From e1a000f7a5a01023e4a2bcfafa8bcc89762059f7 Mon Sep 17 00:00:00 2001
From: jgarnek <jgarnek@amu.edu.pl>
Date: Fri, 24 Feb 2023 16:57:49 +0000
Subject: [PATCH] lift kocykli do drw zrobiony z drobnymi bledami

---
 sage/.run.term-0.term                         | 436 +++++++++++++++++-
 sage/drafty/superelliptic_drw.sage            |  80 ++++
 .../decomposition_into_g0_g8.sage             |   7 +-
 sage/superelliptic/superelliptic_class.sage   |   4 +-
 .../superelliptic_function_class.sage         |   2 +-
 5 files changed, 524 insertions(+), 5 deletions(-)

diff --git a/sage/.run.term-0.term b/sage/.run.term-0.term
index ef85aec..f16ccdb 100644
--- a/sage/.run.term-0.term
+++ b/sage/.run.term-0.term
@@ -39865,4 +39865,438 @@ Untracked files:
 
 no changes added to commit (use "git add" and/or "git commit -a")
 ]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add sage/drqaafty/second_patch.sage 
-]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u
\ No newline at end of file
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m ""r"o"z"n"i"c"z"k"o"w"a"n"i"e" "f"o"r"m" "d"r"w" "z"r"o"b"i"o"n"e" "("?")"
+[master 22872e2] rozniczkowanie form drw zrobione (?)
+ 6 files changed, 1514 insertions(+), 117 deletions(-)
+ create mode 100644 sage/drafty/second_patch.sage
+ rewrite sage/drafty/superelliptic_drw.sage (68%)
+]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: 19, done.
+Counting objects:   5% (1/19)
Counting objects:  10% (2/19)
Counting objects:  15% (3/19)
Counting objects:  21% (4/19)
Counting objects:  26% (5/19)
Counting objects:  31% (6/19)
Counting objects:  36% (7/19)
Counting objects:  42% (8/19)
Counting objects:  47% (9/19)
Counting objects:  52% (10/19)
Counting objects:  57% (11/19)
Counting objects:  63% (12/19)
Counting objects:  68% (13/19)
Counting objects:  73% (14/19)
Counting objects:  78% (15/19)
Counting objects:  84% (16/19)
Counting objects:  89% (17/19)
Counting objects:  94% (18/19)
Counting objects: 100% (19/19)
Counting objects: 100% (19/19), done.
+Delta compression using up to 4 threads
+Compressing objects:   9% (1/11)
Compressing objects:  18% (2/11)
Compressing objects:  27% (3/11)
Compressing objects:  36% (4/11)
Compressing objects:  45% (5/11)
Compressing objects:  54% (6/11)
Compressing objects:  63% (7/11)
Compressing objects:  72% (8/11)
Compressing objects:  81% (9/11)
Compressing objects:  90% (10/11)
Compressing objects: 100% (11/11)
Compressing objects: 100% (11/11), done.
+Writing objects:   9% (1/11)
Writing objects:  18% (2/11)
Writing objects:  27% (3/11)
Writing objects:  36% (4/11)
Writing objects:  45% (5/11)
Writing objects:  54% (6/11)
Writing objects:  63% (7/11)
Writing objects:  72% (8/11)
Writing objects:  81% (9/11)
Writing objects:  90% (10/11)
Writing objects: 100% (11/11)
Writing objects: 100% (11/11), 18.02 KiB | 271.00 KiB/s, done.
+Total 11 (delta 6), reused 0 (delta 0)
+remote: . Processing 1 references
+remote: Processed 1 references in total
+To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
+   856d742..22872e2  master -> master
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 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[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7ldx == C.dx[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_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[?7laC.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l=C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l C.de_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.diffn()[?7h[?12l[?25h[?25l[?7lsage: a.diffn()

+ a.coordinates  a.frobenius    a.omega8      

+ a.curve        a.is_cocycle   a.verschiebung

+ a.f            a.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[?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[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lx^3 - C.x[?7h[?12l[?25h[?25l[?7l.teichmuller()*C.y.teichmuller()[?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: C.x.verschiebung()

