?7h[?12l[?25h[?25l[?7l

+ ffff.expansion         

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l_at_infty

+ ffff.expansion         

+ ffff.expansion_at_infty[?7h[?12l[?25h[?25l[?7l(

+

+

+[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ffff.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^3 + t^13 + t^21 + O(t^23)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?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[?7lffff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = (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.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + 
C

+....: .x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - C.one)[?7h[?12l[?25h[?25l[?7lf = (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.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 +


+C.x^1 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7l)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 
+

+ C.x^1 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7lC.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.y

+ [?7h[?12l[?25h[?25l[?7l.numerator().quo_rem(fffff.denominator())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = Fxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=Cct_feld[?7h[?12l[?25h[?25l[?7lgg =C.x^9 +C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lxi.f.coordines(prec = 500)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11).quo_rem(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lgg[?7h[?12l[?25h[?25l[?7l = (C.x^24 + C.x^22 + C.x^20 + C.x^18 + 2*C.x^15 + 2*C.x^13 + 2*C.x^11)/(C.x^14 + C.x^12 + C.x^10 + C.x^8 + 2*C.x^6 + 2*C.x^4 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7lxi.coordnates()[?7h[?12l[?25h[?25l[?7l((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2*C.x
^

+....: 9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.x^7 
+

+....:  2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lf.coordinates()

+ 

+ [?7h[?12l[?25h[?25l[?7lxi.cordinates()[?7h[?12l[?25h[?25l[?7lomega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l00()[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7lf = ((C.x^25 + C.x^24 + .x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

+....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9+ C.x^8+ 2*C.
x

+^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^ + 2*C.x+ 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l))*C.y[?7h[?12l[?25h[?25l[?7lC

+ 

+ [?7h[?12l[?25h[?25l[?7lom1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx[?7h[?12l[?25h[?25l[?7lB =C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l); autom(B[3]).cordinates(bass=B)[?7h[?12l[?25h[?25l[?7lprec = 100); autm(B[3]).coordnates(basis=B)[?7h[?12l[?25h[?25l[?7lom1= ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lom1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx[?7h[?12l[?25h[?25l[?7lsage: om1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7lom1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lffff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = (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.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + 
C

+....: .x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - C.one)[?7h[?12l[?25h[?25l[?7lf = (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.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 +


+C.x^1 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7l)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 
+

+ C.x^1 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7lC.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.y

+ [?7h[?12l[?25h[?25l[?7l.numerator().quo_rem(fffff.denominator())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = Fxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=Cct_feld[?7h[?12l[?25h[?25l[?7lgg =C.x^9 +C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lxi.f.coordines(prec = 500)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11).quo_rem(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lgg[?7h[?12l[?25h[?25l[?7l = (C.x^24 + C.x^22 + C.x^20 + C.x^18 + 2*C.x^15 + 2*C.x^13 + 2*C.x^11)/(C.x^14 + C.x^12 + C.x^10 + C.x^8 + 2*C.x^6 + 2*C.x^4 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7lxi.coordnates()[?7h[?12l[?25h[?25l[?7l((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2*C.x
^

+....: 9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.x^7 
+

+....:  2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lf.coordinates()

+ 

+ [?7h[?12l[?25h[?25l[?7lxi.cordinates()[?7h[?12l[?25h[?25l[?7lomega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l00()[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7lf = ((C.x^25 + C.x^24 + .x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

+....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

+....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

+....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l.coordinates()

+ 

+ [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7lsage: f.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_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[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7l = superelliptc((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic((x^3 - x)^3 + x^3 - x, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lf.coordinates()[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

+....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1= ((C.x^18- C.x^10- C.x^9 + C.x)/C.y) * C.dx

+ 

+ [?7h[?12l[?25h[?25l[?7lf =((C.x^25 +C.x^24 +C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

+....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1= ((C.x^18- C.x^10- C.x^9 + C.x)/C.y) * C.dx

+ 

+ [?7h[?12l[?25h[?25l[?7lsage: om1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7lom1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx[?7h[?12l[?25h[?25l[?7lC =superelliptic((3 - x)^3 +x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lf.coordinates()[?7h[?12l[?25h[?25l[?7l = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

+....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

+....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

+....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l.coordinates()

+ 

+ [?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lordinates()[?7h[?12l[?25h[?25l[?7lsage: f.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.f.coordinates(prec = 500)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_cech(C, om1, f)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.f.coordinates(prec = 500)[?7h[?12l[?25h[?25l[?7lomega8.s_rgular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lga8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lsage: xi.omega8.is_regular_on_Uinfty()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

+[?7h[?12l[?25h[?2004l[?7h(0, 1, 1, 0, 0, 0, 0, 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.coordinates()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(xi.f)

+[?7h[?12l[?25h[?2004l[?7h((x^10 + x^2 + 2*x)*y,
+ ((2*x^9 + 2*x^8 + 2*x^7 + 2*x^6 + 2*x^5 + x^4 + x^3 + x^2 + 2*x + 1)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2))*y,
+ 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7lxi.coordnates()[?7h[?12l[?25h[?25l[?7lomega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7lf.coordinates()[?7h[?12l[?25h[?25l[?7lsage: f = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

+....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1= ((C.x^18- C.x^10- C.x^9 + C.x)/C.y) * C.dx

+ 

+ [?7h[?12l[?25h[?25l[?7lC =superelliptic((3 - x)^3 +x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lf.coordinates()[?7h[?12l[?25h[?25l[?7l = ((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

+....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lom1= ((C.x^18- C.x^10- C.x^9 + C.x)/C.y) * C.dx

+ 

+ [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lffff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l = (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.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + 
C

+....: .x^11 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - C.one)[?7h[?12l[?25h[?25l[?7lf = (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.y)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 +


+C.x^1 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7l)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 
+

+ C.x^1 + C.x^10 + C.x^9 + C.x^8 - C.x^7 - C.x^6 - C.x^5 - C.x^4 - C.x^3 - C.x^2 - C.x - 1)[?7h[?12l[?25h[?25l[?7lC.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.y

