From 7e8546b2c366fe016334142d63b124d38430197e Mon Sep 17 00:00:00 2001
From: jgarnek <jgarnek@amu.edu.pl>
Date: Mon, 27 Feb 2023 11:51:16 +0000
Subject: [PATCH] poprawiony rozklad na omega0 - omega8

---
 sage/.run.term-0.term                         | 2466 ++++++++++++++++-
 sage/drafty/draft.sage                        |    7 +-
 sage/drafty/superelliptic_drw.sage            |   59 +-
 .../decomposition_into_g0_g8.sage             |   33 +-
 .../superelliptic_cech_class.sage             |    2 +-
 .../superelliptic_form_class.sage             |   15 +-
 6 files changed, 2553 insertions(+), 29 deletions(-)

diff --git a/sage/.run.term-0.term b/sage/.run.term-0.term
index d311ba7..11e32c3 100644
--- a/sage/.run.term-0.term
+++ b/sage/.run.term-0.term
@@ -40596,4 +40596,2468 @@ omega8_regular (0, 2/x)
 [?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a.omega0 - mult_by_p(C.x*C.y.diffn())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7lsage: a

 [?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([(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[?7l[?7h[?12l[?25h[?25l[?7lquo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1)[?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
\ No newline at end of file
+[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd ..
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -ucd ..sagegit pushcommit -m "lift kocykli do drw zrobiony z drobnymi bledami"""""""""""""""""""" "c"h"y"b"a" "o"k"
+[master 8719e64] lift kocykli do drw zrobiony chyba ok
+ 2 files changed, 305 insertions(+), 3 deletions(-)
+]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: 11, done.
+Counting objects:   9% (1/11)
Counting objects:  18% (2/11)
Counting objects:  27% (3/11)
Counting objects:  36% (4/11)
Counting objects:  45% (5/11)
Counting objects:  54% (6/11)
Counting objects:  63% (7/11)
Counting objects:  72% (8/11)
Counting objects:  81% (9/11)
Counting objects:  90% (10/11)
Counting objects: 100% (11/11)
Counting objects: 100% (11/11), done.
+Delta compression using up to 4 threads
+Compressing objects:  16% (1/6)
Compressing objects:  33% (2/6)
Compressing objects:  50% (3/6)
Compressing objects:  66% (4/6)
Compressing objects:  83% (5/6)
Compressing objects: 100% (6/6)
Compressing objects: 100% (6/6), done.
+Writing objects:  16% (1/6)
Writing objects:  33% (2/6)
Writing objects:  50% (3/6)
Writing objects:  66% (4/6)
Writing objects:  83% (5/6)
Writing objects: 100% (6/6)
Writing objects: 100% (6/6), 8.38 KiB | 158.00 KiB/s, done.
+Total 6 (delta 5), reused 0 (delta 0)
+remote: . Processing 1 references
+remote: Processed 1 references in total
+To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
+   e1a000f..8719e64  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'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('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[?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'); xi = C.de_rham_basis()[Integer(1)]; a = de_rham_witt_lift(xi)
+
+  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>:26 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>:322
+    coord_lifted =
+                   ^
+SyntaxError: invalid syntax
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('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[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.reduce()[?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[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinted()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [3], in <cell line: 1>()
+----> 1 xi.coordinted()
+
+AttributeError: 'superelliptic_cech' object has no attribute 'coordinted'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinted()[?7h[?12l[?25h[?25l[?7l)[?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[?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[?7lsage: xi.coordinates()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [4], in <cell line: 1>()
+----> 1 xi.coordinates()
+
+File <string>:75, in coordinates(self)
+
+File <string>:113, in degree_of_rational_fctn(f, F)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554, in 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):
+--> 554     raise TypeError("base_ring {!r} must be a ring".format(base_ring))
+    556 n = -1  # Unknown number of variables
+    557 names = None  # Unknown variable names
+
+TypeError: base_ring 3 must be a ring
+[?2004h[?25l[?7lsage: [?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/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?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/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?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: xi[0].coordinates()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [7], in <cell line: 1>()
+----> 1 xi[Integer(0)].coordinates()
+
+TypeError: 'superelliptic_cech' object is not subscriptable
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[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[0.cordinates()[?7h[?12l[?25h[?25l[?7l.cordinates()[?7h[?12l[?25h[?25l[?7l.cordinates()[?7h[?12l[?25h[?25l[?7l.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[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.coordinates()[?7h[?12l[?25h[?25l[?7lted()[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; a = 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[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]; a = de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l0]; a = de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[0]; a = de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi[0].coordinates()[?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[?7lxi[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[0].coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.coordinates()[?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: xi.omega0

+[?7h[?12l[?25h[?2004l[?7h(1/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega0[?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.omega0.coordinates()

+[?7h[?12l[?25h[?2004l[?7h[1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega0.coordinates()[?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[?7h(1, 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lor a in range(25):[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: for xi in 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[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l

+....: [?7h[?12l[?25h[?25l[?7lprint('b')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?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[?7la[?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[?7l(())[?7h[?12l[?25h[?25l[?7l()

+....: [?7h[?12l[?25h[?25l[?7lsage: for xi in C.de_rham_basis():

+....:     print(xi.coordinates())

+....: 

+[?7h[?12l[?25h[?2004l(1, 0)
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [13], in <cell line: 1>()
+      1 for xi in C.de_rham_basis():
+----> 2     print(xi.coordinates())
+
+File <string>:75, in coordinates(self)
+
+File <string>:113, in degree_of_rational_fctn(f, F)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554, in 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):
+--> 554     raise TypeError("base_ring {!r} must be a ring".format(base_ring))
+    556 n = -1  # Unknown number of variables
+    557 names = None  # Unknown variable names
+
+TypeError: base_ring 3 must be a ring
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); xi = C.de_rham_basis()[0]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[0]; a = de_rham_witt_lift(xi)

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; a = 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[?7l];[?7h[?12l[?25h[?25l[?7l1];[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[] a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l 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[?7lload('init.sage'); xi = C.de_rham_basis()[1]; a = 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[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1];

+[?7h[?12l[?25h[?2004l0
+[?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[?7lc[?7h[?12l[?25h[?25l[?7loordinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

+[?7h[?12l[?25h[?2004lf, F 2/x 3
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [17], in <cell line: 1>()
+----> 1 xi.coordinates()
+
+File <string>:75, in coordinates(self)
+
+File <string>:114, in degree_of_rational_fctn(f, F)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554, in 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):
+--> 554     raise TypeError("base_ring {!r} must be a ring".format(base_ring))
+    556 n = -1  # Unknown number of variables
+    557 names = None  # Unknown variable names
+
+TypeError: base_ring 3 must be a ring
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1];[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l];[?7h[?12l[?25h[?25l[?7l0];[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[0];

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

+[?7h[?12l[?25h[?2004l  Input In [19]
+    xi.
+       ^
+SyntaxError: invalid syntax
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lordinates()[?7h[?12l[?25h[?25l[?7lsage: xi.coordinates()

+[?7h[?12l[?25h[?2004lf, F 1 Finite Field of size 3
+[?7h(1, 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.x.teichmuller() * C.y.teichmuller().diffn() + 3 * (C.x^3).teichmuller() * C.y.tecihmuller().diffn() + (2*(C.x^4 + C.x^2 + C.one) * C.y).verschiebung().dif
f

+....: n()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology()

+ [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le_ring[?7h[?12l[?25h[?25l[?7l_ring[?7h[?12l[?25h[?25l[?7lsage: C.base_ring

+[?7h[?12l[?25h[?2004l[?7hFinite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.base_ring[?7h[?12l[?25h[?25l[?7lxi.coordates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = 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[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7l()xi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7l(xi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lxi = 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[?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[?7lx[?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 = C.de_rham_basis()[1];xi.coordinates()

+[?7h[?12l[?25h[?2004lf, F 2/x 3
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [22], in <cell line: 1>()
+----> 1 xi = C.de_rham_basis()[Integer(1)];xi.coordinates()
+
+File <string>:75, in coordinates(self)
+
+File <string>:114, in degree_of_rational_fctn(f, F)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554, in 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):
+--> 554     raise TypeError("base_ring {!r} must be a ring".format(base_ring))
+    556 n = -1  # Unknown number of variables
+    557 names = None  # Unknown variable names
+
+TypeError: base_ring 3 must be a ring
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); xi = C.de_rham_basis()[0];[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[0];

+[?7h[?12l[?25h[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0];[?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[?7l[?7h[?12l[?25h[?25l[?7lx[?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[?7ldinates[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1];xi.coordinates()

+[?7h[?12l[?25h[?2004l0
+f, F 2/x Finite Field of size 3
+[?7h(0, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1];xi.coordinates()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); xi = C.de_rham_basis()[1];xi.coordinates()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1];xi.coordinates()

+[?7h[?12l[?25h[?2004l0
+[?7h(0, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[1];xi.coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.coorinates()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrdinates()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?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.cordinates()[?7h[?12l[?25h[?25l[?7loxi.cordinates()[?7h[?12l[?25h[?25l[?7lrxi.cordinates()[?7h[?12l[?25h[?25l[?7lfor xi.cordinates()[?7h[?12l[?25h[?25l[?7laxi.cordinates()[?7h[?12l[?25h[?25l[?7l xi.cordinates()[?7h[?12l[?25h[?25l[?7lixi.cordinates()[?7h[?12l[?25h[?25l[?7lnxi.cordinates()[?7h[?12l[?25h[?25l[?7lin xi.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[?7lsage: for a in xi.coordinates():

+....: [?7h[?12l[?25h[?25l[?7lprint(xi.coordinates())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ltype[?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....:     print(type(a))

+....: [?7h[?12l[?25h[?25l[?7lsage: for a in xi.coordinates():

+....:     print(type(a))

+....: 

+[?7h[?12l[?25h[?2004l<class 'sage.rings.finite_rings.integer_mod.IntegerMod_int'>
+<class 'sage.rings.finite_rings.integer_mod.IntegerMod_int'>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for a in xi.coordinates():

+....:     print(type(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[?7ltyp(a))[?7h[?12l[?25h[?25l[?7l(a))[?7h[?12l[?25h[?25l[?7l(a))[?7h[?12l[?25h[?25l[?7l(a))[?7h[?12l[?25h[?25l[?7ll(a))[?7h[?12l[?25h[?25l[?7li(a))[?7h[?12l[?25h[?25l[?7lt(a))[?7h[?12l[?25h[?25l[?7l(a))[?7h[?12l[?25h[?25l[?7lf(a))[?7h[?12l[?25h[?25l[?7lt(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....:     print(lift(a))

+....: [?7h[?12l[?25h[?25l[?7lsage: for a in xi.coordinates():

+....:     print(lift(a))

+....: 

+[?7h[?12l[?25h[?2004l0
+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$ losage
+┌────────────────────────────────────────────────────────────────────┐
+│ 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'); xi = C.de_rham_basis()[1];xi.coordinates()[?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[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.base_ring[?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[?7lC[?7h[?12l[?25h[?25l[?7l.base_ring[?7h[?12l[?25h[?25l[?7lcrtier_matrix()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lystalline_cohomology_basis[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()

+[?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([((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])),
+ ([(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[?7la[?7h[?12l[?25h[?25l[?7la[?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[?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[?7laC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7laC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7laC.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[?7lsage: aaa = C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laaa = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7la[?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[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7llen[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: len(aaa)

+[?7h[?12l[?25h[?2004l[?7h2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8((3*a).f)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ldef[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?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[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7lsage: def chang(a):

+....: [?7h[?12l[?25h[?25l[?7la[?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[?7l1[?7h[?12l[?25h[?25l[?7l....:     a = a+1

