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)
 [6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m3[0;38;5;241m*a.omega0 - mult_by_p(C.x*C.y.diffn())[38D[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ma[0;38;5;241m.omega0[7D[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0ma[7D[0m

 [J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m([(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]))
 [6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mq[0;38;5;241muo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1)[39D[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mi[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[12D[0m[J[0;94msage: [0mquit()[12D[0m

-[J[?7h[0m[?12l[?25h[?2004l[23;0t
\ No newline at end of file
+[J[?7h[0m[?12l[?25h[?2004l[23;0t]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ cd ..
+]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ git add -u
+]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ git add -u[5Pcd ..[1Psagegit pushcommit -m "lift kocykli do drw zrobiony z drobnymi bledami"[1P"[1P"[1P"[1P"[1P"[1P"[1P"[1P"[1P"[1P"[1P"[1P"[1P"[1P"[1P"[1P"[1P"[1P"[1P" "c"h"y"b"a" "o"k"[C
+[master 8719e64] lift kocykli do drw zrobiony chyba ok
+ 2 files changed, 305 insertions(+), 3 deletions(-)
+]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ 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[K
+remote: Processed 1 references in total[K
+To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
+   e1a000f..8719e64  master -> master
+]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ 
[K]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+[22;0t]0;IPython: DeRhamComputation/sage[6n[?2004h[?1l[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[70D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m]; a = de_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[77D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m]; a = de_rham_witt_lift(xi)[77D[0m

+[J[?7h[0m[?12l[?25h[?2004lTraceback [0;36m(most recent call last)[0m:
+
+  File [1;32m/ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398[0m in [1;35mrun_code[0m
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input [1;32mIn [1][0m in [1;35m<cell line: 1>[0m
+    load('init.sage'); xi = C.de_rham_basis()[Integer(1)]; a = de_rham_witt_lift(xi)
+
+  File [1;32msage/misc/persist.pyx:175[0m in [1;35msage.misc.persist.load[0m
+    sage.repl.load.load(filename, globals())
+
+  File [1;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m in [1;35mload[0m
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File [1;32m<string>:26[0m in [1;35m<module>[0m
+
+  File [1;32msage/misc/persist.pyx:175[0m in [1;35msage.misc.persist.load[0m
+    sage.repl.load.load(filename, globals())
+
+[0;36m  File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0;36m in [0;35mload[0;36m[0m
+[0;31m    exec(preparse_file(f.read()) + "\n", globals)[0m
+
+[0;36m  File [0;32m<string>:322[0;36m[0m
+[0;31m    coord_lifted =[0m
+[0m                   ^[0m
+[0;31mSyntaxError[0m[0;31m:[0m invalid syntax
+
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m]; a = de_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[77D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m]; a = de_rham_witt_lift(xi)[77D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241mi[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mreduce()[8D[?7h[0m[?12l[?25h[?25l[?7l[0mc[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[21D[0m[J[0;94msage: [0mxi.coordinted()[21D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [3][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mxi[49m[38;5;241;43m.[39;49m[43mcoordinted[49m()
+
+[0;31mAttributeError[0m: 'superelliptic_cech' object has no attribute 'coordinted'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mxi.coordinted[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0ma[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0mt[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0me[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0ms[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[22D[0m[J[0;94msage: [0mxi.coordinates()[22D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [4][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mxi[49m[38;5;241;43m.[39;49m[43mcoordinates[49m[43m([49m[43m)[49m
+
+File [0;32m<string>:75[0m, in [0;36mcoordinates[0;34m(self)[0m
+
+File [0;32m<string>:113[0m, in [0;36mdegree_of_rational_fctn[0;34m(f, F)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554[0m, in [0;36mPolynomialRing[0;34m(base_ring, *args, **kwds)[0m
+[1;32m     52[0m [38;5;124mr[39m[38;5;124;03m"""[39;00m
+[1;32m     53[0m [38;5;124;03mReturn the globally unique univariate or multivariate polynomial[39;00m
+[1;32m     54[0m [38;5;124;03mring with given properties and variable name or names.[39;00m
+[0;32m   (...)[0m
+[1;32m    551[0m [38;5;124;03m    TypeError: unable to convert 'x' to an integer[39;00m
+[1;32m    552[0m [38;5;124;03m"""[39;00m
+[1;32m    553[0m [38;5;28;01mif[39;00m [38;5;129;01mnot[39;00m ring[38;5;241m.[39mis_Ring(base_ring):
+[0;32m--> 554[0m     [38;5;28;01mraise[39;00m [38;5;167;01mTypeError[39;00m([38;5;124m"[39m[38;5;124mbase_ring [39m[38;5;132;01m{!r}[39;00m[38;5;124m must be a ring[39m[38;5;124m"[39m[38;5;241m.[39mformat(base_ring))
+[1;32m    556[0m n [38;5;241m=[39m [38;5;241m-[39m[38;5;241m1[39m  [38;5;66;03m# Unknown number of variables[39;00m
+[1;32m    557[0m names [38;5;241m=[39m [38;5;28;01mNone[39;00m  [38;5;66;03m# Unknown variable names[39;00m
+
+[0;31mTypeError[0m: base_ring 3 must be a ring
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241mi.coordinates()[15D[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[8D[0m[J[0;94msage: [0mxi[8D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241mi[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[8D[0m[J[0;94msage: [0mxi[8D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241mi[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0m[[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C].[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[25D[0m[J[0;94msage: [0mxi[[0;38;5;20;1m0[0m].coordinates()[25D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [7][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mxi[49m[43m[[49m[43mInteger[49m[43m([49m[38;5;241;43m0[39;49m[43m)[49m[43m][49m[38;5;241m.[39mcoordinates()
+
+[0;31mTypeError[0m: 'superelliptic_cech' object is not subscriptable
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mxi[[0;38;5;20;1m0[0m].coordinates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m()[3D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[0;38;5;20;1m0.[0mco[Crdinates()[0m[K[14D[?7h[0m[?12l[?25h[?25l[?7l[0m.co[Crdinates()[0m[K[14D[?7h[0m[?12l[?25h[?25l[?7l[0m.co[Crdinates()[0m[K[14D[?7h[0m[?12l[?25h[?25l[?7l[C[0m.c[Cordinates()[14D[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m([0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mxi[?7h[0m[?12l[?25h[?25l[?7l[0m.coordinates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[6D[0mted[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[15D[0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m]; a = de_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[3D[0m([2C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([2C[0;38;5;16;48;5;152m)[4D[?7h[0m[?12l[?25h[?25l[?7l[0m([2C)[5D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m[[C[0;38;5;16;48;5;152m][3D[?7h[0m[?12l[?25h[?25l[?7l[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m[[C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m; a = de_rham_wit[C_lift(xi)[0m[K[28D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[0;38;5;210;48;5;88m][0m; a = de_rham_wi[Ct_lift(xi)[28D[?7h[0m[?12l[?25h[?25l[?7l[49D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m0[0m]; a = de_rham_witt_lift(xi)[77D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241mi[0].coordinates()[18D[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[8D[0m[J[0;94msage: [0mxi[8D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m((1/y) dx, 0, (1/y) dx)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241mi[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0m[[0;38;5;241m0].coordinates()[16D[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mcoordinates()[13D[?7h[0m[?12l[?25h[?25l[?7l[0mo[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0m0[?7h[0m[?12l[?25h[?25l[?7l[15D[0m[J[0;94msage: [0mxi.omega0[15D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(1/y) dx
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mxi.omega0[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[29D[0m[J[0;94msage: [0mxi.omega0.coordinates()[29D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[1]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241mi.omega0.coordinates()[22D[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mc[0;38;5;241moordinates()[0m[K[12D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mrdinates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[22D[0m[J[0;94msage: [0mxi.coordinates()[22D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(1, 0)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mo[0;38;5;241mr a in range(25):[17D[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;28;1mfor[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mx[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;28min[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[20D[0;94msage: [0;38;5;28;1mfor[0m xi [0;38;5;28min[0m C.de[0m

+[20C[0;38;5;16;48;5;250m C.de_rham_basis                     C.degrees_de_rham1                 [0m

+[20C[0;38;5;16;48;5;250m C.degrees_de_rham0                  C.degrees_holomorphic_differentials[0m

+

+

+[0m [5A[20C[?7h[0m[?12l[?25h[?25l[?7l[0m_rham_basis[0m

+[20C[0;38;5;231;48;5;102m C.de_rham_basis                    [0m

+

+[20C[0;38;5;16;48;5;248m <unknown> [3A[?7h[0m[?12l[?25h[?25l[?7l[0m

+[C[0m[K[0m

+[C[0m[K[0m

+[C[0m[K[3A[30C[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[2D[0m():[?7h[0m[?12l[?25h[?25l[?7l[0m

+[0;94m....: [4C[?7h[0m[?12l[?25h[?25l[?7l[0mp[0;38;5;241mrint('b')[9D[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;24mprint[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mx[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[17D[0;38;5;16;48;5;152m([14C[0m()[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[18D[0m([16C)[0m

+[0;94m....: [4C[?7h[0m[?12l[?25h[?25l[?7l[2A[10D[0m[J[0;94msage: [0;38;5;28;1mfor[0m xi [0;38;5;28min[0m C.de_rham_basis():[0m

+[0;94m....: [0m    [0;38;5;24mprint[0m(xi.coordinates())[0m

+[0;94m....: [6D[0m

+[J[?7h[0m[?12l[?25h[?2004l(1, 0)
+[0;31m---------------------------------------------------------------------------[0m
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [13][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[1;32m      1[0m [38;5;28;01mfor[39;00m xi [38;5;129;01min[39;00m C[38;5;241m.[39mde_rham_basis():
+[0;32m----> 2[0m     [38;5;28mprint[39m([43mxi[49m[38;5;241;43m.[39;49m[43mcoordinates[49m[43m([49m[43m)[49m)
+
+File [0;32m<string>:75[0m, in [0;36mcoordinates[0;34m(self)[0m
+
+File [0;32m<string>:113[0m, in [0;36mdegree_of_rational_fctn[0;34m(f, F)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554[0m, in [0;36mPolynomialRing[0;34m(base_ring, *args, **kwds)[0m
+[1;32m     52[0m [38;5;124mr[39m[38;5;124;03m"""[39;00m
+[1;32m     53[0m [38;5;124;03mReturn the globally unique univariate or multivariate polynomial[39;00m
+[1;32m     54[0m [38;5;124;03mring with given properties and variable name or names.[39;00m
+[0;32m   (...)[0m
+[1;32m    551[0m [38;5;124;03m    TypeError: unable to convert 'x' to an integer[39;00m
+[1;32m    552[0m [38;5;124;03m"""[39;00m
+[1;32m    553[0m [38;5;28;01mif[39;00m [38;5;129;01mnot[39;00m ring[38;5;241m.[39mis_Ring(base_ring):
+[0;32m--> 554[0m     [38;5;28;01mraise[39;00m [38;5;167;01mTypeError[39;00m([38;5;124m"[39m[38;5;124mbase_ring [39m[38;5;132;01m{!r}[39;00m[38;5;124m must be a ring[39m[38;5;124m"[39m[38;5;241m.[39mformat(base_ring))
+[1;32m    556[0m n [38;5;241m=[39m [38;5;241m-[39m[38;5;241m1[39m  [38;5;66;03m# Unknown number of variables[39;00m
+[1;32m    557[0m names [38;5;241m=[39m [38;5;28;01mNone[39;00m  [38;5;66;03m# Unknown variable names[39;00m
+
+[0;31mTypeError[0m: base_ring 3 must be a ring
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage'); xi = C.de_rham_basis()[0]; a = de_rham_witt_lift(xi)[70D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m0[0m]; a = de_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[77D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m0[0m]; a = de_rham_witt_lift(xi)[77D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m0[0m]; a = de_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([2C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m;[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[0;38;5;210;48;5;88m][0m;[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C][C[0;38;5;241m a = de_rham_witt_lift(xi)[26D[?7h[0m[?12l[?25h[?25l[?7l[0m a = de_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[77D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m]; a = de_rham_witt_lift(xi)[77D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m]; a = de_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([2C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[51D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m];[51D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241mi.coordinates()[15D[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0moordinates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[22D[0m[J[0;94msage: [0mxi.coordinates()[22D[0m