+ [?7h[?12l[?25h[?25l[?7l.numerator().quo_rem(fffff.denominator())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = Fxy(xi.f.function)[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=Cct_feld[?7h[?12l[?25h[?25l[?7lgg =C.x^9 +C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lxi.f.coordines(prec = 500)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^24 + x^22 + x^20 + x^18 + 2*x^15 + 2*x^13 + 2*x^11).quo_rem(x^14 + x^12 + x^10 + x^8 + 2*x^6 + 2*x^4 + 2*x^2 + 2)[?7h[?12l[?25h[?25l[?7lgg[?7h[?12l[?25h[?25l[?7l = (C.x^24 + C.x^22 + C.x^20 + C.x^18 + 2*C.x^15 + 2*C.x^13 + 2*C.x^11)/(C.x^14 + C.x^12 + C.x^10 + C.x^8 + 2*C.x^6 + 2*C.x^4 + 2*C.x^2 + 2*C.one)[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(xi.f)[?7h[?12l[?25h[?25l[?7lxi.coordnates()[?7h[?12l[?25h[?25l[?7l((C.x^25 + C.x^24 + C.x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2*C.x
^

+....: 9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 + 2*C.x^7 
+

+....:  2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7lf.coordinates()

+ 

+ [?7h[?12l[?25h[?25l[?7lxi.cordinates()[?7h[?12l[?25h[?25l[?7lomega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7l00()[?7h[?12l[?25h[?25l[?7l = superelliptic_cech(C, om1, f)[?7h[?12l[?25h[?25l[?7lf = ((C.x^25 + C.x^24 + .x^23 + C.x^22 + C.x^21 + C.x^20 + C.x^19 + C.x^18 + 2*C.x^16 + 2*C.x^15 + 2*C.x^14 + 2*C.x^13 + 2*C.x^12 + 2*C.x^11 + 2*C.x^10 + 2
*

+....: C.x^9 + C.x^8 + C.x^7 + C.x^6 + C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9 + C.x^8 
+

+....:  2*C.x^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^2 + 2*C.x + 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l)/(C.x^15 + C.x^14 + C.x^13 + C.x^12 + C.x^11 + C.x^10 + C.x^9+ C.x^8+ 2*C.
x

+^7 + 2*C.x^6 + 2*C.x^5 + 2*C.x^4 + 2*C.x^3 + 2*C.x^ + 2*C.x+ 2*C.one))*C.y[?7h[?12l[?25h[?25l[?7l))*C.y[?7h[?12l[?25h[?25l[?7lC

+ 

+ [?7h[?12l[?25h[?25l[?7lom1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx[?7h[?12l[?25h[?25l[?7lB =C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7l); autom(B[3]).cordinates(bass=B)[?7h[?12l[?25h[?25l[?7lprec = 100); autm(B[3]).coordnates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: 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)
+aux (V(((x^63 - x^55 - x^39 - x^36 + x^31 + x^28 + x^12 - x^4)/y) dx), V(((x^76 + x^73 + x^70 + x^67 + x^64 + x^61 + x^58 + x^55 + 2*x^49 + 2*x^46 + 2*x^43 + 2*x^40 + 2*x^37 + 2*x^34 + 2*x^31 + 2*x^28 + x^25 + x^22 + x^19 + x^16 + 2*x^13 + 2*x^10 + 2*x^7 + 2*x^4 + 2*x)/(x^37 + x^34 + x^31 + x^29 + x^28 + x^26 + x^25 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^12 + x^11 + x^9 + x^8 + x^6 + x^3 + 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^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + x^7 + x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2)/(x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 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[1, 3, 3, 1, 0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = 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[?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]).coordinates(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]).coordinates(basi=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]).coordinates(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[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: autom(B[4]).coordinates(basis=B)

+[?7h[?12l[?25h[?2004l(1, 1, 0, 2, 1, 2, 1, 2)
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [52], in <cell line: 1>()
+----> 1 autom(B[Integer(4)]).coordinates(basis=B)
+
+File <string>:102, in coordinates(self, basis)
+
+AttributeError: 'NoneType' object has no attribute 'coordinates'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrr = autom(Bcrys[1]) - Bcrys[0] - Bcrys[1][?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lraise[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lE[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lValueError[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: raise ValueError("Test")

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [53], in <cell line: 1>()
+----> 1 raise ValueError("Test")
+
+ValueError: Test
+[?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[?7lraise ValueError("Test")[?7h[?12l[?25h[?25l[?7lautom(B[4]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: B = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)

+[?7h[?12l[?25h[?2004lomega0_lift, omega8_lift [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 + x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) [(1/(x^3 + 2*x))*y] d[x] + V(((x^6 + x^4 - 1)/(x^7*y - x^5*y)) dx) + dV([(1/(x^5 + 2*x^3))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+omega0_lift, omega8_lift [(1/(x^2 + 2))*y] d[x] + V(((-x^10 - x^8 - x^6 + x^4)/(x^2*y - y)) dx) + dV([(x^6/(x^2 + 2))*y]) [(2/(x^4 + 2*x^2))*y] d[x] + V(((-x^6 + x^4 + x^2 + 1)/(x^10*y - x^8*y)) dx) + dV([(2/(x^8 + 2*x^6))*y])
+result.omega8 == compare True
+result.omega8 - compare 0
+---------------------------------------------------------------------------
+IndexError                                Traceback (most recent call last)
+Input In [55], in <cell line: 1>()
+----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B)
+
+IndexError: list index out of range
+[?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 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[?7lBC.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: 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 [57], in <cell line: 1>()
+----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B)
+
+File <string>:107, in coordinates(self, basis)
+
+File <string>:94, in div_by_p(self)
+
+ValueError: aux.omega0.h2.function not in Rxy
+[?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[?2004lTraceback (most recent call last):
+
+  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input In [58] in <cell line: 1>
+    load('init.sage')
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:20 in <module>
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:94
+    raise ValueError("aux.omega0.h2.function not in Rxy":, aux.omega0.h2.function)
+                                                        ^
+SyntaxError: invalid syntax
+
+[?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[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?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[?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[?7lC = superelliptic((x^3 - x)^3 + x^3 - x, 2)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lB = C.crystalline_cohomology_basis(prec = 100); autom(B[3]).coordinates(basis=B)[?7h[?12l[?25h[?25l[?7lsage: 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 [61], in <cell line: 1>()
+----> 1 B = C.crystalline_cohomology_basis(prec = Integer(100)); autom(B[Integer(3)]).coordinates(basis=B)
+
+File <string>:107, in coordinates(self, basis)
+
+File <string>: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[?7lom1 = ((C.x^18 - C.x^10 - C.x^9 + C.x)/C.y) * C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l - aux.f.t.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l=omega8[?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 + 1))*C.y)[?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 + 1))*C.y)