+....: [?7h[?12l[?25h[?25l[?7lsage: def chang(a):

+....:     a = a+1

+....: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc.frobenius()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = (a+a+a).omega0.omega[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: b = 3

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc.frobenius()[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: chang(b)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = 3[?7h[?12l[?25h[?25l[?7lsage: b

+[?7h[?12l[?25h[?2004l[?7h3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llen(aaa)[?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[?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 [10] 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>:26 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>:323
+    if basis = _sage_const_0 :
+       ^
+SyntaxError: invalid syntax. Maybe you meant '==' or ':=' instead of '='?
+
+[?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[?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[?7laaa = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lux.h2.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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(C.x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [12], in <cell line: 1>()
+----> 1 autom(C.x)
+
+File <string>:359, in autom(self)
+
+NameError: name 'y' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(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[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7lsage: autom(C.x)

+[?7h[?12l[?25h[?2004l[?7hx + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ly)[?7h[?12l[?25h[?25l[?7lsage: autom(C.y)

+[?7h[?12l[?25h[?2004l[?7hy
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.y)[?7h[?12l[?25h[?25l[?7l)[?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[?7lsage: autom(C.dx)

+[?7h[?12l[?25h[?2004l[?7h1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(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.dx)[?7h[?12l[?25h[?25l[?7l.C.dx)[?7h[?12l[?25h[?25l[?7lxC.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[?7lsage: autom(C.x*C.dx)

+[?7h[?12l[?25h[?2004l[?7h(x - 1) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x*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(3*a).reduce()[?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[?7lD)[?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.dx)[?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[?7l[?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[?7lsage: (C.x*C.dx).function()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [18], in <cell line: 1>()
+----> 1 (C.x*C.dx).function()
+
+AttributeError: 'superelliptic_form' object has no attribute 'function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).function()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.dx).function

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [19], in <cell line: 1>()
+----> 1 (C.x*C.dx).function
+
+AttributeError: 'superelliptic_form' object has no attribute 'function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).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[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.dx).form

+[?7h[?12l[?25h[?2004l[?7hx + 1
+[?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[?7lx.teichmuller() * C.y.teichmuller().diffn() + 3 * (C.x^3).teichmuller() * C.y.tecihmuller().diffn() + (2*(C.x^4 + C.x^2 + C.one) * C.y).verschiebung().diffn()[?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[?7lsage: C.x.function

+[?7h[?12l[?25h[?2004l[?7hx + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x*C.dx)[?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[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(C.x)

+[?7h[?12l[?25h[?2004l[?7hx - 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7lsage: autom(C.x)

+[?7h[?12l[?25h[?2004l[?7hx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7lsage: autom(C.x)

+[?7h[?12l[?25h[?2004l[?7hx + 1
+[?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[?7lautom(C.x)[?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[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l(x)[?7h[?12l[?25h[?25l[?7lsage: autom(C.x)

+[?7h[?12l[?25h[?2004l[?7hx + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7lsage: autom(C.x)

+[?7h[?12l[?25h[?2004l[?7hx + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7lC.x.function[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).form[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.dx).form

+[?7h[?12l[?25h[?2004l[?7hx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).form[?7h[?12l[?25h[?25l[?7lautom(C.)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lautom(C.x)[?7h[?12l[?25h[?25l[?7lC.x.function[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).form[?7h[?12l[?25h[?25l[?7lunction[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lautom(C.*C.dx)[?7h[?12l[?25h[?25l[?7lsage: autom(C.x*C.dx)

+[?7h[?12l[?25h[?2004l[?7h(x + 1) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(C.x*C.dx)[?7h[?12l[?25h[?25l[?7lsage: autom(C.x*C.dx)

+[?7h[?12l[?25h[?2004l[?7h(x + 1) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = 3[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.x.teichmuller().diffn() + C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lystalline_cohomology_basis[?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[?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[0].coordinates()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [32], in <cell line: 1>()
+----> 1 b[Integer(0)].coordinates()
+
+File <string>:321, in coordinates(self, basis)
+
+AttributeError: 'function' 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[?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[?7lb[0].coordinates()[?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[?7lb[0].coordinates()[?7h[?12l[?25h[?25l[?7lsage: b[0].coordinates()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [35], in <cell line: 1>()
+----> 1 b[Integer(0)].coordinates()
+
+File <string>:321, in coordinates(self, basis)
+
+AttributeError: 'function' 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[?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[?7lb[0].coordinates()[?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[?7lb = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7lb[0].coordinates()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[0].coordinates()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[0].coordinates()[?7h[?12l[?25h[?25l[?7l = C.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[0].coordinates()[?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[?7l[?7h[?12l[?25h[?25l[?7lsage: b[0].coordinates(basis = b)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [38], in <cell line: 1>()
+----> 1 b[Integer(0)].coordinates(basis = b)
+
+File <string>:321, in coordinates(self, basis)
+
+File <string>:318, in r(self)
+
+File <string>:5, in __init__(self, C, omega, fct)
+
+File <string>:50, in __sub__(self, other)
+
+AttributeError: 'superelliptic_form' object has no attribute 'function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[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[?7lsage: b[0].coordinates()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [39], in <cell line: 1>()
+----> 1 b[Integer(0)].coordinates()
+
+File <string>:321, in coordinates(self, basis)
+
+File <string>:318, in r(self)
+
+File <string>:5, in __init__(self, C, omega, fct)
+
+File <string>:50, in __sub__(self, other)
+
+AttributeError: 'superelliptic_form' object has no attribute 'function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].coordinates()[?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[].coordinates()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b[0].r()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [40], in <cell line: 1>()
+----> 1 b[Integer(0)].r()
+
+File <string>:318, in r(self)
+
+File <string>:5, in __init__(self, C, omega, fct)
+
+File <string>:50, in __sub__(self, other)
+
+AttributeError: 'superelliptic_form' object has no attribute 'function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].r()[?7h[?12l[?25h[?25l[?7lcoordinates()[?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[?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[?7lb[0].r()[?7h[?12l[?25h[?25l[?7lcoordinates()[?7h[?12l[?25h[?25l[?7lbasis = b)[?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[?7lb[0].r()[?7h[?12l[?25h[?25l[?7lsage: b[0].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[0].r()[?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[].r()[?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[?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[?7l[?7h[?12l[?25h[?25l[?7lsage: b[0].coordinates(basis = b)

+[?7h[?12l[?25h[?2004l(1, 0)
+[?7h(0, [0], 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[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[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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].cordinates(basis = b)[?7h[?12l[?25h[?25l[?7lub[0].cordinates(basis = b)[?7h[?12l[?25h[?25l[?7ltb[0].cordinates(basis = b)[?7h[?12l[?25h[?25l[?7lob[0].cordinates(basis = b)[?7h[?12l[?25h[?25l[?7lmb[0].cordinates(basis = b)[?7h[?12l[?25h[?25l[?7l(b[0].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([]).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: autom(b[0]).coordinates(basis = b)

+[?7h[?12l[?25h[?2004l(1, 0)
+[?7h(V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), V((2/(x^2 + x))*y), V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([2*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreduce(xi)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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(b[0]).cordinates(basis = b)[?7h[?12l[?25h[?25l[?7leautom(b[0]).cordinates(basis = b)[?7h[?12l[?25h[?25l[?7lsautom(b[0]).cordinates(basis = b)[?7h[?12l[?25h[?25l[?7l autom(b[0]).cordinates(basis = b)[?7h[?12l[?25h[?25l[?7l=autom(b[0]).cordinates(basis = b)[?7h[?12l[?25h[?25l[?7l autom(b[0]).cordinates(basis = b)[?7h[?12l[?25h[?25l[?7lsage: res = autom(b[0]).coordinates(basis = b)

+[?7h[?12l[?25h[?2004l(1, 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lres = autom(b[0]).coordinates(basis = b)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l1[?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[?7ls[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: res1 = res.f.f

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lres1 = res.f.f[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: res1

+[?7h[?12l[?25h[?2004l[?7h(2/(x^2 + x))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lres1[?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[?7lroot[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: res1.pth_root()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [49], in <cell line: 1>()
+----> 1 res1.pth_root()
+
+File <string>:144, in pth_root(self)
+
+ValueError: Function is not a p-th power.
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lres1.pth_root()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1.pth_root()[?7h[?12l[?25h[?25l[?7l1.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[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()|[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: res.reduce()

+[?7h[?12l[?25h[?2004l[?7h(V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]), [0], V(((-x^6 - x^4 + x^2 - x + 1)/(x^2*y + x*y)) dx) + dV([((2*x^2 + 2*x + 2)/(x^2 + x))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]).coordinates(basis = b)[?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[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()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?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[?7l6[?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: autom(b[0]) == 4*b[0] + 6*b[1]

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]) == 4*b[0] + 6*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(). = 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7lr = 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7le = 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7ld = 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7lu = 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7lc = 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7le = 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7l( = 4*b[0] + 6*b[1][?7h[?12l[?25h[?25l[?7l() = 4*b[0] + 6*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(4*b[0] + 6*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[?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: autom(b[0]).reduce() == (4*b[0] + 6*b[1]).reduce()

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(b[0]).reduce() == (4*b[0] + 6*b[1]).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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l (4*b[0] + 6*b[1]).reduce()[?7h[?12l[?25h[?25l[?7l (4*b[0] + 6*b[1]).reduce()[?7h[?12l[?25h[?25l[?7l()(4*b[0] + 6*b[1]).reduce()[?7h[?12l[?25h[?25l[?7l(), (4*b[0] + 6*b[1]).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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[0]).reduce(), (4*b[0] + 6*b[1]).reduce()

+[?7h[?12l[?25h[?2004l[?7h(([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 + x^6 - x^4 + x^3 - 1)/(x^2*y - x*y)) dx) + dV([((2*x^3 + 2*x + 1)/(x^2 + 2*x))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 + x^6 - x^4 + x^3 - 1)/(x^2*y - x*y)) dx) + dV([((2*x^3 + x + 2)/(x^2 + 2*x))*y])),
+ ([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^4 - x^3)/(x^2*y - y)) dx) + dV([((2*x^3 + 2*x^2 + 2*x + 1)/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^4 - x^3)/(x^2*y - y)) dx) + dV([((2*x^4 + 2*x^3 + x^2 + x + 1)/(x^3 + 2*x))*y])))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.function[?7h[?12l[?25h[?25l[?7l = sperelliptic(x^4 + x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^4 + 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[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4 + x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + x, 2)[?7h[?12l[?25h[?25l[?7l^ + x, 2)[?7h[?12l[?25h[?25l[?7l3 + x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l x, 2)[?7h[?12l[?25h[?25l[?7l- x, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l+, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x + 1, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(f)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ltch(C)[?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 = x^4 + 2*x^3 + x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?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[?7lsage: C1 = patch(C)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = patch(C)[?7h[?12l[?25h[?25l[?7l1[?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[?7la[?7h[?12l[?25h[?25l[?7llline_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [57], in <cell line: 1>()
+----> 1 C1.crystalline_cohomology_basis()
+
+File <string>:354, in crystalline_cohomology_basis(self)
+
+File <string>:348, in de_rham_witt_lift(cech_class)
+
+File <string>:50, in decomposition_omega0_omega8(omega, prec)
+
+NameError: name 'Error' 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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l = pach(C)[?7h[?12l[?25h[?25l[?7l.crysalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: C1.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [58], in <cell line: 1>()
+----> 1 C1.crystalline_cohomology_basis()
+
+File <string>:354, in crystalline_cohomology_basis(self)
+
+File <string>:348, in de_rham_witt_lift(cech_class)
+
+File <string>:50, in decomposition_omega0_omega8(omega, prec)
+
+NameError: name 'Error' 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[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l = pach(C)[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7lC1 = patch(C)[?7h[?12l[?25h[?25l[?7lsage: C1 = patch(C)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = patch(C)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.crysalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lrystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: C1.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l[?7h[([(2/(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), [(2/(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])),
+ ([(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*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([(x^4 + x^2 + 1)*y]))]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: C1