+[J[?7h[0m[?12l[?25h[?2004lf, F 2/x 3
+[0;31m---------------------------------------------------------------------------[0m
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [17][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mxi[49m[38;5;241;43m.[39;49m[43mcoordinates[49m[43m([49m[43m)[49m
+
+File [0;32m<string>:75[0m, in [0;36mcoordinates[0;34m(self)[0m
+
+File [0;32m<string>:114[0m, in [0;36mdegree_of_rational_fctn[0;34m(f, F)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554[0m, in [0;36mPolynomialRing[0;34m(base_ring, *args, **kwds)[0m
+[1;32m     52[0m [38;5;124mr[39m[38;5;124;03m"""[39;00m
+[1;32m     53[0m [38;5;124;03mReturn the globally unique univariate or multivariate polynomial[39;00m
+[1;32m     54[0m [38;5;124;03mring with given properties and variable name or names.[39;00m
+[0;32m   (...)[0m
+[1;32m    551[0m [38;5;124;03m    TypeError: unable to convert 'x' to an integer[39;00m
+[1;32m    552[0m [38;5;124;03m"""[39;00m
+[1;32m    553[0m [38;5;28;01mif[39;00m [38;5;129;01mnot[39;00m ring[38;5;241m.[39mis_Ring(base_ring):
+[0;32m--> 554[0m     [38;5;28;01mraise[39;00m [38;5;167;01mTypeError[39;00m([38;5;124m"[39m[38;5;124mbase_ring [39m[38;5;132;01m{!r}[39;00m[38;5;124m must be a ring[39m[38;5;124m"[39m[38;5;241m.[39mformat(base_ring))
+[1;32m    556[0m n [38;5;241m=[39m [38;5;241m-[39m[38;5;241m1[39m  [38;5;66;03m# Unknown number of variables[39;00m
+[1;32m    557[0m names [38;5;241m=[39m [38;5;28;01mNone[39;00m  [38;5;66;03m# Unknown variable names[39;00m
+
+[0;31mTypeError[0m: base_ring 3 must be a ring
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mxi.coordinates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[15D[0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m];[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m;[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[0;38;5;210;48;5;88m][0m;[2D[?7h[0m[?12l[?25h[?25l[?7l[49D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m0[0m];[51D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241mi.coordinates()[15D[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[9D[0m[J[0;94msage: [0mxi.[9D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;36m  Input [0;32mIn [19][0;36m[0m
+[0;31m    xi.[0m
+[0m       ^[0m
+[0;31mSyntaxError[0m[0;31m:[0m invalid syntax
+
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241mi.[2D[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mc[0;38;5;241moordinates()[12D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mordinates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[22D[0m[J[0;94msage: [0mxi.coordinates()[22D[0m

+[J[?7h[0m[?12l[?25h[?2004lf, F 1 Finite Field of size 3
+[0m[?7h[0;91m[0m[0m(1, 0)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[6D[0;94msage: [0mC[0;38;5;241m.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
[162Cf[0m

+[0;94m....: [0;38;5;241mn()[9D[A[7C[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mb[0;38;5;241masis_of_cohomology()[0m[K[0m

+[0m [0m[K[A[8C[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0me[0;38;5;241m_ring[0m[K[5D[?7h[0m[?12l[?25h[?25l[?7l[0m_ring[?7h[0m[?12l[?25h[?25l[?7l[17D[0m[J[0;94msage: [0mC.base_ring[17D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mFinite Field of size 3
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC.base_ring[?7h[0m[?12l[?25h[?25l[?7l[11D[0mxi.coord[2Cates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[13D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[3D[0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m0[0m];[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m[[C[0;38;5;16;48;5;152m][3D[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m([0;38;5;210;48;5;88m)[0m[[C][4D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m()[3D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mxi = C.de_rham_basis()[[0;38;5;20;1m0[0m];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[14D[0;38;5;16;48;5;152m([11C)[0mxi = C.de_rham_basis()[[0;38;5;20;1m0[0m];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[13D[0m([11Cxi = C.de_rham_basis()[[0;38;5;20;1m0[0m];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231mxi = C.de_rham_basis()[0];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231mxi = C.de_rham_basis()[0];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231mxi = C.de_rham_basis()[0];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231mxi = C.de_rham_basis()[0];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231mxi = C.de_rham_basis()[0];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231mxi = C.de_rham_basis()[0];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231mxi = C.de_rham_basis()[0];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231mxi = C.de_rham_basis()[0];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231mxi = C.de_rham_basis()[0];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231mxi = C.de_rham_basis()[0];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[0mxi = C.de_rham_basis()[[0;38;5;20;1m0[0m];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[0mxi = C.de_rham_basis()[[0;38;5;20;1m0[0m];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[0mxi = C.de_rham_basis()[[0;38;5;20;1m0[0m];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[0mxi = C.de_rham_basis()[[0;38;5;20;1m0[0m];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[0mxi = C.de_rham_basis()[[0;38;5;20;1m0[0m];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[0mxi = C.de_rham_basis()[[0;38;5;20;1m0[0m];[0m[K[26D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[14C[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m()[C[?7h[0m[?12l[?25h[?25l[?7l[3C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m[[C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m;[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[0;38;5;210;48;5;88m][0m;[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C][C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[48D[0m[J[0;94msage: [0mxi = C.de_rham_basis()[[0;38;5;20;1m1[0m];xi.coordinates()[48D[0m

+[J[?7h[0m[?12l[?25h[?2004lf, F 2/x 3
+[0;31m---------------------------------------------------------------------------[0m
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [22][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m xi [38;5;241m=[39m C[38;5;241m.[39mde_rham_basis()[Integer([38;5;241m1[39m)];[43mxi[49m[38;5;241;43m.[39;49m[43mcoordinates[49m[43m([49m[43m)[49m
+
+File [0;32m<string>:75[0m, in [0;36mcoordinates[0;34m(self)[0m
+
+File [0;32m<string>:114[0m, in [0;36mdegree_of_rational_fctn[0;34m(f, F)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554[0m, in [0;36mPolynomialRing[0;34m(base_ring, *args, **kwds)[0m
+[1;32m     52[0m [38;5;124mr[39m[38;5;124;03m"""[39;00m
+[1;32m     53[0m [38;5;124;03mReturn the globally unique univariate or multivariate polynomial[39;00m
+[1;32m     54[0m [38;5;124;03mring with given properties and variable name or names.[39;00m
+[0;32m   (...)[0m
+[1;32m    551[0m [38;5;124;03m    TypeError: unable to convert 'x' to an integer[39;00m
+[1;32m    552[0m [38;5;124;03m"""[39;00m
+[1;32m    553[0m [38;5;28;01mif[39;00m [38;5;129;01mnot[39;00m ring[38;5;241m.[39mis_Ring(base_ring):
+[0;32m--> 554[0m     [38;5;28;01mraise[39;00m [38;5;167;01mTypeError[39;00m([38;5;124m"[39m[38;5;124mbase_ring [39m[38;5;132;01m{!r}[39;00m[38;5;124m must be a ring[39m[38;5;124m"[39m[38;5;241m.[39mformat(base_ring))
+[1;32m    556[0m n [38;5;241m=[39m [38;5;241m-[39m[38;5;241m1[39m  [38;5;66;03m# Unknown number of variables[39;00m
+[1;32m    557[0m names [38;5;241m=[39m [38;5;28;01mNone[39;00m  [38;5;66;03m# Unknown variable names[39;00m
+
+[0;31mTypeError[0m: base_ring 3 must be a ring
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage'); xi = C.de_rham_basis()[0];[44D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m0[0m];[?7h[0m[?12l[?25h[?25l[?7l[51D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m0[0m];[51D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m0[0m];[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m;[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[0;38;5;210;48;5;88m][0m;[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C][C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mdinates[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[67D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m];xi.coordinates()[67D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+f, F 2/x Finite Field of size 3
+[0m[?7h[0;91m[0m[0m(0, 1)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage'); xi = C.de_rham_basis()[1];xi.coordinates()[60D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m];xi.coordinates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[67D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m];xi.coordinates()[67D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[0m[?7h[0;91m[0m[0m(0, 1)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241mi = C.de_rham_basis()[1];xi.coordinates()[41D[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mcoor[Cinates()[0m[K[13D[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mrdinates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;210;48;5;88m([?7h[0m[?12l[?25h[?25l[?7l[0m()[13D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mfxi.c[Cordinates()[16D[?7h[0m[?12l[?25h[?25l[?7l[0moxi.c[Cordinates()[16D[?7h[0m[?12l[?25h[?25l[?7l[0mrxi.c[Cordinates()[16D[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;28;1mfor[0m xi.c[Cordinates()[16D[?7h[0m[?12l[?25h[?25l[?7l[0maxi.c[Cordinates()[16D[?7h[0m[?12l[?25h[?25l[?7l[0m xi.c[Cordinates()[16D[?7h[0m[?12l[?25h[?25l[?7l[0mixi.c[Cordinates()[16D[?7h[0m[?12l[?25h[?25l[?7l[0mnxi.c[Cordinates()[16D[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;28min[0m xi.c[Cordinates()[16D[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[12C[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m():[?7h[0m[?12l[?25h[?25l[?7l[32D[0;94msage: [0;38;5;28;1mfor[0m a [0;38;5;28min[0m xi.coordinates():[0m

+[0;94m....: [6D[10C[?7h[0m[?12l[?25h[?25l[?7l[0mp[0;38;5;241mrint(xi.coordinates())[22D[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;24mprint[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mt[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;24mtype[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m([C)[?7h[0m[?12l[?25h[?25l[?7l[8D[0;38;5;16;48;5;152m([4C[0m([C)[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[24D[0;94m....: [0m    [0;38;5;24mprint[0m([0;38;5;24mtype[0m(a))[0m

+[0;94m....: [6D[10C[?7h[0m[?12l[?25h[?25l[?7l[2A[10D[0m[J[0;94msage: [0;38;5;28;1mfor[0m a [0;38;5;28min[0m xi.coordinates():[0m

+[0;94m....: [0m    [0;38;5;24mprint[0m([0;38;5;24mtype[0m(a))[0m

+[0;94m....: [6D[0m

+[J[?7h[0m[?12l[?25h[?2004l<class 'sage.rings.finite_rings.integer_mod.IntegerMod_int'>
+<class 'sage.rings.finite_rings.integer_mod.IntegerMod_int'>
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[6D[0;94msage: [0;38;5;28;1mfor[0m a [0;38;5;28min[0m xi.coordinates():[0m

+[0;94m....: [0m    [0;38;5;24mprint[0;38;5;16;48;5;152m([0;38;5;24mtype[0m(a)[0;38;5;16;48;5;152m)[24D[24C[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[8D[0m([4C[0;38;5;16;48;5;152m([C[0;38;5;210;48;5;88m)[0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[0m([C)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([C[0;38;5;16;48;5;152m)[3D[?7h[0m[?12l[?25h[?25l[?7l[4D[0mtyp[0;38;5;210;48;5;88m([0ma[0;38;5;16;48;5;152m)[0m)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0ma[0;38;5;16;48;5;152m)[0m)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0ma[0;38;5;16;48;5;152m)[0m)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0ma[0;38;5;16;48;5;152m)[0m)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;210;48;5;88m([0ma[0;38;5;16;48;5;152m)[0m)[4D[?7h[0m[?12l[?25h[?25l[?7l[0mi[0;38;5;210;48;5;88m([0ma[0;38;5;16;48;5;152m)[0m)[4D[?7h[0m[?12l[?25h[?25l[?7l[0mt[0;38;5;210;48;5;88m([0ma[0;38;5;16;48;5;152m)[0m)[4D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0ma[0;38;5;16;48;5;152m)[0m)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0mf[0;38;5;210;48;5;88m([0ma[0;38;5;16;48;5;152m)[0m)[4D[?7h[0m[?12l[?25h[?25l[?7l[0mt[0;38;5;210;48;5;88m([0ma[0;38;5;16;48;5;152m)[0m)[4D[?7h[0m[?12l[?25h[?25l[?7l[0m([C)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[7D[0;38;5;16;48;5;152m([4C[0m([C)[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[24D[0;94m....: [0m    [0;38;5;24mprint[0m(lift(a))[0m