+[?7h[?12l[?25h[?2004l  Input In [62]
+    om = ((Integer(2)*C.x**Integer(74) + C.x**Integer(73) + C.x**Integer(71) + Integer(2)*C.x**Integer(70) + Integer(2)*C.x**Integer(65) + C.x**Integer(64) + C.x**Integer(62) + Integer(2)*C.x**Integer(61) + Integer(2)*C.x**Integer(56) + C.x**Integer(55) + C.x**Integer(53) + Integer(2)*C.x**Integer(52) + C.x**Integer(50) + Integer(2)*C.x**Integer(49) + Integer(2)*C.x**Integer(47) + C.x**Integer(46) + C.x**Integer(44) + Integer(2)*C.x**Integer(43) + Integer(2)*C.x**Integer(38) + C.x**Integer(37) + C.x**Integer(32) + Integer(2)*C.x**Integer(31) + Integer(2)*C.x**Integer(29) + C.x**Integer(28) + C.x**Integer(26) + Integer(2)*C.x**Integer(25) + C.x**Integer(23) + Integer(2)*C.x**Integer(22) + Integer(2)*C.x**Integer(17) + C.x**Integer(16) + C.x**Integer(14) + Integer(2)*C.x**Integer(13) + Integer(2)*C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(2) + C.x)/(C.x**Integer(35) + Integer(2)*C.x**Integer(34) + Integer(2)*C.x**Integer(32) + C.x**Integer(31) + C.x**Integer(27) + Integer(2)*C.x**Integer(25) + Integer(2)*C.x**Integer(24) + C.x**Integer(22) + C.x**Integer(19) + C.x**Integer(16) + C.x**Integer(13) + Integer(2)*C.x**Integer(11) + Integer(2)*C.x**Integer(10) + C.x**Integer(8) + C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x + Integer(1)))*C.y)
+                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       ^
+SyntaxError: unmatched ')'
+
+[?2004h[?25l[?7lsage: [?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 + 1))*C.y)[?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((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 + 1))*C.y[?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 + 1))*C.y

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [63], in <cell line: 1>()
+----> 1 om = ((Integer(2)*C.x**Integer(74) + C.x**Integer(73) + C.x**Integer(71) + Integer(2)*C.x**Integer(70) + Integer(2)*C.x**Integer(65) + C.x**Integer(64) + C.x**Integer(62) + Integer(2)*C.x**Integer(61) + Integer(2)*C.x**Integer(56) + C.x**Integer(55) + C.x**Integer(53) + Integer(2)*C.x**Integer(52) + C.x**Integer(50) + Integer(2)*C.x**Integer(49) + Integer(2)*C.x**Integer(47) + C.x**Integer(46) + C.x**Integer(44) + Integer(2)*C.x**Integer(43) + Integer(2)*C.x**Integer(38) + C.x**Integer(37) + C.x**Integer(32) + Integer(2)*C.x**Integer(31) + Integer(2)*C.x**Integer(29) + C.x**Integer(28) + C.x**Integer(26) + Integer(2)*C.x**Integer(25) + C.x**Integer(23) + Integer(2)*C.x**Integer(22) + Integer(2)*C.x**Integer(17) + C.x**Integer(16) + C.x**Integer(14) + Integer(2)*C.x**Integer(13) + Integer(2)*C.x**Integer(8) + C.x**Integer(7) + C.x**Integer(5) + Integer(2)*C.x**Integer(4) + Integer(2)*C.x**Integer(2) + C.x)/(C.x**Integer(35) + Integer(2)*C.x**Integer(34) + Integer(2)*C.x**Integer(32) + C.x**Integer(31) + C.x**Integer(27) + Integer(2)*C.x**Integer(25) + Integer(2)*C.x**Integer(24) + C.x**Integer(22) + C.x**Integer(19) + C.x**Integer(16) + C.x**Integer(13) + Integer(2)*C.x**Integer(11) + Integer(2)*C.x**Integer(10) + C.x**Integer(8) + C.x**Integer(4) + Integer(2)*C.x**Integer(3) + Integer(2)*C.x + Integer(1)))*C.y
+
+File <string>: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 = <object>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 = ((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 + 1))*C.y[?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((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: 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[?2004l[?2004h[?25l[?7lsage: [?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[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lom.regular_form()

+ 

+ 

+ [?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ldiffn()[?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 = om.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+ [?7h[?12l[?25h[?25l[?7lom = om.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: om

+[?7h[?12l[?25h[?2004l[?7h0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom[?7h[?12l[?25h[?25l[?7l = om.diffn()[?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[?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[?2004l[?2004h[?25l[?7lsage: [?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[?7lm[?7h[?12l[?25h[?25l[?7l.is_regular_on_U0()

+ 

+ 

+ [?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.[?7h[?12l[?25h[?25l[?7lmom.[?7h[?12l[?25h[?25l[?7l1om.[?7h[?12l[?25h[?25l[?7l om.[?7h[?12l[?25h[?25l[?7l=om.[?7h[?12l[?25h[?25l[?7l om.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7lregular_form()[?7h[?12l[?25h[?25l[?7l()p[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l_root[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om1 = om.pth_root()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+ [?7h[?12l[?25h[?25l[?7lom1 = om.pth_root()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = om.pth_root()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.pth_rot()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = om1.pth_root()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [69], in <cell line: 1>()
+----> 1 om1 = om1.pth_root()
+
+File <string>:168, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom1 = om1.pth_root()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: om1

+[?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[?7lom1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.omega.cartier().is_regular_on_Uinfty()[?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: om1.diffn()

+[?7h[?12l[?25h[?2004l[?7h((-x^18 + x^10 + x^9 + x^2 - 1)/y) dx
+[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: loa

+[?7h[?12l[?25h[?2004l^[[C---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [1], in <cell line: 1>()
+----> 1 loa
+
+NameError: name 'loa' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lloa[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?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[?7lgg = C.x^9 + C.x^8 + 2*C.x^7 + C.x^6 + 2*C.x^5 + C.x^4 + 2*C.x^3 + C.x^2 + 2*C.x[?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 C.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[?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().int()[?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[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