+[?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[?7h[?12l[?25h[?25l[?7lC1[?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[?7lC1[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x + 1, 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 + 1, 2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l = pach(C)[?7h[?12l[?25h[?25l[?7lsage: C1 = patch(C)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = patch(C)[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: C1.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [65], in <cell line: 1>()
+----> 1 C1.crystalline_cohomology_basis()
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:50, in decomposition_omega0_omega8(omega, prec)
+
+ValueError: Something went wrong.((x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx((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^2*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[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l.x.function[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lx.verschiebung()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.dx.residue()

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.residue()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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.residue()[?7h[?12l[?25h[?25l[?7lC.dx.residue()[?7h[?12l[?25h[?25l[?7l.C.dx.residue()[?7h[?12l[?25h[?25l[?7lxC.dx.residue()[?7h[?12l[?25h[?25l[?7l()C.dx.residue()[?7h[?12l[?25h[?25l[?7l()^C.dx.residue()[?7h[?12l[?25h[?25l[?7l(C.dx.residue()[?7h[?12l[?25h[?25l[?7l-C.dx.residue()[?7h[?12l[?25h[?25l[?7l0C.dx.residue()[?7h[?12l[?25h[?25l[?7l1C.dx.residue()[?7h[?12l[?25h[?25l[?7lC.dx.residue()[?7h[?12l[?25h[?25l[?7lC.dx.residue()[?7h[?12l[?25h[?25l[?7lC.dx.residue()[?7h[?12l[?25h[?25l[?7l-C.dx.residue()[?7h[?12l[?25h[?25l[?7l1C.dx.residue()[?7h[?12l[?25h[?25l[?7l()C.dx.residue()[?7h[?12l[?25h[?25l[?7l()*C.dx.residue()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?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.dx.residue()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().residue()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?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)*C.dx).residue()

+[?7h[?12l[?25h[?2004l[?7h1
+[?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[?7l((C.x)^(-1)*C.dx).residue()[?7h[?12l[?25h[?25l[?7lC.dx.residue()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l = pach(C)[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x + 1, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)*C.dx).residue()[?7h[?12l[?25h[?25l[?7lC.dx.residue()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l = pach(C)[?7h[?12l[?25h[?25l[?7lsage: C1 = patch(C)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = patch(C)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.crysalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lcrystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: C1.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [72], in <cell line: 1>()
+----> 1 C1.crystalline_cohomology_basis()
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:32, in decomposition_omega0_omega8(omega, prec)
+
+ValueError: Non zero residue!
+[?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[?2004l0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l = supereliptic(x^3 - x + 1, 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxy.<x, y> = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.<x> = PolynmialRng(GF(4))[?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 = PolynomialRing(GF(4))[?7h[?12l[?25h[?25l[?7l = PolynomialRing(GF(4))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?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[?7lsage: Rx.<x> = PolynomialRing(GF(2))

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l = supereliptic(x^3 - x + 1, 2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 - x + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l(, 2)[?7h[?12l[?25h[?25l[?7lx, 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[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x, 1)

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

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(C.y)^(-1)])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7las_cover(C, [(C.y)^(-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[?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(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[?7l3])[?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[?7lsage: AS = as_cover(C, [(C.x)^3, (C.x)])

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.x)^3, (C.x)])[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.exponent_of_different_prim()[?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[?7la[?7h[?12l[?25h[?25l[?7lm[?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[?7lsage: AS.de_rham_basis()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+IndexError                                Traceback (most recent call last)
+Input In [6], in <cell line: 1>()
+----> 1 AS.de_rham_basis()
+
+File <string>:389, in de_rham_basis(self, threshold)
+
+File <string>:342, in cohomology_of_structure_sheaf_basis(self, threshold)
+
+File <string>:342, in <listcomp>(.0)
+
+File <string>:109, in serre_duality_pairing(self, fct)
+
+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>:109, in <genexpr>(.0)
+
+File <string>:102, in residue(self, place)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:618, in sage.rings.laurent_series_ring_element.LaurentSeries.residue()
+    616         Integer Ring
+    617     """
+--> 618     return self[-1]
+    619 
+    620 def exponents(self):
+
+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[?7lAS.de_rham_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[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis(prec=100)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [7], in <cell line: 1>()
+----> 1 AS.de_rham_basis(prec=Integer(100))
+
+TypeError: as_cover.de_rham_basis() got an unexpected keyword argument 'prec'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis(prec=100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(C.x)^3, (C.x)])[?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[?7l5)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(C.x)^3, (C.x)], prec = 50)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.x)^3, (C.x)], prec = 50)[?7h[?12l[?25h[?25l[?7l.de_rham_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[?7l)[?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: AS.de_rham_basis()

+[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
+ ( (z1) * dx, 0 ),
+ ( (x) * dx, z0/x ),
+ ( (x*z1) * dx, z0*z1/x )]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(C.x)^3, (C.x)], prec = 50)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l[()][?7h[?12l[?25h[?25l[?7l ], prec = 50)[?7h[?12l[?25h[?25l[?7l+], prec = 50)[?7h[?12l[?25h[?25l[?7l ], prec = 50)[?7h[?12l[?25h[?25l[?7l(], prec = 50)[?7h[?12l[?25h[?25l[?7lC], prec = 50)[?7h[?12l[?25h[?25l[?7l.], prec = 50)[?7h[?12l[?25h[?25l[?7lx], prec = 50)[?7h[?12l[?25h[?25l[?7l)], prec = 50)[?7h[?12l[?25h[?25l[?7l^], prec = 50)[?7h[?12l[?25h[?25l[?7l5], prec = 50)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(C.x)^3, (C.x) + (C.x)^5], prec = 50)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.x)^3, (C.x) + (C.x)^5], prec = 50)[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()

+[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
+ ( (x*z0 + z1) * dx, 0 ),
+ ( (z0) * dx, 0 ),
+ ( (x) * dx, 0 ),
+ ( (x^2) * dx, 0 ),
+ ( (x^3) * dx, z1/x ),
+ ( (0) * dx, z0/x ),
+ ( (x^3*z0 + x*z1) * dx, z0*z1/x ),
+ ( (x^2*z0 + x*z0) * dx, z0*z1/x^2 ),
+ ( (x*z0) * dx, z0*z1/x^3 )]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: group_action_matrices

+ group_action_matrices      group_action_matrices_log 

+ group_action_matrices_dR   group_action_matrices_old 

+ group_action_matrices_holo                           

+

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

+ group_action_matrices     

+

+

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

+ group_action_matrices     

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

+

+

+

+[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: group_action_matrices_dR(AS)

+[?7h[?12l[?25h[?2004l[?7h[
+[1 0 1 0 0 0 0 0 0 0]  [1 1 0 0 0 0 0 0 0 0]
+[0 1 0 0 0 0 0 0 0 0]  [0 1 0 0 0 0 0 0 0 0]
+[0 0 1 0 0 0 0 0 0 0]  [0 0 1 0 0 0 0 0 0 0]
+[0 1 0 1 0 0 0 0 1 1]  [0 0 0 1 0 0 0 1 0 0]
+[0 0 0 0 1 0 0 0 1 0]  [0 0 0 0 1 0 0 0 0 0]
+[0 0 0 0 0 1 0 1 0 0]  [0 0 0 0 0 1 0 0 0 0]
+[0 0 0 0 0 0 1 0 1 0]  [0 0 0 0 0 0 1 1 0 0]
+[0 0 0 0 0 0 0 1 0 0]  [0 0 0 0 0 0 0 1 0 0]
+[0 0 0 0 0 0 0 0 1 0]  [0 0 0 0 0 0 0 0 1 0]
+[0 0 0 0 0 0 0 0 0 1], [0 0 0 0 0 0 0 0 0 1]
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgroup_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAgroup_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l,group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lBgroup_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l=group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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, B = group_action_matrices_dR(AS)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm = 3[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: magma

+ magma     

+ magma_free

+ magmathis 

+

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

+ magma     

+

+

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

+ magma     

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

+

+ magma_free

+ magmathis [?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[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B)

+[?7h[?12l[?25h[?2004l[?7h[
+RModule of dimension 2 over GF(3),
+RModule of dimension 2 over GF(3),
+RModule of dimension 3 over GF(3),
+RModule of dimension 3 over GF(3)
+]
+{
+[1 0]
+[0 1],
+[1 0]
+[1 1]
+}
+{
+[1 0]
+[0 1],
+[1 0]
+[2 1]
+}
+{
+[1 0 1]
+[0 1 0]
+[0 0 1],
+[1 1 0]
+[0 1 0]
+[0 0 1]
+}
+{
+[1 0 2]
+[0 1 1]
+[0 0 1],
+[1 0 0]
+[0 1 1]
+[0 0 1]
+}
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS

+[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
+z0^2 - z0 = x^3
+z1^2 - z1 = x^5 + x
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lsage: AS.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[?7lAS.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lgroup_actionmarices_dR(AS)[?7h[?12l[?25h[?25l[?7lAS.derham_basis()[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(C.x)^3, (C.x) + (C.x)^5], prec = 50)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l], prec = 50)[?7h[?12l[?25h[?25l[?7l7], prec = 50)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS = as_cover(C, [(C.x)^3, (C.x) + (C.x)^7], prec = 50)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.x)^3, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lgroup_actionmarices_dR(AS)[?7h[?12l[?25h[?25l[?7lAS.derham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()

+[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
+ ( (x^2*z0 + z1) * dx, 0 ),
+ ( (z0) * dx, 0 ),
+ ( (x) * dx, 0 ),
+ ( (x*z0) * dx, 0 ),
+ ( (x^2) * dx, 0 ),
+ ( (x^3) * dx, 0 ),
+ ( (x^5) * dx, z1/x ),
+ ( (0) * dx, z0/x ),
+ ( (x^5*z0 + x*z1) * dx, z0*z1/x ),
+ ( (x^4) * dx, z1/x^2 ),
+ ( (x^4*z0 + x^2*z0) * dx, z0*z1/x^2 ),
+ ( (x^3*z0) * dx, z0*z1/x^3 ),
+ ( (x^2*z0) * dx, z0*z1/x^4 )]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = as_cover(C, [(C.x)^3, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?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.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l+, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l , (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l(, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7lC, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l., (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7lx, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l(), (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l()^, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l5, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: AS = as_cover(C, [(C.x)^3 + (C.x)^5, (C.x) + (C.x)^7], prec = 50)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS = as_cover(C, [(C.x)^3 + (C.x)^5, (C.x) + (C.x)^7], prec = 50)[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()

+[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
+ ( (z1) * dx, 0 ),
+ ( (z0) * dx, 0 ),
+ ( (x) * dx, 0 ),
+ ( (x^2*z0 + x*z1) * dx, 0 ),
+ ( (x*z0) * dx, 0 ),
+ ( (x^2) * dx, 0 ),
+ ( (x^3) * dx, 0 ),
+ ( (x^5) * dx, z1/x ),
+ ( (0) * dx, z0/x ),
+ ( (x^5*z0 + x^4 + x^3*z1 + x^2*z0) * dx, z0*z1/x ),
+ ( (x^4) * dx, z1/x^2 ),
+ ( (x^2 + 1) * dx, z0/x^2 ),
+ ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ),
+ ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ),
+ ( (x^2*z0) * dx, z0*z1/x^4 )]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)*C.dx).residue()[?7h[?12l[?25h[?25l[?7lz[?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[?7lC[?7h[?12l[?25h[?25l[?7l.dx.residue()[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.z[0]/C.x[?7h[?12l[?25h[?25l[?7lA.z[0]/C.x[?7h[?12l[?25h[?25l[?7lS.z[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.x[?7h[?12l[?25h[?25l[?7lA.x[?7h[?12l[?25h[?25l[?7lS.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS.z[0]/AS.x