+[?7h[?12l[?25h[?2004l[?7hV(x)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7lC.x.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[?7ldx.verschiebung()[?7h[?12l[?25h[?25l[?7lsage: C.dx.verschiebung()

+[?7h[?12l[?25h[?2004l[?7h<repr(<__main__.superelliptic_drw_form at 0x7f09bae4bf10>) failed: AttributeError: 'superelliptic_form' object has no attribute 'function'>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.verschiebung()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ltichmuller()*C.y.teichmuller()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7ln[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.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[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7lx.verschiebung()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7lsage: C.dx.verschiebung()

+[?7h[?12l[?25h[?2004l[?7hV(1 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[?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 [9] 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>:6 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>:7
+    for a in
+             ^
+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[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.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[?7ldiffn(C.y.teichmuller())[?7h[?12l[?25h[?25l[?7lenominator(((C.y)^(-1*C.dx).form) == y[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: decomposition

+ decomposition              

+ decomposition_g0_g8        

+ decomposition_omega0_omega8

+

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

+ decomposition              

+

+

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

+ decomposition              

+ decomposition_g0_g8        [?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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(C.y/C.x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [11], in <cell line: 1>()
+----> 1 decomposition_g0_g8(C.y/C.x)
+
+File <string>:6, in decomposition_g0_g8(fct)
+
+File <string>:101, in coordinates(self, basis, basis_holo, prec)
+
+AttributeError: 'superelliptic' object has no attribute 'basis_of_cohomology'
+[?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[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(C.y/C.x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [13], in <cell line: 1>()
+----> 1 decomposition_g0_g8(C.y/C.x)
+
+File <string>:8, in decomposition_g0_g8(fct)
+
+NameError: name 'enumeratate' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(C.y/C.x)

+[?7h[?12l[?25h[?2004l[?7h(0, 0, 1/x*y)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.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[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

+[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?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[?7lxC.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7liC.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l=C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift_form_to_drw(omega)[?7h[?12l[?25h[?25l[?7lsage: lift_form_to_drw(omega)

+  li                                lie                               lift_form_to_drw                  line                              linear_relation                   list                               

+  libgap                            lie_algebras                      lift_to_sl2z                      line2d                            linear_representation_polynomials list_plot                          

+  libgiac                           lie_conformal_algebras            lim                               line3d                            linear_transformation             list_plot3d                       >

+  license                           lift                              limit                             linear_program                    lisp                              list_plot_loglog                   

+ [?7h[?12l[?25h[?25l[?7lft_form_to_drw(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[?7lx)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: lift_form_to_drw(xi)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [18], in <cell line: 1>()
+----> 1 lift_form_to_drw(xi)
+
+File <string>:29, in lift_form_to_drw(omega)
+
+File <string>:10, in regular_form(omega)
+
+AttributeError: 'superelliptic_cech' object has no attribute 'form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(C.y/C.x)[?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[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [19], in <cell line: 1>()
+----> 1 de_rham_witt_lift(xi)
+
+File <string>:270, in de_rham_witt_lift(cech_class)
+
+File <string>:88, in diffn(self)
+
+TypeError: unsupported operand type(s) for -: 'superelliptic_drw_form' and 'superelliptic_drw_form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_form_to_drw(xi)[?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[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [21], in <cell line: 1>()
+----> 1 de_rham_witt_lift(xi)
+
+File <string>:269, in de_rham_witt_lift(cech_class)
+
+File <string>:5, in regular_form(omega)
+
+AttributeError: 'NoneType' object has no attribute 'curve'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi

+[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx)
+[?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[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi[?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[?7lxi[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7llift_form_odrw(xi)[?7h[?12l[?25h[?25l[?7lx = C.derham_bass()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [25], in <cell line: 1>()
+----> 1 de_rham_witt_lift(xi)
+
+File <string>:275, in de_rham_witt_lift(cech_class)
+
+TypeError: unsupported operand type(s) for -: 'tuple' and 'tuple'
+[?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[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [28], in <cell line: 1>()
+----> 1 de_rham_witt_lift(xi)
+
+File <string>:276, in de_rham_witt_lift(cech_class)
+
+AttributeError: 'superelliptic_function' object has no attribute 'decomposition_g0_g8'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [31], in <cell line: 1>()
+----> 1 de_rham_witt_lift(xi)
+
+File <string>:278, in de_rham_witt_lift(cech_class)
+
+AttributeError: 'superelliptic_form' object has no attribute 'decomposition_omega0_omega8'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
+[?7h<__main__.superelliptic_drw_cech object at 0x7f09ba3d4f40>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
+[?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]), [0], [0])
+<repr(<__main__.superelliptic_drw_cech at 0x7f09bad3fbe0>) failed: TypeError: __repr__ returned non-string (type NoneType)>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
+[?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]), [0], [0])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l[?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(xi)[?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

+I-search:[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi).omega0

+ [?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi).omega0

+[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
+[?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[?7lde_rham_witt_lift(xi).omega0[?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: de_rham_witt_lift(xi).omega0.omega

+[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
+[?7h((x^7 - x^3 - x)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi).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[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lade_rham_wit_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7lsage: a = de_rham_witt_lift(xi).omega0.omega

+[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lsage: a.diffn()

+ a.cartier               a.expansion_at_infty    a.is_regular_on_Uinfty  a.verschiebung         

+ a.coordinates           a.form                  a.jth_component                                

+ a.curve                 a.is_regular_on_U0      a.serre_duality_pairing                        

+

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

+ a.cartier              

+

+

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

+ a.cartier              

+ a.coordinates          [?7h[?12l[?25h[?25l[?7lurve

+

+ a.coordinates          

+ a.curve                [?7h[?12l[?25h[?25l[?7lis_rgular_on_U0

+

+

+ a.curve                 a.is_regular_on_U0     [?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^7 - x^3 - x)/(x^2*y - y)) dx>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+

+

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

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

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

+[?7h[?12l[?25h[?2004l[?7h((x^7 - x^3 - x)/(x^2*y - y)) dx
+[?2004h[?25l[?7lsage: [?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[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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(xi).omega0.omega[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_g8(Cy/C.x)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_g8(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_g0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lga0_omega8[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(a)

+[?7h[?12l[?25h[?2004l[?7h(((x^5 + x^3)/y) dx, ((-x)/(x^2*y - y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(a)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7li)[?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[?7lsage: decomposition_omega0_omega8(xi.omega0)

+[?7h[?12l[?25h[?2004l[?7h(0 dx, (1/y) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(xi.omega0)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(a)

+[?7h[?12l[?25h[?2004l[?7h(((x^5 + x^3)/y) dx, ((-x)/(x^2*y - y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(a)[?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[?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[?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: decomposition_omega0_omega8(a)[1].expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h2*t^2 + t^6 + 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[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(a)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_witt_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7lrham_witt_lift(xi).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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
+((-x^5 - x^3)/y) dx
+[?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]), [0], [0])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
+[(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])
+[?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]), [0], [0])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
+0
+[?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]), [0], [0])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
+[1]
+[?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]), [0], [0])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
+[1]
+[?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]), [0], [(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[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?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(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
+aux V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
+[1]
+[?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]), [0], [(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.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.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[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
+aux V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
+[?7hV(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lade_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7lude_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7lxde_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
+aux V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_omega0_omega8(a)[1].expansion_at_infty()[?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[?7lg0_8(C.y/C.x)[?7h[?12l[?25h[?25l[?7l0_g8(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[?7la)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(aux)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [73], in <cell line: 1>()
+----> 1 decomposition_g0_g8(aux)
+
+File <string>:6, in decomposition_g0_g8(fct)
+
+AttributeError: 'superelliptic_drw_form' object has no attribute 'coordinates'
+[?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[?7l.)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(aux.h1)

+[?7h[?12l[?25h[?2004l[?7h(0, 0, 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?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: aux.h1.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.h1.coordinates()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: aux.h1

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.h1[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux

+[?7h[?12l[?25h[?2004l[?7hV(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7l.h1[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: aux.h2

+[?7h[?12l[?25h[?2004l[?7h((x^4 + x^2 + 1)/x^3)*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.h2[?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: aux.h2.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[2]
+[?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[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l[];[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[0]; de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l0
+(1/y) dx ((-1)/y) dx (0, 1)
+aux V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
+[1]
+[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^3 + 2*x)/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^4 + x^2 + 1)/(x^3 + 2*x))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7laux.h2.coordinates()[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]; de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l1]; de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l0
+(x/y) dx ((-1)/(x*y)) dx None
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [81], in <cell line: 1>()
+----> 1 load('init.sage'); xi = C.de_rham_basis()[Integer(1)]; de_rham_witt_lift(xi)
+
+File <string>:304, in de_rham_witt_lift(cech_class)
+
+TypeError: 'NoneType' object is not subscriptable
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l0
+(x/y) dx ((-1)/(x*y)) dx None
+None
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [82], in <cell line: 1>()
+----> 1 load('init.sage'); xi = C.de_rham_basis()[Integer(1)]; de_rham_witt_lift(xi)
+
+File <string>:305, in de_rham_witt_lift(cech_class)
+
+TypeError: 'NoneType' object is not subscriptable
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l0
+omega8_re None
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [83], in <cell line: 1>()
+----> 1 load('init.sage'); xi = C.de_rham_basis()[Integer(1)]; de_rham_witt_lift(xi)
+
+File <string>:304, in de_rham_witt_lift(cech_class)
+
+TypeError: 'NoneType' object is not subscriptable
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7laux.h2.coordinates()[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l0
+omega8_re None
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [84], in <cell line: 1>()
+----> 1 load('init.sage'); xi = C.de_rham_basis()[Integer(1)]; de_rham_witt_lift(xi)
+
+File <string>:304, in de_rham_witt_lift(cech_class)
+
+TypeError: 'NoneType' object is not subscriptable
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l0
+second_patch(omega0) ((-1)/(x*y)) dx
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [85], in <cell line: 1>()
+----> 1 load('init.sage'); xi = C.de_rham_basis()[Integer(1)]; de_rham_witt_lift(xi)
+
+File <string>:304, in de_rham_witt_lift(cech_class)
+
+TypeError: 'NoneType' object is not subscriptable
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?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[?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[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1].omega8; second_patch(xi)

+[?7h[?12l[?25h[?2004l0
+[?7h(x/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1].omega8; second_patch(xi)[?7h[?12l[?25h[?25l[?7l; d_rham_witt_lif(xi)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7laux.h2.coordinates()[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l0
+second_patch(omega0) ((-1)/(x*y)) dx
+g0, g8 ((-x^8 + x^6)/y) dx ((-1)/(x^2*y - y)) dx
+[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^10 + x^8 + x^6 - x^4)/(x^2*y - y)) dx) + dV([(2*x^6/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((x^10 + x^8 + x^6 + x^4 - x^2 - 1)/(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[?7ldecomposition_g0_g8(aux.h1)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lrham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004lsecond_patch(omega0) ((-1)/(x*y)) dx
+g0, g8 ((-x^8 + x^6)/y) dx ((-1)/(x^2*y - y)) dx
+[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^10 + x^8 + x^6 - x^4)/(x^2*y - y)) dx) + dV([(2*x^6/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((x^10 + x^8 + x^6 + x^4 - x^2 - 1)/(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[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l.omga8; second_pach(xi)[?7h[?12l[?25h[?25l[?7l; d_rham_witt_lif(xi)[?7h[?12l[?25h[?25l[?7l.omga8; second_pach(xi)[?7h[?12l[?25h[?25l[?7l; d_rham_witt_lif(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lade_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.h2.coordinates()[?7h[?12l[?25h[?25l[?7l+a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a+a+a