+[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git status
+On branch master
+Your branch is up to date with 'origin/master'.
+
+Changes not staged for commit:
+  (use "git add <file>..." to update what will be committed)
+  (use "git restore <file>..." to discard changes in working directory)
+	modified:   sage/.run.term-0.term
+	modified:   sage/drafty/draft.sage
+	modified:   sage/init.sage
+	modified:   sage/superelliptic/superelliptic_cech_class.sage
+	modified:   sage/superelliptic/superelliptic_class.sage
+	modified:   sage/superelliptic/superelliptic_form_class.sage
+	modified:   sage/superelliptic_drw/automorphism.sage
+	modified:   sage/superelliptic_drw/de_rham_witt_lift.sage
+	modified:   sage/superelliptic_drw/decomposition_into_g0_g8.sage
+	modified:   sage/superelliptic_drw/second_patch.sage
+	modified:   sage/superelliptic_drw/superelliptic_drw_cech.sage
+	modified:   sage/superelliptic_drw/superelliptic_drw_form.sage
+	modified:   sage/tests.sage
+
+Untracked files:
+  (use "git add <file>..." to include in what will be committed)
+	.crystalline_p2.ipynb.sage-jupyter2
+	.deRhamComputation.ipynb.sage-jupyter2
+	.elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2
+	.git.x11-0.term
+	.superelliptic.ipynb.sage-jupyter2
+	.superelliptic_alpha.ipynb.sage-jupyter2
+	.superelliptic_arbitrary_field.ipynb.sage-jupyter2
+	git.x11
+	sage/as_covers/tests/cartier_test.sage
+	sage/drafty/.2023-03-06-file-1.ipynb.sage-jupyter2
+	sage/drafty/2gpcovers.sage
+	sage/drafty/as_cartier.sage
+	sage/drafty/better_trace.sage
+	sage/drafty/cartier_image_representation.sage
+	sage/drafty/convert_superelliptic_into_AS.sage
+	sage/drafty/draft4.sage
+	sage/drafty/draft5.sage
+	sage/drafty/draft6.sage
+	sage/drafty/draft7.sage
+	sage/drafty/draft8.sage
+	sage/drafty/draft_klein_covers.sage
+	sage/drafty/lift_to_de_rham.sage
+	sage/drafty/pole_numbers.sage
+	sage/superelliptic/frobenius_kernel.sage
+	sage/superelliptic/tests/
+	sage/superelliptic_drw/regular_form.sage
+	sage/superelliptic_drw/tests/
+	superelliptic_arbitrary_field.ipynb
+
+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/
diff --git a/sage/as_covers/tests/cartier_test.sage b/sage/as_covers/tests/cartier_test.sage
new file mode 100644
index 0000000..a01ba7d
--- /dev/null
+++ b/sage/as_covers/tests/cartier_test.sage
@@ -0,0 +1,11 @@
+p = 5
+m = 2
+F = GF(p)
+Rx.<x> = PolynomialRing(F)
+f = x^3 + x + 1
+C = superelliptic(f, m)
+g = f(x^p - x)
+C1 = superelliptic(g, m)
+ff = superelliptic_function(C, x)
+AS = as_cover(C, [ff])
+print(C1.cartier_matrix().rank() == AS.cartier_matrix().rank())
\ No newline at end of file
diff --git a/sage/drafty/draft.sage b/sage/drafty/draft.sage
index 54433d1..2e74027 100644
--- a/sage/drafty/draft.sage
+++ b/sage/drafty/draft.sage
@@ -15,8 +15,14 @@ C = superelliptic(f, m)
 #b = C.crystalline_cohomology_basis()
 #print(autom(b[0]).coordinates(basis = b))
 #eta1 = (dy + dV(2xy) + V(x^5 \, dy), V(y/x))
-eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
+#eta1 = superelliptic_drw_cech(C.y.teichmuller().diffn() + (2*C.x*C.y).verschiebung().diffn() + (C.x^5*C.y.diffn()).verschiebung(), (C.y/C.x).verschiebung())
 #eta2 =  (  x \, dy + 3 x^3 \, dy + dV((2x^4 + 2x^2 + 2) y) + V( (x^4 + x^2 + 1) dy), -[y/x])
-eta2 = superelliptic_drw_cech(C.x.teichmuller()*(C.y.teichmuller()).diffn() + ((2*C.x^4 + 2*C.x^2 + 2*C.one) * C.y).verschiebung().diffn(), - (C.y/C.x).teichmuller())
-aux = de_rham_witt_lift(C.de_rham_basis()[1])
-print(aux)
+#eta2 = superelliptic_drw_cech(C.x.teichmuller()*(C.y.teichmuller()).diffn() + ((2*C.x^4 + 2*C.x^2 + 2*C.one) * C.y).verschiebung().diffn(), - (C.y/C.x).teichmuller())
+#omega8_lift0, compare = de_rham_witt_lift(C.de_rham_basis()[1])
+#omega8_lift = -(C.x^(-3)).teichmuller()*C.y.teichmuller().diffn() + 2*C.y.teichmuller()*(C.x^(-4)).teichmuller()*C.x.teichmuller().diffn()
+#eta2 = de_rham_witt_lift(C.de_rham_basis()[1])
+#b = autom(eta2)
+#print(autom(C.crystalline_cohomology_basis()[1]).coordinates())
+
+
+
diff --git a/sage/init.sage b/sage/init.sage
index 8ea4d20..f4efe85 100644
--- a/sage/init.sage
+++ b/sage/init.sage
@@ -18,6 +18,7 @@ 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/regular_form.sage')
 load('superelliptic_drw/de_rham_witt_lift.sage')
 load('superelliptic_drw/automorphism.sage')
 load('auxilliaries/reverse.sage')
@@ -26,8 +27,6 @@ load('auxilliaries/linear_combination_polynomials.sage')
 ##############
 ##############
 load('drafty/convert_superelliptic_into_AS.sage')
-load('drafty/regular_on_U0.sage')
-load('drafty/lift_to_de_rham.sage')
 load('drafty/draft.sage')
 #load('drafty/draft_klein_covers.sage')
 #load('drafty/2gpcovers.sage')
diff --git a/sage/superelliptic/superelliptic_cech_class.sage b/sage/superelliptic/superelliptic_cech_class.sage
index 12af23d..05c7ed6 100644
--- a/sage/superelliptic/superelliptic_cech_class.sage
+++ b/sage/superelliptic/superelliptic_cech_class.sage
@@ -46,52 +46,30 @@ class superelliptic_cech:
         Fx = FractionField(Rx)
         FxRy.<y> = PolynomialRing(Fx)
         g = C.genus()
-        degrees_holo = C.degrees_holomorphic_differentials()
-        degrees_holo_inv = {b:a for a, b in degrees_holo.items()}
-        degrees0 = C.degrees_de_rham0()
-        degrees0_inv = {b:a for a, b in degrees0.items()}
-        degrees1 = C.degrees_de_rham1()
-        degrees1_inv = {b:a for a, b in degrees1.items()}
         basis = C.de_rham_basis()
         