+[?7h[?12l[?25h[?2004l[?7hz0/x
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]/AS.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(AS.z[0]/AS.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[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?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: (AS.z[0]/AS.x).pth_root()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [22], in <cell line: 1>()
+----> 1 (AS.z[Integer(0)]/AS.x).pth_root()
+
+AttributeError: 'as_function' object has no attribute 'pth_root'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]/AS.x).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[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?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: (AS.z[0]/AS.x).expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-2 + t^2 + t^3 + t^7 + t^8 + t^10 + t^11 + t^14 + t^19 + t^21 + t^22 + t^23 + t^26 + t^28 + t^29 + t^31 + t^32 + t^34 + t^35 + t^36 + t^37 + t^39 + t^40 + t^42 + t^43 + O(t^44)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]/AS.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[?7ldexpansion_at_infty()[?7h[?12l[?25h[?25l[?7liexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lfexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lfexpansion_at_infty()[?7h[?12l[?25h[?25l[?7lnexpansion_at_infty()[?7h[?12l[?25h[?25l[?7l(expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()expansion_at_infty()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]/AS.x).diffn().expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^2 + t^6 + t^10 + t^18 + t^20 + t^22 + t^28 + t^30 + O(t^33)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]/AS.x).diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]/AS.x[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

+[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
+z0^2 - z0 = x^5 + x^3
+z1^2 - z1 = x^7 + x
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]/AS.x).diffn().expansion_at_infty()[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?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(AS.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[?7l4[?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: (AS.z[0]*AS.z[1]/(AS.x)^4).diffn()

+[?7h[?12l[?25h[?2004l[?7h((x^6*z0 + x^4*z1 + x^2*z1 + z0)/x^4) * 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[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            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>:27, 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>:9, in <module>
+
+AttributeError: 'superelliptic' object has no attribute 'crystalline_cohomology'
+[?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---------------------------------------------------------------------------
+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>:27, 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>:9, in <module>
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:32, in decomposition_omega0_omega8(omega, prec)
+
+ValueError: Non zero residue!
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx.residue()[?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[?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 [4] 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>:33
+    if sum(omega.residue(place = i) i in range(delta)) != _sage_const_0 :
+           ^
+SyntaxError: invalid syntax. Perhaps you forgot a comma?
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lsum[?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[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7la[?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[?7li[?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[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: sum(omega.residue(place = i) for i in range(2))

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [5], in <cell line: 1>()
+----> 1 sum(omega.residue(place = i) for i in range(Integer(2)))
+
+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
+
+Input In [5], in <genexpr>(.0)
+----> 1 sum(omega.residue(place = i) for i in range(Integer(2)))
+
+NameError: name 'omega' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsum(omega.residue(place = i) for i in range(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.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7l.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7l.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7l.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7l.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7lC.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7l.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7ld.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7lx.residue(place = i) for i in range(2)[?7h[?12l[?25h[?25l[?7lsage: sum(C.dx.residue(place = i) for i in range(2))

+[?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[?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 [7] 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>:33
+    if sum(omega.residue(place = i) i in range(delta)) != _sage_const_0 :
+           ^
+SyntaxError: invalid syntax. Perhaps you forgot a comma?
+
+[?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---------------------------------------------------------------------------
+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>:27, 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>:9, in <module>
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:54, in decomposition_omega0_omega8(omega, prec)
+
+ValueError: Something went wrong.((x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx((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^2*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---------------------------------------------------------------------------
+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>:27, 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>:9, in <module>
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:54, in decomposition_omega0_omega8(omega, prec)
+
+ValueError: Something went wrong for ((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + 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^2*y)) dx. Result would be ((x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx and ((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^2*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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^15 - x^14 + x^13 + x^12 + x^1 + x^10 - x^8)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + 1)[?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 + x^2 + 1)[?7h[?12l[?25h[?25l[?7l + x^2 + 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 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7l - x^3 + x^2 + 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 + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7l + x^4 - x^3 + x^2 + 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 + x^5 + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7l + x^5 + x^4 - x^3 + x^2 + 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[?7lsage: (x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8).quo_rem(x^6 + x^5 + x^4 - x^3 + x^2 + 1)

+[?7h[?12l[?25h[?2004l[?7h(x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^3 + 2*x + 1, x^5 + x^4 + 2*x^2 + x + 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in xi.coordinates():[?7h[?12l[?25h[?25l[?7lfffff.coordinates()[?7h[?12l[?25h[?25l[?7l = ((C.y)^3/(C.x)^2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx^5 + x^4 + 2*x^2 + 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(x^5 + x^4 + 2*x^2 + 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[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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^6 + x^5 + x^4 - x^3 + x^2 + 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(x^6 + x^5 + x^4 - x^3 + x^2 + 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[?7lsage: ff = (x^5 + x^4 + 2*x^2 + x + 2)/(x^6 + x^5 + x^4 - x^3 + x^2 + 1)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = (x^5 + x^4 + 2*x^2 + x + 2)/(x^6 + x^5 + x^4 - x^3 + x^2 + 1)[?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^5 + x^4 + 2*x^2 + x + 2)/(x^6 + x^5 + x^4 - x^3 + x^2 + 1)[?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[?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[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ff = superelliptic_function(C, ff)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = superelliptic_function(C, ff)[?7h[?12l[?25h[?25l[?7lf[?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: ff/C.y

+[?7h[?12l[?25h[?2004l[?7h((x^5 + x^4 + 2*x^2 + x + 2)/(x^9 + x^8 + 2*x^6 + x^5 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1))*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff/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[?7lf/C.y[?7h[?12l[?25h[?25l[?7lf/C.y[?7h[?12l[?25h[?25l[?7l f/C.y[?7h[?12l[?25h[?25l[?7l=f/C.y[?7h[?12l[?25h[?25l[?7l f/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[?7lsage: ff = ff/C.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = ff/C.y[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: ff.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^5 + t^9 + 2*t^11 + 2*t^13 + t^21 + 2*t^23 + O(t^25)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7la)[?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[?7l0)[?7h[?12l[?25h[?25l[?7lsage: ff.expansion_at_infty(place = 0)

+[?7h[?12l[?25h[?2004l[?7ht^5 + t^9 + 2*t^11 + 2*t^13 + t^21 + 2*t^23 + O(t^25)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty(place = 0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7lsage: ff.expansion_at_infty(place = 1)

+[?7h[?12l[?25h[?2004l[?7ht^5 + t^9 + 2*t^11 + 2*t^13 + t^21 + 2*t^23 + O(t^25)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = ff/C.y[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: ff = ff*C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff = ff*C.dx[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7lsage: ff.expansion_at_infty(place = 1)

+[?7h[?12l[?25h[?2004l[?7ht^2 + t^8 + t^10 + O(t^12)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: ff.expansion_at_infty(place = 0)

+[?7h[?12l[?25h[?2004l[?7ht^2 + t^8 + 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[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    705 try:
+--> 706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
+    682 def resolve_fractions(x, y):
+--> 683     xn = x.numerator()
+    684     xd = x.denominator()
+
+AttributeError: 'superelliptic_function' object has no attribute 'numerator'
+
+During handling of the above exception, another exception occurred:
+
+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>:27, 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>:9, in <module>
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:51, in decomposition_omega0_omega8(omega, prec)
+
+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:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+--> 708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
+    709                     x0, y0, self))
+    710 try:
+    711     return self._element_class(self, x, y, coerce=coerce)
+
+TypeError: cannot convert ((x^14 + 2*x^13 + x^12 + x^11 + x^10 + x^9 + 2*x^7)/(x^9 + 2*x^6 + 1))*y/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+ValueError                                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>:27, 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>:9, in <module>
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:60, in decomposition_omega0_omega8(omega, prec)
+
+ValueError: Something went wrong for (((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y) dx. Result would be ((x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx and ((x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8).quo_rem(x^6 + x^5 + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7l().quo_rem(x^6 + x^5 + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7lsage: (x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8).quo_rem(x^6 + x^5 + x^4 - x^3 + x^2 + 1)

+[?7h[?12l[?25h[?2004l[?7h(x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^3 + 2*x + 1, x^5 + x^4 + 2*x^2 + x + 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8).quo_rem(x^6 + x^5 + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lff.expansion_at_infty(place = 0)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = ff*C.dx[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = ff/C.y[?7h[?12l[?25h[?25l[?7l/C.y[?7h[?12l[?25h[?25l[?7l = superelliptic_function(C, ff)[?7h[?12l[?25h[?25l[?7l/C.y[?7h[?12l[?25h[?25l[?7l = ff/C.y[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lplace = 0)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = ff*C.dx[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(place = 1)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8).quo_rem(x^6 + x^5 + x^4 - x^3 + x^2 + 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]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---------------------------------------------------------------------------
+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>:27, 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>:9, in <module>
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:60, in decomposition_omega0_omega8(omega, prec)
+
+ValueError: Something went wrong for (((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y) dx. Result would be ((x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx and ((x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x + 1 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.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7ldx.residue()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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 = C.holomorphic_differentials_basis()[0][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = gg^8*gg.diffn()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: om = C.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.expansion_at_infty(prec = 30)[?7h[?12l[?25h[?25l[?7li[?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[?7lom = 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[?7lC.dx[?7h[?12l[?25h[?25l[?7l.C.dx[?7h[?12l[?25h[?25l[?7lyC.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-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[?7lsage: om = (C.y)^(-1)*C.dx

+[?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[?7lm[?7h[?12l[?25h[?25l[?7l.expansion_at_infty(prec = 30)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: om.is_regular_on_U

+ om.is_regular_on_U0    

+ om.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[?7lis[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

+ om.cartier               om.expansion_at_infty    om.is_regular_on_Uinfty  om.serre_duality_pairing

+ om.coordinates           om.form                  om.jth_component         om.verschiebung         

+ om.curve                 om.is_regular_on_U0      om.residue                                       [?7h[?12l[?25h[?25l[?7lcartier

+ om.cartier              

+

+

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

+ om.cartier              

+ om.coordinates          [?7h[?12l[?25h[?25l[?7lfrm

+

+ om.coordinates           om.form                 [?7h[?12l[?25h[?25l[?7ljth_component

+

+ om.form                  om.jth_component        [?7h[?12l[?25h[?25l[?7lvershiebung

+

+ om.jth_component         om.verschiebung         [?7h[?12l[?25h[?25l[?7ljth_omponent

+

+ om.jth_component         om.verschiebung         [?7h[?12l[?25h[?25l[?7l

+

+

+

+[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.jth_component()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [5], in <cell line: 1>()
+----> 1 om.jth_component()
+
+TypeError: superelliptic_form.jth_component() missing 1 required positional argument: 'j'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.jth_component()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7lsage: om.jth_component(1)

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom.jth_component(1)[?7h[?12l[?25h[?25l[?7l)[?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[?7lC.dx[?7h[?12l[?25h[?25l[?7l.C.dx[?7h[?12l[?25h[?25l[?7lxC.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[?7lsage: om = (C.y)^(-1)*C.x*C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (C.y)^(-1)*C.x*C.dx[?7h[?12l[?25h[?25l[?7l.jth_component(1)[?7h[?12l[?25h[?25l[?7lsage: om.jth_component(1)