+[0;94m....: [6D[10C[?7h[0m[?12l[?25h[?25l[?7l[2A[10D[0m[J[0;94msage: [0;38;5;28;1mfor[0m a [0;38;5;28min[0m xi.coordinates():[0m

+[0;94m....: [0m    [0;38;5;24mprint[0m(lift(a))[0m

+[0;94m....: [6D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+1
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ 
[K]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ lo[K[Ksage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+[22;0t]0;IPython: DeRhamComputation/sage[6n[?2004h[?1l[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage'); xi = C.de_rham_basis()[1];xi.coordinates()[60D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231m'[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231mi[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231mn[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231mi[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231mt[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231m.[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231ms[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231ma[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231mg[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231me[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231m'[?7h[0m[?12l[?25h[?25l[?7l[12D[0;38;5;16;48;5;152m([11C)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.base_ring[10D[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mC[7D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mbase_ring[9D[?7h[0m[?12l[?25h[?25l[?7l[0mc[C[0;38;5;241mrtier_matrix()[15D[?7h[0m[?12l[?25h[?25l[?7l[0mr[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mystalline_cohomology_basis[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[38D[0m[J[0;94msage: [0mC.crystalline_cohomology_basis()[38D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[([(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]))]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;210;48;5;88m([?7h[0m[?12l[?25h[?25l[?7l[0m()[30D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0maC.crysta[Cline_cohomology_basis()[32D[?7h[0m[?12l[?25h[?25l[?7l[0maC.crysta[Cline_cohomology_basis()[32D[?7h[0m[?12l[?25h[?25l[?7l[0maC.crysta[Cline_cohomology_basis()[32D[?7h[0m[?12l[?25h[?25l[?7l[0m C.crysta[Cline_cohomology_basis()[32D[?7h[0m[?12l[?25h[?25l[?7l[0m=C.crysta[Cline_cohomology_basis()[32D[?7h[0m[?12l[?25h[?25l[?7l[0m C.crysta[Cline_cohomology_basis()[32D[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[28C[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[44D[0m[J[0;94msage: [0maaa = C.crystalline_cohomology_basis()[44D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ma[0;38;5;241maa = C.crystalline_cohomology_basis()[37D[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0me[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;24mlen[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0m_[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m([3C)[?7h[0m[?12l[?25h[?25l[?7l[14D[0m[J[0;94msage: [0;38;5;24mlen[0m(aaa)[14D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m2
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;241mecomposition_g0_g8((3*a).f)[27D[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mf[0m[K[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;28;1mdef[C[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;25;1mc[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;25;1mh[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;25;1ma[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;25;1mn[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;25;1mg[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;25;1me[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m([C)[?7h[0m[?12l[?25h[?25l[?7l[3D[0m([C):[?7h[0m[?12l[?25h[?25l[?7l[19D[0;94msage: [0;38;5;28;1mdef[0m [0;38;5;25;1mchang[0m(a):[0m

+[0;94m....: [6D[10C[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0m+[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[?7h[0m[?12l[?25h[?25l[?7l[17D[0;94m....: [0m    a = a+[0;38;5;20;1m1[0m

+[0;94m....: [6D[10C[?7h[0m[?12l[?25h[?25l[?7l[2A[10D[0m[J[0;94msage: [0;38;5;28;1mdef[0m [0;38;5;25;1mchang[0m(a):[0m

+[0;94m....: [0m    a = a+[0;38;5;20;1m1[0m

+[0;94m....: [6D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mc[0;38;5;241m.frobenius()[12D[?7h[0m[?12l[?25h[?25l[?7l[0mh[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mb[0;38;5;241m = (a+a+a).omega0.omega[23D[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m3[0m[K[?7h[0m[?12l[?25h[?25l[?7l[11D[0m[J[0;94msage: [0mb = [0;38;5;20;1m3[11D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mc[0;38;5;241m.frobenius()[12D[?7h[0m[?12l[?25h[?25l[?7l[0mh[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mb[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m([C)[?7h[0m[?12l[?25h[?25l[?7l[14D[0m[J[0;94msage: [0mchang(b)[14D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mb[0;38;5;241m = 3[4D[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mb[7D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m3
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241men(aaa)[7D[?7h[0m[?12l[?25h[?25l[?7l[0mo[0;38;5;241mad('init.sage')[15D[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004lTraceback [0;36m(most recent call last)[0m:
+
+  File [1;32m/ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398[0m in [1;35mrun_code[0m
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input [1;32mIn [10][0m in [1;35m<cell line: 1>[0m
+    load('init.sage')
+
+  File [1;32msage/misc/persist.pyx:175[0m in [1;35msage.misc.persist.load[0m
+    sage.repl.load.load(filename, globals())
+
+  File [1;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m in [1;35mload[0m
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File [1;32m<string>:26[0m in [1;35m<module>[0m
+
+  File [1;32msage/misc/persist.pyx:175[0m in [1;35msage.misc.persist.load[0m
+    sage.repl.load.load(filename, globals())
+
+[0;36m  File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0;36m in [0;35mload[0;36m[0m
+[0;31m    exec(preparse_file(f.read()) + "\n", globals)[0m
+
+[0;36m  File [0;32m<string>:323[0;36m[0m
+[0;31m    if basis = _sage_const_0 :[0m
+[0m       ^[0m
+[0;31mSyntaxError[0m[0;31m:[0m invalid syntax. Maybe you meant '==' or ':=' instead of '='?
+
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.crystalline_cohomology_basis()[31D[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ma[0;38;5;241maa = C.crystalline_cohomology_basis()[37D[?7h[0m[?12l[?25h[?25l[?7l[0mu[0;38;5;241mx.h2.coordinates()[0m[K[18D[?7h[0m[?12l[?25h[?25l[?7l[0mt[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m([3C)[?7h[0m[?12l[?25h[?25l[?7l[16D[0m[J[0;94msage: [0mautom(C.x)[16D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mNameError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [12][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mautom[49m[43m([49m[43mC[49m[38;5;241;43m.[39;49m[43mx[49m[43m)[49m
+
+File [0;32m<string>:359[0m, in [0;36mautom[0;34m(self)[0m
+
+[0;31mNameError[0m: name 'y' is not defined
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mautom[0;38;5;16;48;5;152m([0mC.x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[10D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[17D[0mautom[0;38;5;16;48;5;152m([0mC.x[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[16D[0m[J[0;94msage: [0mautom(C.x)[16D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mx + 1
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mautom[0;38;5;16;48;5;152m([0mC.x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0my[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[15D[0m[J[0;94msage: [0mautom(C.y)[16D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0my
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mautom[0;38;5;16;48;5;152m([0mC.y[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[17D[0m[J[0;94msage: [0mautom(C.dx)[17D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m1 dx
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mautom[0;38;5;16;48;5;152m([0mC.dx[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[5D[0m([4C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[C[0mC.dx)[5D[?7h[0m[?12l[?25h[?25l[?7l[0m.C.dx)[5D[?7h[0m[?12l[?25h[?25l[?7l[0mxC.dx)[5D[?7h[0m[?12l[?25h[?25l[?7l[0m*C.dx)[5D[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[7D[0;38;5;16;48;5;152m([8C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[20D[0m[J[0;94msage: [0mautom(C.x*C.dx)[21D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(x - 1) dx
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mautom[0;38;5;16;48;5;152m([0mC.x*C.dx[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[15D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m([0;38;5;241m3*a).reduce()[13D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m*[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mD[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[9D[0m([8C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m.dx)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0mC.dx)[4D[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;16;48;5;152m([8C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[10D[0m([8C).[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[27D[0m[J[0;94msage: [0m(C.x*C.dx).function()[27D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [18][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43m([49m[43mC[49m[38;5;241;43m.[39;49m[43mx[49m[38;5;241;43m*[39;49m[43mC[49m[38;5;241;43m.[39;49m[43mdx[49m[43m)[49m[38;5;241;43m.[39;49m[43mfunction[49m()
+
+[0;31mAttributeError[0m: 'superelliptic_form' object has no attribute 'function'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m(C.x*C.dx).function[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[2D[0m([0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[25D[0m[J[0;94msage: [0m(C.x*C.dx).function[25D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [19][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43m([49m[43mC[49m[38;5;241;43m.[39;49m[43mx[49m[38;5;241;43m*[39;49m[43mC[49m[38;5;241;43m.[39;49m[43mdx[49m[43m)[49m[38;5;241;43m.[39;49m[43mfunction[49m
+
+[0;31mAttributeError[0m: 'superelliptic_form' object has no attribute 'function'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m(C.x*C.dx).function[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;28;1mfor[?7h[0m[?12l[?25h[?25l[?7l[3D[0mform[?7h[0m[?12l[?25h[?25l[?7l[21D[0m[J[0;94msage: [0m(C.x*C.dx).form[21D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mx + 1
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.crystalline_cohomology_basis()[31D[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241m.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()[157D[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mf[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[18D[0m[J[0;94msage: [0mC.x.function[18D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mx + 1
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ma[0;38;5;241mutom(C.x*C.dx)[14D[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m([3C)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[16D[0m[J[0;94msage: [0mautom(C.x)[16D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mx - 1
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mautom[0;38;5;16;48;5;152m([0mC.x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[16D[0m[J[0;94msage: [0mautom(C.x)[16D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mx
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mautom[0;38;5;16;48;5;152m([0mC.x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[16D[0m[J[0;94msage: [0mautom(C.x)[16D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mx + 1
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ma[0;38;5;241mutom(C.x)[9D[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;16;48;5;152m([2C[0mx[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[16D[0m[J[0;94msage: [0mautom(C.x)[16D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mx + 1
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mautom[0;38;5;16;48;5;152m([0mC.x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[16D[0m[J[0;94msage: [0mautom(C.x)[16D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mx + 1
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mautom[0;38;5;16;48;5;152m([0mC.x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[10D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[17D[0mautom[0;38;5;16;48;5;152m([0mC.x[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[10D[0mC.x.function[?7h[0m[?12l[?25h[?25l[?7l[12D[0m(C.x*C.dx).form[?7h[0m[?12l[?25h[?25l[?7l[21D[0m[J[0;94msage: [0m(C.x*C.dx).form[21D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mx
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m(C.x*C.dx).form[?7h[0m[?12l[?25h[?25l[?7l[15D[0mautom[0;38;5;16;48;5;152m([0mC.[C[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[10D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[17D[0mautom[0;38;5;16;48;5;152m([0mC.x[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[10D[0mC.x.function[?7h[0m[?12l[?25h[?25l[?7l[12D[0m(C.x*C.dx).form[?7h[0m[?12l[?25h[?25l[?7l[3D[0munction[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[21D[0mautom[0;38;5;16;48;5;152m([0mC.[C*C.dx[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[21D[0m[J[0;94msage: [0mautom(C.x*C.dx)[21D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(x + 1) dx
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mautom[0;38;5;16;48;5;152m([0mC.x*C.dx[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0m[J[0;94msage: [0mautom(C.x*C.dx)[21D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(x + 1) dx
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mb[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= 3[3D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.x.teichmuller().diffn() + C.y.teichmuller().diffn()[52D[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mc[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mystalline_cohomology_basis[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[42D[0m[J[0;94msage: [0mb = C.crystalline_cohomology_basis()[42D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mb[0;38;5;241m = C.crystalline_cohomology_basis()[35D[?7h[0m[?12l[?25h[?25l[?7l[0m[[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C].[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[24D[0m[J[0;94msage: [0mb[[0;38;5;20;1m0[0m].coordinates()[24D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [32][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mb[49m[43m[[49m[43mInteger[49m[43m([49m[38;5;241;43m0[39;49m[43m)[49m[43m][49m[38;5;241;43m.[39;49m[43mcoordinates[49m[43m([49m[43m)[49m
+
+File [0;32m<string>:321[0m, in [0;36mcoordinates[0;34m(self, basis)[0m
+
+[0;31mAttributeError[0m: 'function' object has no attribute 'coordinates'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[17D[0mb[[0;38;5;20;1m0[0m].coordinates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[17D[0m = C.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[42D[0m[J[0;94msage: [0mb = C.crystalline_cohomology_basis()[42D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mb = C.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[36D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[17D[0mb[[0;38;5;20;1m0[0m].coordinates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[24D[0m[J[0;94msage: [0mb[[0;38;5;20;1m0[0m].coordinates()[24D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [35][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mb[49m[43m[[49m[43mInteger[49m[43m([49m[38;5;241;43m0[39;49m[43m)[49m[43m][49m[38;5;241;43m.[39;49m[43mcoordinates[49m[43m([49m[43m)[49m
+
+File [0;32m<string>:321[0m, in [0;36mcoordinates[0;34m(self, basis)[0m
+
+[0;31mAttributeError[0m: 'function' object has no attribute 'coordinates'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[17D[0mb[[0;38;5;20;1m0[0m].coordinates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[17D[0m = C.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[42D[0m[J[0;94msage: [0mb = C.crystalline_cohomology_basis()[42D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mb = C.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[36D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[17D[0mb = C.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[36D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mb = C.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[36D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[17D[0mb[[0;38;5;20;1m0[0m].coordinates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[17D[0m = C.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[35D[0m[[0;38;5;20;1m0[0m].coordinates[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[17D[0m = C.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[36D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[17D[0mb[[0;38;5;20;1m0[0m].coordinates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[17D[0m = C.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[35D[0m[[0;38;5;20;1m0[0m].coordinates[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mb[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0ma[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0ms[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mi[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0ms[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m=[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mb[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[33D[0m[J[0;94msage: [0mb[[0;38;5;20;1m0[0m].coordinates(basis = b)[33D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [38][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mb[49m[43m[[49m[43mInteger[49m[43m([49m[38;5;241;43m0[39;49m[43m)[49m[43m][49m[38;5;241;43m.[39;49m[43mcoordinates[49m[43m([49m[43mbasis[49m[43m [49m[38;5;241;43m=[39;49m[43m [49m[43mb[49m[43m)[49m
+
+File [0;32m<string>:321[0m, in [0;36mcoordinates[0;34m(self, basis)[0m
+
+File [0;32m<string>:318[0m, in [0;36mr[0;34m(self)[0m
+
+File [0;32m<string>:5[0m, in [0;36m__init__[0;34m(self, C, omega, fct)[0m
+
+File [0;32m<string>:50[0m, in [0;36m__sub__[0;34m(self, other)[0m
+
+[0;31mAttributeError[0m: 'superelliptic_form' object has no attribute 'function'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mb[[0;38;5;20;1m0[0m].coordinates[0;38;5;16;48;5;152m([0mbasis = b[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[24D[0m[J[0;94msage: [0mb[[0;38;5;20;1m0[0m].coordinates()[24D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [39][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mb[49m[43m[[49m[43mInteger[49m[43m([49m[38;5;241;43m0[39;49m[43m)[49m[43m][49m[38;5;241;43m.[39;49m[43mcoordinates[49m[43m([49m[43m)[49m
+
+File [0;32m<string>:321[0m, in [0;36mcoordinates[0;34m(self, basis)[0m
+
+File [0;32m<string>:318[0m, in [0;36mr[0;34m(self)[0m
+
+File [0;32m<string>:5[0m, in [0;36m__init__[0;34m(self, C, omega, fct)[0m
+
+File [0;32m<string>:50[0m, in [0;36m__sub__[0;34m(self, other)[0m
+
+[0;31mAttributeError[0m: 'superelliptic_form' object has no attribute 'function'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mb[0;38;5;241m[0].coordinates()[17D[?7h[0m[?12l[?25h[?25l[?7l[0m[[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C]/[0m[K[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C][0m[K[?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C].[0;38;5;241mcoordinates()[13D[?7h[0m[?12l[?25h[?25l[?7l[0mr[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[14D[0m[J[0;94msage: [0mb[[0;38;5;20;1m0[0m].r()[14D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [40][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mb[49m[43m[[49m[43mInteger[49m[43m([49m[38;5;241;43m0[39;49m[43m)[49m[43m][49m[38;5;241;43m.[39;49m[43mr[49m[43m([49m[43m)[49m
+
+File [0;32m<string>:318[0m, in [0;36mr[0;34m(self)[0m
+
+File [0;32m<string>:5[0m, in [0;36m__init__[0;34m(self, C, omega, fct)[0m
+
+File [0;32m<string>:50[0m, in [0;36m__sub__[0;34m(self, other)[0m
+
+[0;31mAttributeError[0m: 'superelliptic_form' object has no attribute 'function'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mb[[0;38;5;20;1m0[0m].r[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[3D[0mcoordinates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[13D[0mr[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[8D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[17D[0mb[[0;38;5;20;1m0[0m].r[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[3D[0mcoordinates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0mbasis = b[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[26D[0m = C.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[42D[0m[J[0;94msage: [0mb = C.crystalline_cohomology_basis()[42D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mb = C.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[36D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[17D[0mb[[0;38;5;20;1m0[0m].r[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[14D[0m[J[0;94msage: [0mb[[0;38;5;20;1m0[0m].r()[14D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m((1/y) dx, 0, (1/y) dx)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mb[0;38;5;241m[0].r()[7D[?7h[0m[?12l[?25h[?25l[?7l[0m[[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C]/[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C][0m[K[?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C].[0;38;5;241mr()[3D[?7h[0m[?12l[?25h[?25l[?7l[0mc[0;38;5;241moordinates()[12D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mdinates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mb[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0ma[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0ms[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mi[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0ms[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m=[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mb[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[33D[0m[J[0;94msage: [0mb[[0;38;5;20;1m0[0m].coordinates(basis = b)[33D[0m