         omega = self.omega0
         fct = self.f
         
+        if fct.function == Rx(0) and omega.form == Rx(0):
+            return vector((2*g)*[0])
+        
         if fct.function == Rx(0) and omega.form != Rx(0):
-            for j in range(1, m):
-                omega_j = Fx(omega.jth_component(j))
-                if omega_j != Fx(0):
-                    d = degree_of_rational_fctn(omega_j, F)
-                    index = degrees_holo_inv[(d, j)]
-                    a = coeff_of_rational_fctn(omega_j, F)
-                    a1 = coeff_of_rational_fctn(basis[index].omega0.jth_component(j), F)
-                    elt = self - (a/a1)*basis[index]
-                    return elt.coordinates() + a/a1*vector([F(i == index) for i in range(0, 2*g)])
-                    
-        for j in range(1, m):
-            fct_j = Fx(fct.jth_component(j))
-            if (fct_j != Rx(0)):
-                d = degree_of_rational_fctn(fct_j, F)
-            
-                if (d, j) in degrees1.values():
-                    index = degrees1_inv[(d, j)]
-                    a = coeff_of_rational_fctn(fct_j, F)
-                    elt = self - (a/m)*basis[index]
-                    return elt.coordinates() + a/m*vector([F(i == index) for i in range(0, 2*g)])
-                
-                if d<0:
-                    a = coeff_of_rational_fctn(fct_j, F)
-                    h = superelliptic_function(C, FxRy(a*y^j*x^d))
-                    elt = superelliptic_cech(C, self.omega0, self.f - h)
-                    return elt.coordinates()
-            
-                if (fct_j != Rx(0)):
-                    G = superelliptic_function(C, y^j*x^d)
-                    a = coeff_of_rational_fctn(fct_j, F)
-                    elt =self - a*superelliptic_cech(C, diffn(G), G)
-                    return elt.coordinates()
-
-        return vector(2*g*[0])
+            result = list(omega.coordinates()) + g*[0]
+            result = vector([F(a) for a in result])
+            return result
+        
+        coord = fct.coordinates()
+        coord = g*[0] + list(coord)
+        coord = vector([F(a) for a in coord])
+        aux = self
+        for i in range(g, 2*g):
+            aux -= coord[i]*basis[i]
+        aux_f = decomposition_g0_g8(aux.f)[0]
+        aux.omega0 -= aux_f.diffn()
+        aux.f = 0*C.x
+        aux.omega8 = aux.omega0
+        return coord + aux.coordinates()
     
     def is_cocycle(self):
         w0 = self.omega0
diff --git a/sage/superelliptic/superelliptic_class.sage b/sage/superelliptic/superelliptic_class.sage
index b2cb919..1a43896 100644
--- a/sage/superelliptic/superelliptic_class.sage
+++ b/sage/superelliptic/superelliptic_class.sage
@@ -196,9 +196,9 @@ class superelliptic:
         Fxy = FractionField(Rxy)
         basis = []
         for j in range(1, m):
-                for i in range(1, r):
-                    if (r*j - m*i >= delta):
-                        basis += [superelliptic_function(self, Fxy(m*y^(j)/x^i))]
+            for i in range(1, r):
+                if (r*(m-j) - m*i >= delta): 
+                    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)
diff --git a/sage/superelliptic/superelliptic_form_class.sage b/sage/superelliptic/superelliptic_form_class.sage
index 85164cc..6c0763d 100644
--- a/sage/superelliptic/superelliptic_form_class.sage
+++ b/sage/superelliptic/superelliptic_form_class.sage
@@ -6,7 +6,12 @@ class superelliptic_form:
         g = Fxy(reduction_form(C, g))
         self.form = g
         self.curve = C
-        
+    
+    def __eq__(self, other):
+        if self.reduce().form == other.reduce().form:
+            return True
+        return False
+    
     def __add__(self, other):
         C = self.curve
         g1 = self.form
@@ -37,9 +42,6 @@ class superelliptic_form:
         omega = self.form
         return superelliptic_form(C, constant*omega)
     
-    def __eq__(self, other):
-        return self.form == other.form
-    
     def cartier(self):
         '''Computes Cartier operator on the form. Idea: y^m = f(x) -> y^(p^r - 1) = f(x)^M, where r = ord_p(m),
         M = (p^r - 1)/m. Thus h(x)/y^j dx = h(x) f(x)^(M*j)/y^(p^r * j) dx. Thus C(h(x)/y^j dx) = 1/y^(p^(r-1)*j) C(h(x) f(x)^(M*j) dx).'''
@@ -52,7 +54,7 @@ class superelliptic_form:
         Fx = FractionField(Rx)
         FxRy.<y> = PolynomialRing(Fx)
         Fxy = FractionField(FxRy)
-        result = superelliptic_form(C, FxRy(0))
+        result = 0*C.dx
         mult_order = Integers(m)(p).multiplicative_order()
         M = Integer((p^(mult_order)-1)/m)
         
@@ -111,8 +113,8 @@ class superelliptic_form:
         Rx.<x> = PolynomialRing(F)
         for j in range(0, m):
             if self.jth_component(j) not in Rx:
-                return 0
-        return 1
+                return False
+        return True
     
     def is_regular_on_Uinfty(self):
         C = self.curve
@@ -128,8 +130,8 @@ class superelliptic_form:
             A = self.jth_component(j)
             d = degree_of_rational_fctn(A, F)
             if(-d*M + j*R -(M+1)<0):
-                return 0
-        return 1
+                return False
+        return True
 