+[?7h[?12l[?25h[?2004l[?7h(V((x^4/(x^2*y - y)) dx), V(((2*x^2 + 1)/x^2)*y), V((x^4/(x^2*y - y)) dx) + dV([((x^2 + 2)/x^2)*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la+a+a[?7h[?12l[?25h[?25l[?7llod('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn().frobenius() == C.y^2*C.y.diffn()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?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: (a+a+a).reduce()

+[?7h[?12l[?25h[?2004l[?7h(dV([y]), [0], dV([y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h
\ No newline at end of file
diff --git a/sage/drafty/superelliptic_drw.sage b/sage/drafty/superelliptic_drw.sage
index ed4e80b..c0aed74 100644
--- a/sage/drafty/superelliptic_drw.sage
+++ b/sage/drafty/superelliptic_drw.sage
@@ -214,6 +214,9 @@ class superelliptic_drw_form:
         omega = self.omega
         return superelliptic_drw_form(-h1, -omega, -h2)
     
+    def __sub__(self, other):
+        return self + (-other)
+    
     def __add__(self, other):
         C = self.curve
         h1 = self.h1
@@ -243,3 +246,80 @@ def mult_by_p(omega):
     result = superelliptic_drw_form(C, 0*C.dx, omega, 0*C.x)
     return result
 
+def verschiebung(elt):
+    C = elt.curve
+    if isinstance(elt, superelliptic_function):
+        return superelliptic_witt(0*C.x, elt)
+
+    if isinstance(elt, superelliptic_form):
+        return superelliptic_drw_form(0*C.x, elt, 0*C.x)
+
+superelliptic_form.verschiebung = verschiebung
+superelliptic_function.verschiebung = verschiebung
+
+
+class superelliptic_drw_cech:
+    def __init__(self, omega0, f):
+        self.curve = omega0.curve
+        self.omega0 = omega0
+        self.omega8 = omega0 - f.diffn()
+        self.f = f
+        
+        
+    def reduce(self):
+        C = self.curve
+        fct = self.f
+        f_first_comp = fct.t
+        f_second_comp = fct.f
+        decomp_first_comp = decomposition_g0_g8(f_first_comp)
+        decomp_second_comp = decomposition_g0_g8(f_second_comp)
+        new = superelliptic_drw_cech(0*C.dx.verschiebung(), 0*C.x.verschiebung())
+        new.omega0 -= decomposition_g0_g8(f_first_comp)[0].teichmuller().diffn()
+        new.omega0 -= decomposition_g0_g8(f_second_comp)[0].verschiebung().diffn()
+        new.f = decomposition_g0_g8(f_first_comp)[2].teichmuller() + decomposition_g0_g8(f_second_comp)[2].verschiebung()
+        new.omega8 = new.omega0 - new.f.diffn()
+        return new
+        
+    def __repr__(self):
+        return("(" + str(self.omega0) + ", "+ str(self.f) + ", " + str(self.omega8) + ")")
+
+    def __add__(self, other):
+        C = self.curve
+        omega0 = self.omega0
+        f = self.f
+        omega0_1 = other.omega0
+        f_1 = other.f
+        return superelliptic_drw_cech(omega0 + omega0_1, f + f_1)
+    
+    def __sub__(self, other):
+        C = self.curve
+        omega0 = self.omega0
+        f = self.f
+        omega0_1 = other.omega0
+        f_1 = other.f
+        return superelliptic_drw_cech(omega0 - omega0_1, f - f_1)
+        
+    def __neg__(self):
+        C = self.curve
+        omega0 = self.omega0
+        f = self.f
+        return superelliptic_drw_cech(-omega0, -f)
+
+def de_rham_witt_lift(cech_class):
+    C = cech_class.curve
+    g = C.genus()
+    omega0 = cech_class.omega0
+    omega8 = cech_class.omega8
+    fct = cech_class.f
+    omega0_regular = regular_form(omega0)
+    omega0_lift = omega0_regular[0].teichmuller()*(C.x.teichmuller().diffn()) + omega0_regular[1].teichmuller()*(C.y.teichmuller().diffn())
+    omega8_regular = regular_form(second_patch(omega8))
+    omega8_regular = (second_patch(omega8_regular[0]), second_patch(omega8_regular[1]))
+    u = (C.x)^(-1)
+    v = (C.y)/(C.x)^(g+1)
+    omega8_lift = omega0_regular[0].teichmuller()*(u.teichmuller().diffn()) + omega0_regular[1].teichmuller()*(v.teichmuller().diffn())
+    aux = omega0_lift - omega8_lift - fct.teichmuller().diffn()
+    aux_h2 = decomposition_g0_g8(aux.h2)[0]
+    aux_f = decomposition_g0_g8(aux.h2)[2] #do napisania - komponent od kohomologii
+    aux_omega0 = decomposition_omega0_omega8(aux.omega)[0]
+    return superelliptic_drw_cech(omega0_lift + aux_h2.verschiebung().diffn() + aux_omega0.verschiebung(), fct.teichmuller() + aux_f.verschiebung())
\ No newline at end of file
diff --git a/sage/superelliptic/decomposition_into_g0_g8.sage b/sage/superelliptic/decomposition_into_g0_g8.sage
index 845540d..f4b99ee 100644
--- a/sage/superelliptic/decomposition_into_g0_g8.sage
+++ b/sage/superelliptic/decomposition_into_g0_g8.sage
@@ -2,6 +2,11 @@ def decomposition_g0_g8(fct):
     '''Writes fct as a difference g0 - g8, with g0 regular on the affine patch and g8 at the points in infinity.'''
     C = fct.curve
     g = C.genus()
+    coord = fct.coordinates()
+    nontrivial_part = 0*C.x
+    for i, a in enumerate(C.cohomology_of_structure_sheaf_basis()):
+        nontrivial_part += coord[i]*a
+    fct -= nontrivial_part
     if fct.coordinates() != g*[0]:
         raise ValueError("The given function cannot be written as g0 - g8.")
     