+[J[?7h[0m[?12l[?25h[?2004l(1, 0)
+[0m[?7h[0;91m[0m[0m(0, [0], 0)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mb[[0;38;5;20;1m0[0m].coordinates[0;38;5;16;48;5;152m([0mbasis = b[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[10D[0m([9C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([9C[0;38;5;16;48;5;152m)[11D[?7h[0m[?12l[?25h[?25l[?7l[0m([9C)[12D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m[[C[0;38;5;16;48;5;152m][3D[?7h[0m[?12l[?25h[?25l[?7l[0m[[C][4D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mab[[0;38;5;20;1m0[0m].c[Cordinates(basis = b)[27D[?7h[0m[?12l[?25h[?25l[?7l[0mub[[0;38;5;20;1m0[0m].c[Cordinates(basis = b)[27D[?7h[0m[?12l[?25h[?25l[?7l[0mtb[[0;38;5;20;1m0[0m].c[Cordinates(basis = b)[27D[?7h[0m[?12l[?25h[?25l[?7l[0mob[[0;38;5;20;1m0[0m].c[Cordinates(basis = b)[27D[?7h[0m[?12l[?25h[?25l[?7l[0mmb[[0;38;5;20;1m0[0m].c[Cordinates(basis = b)[27D[?7h[0m[?12l[?25h[?25l[?7l[0m(b[[0;38;5;20;1m0[0m].c[Cordinates(basis = b)[27D[?7h[0m[?12l[?25h[?25l[?7l[C[0;38;5;210;48;5;88m[[C[0;38;5;16;48;5;152m][3D[?7h[0m[?12l[?25h[?25l[?7l[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m[[C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m][?7h[0m[?12l[?25h[?25l[?7l[5D[0;38;5;16;48;5;152m([C[0m[[C][0;38;5;16;48;5;152m)[0m.c[Cordinates(basis = b)[23D[?7h[0m[?12l[?25h[?25l[?7l[6D[0m([4C)[12C[0;38;5;210;48;5;88m([9C[0;38;5;16;48;5;152m)[11D[?7h[0m[?12l[?25h[?25l[?7l[0m([9C)[5D[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[8D[0;38;5;16;48;5;152m([9C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[39D[0m[J[0;94msage: [0mautom(b[[0;38;5;20;1m0[0m]).coordinates(basis = b)[40D[0m

+[J[?7h[0m[?12l[?25h[?2004l(1, 0)
+[0m[?7h[0;91m[0m[0m(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]))
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mr[0;38;5;241meduce(xi)[9D[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0ms[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mautom(b[[0;38;5;20;1m0[0m]).coordinates[0;38;5;16;48;5;152m([0mbasis = b[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[10D[0m([9C)[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[6D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([9C[0;38;5;16;48;5;152m)[11D[?7h[0m[?12l[?25h[?25l[?7l[0m([9C)[22D[?7h[0m[?12l[?25h[?25l[?7l[5D[0;38;5;16;48;5;152m[[C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m[[C[0;38;5;16;48;5;152m][3D[?7h[0m[?12l[?25h[?25l[?7l[0m[[C][4D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([4C[0;38;5;16;48;5;152m)[6D[?7h[0m[?12l[?25h[?25l[?7l[0m([4C)[11D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mrautom(b[[0;38;5;20;1m0[0m]).c[Cordinates(basis = b)[34D[?7h[0m[?12l[?25h[?25l[?7l[0meautom(b[[0;38;5;20;1m0[0m]).c[Cordinates(basis = b)[34D[?7h[0m[?12l[?25h[?25l[?7l[0msautom(b[[0;38;5;20;1m0[0m]).c[Cordinates(basis = b)[34D[?7h[0m[?12l[?25h[?25l[?7l[0m autom(b[[0;38;5;20;1m0[0m]).c[Cordinates(basis = b)[34D[?7h[0m[?12l[?25h[?25l[?7l[0m=autom(b[[0;38;5;20;1m0[0m]).c[Cordinates(basis = b)[34D[?7h[0m[?12l[?25h[?25l[?7l[0m autom(b[[0;38;5;20;1m0[0m]).c[Cordinates(basis = b)[34D[?7h[0m[?12l[?25h[?25l[?7l[12D[0m[J[0;94msage: [0mres = autom(b[[0;38;5;20;1m0[0m]).coordinates(basis = b)[46D[0m