     def expansion_at_infty(self, place = 0, prec=10):
         g = self.form
@@ -166,4 +168,38 @@ class superelliptic_form:
         Rxy.<x, y> = PolynomialRing(F, 2)
         Fxy = FractionField(Rxy)
         fct = reduction(C, Fxy(y^m*fct))
-        return superelliptic_form(C, fct/y^m)
\ No newline at end of file
+        return superelliptic_form(C, fct/y^m)
+    
+    def int(self):
+        '''Computes an "integral" of a form dg. Idea: y^m = f(x) -> y^(p^r - 1) = f(x)^M, where r = ord_p(m),
+        M = (p^r - 1)/m. Thus h(x)/y^j dx = h(x) f(x)^(M*j)/y^(p^r * j) dx. Thus int(h(x)/y^j dx) = 1/y^(p^(r-1)*j) int(h(x) f(x)^(M*j) dx).'''
+        C = self.curve
+        m = C.exponent
+        p = C.characteristic
+        f = C.polynomial
+        F = C.base_ring
+        Rx.<x> = PolynomialRing(F)
+        Fx = FractionField(Rx)
+        FxRy.<y> = PolynomialRing(Fx)
+        Fxy = FractionField(FxRy)
+        result = 0*C.x
+        mult_order = Integers(m)(p).multiplicative_order()
+        M = Integer((p^(mult_order)-1)/m)
+        
+        for j in range(0, m):
+            fct_j = self.jth_component(j)
+            h = Fx(fct_j*f^(M*j))
+            h_denom = h.denominator()
+            h *= (h_denom)^(p)
+            h = Rx(h)
+            j1 = (p^(mult_order)*j)%m
+            B = floor(p^(mult_order)*j/m)
+            result += superelliptic_function(C, h.integral()/(f^(B)*y^(j1)*h_denom^p))
+        return result   
+    
+    def inv_cartier(omega):
+        '''If omega is regular, return form eta such that Cartier(eta) = omega'''
+        omega_regular = omega.regular_form()
+        C = omega.curve
+        p = C.characteristic
+        return (omega_regular.dx)^p*C.x^(p-1)*C.dx + (omega_regular.dy)^p*C.y^(p-1)*C.y.diffn()
\ No newline at end of file
diff --git a/sage/superelliptic/tests/a_number_test.sage b/sage/superelliptic/tests/a_number_test.sage
new file mode 100644
index 0000000..556c370
--- /dev/null
+++ b/sage/superelliptic/tests/a_number_test.sage
@@ -0,0 +1,5 @@
+F = GF(67)
+P.<x>= PolynomialRing(F)
+X = HyperellipticCurve(x^7 + x^3 + x)
+C = superelliptic(x^7 + x^3 + x, 2)
+print(X.a_number() == C.a_number())
\ No newline at end of file
diff --git a/sage/superelliptic/tests/form_coordinates_test.sage b/sage/superelliptic/tests/form_coordinates_test.sage
new file mode 100644
index 0000000..ae6d1cf
--- /dev/null
+++ b/sage/superelliptic/tests/form_coordinates_test.sage
@@ -0,0 +1,12 @@
+p = 7
+m = 4
+F = GF(p)
+Rx.<x> = PolynomialRing(F)
+f = x^5 + x
+C = superelliptic(f, m)
+bbb = C.holomorphic_differentials_basis()
+v = [GF(p).random_element() for _ in range(C.genus())]
+aaa = 0*C.dx
+for i in range(C.genus()):
+    aaa += v[i]*bbb[i]
+print(vector(aaa.coordinates()) == vector(v))
\ No newline at end of file
diff --git a/sage/superelliptic/tests/p_rank_test.sage b/sage/superelliptic/tests/p_rank_test.sage
new file mode 100644
index 0000000..e85eb18
--- /dev/null
+++ b/sage/superelliptic/tests/p_rank_test.sage
@@ -0,0 +1,6 @@
+print("Nie działa!")
+F = GF(67)
+P.<x>= PolynomialRing(F)
+X = HyperellipticCurve(x^7 + x^3 + x)
+C = superelliptic(x^7 + x^3 + x, 2)
+print(X.p_rank() == C.p_rank())
\ No newline at end of file
diff --git a/sage/superelliptic/tests/pth_root_test.sage b/sage/superelliptic/tests/pth_root_test.sage
new file mode 100644
index 0000000..d135731
--- /dev/null
+++ b/sage/superelliptic/tests/pth_root_test.sage
@@ -0,0 +1,11 @@
+p = 3
+m = 4
+F = GF(p)
+Rx.<x> = PolynomialRing(F)
+f = x^5 + x
+C = superelliptic(f, m)
+g = (C.x)^5 * (C.y)^2 + 2*(C.x)^2 * (C.y)^3
+g = g^p
+print(g.pth_root()==(C.x)^5 * (C.y)^2 + 2*(C.x)^2 * (C.y)^3)
+g = C.x
+print(g.pth_root())
\ No newline at end of file
diff --git a/sage/superelliptic_drw/automorphism.sage b/sage/superelliptic_drw/automorphism.sage
index 47ddf25..bba812e 100644
--- a/sage/superelliptic_drw/automorphism.sage
+++ b/sage/superelliptic_drw/automorphism.sage
@@ -11,6 +11,9 @@ def autom(self):
     if isinstance(self, superelliptic_form):
         result = superelliptic_form(C, Fxy(self.form).subs({x:x+1, y:y}))
         return result
+    if isinstance(self, superelliptic_cech):
+        result = superelliptic_cech(C, autom(self.omega0), autom(self.f))
+        return result
     if isinstance(self, superelliptic_witt):
         result = superelliptic_witt(autom(self.t), autom(self.f))
         return result
diff --git a/sage/superelliptic_drw/de_rham_witt_lift.sage b/sage/superelliptic_drw/de_rham_witt_lift.sage
index b4d4e2d..22295a5 100644
--- a/sage/superelliptic_drw/de_rham_witt_lift.sage
+++ b/sage/superelliptic_drw/de_rham_witt_lift.sage
@@ -1,31 +1,50 @@
+def de_rham_witt_lift_form0(omega):
+    C = omega.curve
+    omega_regular = omega.regular_form() #Present omega0 in the form P dx + Q dy
+    #Now the obvious lift of omega0 = P dx + Q dy to de Rham-Witt is [P] d[x] + [Q] d[y]
+    return omega_regular.dx.teichmuller()*(C.x.teichmuller().diffn()) + omega_regular.dy.teichmuller()*(C.y.teichmuller().diffn())
+
+def de_rham_witt_lift_form8(omega):
+    C = omega.curve
+    g = C.genus()
+    omega_regular = second_patch(omega).regular_form()
+    omega_regular = (second_patch(omega_regular.dx), second_patch(omega_regular.dy))
+    u = (C.x)^(-1)
+    v = (C.y)/(C.x)^(g+1)
+    omega_lift = omega_regular[0].teichmuller()*(u.teichmuller().diffn()) + omega_regular[1].teichmuller()*(v.teichmuller().diffn())
+    return omega_lift
+    
 def de_rham_witt_lift(cech_class, prec = 50):
     C = cech_class.curve
     g = C.genus()
     omega0 = cech_class.omega0
     omega8 = cech_class.omega8
     fct = cech_class.f
-    omega0_regular = regular_form(omega0) #Present omega0 in the form P dx + Q dy
-    print('omega0_regular', omega0_regular)
-    omega0_lift = omega0_regular[0].teichmuller()*(C.x.teichmuller().diffn()) + omega0_regular[1].teichmuller()*(C.y.teichmuller().diffn())
-    #Now the obvious lift of omega0 = P dx + Q dy to de Rham-Witt is [P] d[x] + [Q] d[y]
-    print('omega8', omega8, 'second_patch(omega8)', second_patch(omega8))
-    omega8_regular = regular_form(second_patch(omega8)) # The same for omega8.
-    print('omega8_regular 1', omega8_regular)
-    omega8_regular = (second_patch(omega8_regular[0]), second_patch(omega8_regular[1]))
-    print('omega8_regular 2', omega8_regular)
-    u = (C.x)^(-1)
-    v = (C.y)/(C.x)^(g+1)
-    omega8_lift = omega8_regular[0].teichmuller()*(u.teichmuller().diffn()) + omega8_regular[1].teichmuller()*(v.teichmuller().diffn())
+    omega0_lift = de_rham_witt_lift_form0(omega0)
+    omega8_lift = de_rham_witt_lift_form8(omega8)
+    print('omega0_lift, omega8_lift', omega0_lift, omega8_lift)
     aux = omega0_lift - omega8_lift - fct.teichmuller().diffn() # now aux is of the form (V(smth) + dV(smth), V(smth))
-    return aux
+    #return aux
     if aux.h1.function != 0:
         raise ValueError('Something went wrong - aux is not of the form (V(smth) + dV(smth), V(smth)).')
     decom_aux_h2 = decomposition_g0_g8(aux.h2, prec=prec) #decompose dV(smth) in aux as smth regular on U0 - smth regular on U8.
     aux_h2 = decom_aux_h2[0]
     aux_f = decom_aux_h2[2]
     aux_omega0 = decomposition_omega0_omega8(aux.omega, prec=prec)[0]
-    result = superelliptic_drw_cech(omega0_lift - aux_h2.verschiebung().diffn() - aux_omega0.verschiebung(), fct.teichmuller() + aux_f.verschiebung())
-    return result.reduce()
+    result = superelliptic_drw_cech(omega0_lift - aux_omega0.verschiebung(), fct.teichmuller() + aux_h2.verschiebung() + aux_f.verschiebung())
+    compare = omega8_lift-decom_aux_h2[1].verschiebung().diffn() - decomposition_omega0_omega8(aux.omega, prec=prec)[1].verschiebung()
+    print("result.omega8 == compare", result.omega8 == compare)
+    print("result.omega8 - compare", result.omega8 - compare)
+    
+    #print('test:', omega0_lift - omega8_lift - fct.teichmuller().diffn() == decom_aux_h2[0].verschiebung().diffn() - decom_aux_h2[1].verschiebung().diffn() + decomposition_omega0_omega8(aux.omega, prec=prec)[0].verschiebung() - decomposition_omega0_omega8(aux.omega, prec=prec)[1].verschiebung())
+    #print('test 1:', omega0_lift - decom_aux_h2[0].verschiebung().diffn() - decomposition_omega0_omega8(aux.omega, prec=prec)[0].verschiebung() - fct.teichmuller().diffn() == omega8_lift - decom_aux_h2[1].verschiebung().diffn() - decomposition_omega0_omega8(aux.omega, prec=prec)[1].verschiebung())
+    #A = omega0_lift - decomposition_omega0_omega8(aux.omega, prec=prec)[0].verschiebung()
+    #B = decom_aux_h2[0].verschiebung() + fct.teichmuller()
+    #C = omega8_lift - decom_aux_h2[1].verschiebung().diffn() - decomposition_omega0_omega8(aux.omega, prec=prec)[1].verschiebung()
+    #print('test 2:', A - B.diffn() == C)
+    #print('test 3:', result.omega0 == A, result.f == B, result.omega8 == C)
+    #print(result.omega8, '\n \n', compare, '\n \n', aux_f, '\n \n')
+    return result#.reduce()
 