+[?7h[?12l[?25h[?2004l[?7hx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7ldx.residue()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lvrschiebung()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.dx.valuation()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [9], in <cell line: 1>()
+----> 1 C.dx.valuation()
+
+AttributeError: 'superelliptic_form' object has no attribute 'valuation'
+[?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---------------------------------------------------------------------------
+TypeError                                 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>:27, 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>:9, in <module>
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:81, in decomposition_omega0_omega8(omega, prec)
+
+File <string>:105, in jth_component(self, j)
+
+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[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [11], 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>:27, 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>:9, in <module>
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:81, in decomposition_omega0_omega8(omega, prec)
+
+File <string>:105, in jth_component(self, j)
+
+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[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [12], 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>:27, 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>:9, in <module>
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:81, in decomposition_omega0_omega8(omega, prec)
+
+File <string>:105, in jth_component(self, j)
+
+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[?2004lself, j (((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y) dx 0
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [13], 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>:27, 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>:9, in <module>
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:81, in decomposition_omega0_omega8(omega, prec)
+
+File <string>:106, in jth_component(self, j)
+
+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[?2004lself, j (((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y) dx 0
+g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))/y_inv
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [14], 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>:27, 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>:9, in <module>
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:81, in decomposition_omega0_omega8(omega, prec)
+
+File <string>:107, in jth_component(self, j)
+
+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[?2004lself, j (((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y) dx 0
+g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))/y_inv <class 'sage.rings.fraction_field_element.FractionFieldElement_1poly_field'>
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [15], 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>:27, 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>:9, in <module>
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:81, in decomposition_omega0_omega8(omega, prec)
+
+File <string>:107, in jth_component(self, j)
+
+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[?2004lself, j (((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y) dx 0
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [16], 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>:27, 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>:9, in <module>
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:81, in decomposition_omega0_omega8(omega, prec)
+
+File <string>:105, in jth_component(self, j)
+
+File <string>:140, in coff(f, d)
+
+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.fraction_field_element.FractionFieldElement_1poly_field' object has no attribute 'coefficients'
+[?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[?2004lself, j (((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y) dx 0
+component 0
+---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [17], 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>:27, 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>:9, in <module>
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:83, in decomposition_omega0_omega8(omega, prec)
+
+NameError: name 'quo_rem' is not defined
+[?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[?2004lcomponent 0
+q, r 0 0
+component 0
+q, r 0 0
+component 0
+q, r 0 0
+component 0
+q, r 0 0
+[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 - x^10 - x^9 - x^8 - x^7 - x^6 + x^5 + x^4)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 + x^10 - x^8 + x^7 - x^6 - x^4 - x^3 - x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^15 - x^14 + x^13 + x^12 + x^11 + x^10 - x^8).quo_rem(x^6 + x^5 + x^4 - x^3 + x^2 + 1)[?7h[?12l[?25h[?25l[?7lC.x*C.d).form[?7h[?12l[?25h[?25l[?7l.x*C.dx).form[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lj[?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[?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[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.dx).jth_component(1)

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).jth_component(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: (C.x*C.dx).jth_component(0)

+[?7h[?12l[?25h[?2004l[?7hx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).jth_component(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/*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7lC*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l.*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7ly*C.dx).jth_component(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[?7lsage: (C.x/C.y*C.dx).jth_component(0)

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x/C.y*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7lsage: (C.x/C.y*C.dx).jth_component(1)

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

+[?7h[?12l[?25h[?2004l((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + 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^2*y)) dx
+component 0
+q, r 0 0
+component 0
+q, r 0 0
+((x^22 - x^21 - x^20 + x^17 - x^16 - x^15 + x^13 - x^10 + x^9 - x^6 - x^4 + x^3 - x^2 + x + 1)/(x^7*y + x^6*y + x^5*y - x^4*y + x^3*y + x*y)) dx
+component 0
+q, r 0 0
+component 0
+q, r 0 0
+[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 - x^10 - x^9 - x^8 - x^7 - x^6 + x^5 + x^4)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 + x^10 - x^8 + x^7 - x^6 - x^4 - x^3 - x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + 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((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + 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^2*y)) dx
+component, j 0 0
+q, r 0 0
+component, j 0 1
+q, r 0 0
+((x^22 - x^21 - x^20 + x^17 - x^16 - x^15 + x^13 - x^10 + x^9 - x^6 - x^4 + x^3 - x^2 + x + 1)/(x^7*y + x^6*y + x^5*y - x^4*y + x^3*y + x*y)) dx
+component, j 0 0
+q, r 0 0
+component, j 0 1
+q, r 0 0
+[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 - x^10 - x^9 - x^8 - x^7 - x^6 + x^5 + x^4)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 + x^10 - x^8 + x^7 - x^6 - x^4 - x^3 - x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))]
+[?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[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?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[?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[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x/C.y*C.dx).jth_component(1)[?7h[?12l[?25h[?25l[?7l(C.x)^(-1)*C.dx).residue()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l)^(-1)*C.dx).residue()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l().residue()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?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[?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[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(-1)*C.dx).jth_component(1)

+[?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[?2004l((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + 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^2*y)) dx
+g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y
+g2 ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y^3
+component, j 0 0
+q, r 0 0
+g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y
+g2 ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y^3
+component, j 0 1
+q, r 0 0
+g 0
+g2 0
+((x^22 - x^21 - x^20 + x^17 - x^16 - x^15 + x^13 - x^10 + x^9 - x^6 - x^4 + x^3 - x^2 + x + 1)/(x^7*y + x^6*y + x^5*y - x^4*y + x^3*y + x*y)) dx
+g ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y
+g2 ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y^3
+component, j 0 0
+q, r 0 0
+g ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y
+g2 ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y^3
+component, j 0 1
+q, r 0 0
+g 0
+g2 0
+[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 - x^10 - x^9 - x^8 - x^7 - x^6 + x^5 + x^4)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 + x^10 - x^8 + x^7 - x^6 - x^4 - x^3 - x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx.<x> = PolynomialRing(GF(2))[?7h[?12l[?25h[?25l[?7lx.<x> = PolynomialRing(GF(2))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l3))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: Rx.<x> = PolynomialRing(GF(3))

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy[?7h[?12l[?25h[?25l[?7lx[?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[?7la[?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[?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[?7l([?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Fx = FractionField(Rx)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFx = FractionField(Rx)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7ly[?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[?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[?7lR[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: FxRy.<y> = PolynomialRing(Fx)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgroup_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7ly[?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: ggg = FxRy(C.y/C.x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    705 try:
+--> 706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_.<locals>.resolve_fractions(x, y)
+    682 def resolve_fractions(x, y):
+--> 683     xn = x.numerator()
+    684     xd = x.denominator()
+
+AttributeError: 'superelliptic_function' object has no attribute 'numerator'
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [30], in <cell line: 1>()
+----> 1 ggg = FxRy(C.y/C.x)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py: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_element_generic.py:1083, in Polynomial_generic_dense_field.__init__(self, parent, x, check, is_gen, construct)
+   1082 def __init__(self, parent, x=None, check=True, is_gen = False, construct=False):
+-> 1083     Polynomial_generic_dense.__init__(self, parent, x, check, is_gen)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:11222, in sage.rings.polynomial.polynomial_element.Polynomial_generic_dense.__init__()
+  11220 #                x = []    # zero polynomial
+  11221         if check:
+> 11222             self.__coeffs = [R(z, **kwds) for z in x]
+  11223             self.__normalize()
+  11224         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/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce)
+    706     x, y = resolve_fractions(x0, y0)
+    707 except (AttributeError, TypeError):
+--> 708     raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
+    709                     x0, y0, self))
+    710 try:
+    711     return self._element_class(self, x, y, coerce=coerce)
+
+TypeError: cannot convert 1/x*y/1 to an element of Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lggg = FxRy(C.y/C.x)[?7h[?12l[?25h[?25l[?7lFxRy.<y> = PolynomialRing(Fx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxRy.<y> = PolynomialRing(Fx)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lR[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: FxRy

+[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in y over Fraction Field of Univariate 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[?7lFxRy[?7h[?12l[?25h[?25l[?7lggg = FxRy(C.y/C.x)[?7h[?12l[?25h[?25l[?7lFxRy.<y> = PolynomialRing(Fx)[?7h[?12l[?25h[?25l[?7lggg = FxRy(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[?7ly)[?7h[?12l[?25h[?25l[?7l/)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: ggg = FxRy(y/x)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lggg = FxRy(y/x)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7licients[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ggg.coefficient(y)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [33], in <cell line: 1>()
+----> 1 ggg.coefficient(y)
+
+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:356, in sage.cpython.getattr.getattr_from_other_class()
+    354     dummy_error_message.cls = type(self)
+    355     dummy_error_message.name = name
+--> 356     raise AttributeError(dummy_error_message)
+    357 cdef PyObject* attr = instance_getattr(cls, name)
+    358 if attr is NULL:
+
+AttributeError: 'PolynomialRing_field_with_category.element_class' object has no attribute 'coefficient'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lggg.coefficient(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[?7lmcoeficient(y)[?7h[?12l[?25h[?25l[?7locoeficient(y)[?7h[?12l[?25h[?25l[?7lncoeficient(y)[?7h[?12l[?25h[?25l[?7locoeficient(y)[?7h[?12l[?25h[?25l[?7lmcoeficient(y)[?7h[?12l[?25h[?25l[?7licoeficient(y)[?7h[?12l[?25h[?25l[?7lacoeficient(y)[?7h[?12l[?25h[?25l[?7llcoeficient(y)[?7h[?12l[?25h[?25l[?7l_coeficient(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: ggg.monomial_coefficient(y)

+[?7h[?12l[?25h[?2004l[?7h1/x
+[?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((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + 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^2*y)) dx
+g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y
+g2 ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y^3
+component, j 0 0
+q, r 0 0
+g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y
+g2 ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y^3
+component, j 0 1
+q, r 0 0
+g 0
+g2 0
+((x^22 - x^21 - x^20 + x^17 - x^16 - x^15 + x^13 - x^10 + x^9 - x^6 - x^4 + x^3 - x^2 + x + 1)/(x^7*y + x^6*y + x^5*y - x^4*y + x^3*y + x*y)) dx
+g ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y
+g2 ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y^3
+component, j 0 0
+q, r 0 0
+g ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y
+g2 ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y^3
+component, j 0 1
+q, r 0 0
+g 0
+g2 0
+[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 - x^10 - x^9 - x^8 - x^7 - x^6 + x^5 + x^4)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 + x^10 - x^8 + x^7 - x^6 - x^4 - x^3 - x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lggg.monomial_coefficient(y)[?7h[?12l[?25h[?25l[?7lceffcient(y)[?7h[?12l[?25h[?25l[?7l = FxRy(y/x)[?7h[?12l[?25h[?25l[?7lFxRy[?7h[?12l[?25h[?25l[?7lggg = FxRy(y/x)[?7h[?12l[?25h[?25l[?7lFxRy[?7h[?12l[?25h[?25l[?7lggg = FxRy(C.y/C.x)[?7h[?12l[?25h[?25l[?7lFxRy.<y> = PolynomialRing(Fx)[?7h[?12l[?25h[?25l[?7l = FractionField(Rx)[?7h[?12l[?25h[?25l[?7lR.<x> = Polynomialing(GF(3))[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)*C.dx).jth_component(1)[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^(-1)*C.dx).jth_component(1)

+[?7h[?12l[?25h[?2004lg 1/x
+g2 1/x*y^2
+[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)*C.dx).jth_component(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[?7lsage: ((C.x)^(-1)*C.dx).jth_component(0)