+[J[?7h[0m[?12l[?25h[?2004l(1, 0)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mr[0;38;5;241mes = autom(b[0]).coordinates(basis = b)[39D[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0m1[0m[K[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[20D[0m[J[0;94msage: [0mres1 = res.f.f[20D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mr[0;38;5;241mes1 = res.f.f[13D[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0m1[?7h[0m[?12l[?25h[?25l[?7l[10D[0m[J[0;94msage: [0mres1[10D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(2/(x^2 + x))*y
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mres1[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mh[?7h[0m[?12l[?25h[?25l[?7l[0m_[?7h[0m[?12l[?25h[?25l[?7l[0mroot[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[21D[0m[J[0;94msage: [0mres1.pth_root()[21D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mValueError[0m                                Traceback (most recent call last)
+Input [0;32mIn [49][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mres1[49m[38;5;241;43m.[39;49m[43mpth_root[49m[43m([49m[43m)[49m
+
+File [0;32m<string>:144[0m, in [0;36mpth_root[0;34m(self)[0m
+
+[0;31mValueError[0m: Function is not a p-th power.
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mr[0;38;5;241mes1.pth_root()[14D[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0m[K[3D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[0;38;5;241m1.pth_root()[12D[?7h[0m[?12l[?25h[?25l[?7l[0m1.pth_root[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m([0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[2D[0m()|[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[18D[0m[J[0;94msage: [0mres.reduce()[18D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(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]))
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+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(([(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])))
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.x.function[11D[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= s[Cperelliptic(x^4 + x, 2)[27D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0msuperelliptic[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m4[0m + x, [0;38;5;20;1m2[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[11D[0m([10C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[10D[0;38;5;16;48;5;152m([10C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[11D[0m([10C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m4 + x, [0;38;5;20;1m2[0m)[0m[K[9D[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m + x, [0;38;5;20;1m2[0m)[0m[K[8D[?7h[0m[?12l[?25h[?25l[?7l[0m^ + x, [0;38;5;20;1m2[0m)[8D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m3[0m + x, [0;38;5;20;1m2[0m)[8D[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m x, [0;38;5;20;1m2[0m)[0m[K[6D[?7h[0m[?12l[?25h[?25l[?7l[0m- x, [0;38;5;20;1m2[0m)[6D[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m , [0;38;5;20;1m2[0m)[4D[?7h[0m[?12l[?25h[?25l[?7l[0m+, [0;38;5;20;1m2[0m)[4D[?7h[0m[?12l[?25h[?25l[?7l[0m , [0;38;5;20;1m2[0m)[4D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[0m, [0;38;5;20;1m2[0m)[4D[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[14D[0;38;5;16;48;5;152m([14C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[39D[0m[J[0;94msage: [0mC = superelliptic(x^[0;38;5;20;1m3[0m - x + [0;38;5;20;1m1[0m, [0;38;5;20;1m2[0m)[39D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mp[0;38;5;241marent(f)[8D[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mt[0;38;5;241mch(C)[0m[K[5D[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mh[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m([C)[?7h[0m[?12l[?25h[?25l[?7l[14D[0m[J[0;94msage: [0mpatch(C)[14D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mSuperelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mpatch[0;38;5;16;48;5;152m([0mC[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[8D[0mC = superelliptic[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m3[0m - x + [0;38;5;20;1m1[0m, [0;38;5;20;1m2[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[15D[0m([14C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[27D[0mpatch[0;38;5;16;48;5;152m([0mC[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[8D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mV[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m = superelliptic(x^3 - x + 1, 2)[32D[?7h[0m[?12l[?25h[?25l[?7l[0m1[0m[K[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mh[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m([C)[?7h[0m[?12l[?25h[?25l[?7l[19D[0m[J[0;94msage: [0mC1 = patch(C)[19D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m1 = patch(C)[12D[?7h[0m[?12l[?25h[?25l[?7l[0m1[?7h[0m[?12l[?25h[?25l[?7l[0m.[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mlline_cohomology_basis[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[39D[0m[J[0;94msage: [0mC1.crystalline_cohomology_basis()[39D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mNameError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [57][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mC1[49m[38;5;241;43m.[39;49m[43mcrystalline_cohomology_basis[49m[43m([49m[43m)[49m
+
+File [0;32m<string>:354[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:348[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:50[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+[0;31mNameError[0m: name 'Error' is not defined
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC1.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[31D[0m = pa[Cch[0;38;5;16;48;5;152m([0mC[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[11D[0m.crys[Calline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[39D[0m[J[0;94msage: [0mC1.crystalline_cohomology_basis()[39D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mNameError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [58][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mC1[49m[38;5;241;43m.[39;49m[43mcrystalline_cohomology_basis[49m[43m([49m[43m)[49m
+
+File [0;32m<string>:354[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:348[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:50[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+[0;31mNameError[0m: name 'Error' is not defined
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[17D[0mC1.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[31D[0m = pa[Cch[0;38;5;16;48;5;152m([0mC[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[13D[0mpatch[0;38;5;16;48;5;152m([0mC[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[8D[0mC1 = patch[0;38;5;16;48;5;152m([0mC[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[19D[0m[J[0;94msage: [0mC1 = patch(C)[19D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m1 = patch(C)[12D[?7h[0m[?12l[?25h[?25l[?7l[0m1[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mcrys[Calline_cohomology_basis()[30D[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mrystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[39D[0m[J[0;94msage: [0mC1.crystalline_cohomology_basis()[39D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[([(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]))]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m1.crystalline_cohomology_basis()[32D[?7h[0m[?12l[?25h[?25l[?7l[0m1[?7h[0m[?12l[?25h[?25l[?7l[8D[0m[J[0;94msage: [0mC1[8D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mSuperelliptic curve with the equation y^2 = 2*x^3 + x over Finite Field of size 3
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m1[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m1[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m1[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= superelliptic(x^3 - x + 1, 2)[31D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0msuperelliptic[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m3[0m - x + [0;38;5;20;1m1[0m, [0;38;5;20;1m2[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[39D[0m[J[0;94msage: [0mC = superelliptic(x^[0;38;5;20;1m3[0m - x + [0;38;5;20;1m1[0m, [0;38;5;20;1m2[0m)[39D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC = superelliptic[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m3[0m - x + [0;38;5;20;1m1[0m, [0;38;5;20;1m2[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[32D[0m1[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[31D[0m = pa[Cch[0;38;5;16;48;5;152m([0mC[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[19D[0m[J[0;94msage: [0mC1 = patch(C)[19D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC1 = patch[0;38;5;16;48;5;152m([0mC[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[12D[0m = superelliptic[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m3[0m - x + [0;38;5;20;1m1[0m, [0;38;5;20;1m2[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[32D[0m1[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[39D[0m[J[0;94msage: [0mC1.crystalline_cohomology_basis()[39D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mValueError[0m                                Traceback (most recent call last)
+Input [0;32mIn [65][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mC1[49m[38;5;241;43m.[39;49m[43mcrystalline_cohomology_basis[49m[43m([49m[43m)[49m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:50[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+[0;31mValueError[0m: 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
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m1.crystalline_cohomology_basis()[32D[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mx.function[0m[K[10D[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;241me_rham_basis()[14D[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241m.verschiebung()[15D[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mr[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[20D[0m[J[0;94msage: [0mC.dx.residue()[20D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC.dx.residue[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m()[3D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m(C.dx.residue()[14D[?7h[0m[?12l[?25h[?25l[?7l[C[0mC.dx.residue()[14D[?7h[0m[?12l[?25h[?25l[?7l[0m.C.dx.residue()[14D[?7h[0m[?12l[?25h[?25l[?7l[0mxC.dx.residue()[14D[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m([3C)[0mC.dx.residue()[14D[?7h[0m[?12l[?25h[?25l[?7l[5D[0m([3C)^C.dx.residue()[14D[?7h[0m[?12l[?25h[?25l[?7l[0m(C.dx.residue()[14D[?7h[0m[?12l[?25h[?25l[?7l[0m-C.dx.residue()[14D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[0mC.dx.residue()[14D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[0mC.dx.residue()[14D[?7h[0m[?12l[?25h[?25l[?7l[0mC.dx.residue()[0m[K[14D[?7h[0m[?12l[?25h[?25l[?7l[0mC.dx.residue()[0m[K[14D[?7h[0m[?12l[?25h[?25l[?7l[0mC.dx.residue()[0m[K[14D[?7h[0m[?12l[?25h[?25l[?7l[0m-C.dx.residue()[14D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[0mC.dx.residue()[14D[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;16;48;5;152m([2C)[0mC.dx.residue()[14D[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([2C)*C.dx.residue()[14D[?7h[0m[?12l[?25h[?25l[?7l[5D[0;38;5;16;48;5;152m([2C)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[3D[0m([2C)[2D[?7h[0m[?12l[?25h[?25l[?7l[8D[0;38;5;16;48;5;152m([3C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([3C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([3C[0;38;5;16;48;5;152m)[5D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m([0;38;5;210;48;5;88m([0mC.x[0;38;5;16;48;5;152m)[0m^(-[0;38;5;20;1m1[0m)*C.dx.residue()[25D[?7h[0m[?12l[?25h[?25l[?7l[0m([3C)[3D[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m([3C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([3C)[3C[?7h[0m[?12l[?25h[?25l[?7l[3C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[16D[0;38;5;16;48;5;152m([15C)[0m.residue()[10D[?7h[0m[?12l[?25h[?25l[?7l[17D[0m([15C)[C[?7h[0m[?12l[?25h[?25l[?7l[7C[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[33D[0m[J[0;94msage: [0m((C.x)^(-[0;38;5;20;1m1[0m)*C.dx).residue()[33D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m1
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[17D[0m((C.x)^(-[0;38;5;20;1m1[0m)*C.dx).residue[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[27D[0mC.dx.residue[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[14D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[17D[0mC1.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[31D[0m = pa[Cch[0;38;5;16;48;5;152m([0mC[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[12D[0m = superelliptic[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m3[0m - x + [0;38;5;20;1m1[0m, [0;38;5;20;1m2[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[39D[0m[J[0;94msage: [0mC = superelliptic(x^[0;38;5;20;1m3[0m - x + [0;38;5;20;1m1[0m, [0;38;5;20;1m2[0m)[39D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC = superelliptic[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m3[0m - x + [0;38;5;20;1m1[0m, [0;38;5;20;1m2[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[33D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[17D[0m((C.x)^(-[0;38;5;20;1m1[0m)*C.dx).residue[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[27D[0mC.dx.residue[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[14D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[17D[0mC1.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[31D[0m = pa[Cch[0;38;5;16;48;5;152m([0mC[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[19D[0m[J[0;94msage: [0mC1 = patch(C)[19D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m1 = patch(C)[12D[?7h[0m[?12l[?25h[?25l[?7l[0m1[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mcrys[Calline_cohomology_basis()[30D[?7h[0m[?12l[?25h[?25l[?7l[0mcrystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[39D[0m[J[0;94msage: [0mC1.crystalline_cohomology_basis()[39D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mValueError[0m                                Traceback (most recent call last)
+Input [0;32mIn [72][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mC1[49m[38;5;241;43m.[39;49m[43mcrystalline_cohomology_basis[49m[43m([49m[43m)[49m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:32[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+[0;31mValueError[0m: Non zero residue!
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ 
[K]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+[22;0t]0;IPython: DeRhamComputation/sage[6n[?2004h[?1l[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m1.crystalline_cohomology_basis()[32D[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= supere[Cliptic(x^3 - x + 1, 2[30D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mR[0;38;5;241mxy.<x, y> = PolynomialRing(GF(3), 2)[36D[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241m<x> = Polyn[CmialR[Cng(GF(4))[0m[K[27D[?7h[0m[?12l[?25h[?25l[?7l[0m<[?7h[0m[?12l[?25h[?25l[?7l[0m>[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mx>[?7h[0m[?12l[?25h[?25l[?7l[C[0;38;5;241m = PolynomialRing(GF(4))[24D[?7h[0m[?12l[?25h[?25l[?7l[0m = PolynomialRing[0;38;5;16;48;5;152m([0mGF([0;38;5;20;1m4[0m)[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[6D[0m([2C[0;38;5;16;48;5;152m([C[0;38;5;210;48;5;88m)[0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[0m([C)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m)[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m2[0;38;5;210;48;5;88m)[0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[5D[0;38;5;16;48;5;152m([2C[0m([C)[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[36D[0m[J[0;94msage: [0mRx.<x> = PolynomialRing(GF([0;38;5;20;1m2[0m))[36D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m1.crystalline_cohomology_basis()[32D[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= supere[Cliptic(x^3 - x + 1, 2[30D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0msuperelliptic[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m3[0m - x + [0;38;5;20;1m1[0m, [0;38;5;20;1m2[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[15D[0m([14C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m, [0;38;5;20;1m2[0m)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0m, [0;38;5;20;1m2[0m)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0m, [0;38;5;20;1m2[0m)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0m, [0;38;5;20;1m2[0m)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0m, [0;38;5;20;1m2[0m)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0m, [0;38;5;20;1m2[0m)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0m, [0;38;5;20;1m2[0m)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0m, [0;38;5;20;1m2[0m)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0m, [0;38;5;20;1m2[0m)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0m, [0;38;5;20;1m2[0m)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0m, [0;38;5;20;1m2[0m)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0m, [0;38;5;20;1m2[0m)[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0m(, [0;38;5;20;1m2[0m)[4D[?7h[0m[?12l[?25h[?25l[?7l[0mx, [0;38;5;20;1m2[0m)[4D[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m([4C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[29D[0m[J[0;94msage: [0mC = superelliptic(x, [0;38;5;20;1m1[0m)[29D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m = superelliptic(x, 1)[22D[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mC[7D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mSuperelliptic curve with the equation y^1 = x over Finite Field of size 2
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mA[0;38;5;241mS.exponent_of_different_prim()[30D[?7h[0m[?12l[?25h[?25l[?7l[0mS[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= as_cover(C, [(C.y)^(-1)])[0m[K[27D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mas_cover[0;38;5;16;48;5;152m([0mC, [(C.y)^(-[0;38;5;20;1m1[0m)][0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[16D[0m([3C[0;38;5;16;48;5;152m[[10C[0;38;5;210;48;5;88m][0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m)[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m)[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m)[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m)[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m)[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m)[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m)[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m)[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m)[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m)[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;210;48;5;88m][0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;210;48;5;88m][0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;210;48;5;88m][0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[4D[0m[[3C][2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m(C.x])[5D[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[4C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[0m)[0;38;5;210;48;5;88m][0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m^[0;38;5;210;48;5;88m][0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m3[0;38;5;210;48;5;88m][0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m,[0;38;5;210;48;5;88m][0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m][0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m([0;38;5;210;48;5;88m][0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;210;48;5;88m][0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;210;48;5;88m][0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;210;48;5;88m][0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m)[0;38;5;210;48;5;88m][0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[19D[0;38;5;16;48;5;152m([3C[0m[[14C][0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[40D[0m[J[0;94msage: [0mAS = as_cover(C, [(C.x)^[0;38;5;20;1m3[0m, (C.x)])[40D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mA[0;38;5;241mS = as_cover(C, [(C.x)^3, (C.x)])[33D[?7h[0m[?12l[?25h[?25l[?7l[0mS[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mexponent_of_different_prim()[0m[K[28D[?7h[0m[?12l[?25h[?25l[?7l[0md[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0m_[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mh[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0m_[?7h[0m[?12l[?25h[?25l[?7l[0mb[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[24D[0m[J[0;94msage: [0mAS.de_rham_basis()[24D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mIndexError[0m                                Traceback (most recent call last)
+Input [0;32mIn [6][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mAS[49m[38;5;241;43m.[39;49m[43mde_rham_basis[49m[43m([49m[43m)[49m
+
+File [0;32m<string>:389[0m, in [0;36mde_rham_basis[0;34m(self, threshold)[0m
+
+File [0;32m<string>:342[0m, in [0;36mcohomology_of_structure_sheaf_basis[0;34m(self, threshold)[0m
+
+File [0;32m<string>:342[0m, in [0;36m<listcomp>[0;34m(.0)[0m
+
+File [0;32m<string>:109[0m, in [0;36mserre_duality_pairing[0;34m(self, fct)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/functional.py:585[0m, in [0;36msymbolic_sum[0;34m(expression, *args, **kwds)[0m
+[1;32m    583[0m     [38;5;28;01mreturn[39;00m expression[38;5;241m.[39msum([38;5;241m*[39margs, [38;5;241m*[39m[38;5;241m*[39mkwds)
+[1;32m    584[0m [38;5;28;01melif[39;00m [38;5;28mmax[39m([38;5;28mlen[39m(args),[38;5;28mlen[39m(kwds)) [38;5;241m<[39m[38;5;241m=[39m [38;5;241m1[39m:
+[0;32m--> 585[0m     [38;5;28;01mreturn[39;00m [38;5;28;43msum[39;49m[43m([49m[43mexpression[49m[43m,[49m[43m [49m[38;5;241;43m*[39;49m[43margs[49m[43m,[49m[43m [49m[38;5;241;43m*[39;49m[38;5;241;43m*[39;49m[43mkwds[49m[43m)[49m
+[1;32m    586[0m [38;5;28;01melse[39;00m:
+[1;32m    587[0m     [38;5;28;01mfrom[39;00m [38;5;21;01msage[39;00m[38;5;21;01m.[39;00m[38;5;21;01msymbolic[39;00m[38;5;21;01m.[39;00m[38;5;21;01mring[39;00m [38;5;28;01mimport[39;00m SR
+
+File [0;32m<string>:109[0m, in [0;36m<genexpr>[0;34m(.0)[0m
+
+File [0;32m<string>:102[0m, in [0;36mresidue[0;34m(self, place)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:618[0m, in [0;36msage.rings.laurent_series_ring_element.LaurentSeries.residue[0;34m()[0m
+[1;32m    616[0m         Integer Ring
+[1;32m    617[0m     """
+[0;32m--> 618[0m     return self[-1]
+[1;32m    619[0m 
+[1;32m    620[0m def exponents(self):
+
+File [0;32m/ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544[0m, in [0;36msage.rings.laurent_series_ring_element.LaurentSeries.__getitem__[0;34m()[0m
+[1;32m    542[0m         return type(self)(self._parent, f, self.__n)
+[1;32m    543[0m 
+[0;32m--> 544[0m     return self.__u[i - self.__n]
+[1;32m    545[0m 
+[1;32m    546[0m def __iter__(self):
+
+File [0;32m/ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453[0m, in [0;36msage.rings.power_series_poly.PowerSeries_poly.__getitem__[0;34m()[0m
+[1;32m    451[0m         return self.base_ring().zero()
+[1;32m    452[0m     else:
+[0;32m--> 453[0m         raise IndexError("coefficient not known")
+[1;32m    454[0m return self.__f[n]
+[1;32m    455[0m 
+
+[0;31mIndexError[0m: coefficient not known
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mAS.de_rham_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mp[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mr[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0me[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mc[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m=[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[32D[0m[J[0;94msage: [0mAS.de_rham_basis(prec=[0;38;5;20;1m100[0m)[32D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [7][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mAS[49m[38;5;241;43m.[39;49m[43mde_rham_basis[49m[43m([49m[43mprec[49m[38;5;241;43m=[39;49m[43mInteger[49m[43m([49m[38;5;241;43m100[39;49m[43m)[49m[43m)[49m
+
+[0;31mTypeError[0m: as_cover.de_rham_basis() got an unexpected keyword argument 'prec'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mAS.de_rham_basis[0;38;5;16;48;5;152m([0mprec=[0;38;5;20;1m100[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[9D[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[16D[0m = as_cover[0;38;5;16;48;5;152m([0mC, [(C.x)^[0;38;5;20;1m3[0m, (C.x)][0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m,[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mp[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mr[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0me[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mc[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m=[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m5[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[51D[0m[J[0;94msage: [0mAS = as_cover(C, [(C.x)^[0;38;5;20;1m3[0m, (C.x)], prec = [0;38;5;20;1m50[0m)[51D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mAS = as_cover[0;38;5;16;48;5;152m([0mC, [(C.x)^[0;38;5;20;1m3[0m, (C.x)], prec = [0;38;5;20;1m50[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[43D[0m.de_rham_basis[0;38;5;16;48;5;152m([0mprec=[0;38;5;20;1m100[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[24D[0m[J[0;94msage: [0mAS.de_rham_basis()[24D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[( (1) * dx, 0 ),
+ ( (z1) * dx, 0 ),
+ ( (x) * dx, z0/x ),
+ ( (x*z1) * dx, z0*z1/x )]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mAS.de_rham_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[15D[0m = as_cover[0;38;5;16;48;5;152m([0mC, [(C.x)^[0;38;5;20;1m3[0m, (C.x)], prec = [0;38;5;20;1m50[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[31D[0m([30C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[17D[0;38;5;16;48;5;152m[[14C][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[15D[0m[[9C[0;38;5;16;48;5;152m([3C[0;38;5;210;48;5;88m)[0m][2D[?7h[0m[?12l[?25h[?25l[?7l[14D[0;38;5;16;48;5;152m[[9C[0m([3C)[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m][0m, prec = [0;38;5;20;1m50[0m)[13D[?7h[0m[?12l[?25h[?25l[?7l[0m+[0;38;5;210;48;5;88m][0m, prec = [0;38;5;20;1m50[0m)[13D[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m][0m, prec = [0;38;5;20;1m50[0m)[13D[?7h[0m[?12l[?25h[?25l[?7l[0m([0;38;5;210;48;5;88m][0m, prec = [0;38;5;20;1m50[0m)[13D[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;210;48;5;88m][0m, prec = [0;38;5;20;1m50[0m)[13D[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;210;48;5;88m][0m, prec = [0;38;5;20;1m50[0m)[13D[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;210;48;5;88m][0m, prec = [0;38;5;20;1m50[0m)[13D[?7h[0m[?12l[?25h[?25l[?7l[0m)[0;38;5;210;48;5;88m][0m, prec = [0;38;5;20;1m50[0m)[13D[?7h[0m[?12l[?25h[?25l[?7l[0m^[0;38;5;210;48;5;88m][0m, prec = [0;38;5;20;1m50[0m)[13D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m5[0;38;5;210;48;5;88m][0m, prec = [0;38;5;20;1m50[0m)[13D[?7h[0m[?12l[?25h[?25l[?7l[25D[0m[[24C][C[?7h[0m[?12l[?25h[?25l[?7l[5C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[38D[0;38;5;16;48;5;152m([40C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[61D[0m[J[0;94msage: [0mAS = as_cover(C, [(C.x)^[0;38;5;20;1m3[0m, (C.x) + (C.x)^[0;38;5;20;1m5[0m], prec = [0;38;5;20;1m50[0m)[61D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mAS = as_cover[0;38;5;16;48;5;152m([0mC, [(C.x)^[0;38;5;20;1m3[0m, (C.x) + (C.x)^[0;38;5;20;1m5[0m], prec = [0;38;5;20;1m50[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[53D[0m.de_rham_basis[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[24D[0m[J[0;94msage: [0mAS.de_rham_basis()[24D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[( (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 )]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mg[0;38;5;241m.change_ring(Integers(9))[25D[?7h[0m[?12l[?25h[?25l[?7l[0mr[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0m_[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[13D[0;94msage: [0mgroup_action_matrices[0m