 def crystalline_cohomology_basis(self, prec = 50):
     result = []
diff --git a/sage/superelliptic_drw/decomposition_into_g0_g8.sage b/sage/superelliptic_drw/decomposition_into_g0_g8.sage
index ed85141..e83858c 100644
--- a/sage/superelliptic_drw/decomposition_into_g0_g8.sage
+++ b/sage/superelliptic_drw/decomposition_into_g0_g8.sage
@@ -3,7 +3,7 @@ def decomposition_g0_g8(fct, prec = 50):
     and f is combination of basis of H^1(X, OX). Output is (g0, g8, f).'''
     C = fct.curve
     g = C.genus()
-    coord = fct.coordinates()
+    coord = fct.coordinates(prec=prec)
     nontrivial_part = 0*C.x
     for i, a in enumerate(C.cohomology_of_structure_sheaf_basis()):
         nontrivial_part += coord[i]*a
@@ -13,8 +13,9 @@ def decomposition_g0_g8(fct, prec = 50):
     fct = Fxy(fct.function)
     num = fct.numerator()
     den = fct.denominator()
+    integral_part, num = num.quo_rem(den)
     aux_den = superelliptic_function(C, Rxy(den))
-    g0 = superelliptic_function(C, 0)
+    g0 = superelliptic_function(C, integral_part)
     g8 = superelliptic_function(C, 0)
     for monomial in num.monomials():
         aux = superelliptic_function(C, monomial)
@@ -31,7 +32,7 @@ def decomposition_omega0_omega8(omega, prec=50):
     F = C.base_ring
     delta = C.nb_of_pts_at_infty
     m = C.exponent
-    if sum(omega.residue(place = i, prec = 50) for i in range(delta)) != 0:
+    if sum(omega.residue(place = i, prec = prec) for i in range(delta)) != 0:
         raise ValueError(str(omega) + " has non zero residue!")
     Fxy, Rxy, x, y = C.fct_field
     Rx.<x> = PolynomialRing(F)
diff --git a/sage/superelliptic_drw/second_patch.sage b/sage/superelliptic_drw/second_patch.sage
index 7a85d09..40ab840 100644
--- a/sage/superelliptic_drw/second_patch.sage
+++ b/sage/superelliptic_drw/second_patch.sage
@@ -23,6 +23,13 @@ def second_patch(argument):
         fct1 = Fxy(fct.subs({x : 1/x, y : y/x^(g+1)}))
         fct1 *= -x^(-2)
         return superelliptic_form(C1, fct1)
+    if isinstance(argument, superelliptic_drw_form):
+        h1 = argument.h1
+        omega = argument.omega
+        h2 = argument.h2
+        C = h1.curve
+        return superelliptic_drw_form(-second_patch(h1)*(C.x)^(-2), second_patch(omega), second_patch(h2))
+    
     
 def lift_form_to_drw(omega):
     A, B = regular_form(omega)
diff --git a/sage/superelliptic_drw/superelliptic_drw_cech.sage b/sage/superelliptic_drw/superelliptic_drw_cech.sage
index ee7ab74..80ed151 100644
--- a/sage/superelliptic_drw/superelliptic_drw_cech.sage
+++ b/sage/superelliptic_drw/superelliptic_drw_cech.sage
@@ -56,6 +56,42 @@ class superelliptic_drw_cech:
         C = self.curve
         return superelliptic_cech(C, omega0.h1*C.dx, f.t)
     