+[?7h[?12l[?25h[?2004lg 1/x
+g2 1/x*y^2
+[?7h1/x
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + 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^2*y)) dx
+g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y
+g2 ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y^3
+g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y
+g2 ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y^3
+component, j 0 0 0
+q, r 0 0
+g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y
+g2 ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y^3
+g ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y
+g2 ((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^12 + 2*x^9 + x^3))*y^3
+component, j 0 1 0
+q, r 0 0
+g 0
+g2 0
+((x^22 - x^21 - x^20 + x^17 - x^16 - x^15 + x^13 - x^10 + x^9 - x^6 - x^4 + x^3 - x^2 + x + 1)/(x^7*y + x^6*y + x^5*y - x^4*y + x^3*y + x*y)) dx
+g ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y
+g2 ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y^3
+g ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y
+g2 ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y^3
+component, j 0 0 0
+q, r 0 0
+g ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y
+g2 ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y^3
+g ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y
+g2 ((x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^11 + 2*x^8 + x^2))*y^3
+component, j 0 1 0
+q, r 0 0
+g 0
+g2 0
+[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((x^15 - x^14 + x^13 + x^12 + x^11 + x^9 - x^7 - x^4 - x^2 - x)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 - x^10 - x^9 - x^8 - x^7 - x^6 + x^5 + x^4)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((x^21 - x^20 - x^19 - x^16 + x^13 + x^12 + x^10 - x^8 + x^7 - x^6 - x^4 - x^3 - x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lres.reduce()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lduc(xi)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: reduce(C, 1/y)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [39], in <cell line: 1>()
+----> 1 reduce(C, Integer(1)/y)
+
+TypeError: reduce() arg 2 must support iteration
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreduce(C, 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(C, 1/y)[?7h[?12l[?25h[?25l[?7lt(C, 1/y)[?7h[?12l[?25h[?25l[?7li(C, 1/y)[?7h[?12l[?25h[?25l[?7lo(C, 1/y)[?7h[?12l[?25h[?25l[?7ln(C, 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[?7lsage: reduction(C, 1/y)

+[?7h[?12l[?25h[?2004l[?7h(1/(x^3 + 2*x + 1))*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((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + 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^2*y)) dx
+component, j 0 0 0
+q, r 0 0
+component, j (x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^8 + x^7 + x^6 + 2*x^5 + x^4 + x^2) 1 (x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^8 + x^7 + x^6 + 2*x^5 + x^4 + x^2)
+q, r x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^3 + 2*x + 1 2*x^7 + 2*x^6 + 2*x^5 + x^4 + x^3 + 2*x + 1
+---------------------------------------------------------------------------
+ValueError                                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/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:
+
+TypeError                                 Traceback (most recent call last)
+Input In [41], 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>:27, 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>:9, in <module>
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:87, in decomposition_omega0_omega8(omega, prec)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/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((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + 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^2*y)) dx
+component, j 0 0 0
+q, r 0 0
+component, j (x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^8 + x^7 + x^6 + 2*x^5 + x^4 + x^2) 1 (x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^8 + x^7 + x^6 + 2*x^5 + x^4 + x^2)
+q, r x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x^3 + 2*x + 1 2*x^7 + 2*x^6 + 2*x^5 + x^4 + x^3 + 2*x + 1
+((x^22 - x^21 - x^20 + x^17 - x^16 - x^15 + x^13 - x^10 + x^9 - x^6 - x^4 + x^3 - x^2 + x + 1)/(x^7*y + x^6*y + x^5*y - x^4*y + x^3*y + x*y)) dx
+component, j 0 0 0
+q, r 0 0
+component, j (x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x) 1 (x^22 + 2*x^21 + 2*x^20 + x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^10 + x^9 + 2*x^6 + 2*x^4 + x^3 + 2*x^2 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x)
+q, r x^15 + x^14 + x^9 + 2*x^7 + 2*x^4 + 2*x^2 + x + 1 2*x^6 + 2*x^5 + 2*x^4 + x^3 + x^2 + 1
+[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^6 + x^5 - x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 - x^3 - 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + 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((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + 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^2*y)) dx
+((x^22 - x^21 - x^20 + x^17 - x^16 - x^15 + x^13 - x^10 + x^9 - x^6 - x^4 + x^3 - x^2 + x + 1)/(x^7*y + x^6*y + x^5*y - x^4*y + x^3*y + x*y)) dx
+[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^6 + x^5 - x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 - x^3 - 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.valuation()[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x + 1 over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + 1)/(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^2*C.y))[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + 1)/(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^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lf((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + 1)/(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^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lf((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + 1)/(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^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + 1)/(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^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l=((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + 1)/(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^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + 1)/(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^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y)*C.dx[?7h[?12l[?25h[?25l[?7lC)/(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^2*C.y)*C.dx[?7h[?12l[?25h[?25l[?7l.)/(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^2*C.y)*C.dx[?7h[?12l[?25h[?25l[?7lo)/(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^2*C.y)*C.dx[?7h[?12l[?25h[?25l[?7ln)/(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^2*C.y)*C.dx[?7h[?12l[?25h[?25l[?7le)/(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^2*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[?7lsage: fff = ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + C.one)/(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^2*C.y))*C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + C.one)/(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^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: fff

+[?7h[?12l[?25h[?2004l[?7h((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + 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^2*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldef chang(a):[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_g8((3*a).f)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_g8((3*a).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[?7lomega0_omega8(a)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(a)[1].expansion_at_infty()

+ decomposition_omega0_omega8 

+ decomposition_omega0_omega82

+ dec…omega0_omega8_old       

+

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

+

+

+[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(fff)

+[?7h[?12l[?25h[?2004l((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + 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^2*y)) dx
+[?7h(((x^9 + x^8 - x^7 - x^6 - x^3 - x + 1)/y) dx,
+ ((x^9 + x^8 - x^7 - x^6 - x^3 - x + 1)/y) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lldecomposition_omega0_omega8(f)[?7h[?12l[?25h[?25l[?7ledecomposition_omega0_omega8(f)[?7h[?12l[?25h[?25l[?7lndecomposition_omega0_omega8(f)[?7h[?12l[?25h[?25l[?7llen(decomposition_omega0_omega8(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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: len(decomposition_omega0_omega8(fff))

+[?7h[?12l[?25h[?2004l(((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^11 + x^10 + 2*x^8 + x^7 + 2*x^6 + 2*x^5 + x^4 + 2*x^3 + x^2))*y) dx
+[?7h2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llen(decomposition_omega0_omega8(fff))[?7h[?12l[?25h[?25l[?7lsage: len(decomposition_omega0_omega8(fff))

+[?7h[?12l[?25h[?2004l(((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^11 + x^10 + 2*x^8 + x^7 + 2*x^6 + 2*x^5 + x^4 + 2*x^3 + x^2))*y) dx
+[?7h2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llen(decomposition_omega0_omega8(fff))[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llendecomposition_omega0_omega8(f)[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(fff)

+[?7h[?12l[?25h[?2004l(((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^11 + x^10 + 2*x^8 + x^7 + 2*x^6 + 2*x^5 + x^4 + 2*x^3 + x^2))*y) dx
+[?7h(((x^9 + x^8 - x^7 - x^6 - x^3 - x + 1)/y) dx,
+ ((x^9 + x^8 - x^7 - x^6 - x^3 - x + 1)/y) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llen(decomposition_omega0_omega8(fff))[?7h[?12l[?25h[?25l[?7load('init.age')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + 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^2*y)) dx
+((x^22 - x^21 - x^20 + x^17 - x^16 - x^15 + x^13 - x^10 + x^9 - x^6 - x^4 + x^3 - x^2 + x + 1)/(x^7*y + x^6*y + x^5*y - x^4*y + x^3*y + x*y)) dx
+[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^6 + x^5 - x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 - x^3 - 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))]
+[?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[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^6 + x^5 - x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 - x^3 - 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[?7h[?12l[?25h[?25l[?7llen(decomposition_omega0_omega8(fff))[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[?7h[?12l[?25h[?25l[?7lfff[?7h[?12l[?25h[?25l[?7l = ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + C.one)/(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^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lfff = ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + C.one)/(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^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: fff = ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + C.one)/(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^2*C.y))*C.dx

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + C.one)/(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^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[?7h[?12l[?25h[?25l[?7llen(decomposition_omega0_omega8(fff))[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[?7h[?12l[?25h[?25l[?7llen(decomposition_omega0_omega8(fff))[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(fff)

+[?7h[?12l[?25h[?2004l[?7h(((x^9 + x^8 - x^7 - x^6 - x^3 - x + 1)/y) dx,
+ ((x^7 + x^6 + x^5 - x^4 - x^3 + x - 1)/(x^8*y + x^7*y + x^6*y - x^5*y + x^4*y + x^2*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[?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[?7lsage: decomposition_omega0_omega8(fff)[0] - ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + 1)/(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^2*C.y
)

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

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

+ [?7h[?12l[?25h[?25l[?7l
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+                                                          decomposition                   decomposition_omega0_omega82   

+ decomposition_g0_g8             decomposition_omega0_omega8_old

+ decomposition_omega0_omega8                                    

+

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

+ decomposition                  

+

+

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

+ decomposition                  

+ decomposition_g0_g8            [?7h[?12l[?25h[?25l[?7lomea0_omega8

+

+ decomposition_g0_g8            

+ decomposition_omega0_omega8    [?7h[?12l[?25h[?25l[?7l

+

+

+

+[?7h[?12l[?25h[?25l[?7l([?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[?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[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(fff)[0] - decomposition_omega0_omega8(fff)[1] == fff

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

+

+

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

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

+

+ [?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[0] - decomposition_omega0_omega8(fff)[1] == fff[?7h[?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[?7h[?12l[?25h[?25l[?7l f[?7h[?12l[?25h[?25l[?7l[]f[?7h[?12l[?25h[?25l[?7l[], 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[?7lsage: decomposition_omega0_omega8(fff)[0] - decomposition_omega0_omega8(fff)[1], fff

+[?7h[?12l[?25h[?2004l[?7h(((x^17 - x^16 + x^15 + x^14 + x^13 + x^12 - x^10 + 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^2*y)) dx,
+ (((x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^10 + x^7 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 1)/(x^11 + x^10 + 2*x^8 + x^7 + 2*x^6 + 2*x^5 + x^4 + 2*x^3 + x^2))*y) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(fff)[0] - decomposition_omega0_omega8(fff)[1], fff[?7h[?12l[?25h[?25l[?7l[?7h[?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[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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(f)[0] - decomposition_omega0_omega8(f)[1]), 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[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()., f[?7h[?12l[?25h[?25l[?7lf, f[?7h[?12l[?25h[?25l[?7lo, f[?7h[?12l[?25h[?25l[?7lfor, f[?7h[?12l[?25h[?25l[?7lform, 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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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(decomposition_omega0_omega8(f)[0] - decomposition_omega0_omega8(f)[1]).form, f[?7h[?12l[?25h[?25l[?7le(decomposition_omega0_omega8(f)[0] - decomposition_omega0_omega8(f)[1]).form, f[?7h[?12l[?25h[?25l[?7ld(decomposition_omega0_omega8(f)[0] - decomposition_omega0_omega8(f)[1]).form, f[?7h[?12l[?25h[?25l[?7lu(decomposition_omega0_omega8(f)[0] - decomposition_omega0_omega8(f)[1]).form, f[?7h[?12l[?25h[?25l[?7lc(decomposition_omega0_omega8(f)[0] - decomposition_omega0_omega8(f)[1]).form, f[?7h[?12l[?25h[?25l[?7le(decomposition_omega0_omega8(f)[0] - decomposition_omega0_omega8(f)[1]).form, f[?7h[?12l[?25h[?25l[?7l((decomposition_omega0_omega8(f)[0] - decomposition_omega0_omega8(f)[1]).form, f[?7h[?12l[?25h[?25l[?7lC(decomposition_omega0_omega8(f)[0] - decomposition_omega0_omega8(f)[1]).form, f[?7h[?12l[?25h[?25l[?7l,(decomposition_omega0_omega8(f)[0] - decomposition_omega0_omega8(f)[1]).form, f[?7h[?12l[?25h[?25l[?7l (decomposition_omega0_omega8(f)[0] - decomposition_omega0_omega8(f)[1]).form, 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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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[?7h[?12l[?25h[?25l[?7l- 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[?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: reduce(C, (decomposition_omega0_omega8(fff)[0] - decomposition_omega0_omega8(fff)[1]).form- fff.form)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [57], in <cell line: 1>()
+----> 1 reduce(C, (decomposition_omega0_omega8(fff)[Integer(0)] - decomposition_omega0_omega8(fff)[Integer(1)]).form- fff.form)
+
+TypeError: reduce() arg 2 must support iteration
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreduce(C, (decomposition_omega0_omega8(fff)[0] - decomposition_omega0_omega8(fff)[1]).form- fff.form)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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, (decomposition_omega0_omega8(f)[0] - decomposition_omega0_omega8(f)[1]).form- f.form)[?7h[?12l[?25h[?25l[?7lt(C, (decomposition_omega0_omega8(f)[0] - decomposition_omega0_omega8(f)[1]).form- f.form)[?7h[?12l[?25h[?25l[?7li(C, (decomposition_omega0_omega8(f)[0] - decomposition_omega0_omega8(f)[1]).form- f.form)[?7h[?12l[?25h[?25l[?7lo(C, (decomposition_omega0_omega8(f)[0] - decomposition_omega0_omega8(f)[1]).form- f.form)[?7h[?12l[?25h[?25l[?7ln(C, (decomposition_omega0_omega8(f)[0] - decomposition_omega0_omega8(f)[1]).form- f.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[?7lsage: reduction(C, (decomposition_omega0_omega8(fff)[0] - decomposition_omega0_omega8(fff)[1]).form- fff.form)