+[27C[0;38;5;16;48;5;250m group_action_matrices      group_action_matrices_log [0m

+[27C[0;38;5;16;48;5;250m group_action_matrices_dR   group_action_matrices_old [0m

+[27C[0;38;5;16;48;5;250m group_action_matrices_holo                           [0m

+

+[0m [5A[27C[?7h[0m[?12l[?25h[?25l[?7l[0m

+[27C[0;38;5;231;48;5;102m group_action_matrices     [0m

+

+

+[27C[0;38;5;16;48;5;248m <unknown> [4A[11D[?7h[0m[?12l[?25h[?25l[?7l[0m_dR[0m

+[27C[0;38;5;16;48;5;250m group_action_matrices     [0m

+[27C[0;38;5;231;48;5;102m group_action_matrices_dR  [2A[24D[?7h[0m[?12l[?25h[?25l[?7l[0m

+[C[0m[K[0m

+[C[0m[K[0m

+[C[0m[K[0m

+[C[0m[K[4A[29C[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mA[?7h[0m[?12l[?25h[?25l[?7l[0mS[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;16;48;5;152m([2C)[?7h[0m[?12l[?25h[?25l[?7l[34D[0m[J[0;94msage: [0mgroup_action_matrices_dR(AS)[34D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[
+[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]
+]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mA[0;38;5;241mS.de_rham_basis()[17D[?7h[0m[?12l[?25h[?25l[?7l[0m,[0m[K[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mB[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mgroup_action_matrices_dR[0;38;5;16;48;5;152m([0mAS[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[3D[0m([2C)[3D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([2C[0;38;5;16;48;5;152m)[4D[?7h[0m[?12l[?25h[?25l[?7l[0m([2C)[28D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mAgroup_action_matrices_dR(AS)[28D[?7h[0m[?12l[?25h[?25l[?7l[0m,group_action_matrices_dR(AS)[28D[?7h[0m[?12l[?25h[?25l[?7l[0m group_action_matrices_dR(AS)[28D[?7h[0m[?12l[?25h[?25l[?7l[0mBgroup_action_matrices_dR(AS)[28D[?7h[0m[?12l[?25h[?25l[?7l[0m group_action_matrices_dR(AS)[28D[?7h[0m[?12l[?25h[?25l[?7l[0m=group_action_matrices_dR(AS)[28D[?7h[0m[?12l[?25h[?25l[?7l[0m group_action_matrices_dR(AS)[28D[?7h[0m[?12l[?25h[?25l[?7l[24C[0;38;5;210;48;5;88m([2C[0;38;5;16;48;5;152m)[4D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([2C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[41D[0m[J[0;94msage: [0mA, B = group_action_matrices_dR(AS)[41D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mm[0;38;5;241m = 3[4D[?7h[0m[?12l[?25h[?25l[?7l[0ma[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[11D[0;94msage: [0mmagma[0m