+    def div_by_p(self):
+        '''Given a regular cocycle of the form (V(omega) + dV(h), [f] + V(t), ...), where [f] = 0 in H^1(X, OX),
+        find de Rham cocycle (xi0, f, xi8) such that (V(omega) + dV(h), [f] + V(t), ...) = p*(xi0, f, xi8).'''
+        C = self.curve
+        aux = self
+        Fxy, Rxy, x, y = C.fct_field
+        aux_f_t_0 = decomposition_g0_g8(aux.f.t, prec=50)[0]
+        aux.f.t = 0*C.x
+        aux.omega0 -= aux_f_t_0.teichmuller().diffn()
+        aux.omega8 = aux.omega0 - aux.f.diffn()
+        #
+        omega = aux.omega0.omega
+        omega1 = omega.cartier().cartier()
+        omega1 = omega1.inv_cartier().inv_cartier()
+        fct = (omega.cartier() - omega1.cartier()).int()
+        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())
+        else:
+            raise ValueError("aux.omega0.h2.function not in Rxy:", aux.omega0.h2.function)
+        
     def coordinates(self, basis = 0):
         C = self.curve
         g = C.genus()
@@ -67,12 +103,7 @@ class superelliptic_drw_cech:
         aux = self
         for i, a in enumerate(basis):
             aux -= coord_lifted[i]*a
-        print('aux before reduce', aux)
-        #aux = aux.reduce() # Now aux = p*cech class.
-        # Now aux should be of the form (V(smth), V(smth), V(smth))
-        print('aux V(smth)', aux)
-        aux_divided_by_p = superelliptic_cech(C, aux.omega0.omega.cartier(), aux.f.f.pth_root())
-        print('aux.omega0.omega.cartier()', aux.omega0.omega.cartier())
+        aux_divided_by_p = aux.div_by_p()
         coord_aux_divided_by_p = aux_divided_by_p.coordinates()
         coord_aux_divided_by_p = [ZZ(a) for a in coord_aux_divided_by_p]
         coordinates = [ (coord_lifted[i] + p*coord_aux_divided_by_p[i])%p^2 for i in range(2*g)]
diff --git a/sage/superelliptic_drw/superelliptic_drw_form.sage b/sage/superelliptic_drw/superelliptic_drw_form.sage
index c01b226..010f36f 100644
--- a/sage/superelliptic_drw/superelliptic_drw_form.sage
+++ b/sage/superelliptic_drw/superelliptic_drw_form.sage
@@ -17,7 +17,7 @@ class superelliptic_drw_form:
             H = (self.h2 - other.h2).pth_root()
         except:
             return False
-        eq2 = ((self.omega - other.omega).cartier() - H.diffn()) == 0*self.curve.dx
+        eq2 = ((other.omega - self.omega).cartier() - H.diffn()) == 0*self.curve.dx
         if eq1 and eq2:
             return True
         return False
@@ -30,7 +30,7 @@ class superelliptic_drw_form:
         result = ""
         if h1.function != 0:
             result += "[" + str(h1) + "] d[x]"
-        if h1.function !=0 and omega.form != 0:
+        if (h1.function !=0 and omega.form != 0) or (h2.function !=0 and omega.form != 0):
             result += " + "
         if omega.form != 0:
             result += "V(" + str(omega) + ")"
diff --git a/sage/superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage b/sage/superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage
new file mode 100644
index 0000000..9963f4a
--- /dev/null
+++ b/sage/superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage
@@ -0,0 +1,11 @@
+p = 3
+m = 2
+F = GF(p)
+Rx.<x> = PolynomialRing(F)
+f = x^3 - x
+C = superelliptic(f, m)
+Rxy.<x, y> = PolynomialRing(F, 2)
+omega = (((2*C.x^18 + 2*C.x^16 + 2*C.x^14 + 2*C.x^10 + 2*C.x^8 + 2*C.x^4 + 2*C.x^2 + 2*C.one)/(C.x^13 + C.x^11 + C.x^9))*C.y) * C.dx
+print(decomposition_omega0_omega8(aux.omega)[0] - decomposition_omega0_omega8(aux.omega)[1] == omega and decomposition_omega0_omega8(aux.omega)[0].is_regular_on_U0() and decomposition_omega0_omega8(aux.omega)[1].is_regular_on_Uinfty())
+h = ((C.x^10 + C.x^8 + C.x^6 + 2*C.x^4 + 2*C.x^2 + 2*C.one)/C.x^6)*C.y
+print(decomposition_g0_g8(h)[0] - decomposition_g0_g8(h)[1] + decomposition_g0_g8(h)[2] == h and decomposition_g0_g8(h)[0].function in Rxy and decomposition_g0_g8(h)[1].expansion_at_infty().valuation() >= 0)
\ No newline at end of file
diff --git a/sage/superelliptic_drw/tests/superelliptic_drw_tests.sage b/sage/superelliptic_drw/tests/superelliptic_drw_tests.sage
new file mode 100644
index 0000000..f514cfd
--- /dev/null
+++ b/sage/superelliptic_drw/tests/superelliptic_drw_tests.sage
@@ -0,0 +1,10 @@
+p = 3
+m = 2
+F = GF(p)
+Rx.<x> = PolynomialRing(F)
+f = x^3 - x
+C = superelliptic(f, m)
+print(auxilliary_derivative((C.x^3 - C.x).teichmuller()))
+print('Result should be: [2] d[x] + V((x^8) dx) + dV([2*x^7 + x^5])')
+print(2*(C.y).teichmuller() * (C.y).teichmuller().diffn() == (C.x^3 - C.x).teichmuller().diffn())
+print(C.y.teichmuller().diffn().frobenius() == (C.y)^2 * C.y.diffn()) #F(d[y]) = y^2*dy
\ No newline at end of file
diff --git a/sage/tests.sage b/sage/tests.sage
index 8405b77..e5d7ba2 100644
--- a/sage/tests.sage
+++ b/sage/tests.sage
@@ -24,4 +24,6 @@ load('superelliptic/tests/a_number_test.sage')
 #print("diffn_test:")
 #load('as_covers/tests/diffn_test.sage')
 #print("Cartier test:")
-#load('as_covers/tests/cartier_test.sage')
\ No newline at end of file
+#load('as_covers/tests/cartier_test.sage')
+#print("Decomposition into g0, g8/ omega0, omega8 test:")
+#load('superelliptic_drw/tests/decomposition_into_g0_g8_tests.sage')
\ No newline at end of file