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lreduction(C, (decomposition_omega0_omega8(fff)[0] - decomposition_omega0_omega8(fff)[1]).form- fff.form)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[1]).form- fff.form)[?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[?7ls[?7h[?12l[?25h[?25l[?7lt[?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[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?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(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[]decomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[decomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()decomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7l(decomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecompositon_omega0_omega8(ff)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7lecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7lecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(f)[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[?7lsage: decomposition_omega0_omega8(fff)[1].expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^2 + t^6 + t^10 + O(t^12)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx.valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x + 1 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,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.dx.valuation()[?7h[?12l[?25h[?25l[?7lcrystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lrystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lsage: C.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l[?7h[([(1/(x^3 + 2*x + 1))*y] d[x] + V(((x^11 - x^9 + x^8 - x^7 + x^6 + x^5 - x^3 - x + 1)/(x^6*y + x^4*y - x^3*y + x^2*y + x*y + y)) dx) + dV([((2*x^7 + x^6 + 2*x^4 + 2*x^3 + 2*x^2 + x)/(x^6 + x^4 + 2*x^3 + x^2 + x + 1))*y]), V(1/x*y), [(1/(x^3 + 2*x + 1))*y] d[x] + V(((x^11 - x^9 + x^8 - x^7 + x^6 + x^5 - x^3 - x + 1)/(x^6*y + x^4*y - x^3*y + x^2*y + x*y + y)) dx) + dV([((2*x^8 + x^7 + 2*x^6 + 2*x^5 + x^4 + 2*x + 2)/(x^7 + x^5 + 2*x^4 + x^3 + x^2 + x))*y])),
+ ([(x/(x^3 + 2*x + 1))*y] d[x] + V(((x^14 - x^9 - x^8 + x^5 + x^4 + x^3 + x^2 - x)/(x^6*y + x^4*y - x^3*y + x^2*y + x*y + y)) dx) + dV([((2*x^10 + x^9 + x^8 + x^7 + x^6 + 2*x^5 + x^4)/(x^6 + x^4 + 2*x^3 + x^2 + x + 1))*y]), [2/x*y] + V(2/x*y), [((2*x + 2)/(x^5 + 2*x^3 + x^2))*y] d[x] + V(((x^15 - x^10 + x^9 + x^6 + x^5 - x^4 + x^3 - x + 1)/(x^7*y + x^5*y - x^4*y + x^3*y + x^2*y + x*y)) dx) + dV([((2*x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^6 + x^4 + 1)/(x^8 + x^6 + 2*x^5 + x^4 + x^3 + x^2))*y]))]
+[?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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7laC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7ltC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lcC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lhC.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l(C.crystaline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().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[?7lsage: patch(C).crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l[?7h[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])),
+ ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^6 + x^5 - x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 - x^3 - 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + 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$ 
]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[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^6 + x^5 - x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 - x^3 - 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + 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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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()[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x + 1 over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l = pach(C)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7lsage: C1 = patch(C)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1 = patch(C)[?7h[?12l[?25h[?25l[?7l.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lp_rank()[?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 + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.polynomial[?7h[?12l[?25h[?25l[?7l1 = patch(C)[?7h[?12l[?25h[?25l[?7l.crysalline_cohomology_basis()[?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: C1.polynomial

+[?7h[?12l[?25h[?2004l[?7hx^4 + 2*x^3 + x
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx.<x> = PolynomialRing(GF(3))[?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[?7lRx[?7h[?12l[?25h[?25l[?7lC1.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[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lgC1.polynomial[?7h[?12l[?25h[?25l[?7l C1.polynomial[?7h[?12l[?25h[?25l[?7l=C1.polynomial[?7h[?12l[?25h[?25l[?7l C1.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[?7lsage: g = C1.polynomial

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = C1.polynomial[?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[?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: g = g(x^3 - x)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg = g(x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: g

+[?7h[?12l[?25h[?2004l[?7hx^12 + 2*x^10 + 2*x^9 + 2*x^6 + x^4 + 2*x^3 + 2*x
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.polynomial[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?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[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C2 = superelliptic(g, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2 = superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: C2

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^12 + 2*x^10 + 2*x^9 + 2*x^6 + x^4 + 2*x^3 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C2.genus()

+[?7h[?12l[?25h[?2004l[?7h5
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.genus()[?7h[?12l[?25h[?25l[?7l2[?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[?7lsage: C2.crystalline_cohomology_basis()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+IndexError                                Traceback (most recent call last)
+Input In [13], in <cell line: 1>()
+----> 1 C2.crystalline_cohomology_basis()
+
+File <string>:355, in crystalline_cohomology_basis(self)
+
+File <string>:349, in de_rham_witt_lift(cech_class)
+
+File <string>:69, 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>:69, in <genexpr>(.0)
+
+File <string>:143, 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[?7lC2.crystalline_cohomology_basis()[?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[?7l(); xi = C.de_rham_basis()[1];xi.coordinates()[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC2 = superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l2[?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[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lne_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); C2 = superelliptic(g, 2); C2.crystalline_cohomology_basis(prec = 100)

+[?7h[?12l[?25h[?2004l[([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^6 + x^5 - x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 - x^3 - 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))]
+---------------------------------------------------------------------------
+IndexError                                Traceback (most recent call last)
+Input In [14], in <cell line: 1>()
+----> 1 load('init.sage'); C2 = superelliptic(g, Integer(2)); C2.crystalline_cohomology_basis(prec = Integer(100))
+
+File <string>:355, in crystalline_cohomology_basis(self, prec)
+
+File <string>:347, in de_rham_witt_lift(cech_class, prec)
+
+File <string>:6, in decomposition_g0_g8(fct)
+
+File <string>:107, in coordinates(self, basis, basis_holo, prec)
+
+File <string>:77, 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[?7lload('init.sage'); C2 = superelliptic(g, 2); C2.crystalline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage'); C2 = superelliptic(g, 2); C2.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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l^[[A    [([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])), ([((2*x + 2)/(x^3 + 2*x^2 + 1))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^6 + x^5 - x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + 2*x^13 + x^12 + x^5)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [2/x*y] + V(2/x*y), [(1/(x^5 + 2*x^4 + x^2))*y] d[x] + V(((-x^21 + x^20 + x^19 - x^15 - x^14 + x^13 - x^12 + x^10 - x^9 + x^7 - x^6 - x^3 - 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((x^19 + 2*x^18 + 2*x^17 + 2*x^16 + 2*x^15 + 2*x^14 + x^13 + x^7 + x^6 + x^3 + x + 1)/(x^7 + x^6 + x^5 + 2*x^4 + x^3 + x))*y]))]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l = superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7l= superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7lsage: C2 = superelliptic(g, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2 = superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: C2

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^12 + 2*x^10 + 2*x^9 + 2*x^6 + x^4 + 2*x^3 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.crystalline_cohomology_basis()[?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[?7lsage: C2.de_rham_basis()

+[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx),
+ ((x/y) dx, 0, (x/y) dx),
+ ((x^2/y) dx, 0, (x^2/y) dx),
+ ((x^3/y) dx, 0, (x^3/y) dx),
+ ((x^4/y) dx, 0, (x^4/y) dx),
+ (((x^10 + x^8 - x^7 - x^4 - x^2 - x)/y) dx, 2/x*y, ((-1)/(x*y)) dx),
+ (((-x^9 + x^6 + x^3 + 1)/y) dx, 2/x^2*y, 0 dx),
+ (((-x^6 + 1)/y) dx, 2/x^3*y, (1/(x^3*y)) dx),
+ (((x^7 + x^5 - x^4 - x)/y) dx, 2/x^4*y, ((x^3 + x^2 - 1)/(x^4*y)) dx),
+ (((-x^6 + x^3 + 1)/y) dx, 2/x^5*y, ((-1)/(x^3*y)) dx)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.de_rham_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laC2.de_rham_basis()[2][?7h[?12l[?25h[?25l[?7l C2.de_rham_basis()[2][?7h[?12l[?25h[?25l[?7l=C2.de_rham_basis()[2][?7h[?12l[?25h[?25l[?7l C2.de_rham_basis()[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[?7lsage: a = C2.de_rham_basis()[2]

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

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [20], in <cell line: 1>()
+----> 1 lift_form_to_drw(a)
+
+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_omega0_omega8(fff)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(xi)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(a)

+[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y]))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C2.de_rham_basis()[2][?7h[?12l[?25h[?25l[?7ldic_expansion(gg, x^3 - x)[?7h[?12l[?25h[?25l[?7lic_expansion(gg, 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, 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[?7lsage: adic_expansion(g, x^3 - x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [22], in <cell line: 1>()
+----> 1 adic_expansion(g, x**Integer(3) - x)
+
+NameError: name 'adic_expansion' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_form_to_drw(a)[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ldrafty/draft.sage')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(afty/draft.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[?7l5.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[?7lsage: load('drafty/draft5.sage')

+[?7h[?12l[?25h[?2004l((-x^18 + x^15 + x^14 + x^11 + x^4*y^2 - 1)/(x^7*y^3)) dx
+t^-40 + O(t^-30)
+[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(g, x^3 - x)

+[?7h[?12l[?25h[?2004l[?7h[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage'[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7llift_form_odrw(a)[?7h[?12l[?25h[?25l[?7la = C2.derham_basis()[2][?7h[?12l[?25h[?25l[?7lC2.de_rham_bsis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx[?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[?7lRx[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage'[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7llift_form_odrw(a)[?7h[?12l[?25h[?25l[?7la = C2.derham_basis()[2][?7h[?12l[?25h[?25l[?7lC2.de_rham_bsis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(); C2 = superelliptic(g, 2); C2.crystalline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7lC2.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = g(x^3 - x)[?7h[?12l[?25h[?25l[?7lC1.polynomial[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7lC1.polynomial[?7h[?12l[?25h[?25l[?7l.polynomial[?7h[?12l[?25h[?25l[?7l1 = patch(C)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1 = patch(C)[?7h[?12l[?25h[?25l[?7l.polynomial[?7h[?12l[?25h[?25l[?7l1.polynomial[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7lg = C1.polynomial[?7h[?12l[?25h[?25l[?7lg(x^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2 = superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lcrystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage'); C2 = superelliptic(g, 2); C2.crystalline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC2 = superelliptic(g, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7la = C2.de_rhm_basis()[2][?7h[?12l[?25h[?25l[?7llift_formto_drw(a)[?7h[?12l[?25h[?25l[?7lde_rham_witlift(a)[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage'[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.de_rham_basis()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: C2