+[11C[0;38;5;16;48;5;250m magma     [0m

+[11C[0;38;5;16;48;5;250m magma_free[0m

+[11C[0;38;5;16;48;5;250m magmathis [0m

+

+[0m [5A[11C[?7h[0m[?12l[?25h[?25l[?7l[0m

+[11C[0;38;5;231;48;5;102m magma     [0m

+

+

+[11C[0;38;5;16;48;5;248m <unknown> [4A[11D[?7h[0m[?12l[?25h[?25l[?7l[0m_free[0m

+[11C[0;38;5;16;48;5;250m magma     [0m

+[11C[0;38;5;231;48;5;102m magma_free[2A[6D[?7h[0m[?12l[?25h[?25l[?7l[5D[0mthis[0m[K[0m

+

+[11C[0;38;5;16;48;5;250m magma_free[0m

+[11C[0;38;5;231;48;5;102m magmathis [3A[7D[?7h[0m[?12l[?25h[?25l[?7l[0m

+[C[0m[K[0m

+[C[0m[K[0m

+[C[0m[K[0m

+[C[0m[K[4A[14C[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mA[?7h[0m[?12l[?25h[?25l[?7l[0m,[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mB[?7h[0m[?12l[?25h[?25l[?7l[5D[0;38;5;16;48;5;152m([4C)[?7h[0m[?12l[?25h[?25l[?7l[21D[0m[J[0;94msage: [0mmagmathis(A, B)[21D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[
+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]
+}
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mA[0;38;5;241m, B = group_action_matrices_dR(AS)[34D[?7h[0m[?12l[?25h[?25l[?7l[0mS[0;38;5;241m.de_rham_basis()[0m[K[16D[?7h[0m[?12l[?25h[?25l[?7l[8D[0m[J[0;94msage: [0mAS[8D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(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
+
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mA[0;38;5;241mS[?7h[0m[?12l[?25h[?25l[?7l[0mS[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mde_rham_basis()[15D[?7h[0m[?12l[?25h[?25l[?7l[0mn[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mb_of_pts_at_infty[?7h[0m[?12l[?25h[?25l[?7l[27D[0m[J[0;94msage: [0mAS.nb_of_pts_at_infty[27D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m1
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mAS.nb_of_pts_at_infty[?7h[0m[?12l[?25h[?25l[?7l[19D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0mmagmathis[0;38;5;16;48;5;152m([0mA, B[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[15D[0mA, B = group_action_matrices_dR[0;38;5;16;48;5;152m([0mAS[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[35D[0mgroup_action[Cma[Crices_dR[0;38;5;16;48;5;152m([0mAS[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[28D[0mAS.de[Crham_basis[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[16D[0m = as_cover[0;38;5;16;48;5;152m([0mC, [(C.x)^[0;38;5;20;1m3[0m, (C.x) + (C.x)^[0;38;5;20;1m5[0m], prec = [0;38;5;20;1m50[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[41D[0m([40C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[27D[0;38;5;16;48;5;152m[[24C][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[25D[0m[[24C][2D[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;16;48;5;152m([3C)[?7h[0m[?12l[?25h[?25l[?7l[5D[0m([3C)[C[?7h[0m[?12l[?25h[?25l[?7l[24D[0;38;5;16;48;5;152m[[24C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][0m, prec = [0;38;5;20;1m50[0m)[0m[K[13D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m7[0;38;5;210;48;5;88m][0m, prec = [0;38;5;20;1m50[0m)[13D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m][?7h[0m[?12l[?25h[?25l[?7l[26D[0m[[24C][C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[40D[0;38;5;16;48;5;152m([40C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[61D[0m[J[0;94msage: [0mAS = as_cover(C, [(C.x)^[0;38;5;20;1m3[0m, (C.x) + (C.x)^[0;38;5;20;1m7[0m], prec = [0;38;5;20;1m50[0m)[61D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mAS = as_cover[0;38;5;16;48;5;152m([0mC, [(C.x)^[0;38;5;20;1m3[0m, (C.x) + (C.x)^[0;38;5;20;1m7[0m], prec = [0;38;5;20;1m50[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[53D[0m.nb_of_pts_at_infty[0m[K[?7h[0m[?12l[?25h[?25l[?7l[19D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0mmagmathis[0;38;5;16;48;5;152m([0mA, B[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[15D[0mA, B = group_action_matrices_dR[0;38;5;16;48;5;152m([0mAS[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[35D[0mgroup_action[Cma[Crices_dR[0;38;5;16;48;5;152m([0mAS[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[28D[0mAS.de[Crham_basis[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[24D[0m[J[0;94msage: [0mAS.de_rham_basis()[24D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[( (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 )]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mAS.de_rham_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[15D[0m = as_cover[0;38;5;16;48;5;152m([0mC, [(C.x)^[0;38;5;20;1m3[0m, (C.x) + (C.x)^[0;38;5;20;1m7[0m], prec = [0;38;5;20;1m50[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[41D[0m([40C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[27D[0;38;5;16;48;5;152m[[24C][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[25D[0m[[24C][2D[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;16;48;5;152m([3C)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([3C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([3C[0;38;5;16;48;5;152m)[5D[?7h[0m[?12l[?25h[?25l[?7l[0m([3C)[6D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;16;48;5;152m([3C)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([3C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([3C[0;38;5;16;48;5;152m)[5D[?7h[0m[?12l[?25h[?25l[?7l[0m([3C)[6D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;16;48;5;152m([3C)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[5D[0m([3C)[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m , (C.x) + (C.x)^[0;38;5;20;1m7[0m], prec = [0;38;5;20;1m50[0m)[30D[?7h[0m[?12l[?25h[?25l[?7l[0m+, (C.x) + (C.x)^[0;38;5;20;1m7[0m], prec = [0;38;5;20;1m50[0m)[30D[?7h[0m[?12l[?25h[?25l[?7l[0m , (C.x) + (C.x)^[0;38;5;20;1m7[0m], prec = [0;38;5;20;1m50[0m)[30D[?7h[0m[?12l[?25h[?25l[?7l[0m(, (C.x) + (C.x)^[0;38;5;20;1m7[0m], prec = [0;38;5;20;1m50[0m)[30D[?7h[0m[?12l[?25h[?25l[?7l[0mC, (C.x) + (C.x)^[0;38;5;20;1m7[0m], prec = [0;38;5;20;1m50[0m)[30D[?7h[0m[?12l[?25h[?25l[?7l[0m., (C.x) + (C.x)^[0;38;5;20;1m7[0m], prec = [0;38;5;20;1m50[0m)[30D[?7h[0m[?12l[?25h[?25l[?7l[0mx, (C.x) + (C.x)^[0;38;5;20;1m7[0m], prec = [0;38;5;20;1m50[0m)[30D[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m([3C)[0m, (C.x) + (C.x)^[0;38;5;20;1m7[0m], prec = [0;38;5;20;1m50[0m)[30D[?7h[0m[?12l[?25h[?25l[?7l[5D[0m([3C)^, (C.x) + (C.x)^[0;38;5;20;1m7[0m], prec = [0;38;5;20;1m50[0m)[30D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m5[0m, (C.x) + (C.x)^[0;38;5;20;1m7[0m], prec = [0;38;5;20;1m50[0m)[30D[?7h[0m[?12l[?25h[?25l[?7l[3C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;16;48;5;152m([3C)[?7h[0m[?12l[?25h[?25l[?7l[5D[0m([3C)[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[3C[?7h[0m[?12l[?25h[?25l[?7l[3C[?7h[0m[?12l[?25h[?25l[?7l[5C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[48D[0;38;5;16;48;5;152m([50C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[71D[0m[J[0;94msage: [0mAS = as_cover(C, [(C.x)^[0;38;5;20;1m3[0m + (C.x)^[0;38;5;20;1m5[0m, (C.x) + (C.x)^[0;38;5;20;1m7[0m], prec = [0;38;5;20;1m50[0m)[71D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mAS = as_cover[0;38;5;16;48;5;152m([0mC, [(C.x)^[0;38;5;20;1m3[0m + (C.x)^[0;38;5;20;1m5[0m, (C.x) + (C.x)^[0;38;5;20;1m7[0m], prec = [0;38;5;20;1m50[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[63D[0m.de_rham_basis[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[24D[0m[J[0;94msage: [0mAS.de_rham_basis()[24D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[( (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 )]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m([0;38;5;241m(C.x)^(-1)*C.dx).residue()[26D[?7h[0m[?12l[?25h[?25l[?7l[0mz[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m0[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mdx.residue()[12D[?7h[0m[?12l[?25h[?25l[?7l[0mz[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C]/[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m[[C[0;38;5;16;48;5;152m][3D[?7h[0m[?12l[?25h[?25l[?7l[0m[[C][4D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m.z[[0;38;5;20;1m0[0m]/C.x[0m[K[9D[?7h[0m[?12l[?25h[?25l[?7l[0mA.z[[0;38;5;20;1m0[0m]/C.x[9D[?7h[0m[?12l[?25h[?25l[?7l[0mS.z[[0;38;5;20;1m0[0m]/C.x[9D[?7h[0m[?12l[?25h[?25l[?7l[2C[0;38;5;210;48;5;88m[[C[0;38;5;16;48;5;152m][3D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m[[C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m.x[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0mA.x[2D[?7h[0m[?12l[?25h[?25l[?7l[0mS.x[2D[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[18D[0m[J[0;94msage: [0mAS.z[[0;38;5;20;1m0[0m]/AS.x[18D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mz0/x
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mAS.z[[0;38;5;20;1m0[0m]/AS.x[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m[[C[0;38;5;16;48;5;152m][3D[?7h[0m[?12l[?25h[?25l[?7l[0m[[C][4D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m(AS.z[[0;38;5;20;1m0[0m]/AS.x[12D[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[0;38;5;210;48;5;88m[[C[0;38;5;16;48;5;152m][3D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m[[C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[13D[0;38;5;16;48;5;152m([12C)[?7h[0m[?12l[?25h[?25l[?7l[14D[0m([12C).[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mh[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m_[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[31D[0m[J[0;94msage: [0m(AS.z[[0;38;5;20;1m0[0m]/AS.x).pth_root()[31D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [22][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43m([49m[43mAS[49m[38;5;241;43m.[39;49m[43mz[49m[43m[[49m[43mInteger[49m[43m([49m[38;5;241;43m0[39;49m[43m)[49m[43m][49m[38;5;241;43m/[39;49m[43mAS[49m[38;5;241;43m.[39;49m[43mx[49m[43m)[49m[38;5;241;43m.[39;49m[43mpth_root[49m()
+
+[0;31mAttributeError[0m: 'as_function' object has no attribute 'pth_root'
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+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mt^-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)
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+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mt^2 + t^6 + t^10 + t^18 + t^20 + t^22 + t^28 + t^30 + O(t^33)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m(AS.z[[0;38;5;20;1m0[0m]/AS.x).diffn().expansion_at_infty[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[2D[0m([0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m([0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[15D[0;38;5;16;48;5;152m([12C)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[14D[0m([12C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C][0m[K[?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mp[0;38;5;241match(C)[7D[?7h[0m[?12l[?25h[?25l[?7l[0mo[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mz[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mA[0;38;5;241mS.z[0]/AS.x[11D[?7h[0m[?12l[?25h[?25l[?7l[0mS[?7h[0m[?12l[?25h[?25l[?7l[8D[0m[J[0;94msage: [0mAS[8D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(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
+
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m([0;38;5;241mAS.z[0]/AS.x).diffn().expansion_at_infty()[42D[?7h[0m[?12l[?25h[?25l[?7l[0mA[?7h[0m[?12l[?25h[?25l[?7l[0mS[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mz[?7h[0m[?12l[?25h[?25l[?7l[0m[[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C]*[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mA[?7h[0m[?12l[?25h[?25l[?7l[0mS[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mz[?7h[0m[?12l[?25h[?25l[?7l[0m[[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C]/[?7h[0m[?12l[?25h[?25l[?7l[0mA[?7h[0m[?12l[?25h[?25l[?7l[0mS[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m(AS.x[4D[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[5D[0;38;5;16;48;5;152m([4C)[?7h[0m[?12l[?25h[?25l[?7l[6D[0m([4C)^[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m4[?7h[0m[?12l[?25h[?25l[?7l[25D[0;38;5;16;48;5;152m([24C)[?7h[0m[?12l[?25h[?25l[?7l[26D[0m([24C).[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[40D[0m[J[0;94msage: [0m(AS.z[[0;38;5;20;1m0[0m]*AS.z[[0;38;5;20;1m1[0m]/(AS.x)^[0;38;5;20;1m4[0m).diffn()[40D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m((x^6*z0 + x^4*z1 + x^2*z1 + z0)/x^4) * dx