@@ -18,7 +23,7 @@ def decomposition_g0_g8(fct):
             g8 += num.monomial_coefficient(monomial)*aux/aux_den
         else:
             g0 += num.monomial_coefficient(monomial)*aux/aux_den
-    return (g0, g8)
+    return (g0, g8, nontrivial_part)
     
 def decomposition_omega0_omega8(omega, prec=50):
     '''Writes omega as a difference omega0 - omega8, with omega0 regular on the affine patch and omega8 at the points in infinity.'''
diff --git a/sage/superelliptic/superelliptic_class.sage b/sage/superelliptic/superelliptic_class.sage
index 7681157..b2cb919 100644
--- a/sage/superelliptic/superelliptic_class.sage
+++ b/sage/superelliptic/superelliptic_class.sage
@@ -159,7 +159,7 @@ class superelliptic:
         F = self.base_ring
         p = F.characteristic()
         M = matrix(F, g, g)
-        for i, f in enumerate(self.basis_of_cohomology()):
+        for i, f in enumerate(self.cohomology_of_structure_sheaf_basis()):
             M[i, :] = vector((f^p).coordinates(prec=prec))
         M = M.transpose()
         return M
@@ -184,7 +184,7 @@ class superelliptic:
         p = self.characteristic
         return flag(Fr, V, p, test)
     
-    def basis_of_cohomology(self):
+    def cohomology_of_structure_sheaf_basis(self):
         '''Basis of cohomology of structure sheaf H1(X, OX).'''
         m = self.exponent
         f = self.polynomial
diff --git a/sage/superelliptic/superelliptic_function_class.sage b/sage/superelliptic/superelliptic_function_class.sage
index c83aee1..2771bd5 100644
--- a/sage/superelliptic/superelliptic_function_class.sage
+++ b/sage/superelliptic/superelliptic_function_class.sage
@@ -97,7 +97,7 @@ class superelliptic_function:
         '''Find coordinates in H1(X, OX) in given basis basis with dual basis basis_holo.'''
         C = self.curve
         if basis == 0:
-            basis = C.basis_of_cohomology()
+            basis = C.cohomology_of_structure_sheaf_basis()
         if basis_holo == 0:
             basis_holo = C.holomorphic_differentials_basis()
         g = C.genus()