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^12 + 2*x^10 + 2*x^9 + 2*x^6 + x^4 + 2*x^3 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l = g(x^3 - x)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC1.polynomial[?7h[?12l[?25h[?25l[?7l2[?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: g = C2.polynomial

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion(g, x^3 - x)

+[?7h[?12l[?25h[?2004l[?7h[1, 2, 0, 1, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7lg = C2.olynmial[?7h[?12l[?25h[?25l[?7lC2[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x)[?7h[?12l[?25h[?25l[?7lload('drafty/draft5.sage'[?7h[?12l[?25h[?25l[?7ladic_expansion(g, x^3 - x[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7llift_form_odrw(a)[?7h[?12l[?25h[?25l[?7lde_rham_witlift(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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lade_rham_wit_lift(a)[?7h[?12l[?25h[?25l[?7l1de_rham_wit_lift(a)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(a)[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift(a)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(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[?7lsage: a1 = de_rham_witt_lift(a)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C).crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: p*a1

+[?7h[?12l[?25h[?2004l[?7h(V((x^7/(x^11*y - x^9*y - x^8*y - x^5*y + x^3*y - x^2*y - y)) dx), [0], V((x^7/(x^11*y - x^9*y - x^8*y - x^5*y + x^3*y - x^2*y - y)) dx))
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lquo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1)[?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/drafty/superelliptic_drw.sage
+	modified:   sage/superelliptic/decomposition_into_g0_g8.sage
+	modified:   sage/superelliptic/superelliptic_cech_class.sage
+	modified:   sage/superelliptic/superelliptic_form_class.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/as_cartier.sage
+	sage/drafty/better_trace.sage
+	sage/drafty/cartier_image_representation.sage
+	sage/drafty/draft4.sage
+	sage/drafty/draft5.sage
+	sage/drafty/draft6.sage
+	sage/drafty/draft7.sage
+	sage/drafty/lift_to_de_rham.sage
+	sage/drafty/pole_numbers.sage
+	sage/drafty/regular_on_U0.sage
+	sage/superelliptic/frobenius_kernel.sage
+	sage/superelliptic/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$ 
\ No newline at end of file
diff --git a/sage/drafty/draft.sage b/sage/drafty/draft.sage
index c9739b8..4834464 100644
--- a/sage/drafty/draft.sage
+++ b/sage/drafty/draft.sage
@@ -2,8 +2,7 @@ p = 3
 m = 2
 F = GF(p)
 Rx.<x> = PolynomialRing(F)
-f = x^3 - x
+f = x^3 - x + 1
 C = superelliptic(f, m)
-a = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x)
-b = a+a+a+a+a+a+a+a+a
-print(b)
\ No newline at end of file
+C1 = patch(C)
+print(C1.crystalline_cohomology_basis())
\ No newline at end of file
diff --git a/sage/drafty/superelliptic_drw.sage b/sage/drafty/superelliptic_drw.sage
index 1daeac1..6d00826 100644
--- a/sage/drafty/superelliptic_drw.sage
+++ b/sage/drafty/superelliptic_drw.sage
@@ -309,8 +309,27 @@ class superelliptic_drw_cech:
         omega0 = self.omega0
         f = self.f
         return superelliptic_drw_cech(other*omega0, other*f)
+    
+    def r(self):
+        omega0 = self.omega0
+        f = self.f
+        C = self.curve
+        return superelliptic_cech(C, omega0.h1*C.dx, f.t)
+    
+    def coordinates(self, basis = 0):
+        coord_mod_p = self.r().coordinates()
+        print(coord_mod_p)
+        coord_lifted = [lift(a) for a in coord_mod_p]
+        if basis == 0:
+            basis = self.curve().crystalline_cohomology_basis()
+        aux = self
+        for i, a in enumerate(basis):
+            aux -= coord_lifted[i]*a
+        aux = aux.reduce()
+        return aux
+        
 
-def de_rham_witt_lift(cech_class):
+def de_rham_witt_lift(cech_class, prec = 50):
     C = cech_class.curve
     g = C.genus()
     omega0 = cech_class.omega0
@@ -324,7 +343,37 @@ def de_rham_witt_lift(cech_class):
     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
+    decom_aux_h2 = decomposition_g0_g8(aux.h2, prec=prec)
+    aux_h2 = decom_aux_h2[0]
+    aux_f = decom_aux_h2[2]
+    aux_omega0 = decomposition_omega0_omega8(aux.omega, prec=prec)[0]
+    return superelliptic_drw_cech(omega0_lift + aux_h2.verschiebung().diffn() + aux_omega0.verschiebung(), fct.teichmuller() + aux_f.verschiebung())
+
+def crystalline_cohomology_basis(self, prec = 50):
+    result = []
+    for a in self.de_rham_basis():
+        result += [de_rham_witt_lift(a, prec = prec)]
+    return result
+
+superelliptic.crystalline_cohomology_basis = crystalline_cohomology_basis
+
+def autom(self):
+    C = self.curve
+    F = C.base_ring
+    Rxy.<x, y> = PolynomialRing(F, 2)
+    Fxy = FractionField(Rxy)
+    if isinstance(self, superelliptic_function):
+        result = superelliptic_function(C, Fxy(self.function).subs({x:x+1, y:y}))
+        return result
+    if isinstance(self, superelliptic_form):
+        result = superelliptic_form(C, Fxy(self.form).subs({x:x+1, y:y}))
+        return result
+    if isinstance(self, superelliptic_witt):
+        result = superelliptic_witt(autom(self.t), autom(self.f))
+        return result
+    if isinstance(self, superelliptic_drw_form):
+        result = superelliptic_drw_form(autom(self.h1), autom(self.omega), autom(self.h2))
+        return result
+    if isinstance(self, superelliptic_drw_cech):
+        result = superelliptic_drw_cech(autom(self.omega0), autom(self.f))
+        return result
\ 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 f4b99ee..d39b951 100644
--- a/sage/superelliptic/decomposition_into_g0_g8.sage
+++ b/sage/superelliptic/decomposition_into_g0_g8.sage
@@ -1,4 +1,4 @@
-def decomposition_g0_g8(fct):
+def decomposition_g0_g8(fct, prec = 50):
     '''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()
@@ -7,7 +7,7 @@ def decomposition_g0_g8(fct):
     for i, a in enumerate(C.cohomology_of_structure_sheaf_basis()):
         nontrivial_part += coord[i]*a
     fct -= nontrivial_part
-    if fct.coordinates() != g*[0]:
+    if fct.coordinates(prec=prec) != g*[0]:
         raise ValueError("The given function cannot be written as g0 - g8.")
     
     Fxy, Rxy, x, y = C.fct_field
@@ -24,26 +24,37 @@ def decomposition_g0_g8(fct):
         else:
             g0 += num.monomial_coefficient(monomial)*aux/aux_den
     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.'''
     C = omega.curve
+    omega.form = reduction(C, omega.form)
+    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:
+        raise ValueError(str(omega) + " has non zero residue!")
     Fxy, Rxy, x, y = C.fct_field
+    Rx.<x> = PolynomialRing(F)
+    Fx = FractionField(Rx)
     fct = Fxy(omega.form)
     num = fct.numerator()
     den = fct.denominator()
     aux_den = superelliptic_function(C, Rxy(den))
     g0 = superelliptic_function(C, 0)
     g8 = superelliptic_function(C, 0)
-    dx_valuation = C.dx.expansion_at_infty(prec=prec).valuation()
-    for monomial in num.monomials():
-        aux = superelliptic_function(C, monomial)
-        if aux.expansion_at_infty(prec=prec).valuation() + dx_valuation >= aux_den.expansion_at_infty(prec=prec).valuation():
-            g8 += num.monomial_coefficient(monomial)*aux/aux_den
-        else:
-            g0 += num.monomial_coefficient(monomial)*aux/aux_den
+    for j in range(0, m):
+        component = Fx(omega.jth_component(j))
+        q, r = component.numerator().quo_rem(component.denominator())
+        g0 += (C.y)^(-j)*superelliptic_function(C, Rxy(q))
+        if ((C.y)^(-j)*superelliptic_function(C, Fxy(r/component.denominator()))*C.dx).expansion_at_infty().valuation() < 0:
+            raise ValueError("Something went wrong for "+str(omega))
+        g8 -= (C.y)^(-j)*superelliptic_function(C, Fxy(r/component.denominator()))
     g0, g8  = g0*C.dx, g8*C.dx
     if g0.is_regular_on_U0():
         return (g0, g8)
+    #Rx.<x> = PolynomialRing(F)
+    #Rx.<x> = PolynomialRing(F)
+    #aux_fct = (g0.form)*y
     else:
-        raise Error("Something went wrong.")
\ No newline at end of file
+        raise ValueError("Something went wrong for "+str(omega) +". Result would be "+str(g0)+ " and " + str(g8))
\ No newline at end of file
diff --git a/sage/superelliptic/superelliptic_cech_class.sage b/sage/superelliptic/superelliptic_cech_class.sage
index e9f9af0..12af23d 100644
--- a/sage/superelliptic/superelliptic_cech_class.sage
+++ b/sage/superelliptic/superelliptic_cech_class.sage
@@ -71,7 +71,7 @@ class superelliptic_cech:
         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, p)
+                d = degree_of_rational_fctn(fct_j, F)
             
                 if (d, j) in degrees1.values():
                     index = degrees1_inv[(d, j)]
diff --git a/sage/superelliptic/superelliptic_form_class.sage b/sage/superelliptic/superelliptic_form_class.sage
index 68ddf7f..abbcc6a 100644
--- a/sage/superelliptic/superelliptic_form_class.sage
+++ b/sage/superelliptic/superelliptic_form_class.sage
@@ -93,16 +93,14 @@ class superelliptic_form:
         '''If self = sum_j h_j(x)/y^j dx, output is h_j(x).'''
         g = self.form
         C = self.curve
+        m = C.exponent
         F = C.base_ring
         Rx.<x> = PolynomialRing(F)
         Fx = FractionField(Rx)
         FxRy.<y> = PolynomialRing(Fx)
-        Fxy = FractionField(FxRy)
-        Ryinv.<y_inv> = PolynomialRing(Fx)
-        g = Fxy(g)
-        g = g(y = 1/y_inv)
-        g = Ryinv(g)
-        return coff(g, j)
+        g = reduction(C, y^m*g)
+        g = FxRy(g)
+        return g.monomial_coefficient(y^(m-j))
     
     def is_regular_on_U0(self):
         C = self.curve
@@ -136,6 +134,9 @@ class superelliptic_form:
         C = self.curve
         g = superelliptic_function(C, g)
         g = g.expansion_at_infty(place = place, prec=prec)
-        x_series = superelliptic_function(C, x).expansion_at_infty(place = place, prec=prec)
+        x_series = C.x.expansion_at_infty(place = place, prec=prec)
         dx_series = x_series.derivative()
         return g*dx_series
+    
+    def residue(self, place = 0, prec=30):
+        return self.expansion_at_infty(place = place, prec=prec)[-1]
\ No newline at end of file