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ 
[K]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ 
[K]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+[22;0t]0;IPython: DeRhamComputation/sage[6n[?2004h[?1l[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [1][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:27[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:9[0m, in [0;36m<module>[0;34m[0m
+
+[0;31mAttributeError[0m: 'superelliptic' object has no attribute 'crystalline_cohomology'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mValueError[0m                                Traceback (most recent call last)
+Input [0;32mIn [2][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:27[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:9[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:32[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+[0;31mValueError[0m: Non zero residue!
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mdx.residue()[12D[?7h[0m[?12l[?25h[?25l[?7l[0mn[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mb[?7h[0m[?12l[?25h[?25l[?7l[0m_of_pts_at_infty[?7h[0m[?12l[?25h[?25l[?7l[26D[0m[J[0;94msage: [0mC.nb_of_pts_at_infty[26D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m1
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004lTraceback [0;36m(most recent call last)[0m:
+
+  File [1;32m/ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398[0m in [1;35mrun_code[0m
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input [1;32mIn [4][0m in [1;35m<cell line: 1>[0m
+    load('init.sage')
+
+  File [1;32msage/misc/persist.pyx:175[0m in [1;35msage.misc.persist.load[0m
+    sage.repl.load.load(filename, globals())
+
+  File [1;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m in [1;35mload[0m
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File [1;32m<string>:6[0m in [1;35m<module>[0m
+
+  File [1;32msage/misc/persist.pyx:175[0m in [1;35msage.misc.persist.load[0m
+    sage.repl.load.load(filename, globals())
+
+[0;36m  File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0;36m in [0;35mload[0;36m[0m
+[0;31m    exec(preparse_file(f.read()) + "\n", globals)[0m
+
+[0;36m  File [0;32m<string>:33[0;36m[0m
+[0;31m    if sum(omega.residue(place = i) i in range(delta)) != _sage_const_0 :[0m
+[0m           ^[0m
+[0;31mSyntaxError[0m[0;31m:[0m invalid syntax. Perhaps you forgot a comma?
+
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ms[0;38;5;241muperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[43D[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;24msum[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[10D[0;38;5;16;48;5;152m([9C)[?7h[0m[?12l[?25h[?25l[?7l[11D[0m([9C)[C[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;28;1mfor[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;28min[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;24mrange[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m2[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m([C)[?7h[0m[?12l[?25h[?25l[?7l[43D[0;38;5;16;48;5;152m([39C[0m([C)[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[53D[0m[J[0;94msage: [0;38;5;24msum[0m(omega.residue(place = i) [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m2[0m))[53D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mNameError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [5][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [38;5;28;43msum[39;49m[43m([49m[43momega[49m[38;5;241;43m.[39;49m[43mresidue[49m[43m([49m[43mplace[49m[43m [49m[38;5;241;43m=[39;49m[43m [49m[43mi[49m[43m)[49m[43m [49m[38;5;28;43;01mfor[39;49;00m[43m [49m[43mi[49m[43m [49m[38;5;129;43;01min[39;49;00m[43m [49m[38;5;28;43mrange[39;49m[43m([49m[43mInteger[49m[43m([49m[38;5;241;43m2[39;49m[43m)[49m[43m)[49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/functional.py:585[0m, in [0;36msymbolic_sum[0;34m(expression, *args, **kwds)[0m
+[1;32m    583[0m     [38;5;28;01mreturn[39;00m expression[38;5;241m.[39msum([38;5;241m*[39margs, [38;5;241m*[39m[38;5;241m*[39mkwds)
+[1;32m    584[0m [38;5;28;01melif[39;00m [38;5;28mmax[39m([38;5;28mlen[39m(args),[38;5;28mlen[39m(kwds)) [38;5;241m<[39m[38;5;241m=[39m [38;5;241m1[39m:
+[0;32m--> 585[0m     [38;5;28;01mreturn[39;00m [38;5;28;43msum[39;49m[43m([49m[43mexpression[49m[43m,[49m[43m [49m[38;5;241;43m*[39;49m[43margs[49m[43m,[49m[43m [49m[38;5;241;43m*[39;49m[38;5;241;43m*[39;49m[43mkwds[49m[43m)[49m
+[1;32m    586[0m [38;5;28;01melse[39;00m:
+[1;32m    587[0m     [38;5;28;01mfrom[39;00m [38;5;21;01msage[39;00m[38;5;21;01m.[39;00m[38;5;21;01msymbolic[39;00m[38;5;21;01m.[39;00m[38;5;21;01mring[39;00m [38;5;28;01mimport[39;00m SR
+
+Input [0;32mIn [5][0m, in [0;36m<genexpr>[0;34m(.0)[0m
+[0;32m----> 1[0m [38;5;28msum[39m([43momega[49m[38;5;241m.[39mresidue(place [38;5;241m=[39m i) [38;5;28;01mfor[39;00m i [38;5;129;01min[39;00m [38;5;28mrange[39m(Integer([38;5;241m2[39m)))
+
+[0;31mNameError[0m: name 'omega' is not defined
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;24msum[0;38;5;16;48;5;152m([0momega.residue(place = i) [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m2[0m)[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[43D[0m([39C[0;38;5;16;48;5;152m([C[0;38;5;210;48;5;88m)[0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[0m([C)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([C[0;38;5;16;48;5;152m)[3D[?7h[0m[?12l[?25h[?25l[?7l[0m([C)[4D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[12D[0;38;5;16;48;5;152m([9C)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[10D[0m([9C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([9C[0;38;5;16;48;5;152m)[11D[?7h[0m[?12l[?25h[?25l[?7l[0m([9C)[12D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m.residue(place = i) [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m2[0m)[C[0m[K[38D[?7h[0m[?12l[?25h[?25l[?7l[0m.residue(place = i) [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m2[0m)[C[0m[K[38D[?7h[0m[?12l[?25h[?25l[?7l[0m.residue(place = i) [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m2[0m)[C[0m[K[38D[?7h[0m[?12l[?25h[?25l[?7l[0m.residue(place = i) [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m2[0m)[C[0m[K[38D[?7h[0m[?12l[?25h[?25l[?7l[0m.residue(place = i) [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m2[0m)[C[0m[K[38D[?7h[0m[?12l[?25h[?25l[?7l[0mC.residue(place = i) [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m2[C[0m)[38D[?7h[0m[?12l[?25h[?25l[?7l[C[0m.residue(place = i) [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m2[C[0m)[38D[?7h[0m[?12l[?25h[?25l[?7l[0md.residue(place = i) [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m2[C[0m)[38D[?7h[0m[?12l[?25h[?25l[?7l[0mx.residue(place = i) [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m2[C[0m)[38D[?7h[0m[?12l[?25h[?25l[?7l[14D[0m[J[0;94msage: [0;38;5;24msum[0m(C.dx.residue(place = i) [0;38;5;28;1mfor[0m i [0;38;5;28min[0m [0;38;5;24mrange[0m([0;38;5;20;1m2[0m))[52D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004lTraceback [0;36m(most recent call last)[0m:
+
+  File [1;32m/ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398[0m in [1;35mrun_code[0m
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input [1;32mIn [7][0m in [1;35m<cell line: 1>[0m
+    load('init.sage')
+
+  File [1;32msage/misc/persist.pyx:175[0m in [1;35msage.misc.persist.load[0m
+    sage.repl.load.load(filename, globals())
+
+  File [1;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m in [1;35mload[0m
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File [1;32m<string>:6[0m in [1;35m<module>[0m
+
+  File [1;32msage/misc/persist.pyx:175[0m in [1;35msage.misc.persist.load[0m
+    sage.repl.load.load(filename, globals())
+
+[0;36m  File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0;36m in [0;35mload[0;36m[0m
+[0;31m    exec(preparse_file(f.read()) + "\n", globals)[0m
+
+[0;36m  File [0;32m<string>:33[0;36m[0m
+[0;31m    if sum(omega.residue(place = i) i in range(delta)) != _sage_const_0 :[0m
+[0m           ^[0m
+[0;31mSyntaxError[0m[0;31m:[0m invalid syntax. Perhaps you forgot a comma?
+
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mValueError[0m                                Traceback (most recent call last)
+Input [0;32mIn [8][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:27[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:9[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:54[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+[0;31mValueError[0m: 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
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mValueError[0m                                Traceback (most recent call last)
+Input [0;32mIn [9][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:27[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:9[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:54[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+[0;31mValueError[0m: 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
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x^[0;38;5;20;1m14[0m + x^[0;38;5;20;1m13[0m + x^[0;38;5;20;1m12[0m + x^[0;38;5;20;1m11[0m + x^[0;38;5;20;1m10[0m - x^[0;38;5;20;1m8[0m).quo_rem(x^[0;38;5;20;1m6[0m + x^[0;38;5;20;1m5[0m + x^[0;38;5;20;1m4[0m - x^[0;38;5;20;1m3[0m + x^[0;38;5;20;1m2[0m + [0;38;5;20;1m1[0m)[94D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(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)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mf[0;38;5;241mor a in xi.coordinates():[25D[?7h[0m[?12l[?25h[?25l[?7l[0mf[0;38;5;241mffff.coordinates()[0m[K[18D[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= ((C.y)^3/(C.x)^2)[19D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mx^[0;38;5;20;1m5[0m + x^[0;38;5;20;1m4[0m + [0;38;5;20;1m2[0m*x^[0;38;5;20;1m2[0m + x + [0;38;5;20;1m2[?7h[0m[?12l[?25h[?25l[?7l[0m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m(x^[0;38;5;20;1m5[0m + x^[0;38;5;20;1m4[0m + [0;38;5;20;1m2[0m*x^[0;38;5;20;1m2[0m + x + [0;38;5;20;1m2[0m)[26D[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[25D[0;38;5;16;48;5;152m([25C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[27D[0m([25C)/[?7h[0m[?12l[?25h[?25l[?7l[0mx^[0;38;5;20;1m6[0m + x^[0;38;5;20;1m5[0m + x^[0;38;5;20;1m4[0m - x^[0;38;5;20;1m3[0m + x^[0;38;5;20;1m2[0m + [0;38;5;20;1m1[?7h[0m[?12l[?25h[?25l[?7l[0m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[3D[?7h[0m[?12l[?25h[?25l[?7l[3C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m(x^[0;38;5;20;1m6[0m + x^[0;38;5;20;1m5[0m + x^[0;38;5;20;1m4[0m - x^[0;38;5;20;1m3[0m + x^[0;38;5;20;1m2[0m + [0;38;5;20;1m1[0m)[32D[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[3C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[30D[0;38;5;16;48;5;152m([31C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[72D[0m[J[0;94msage: [0mff = (x^[0;38;5;20;1m5[0m + x^[0;38;5;20;1m4[0m + [0;38;5;20;1m2[0m*x^[0;38;5;20;1m2[0m + x + [0;38;5;20;1m2[0m)/(x^[0;38;5;20;1m6[0m + x^[0;38;5;20;1m5[0m + x^[0;38;5;20;1m4[0m - x^[0;38;5;20;1m3[0m + x^[0;38;5;20;1m2[0m + [0;38;5;20;1m1[0m)[72D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mf[0;38;5;241mf = (x^5 + x^4 + 2*x^2 + x + 2)/(x^6 + x^5 + x^4 - x^3 + x^2 + 1)[65D[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0m[K[2C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m=[0;38;5;241m (x^5 + x^4 + 2*x^2 + x + 2)/(x^6 + x^5 + x^4 - x^3 + x^2 + 1)[62D[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0ms[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;24msuper[?7h[0m[?12l[?25h[?25l[?7l[5D[0msupere[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0m_[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m,[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;16;48;5;152m([5C)[?7h[0m[?12l[?25h[?25l[?7l[40D[0m[J[0;94msage: [0mff = superelliptic_function(C, ff)[40D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mf[0;38;5;241mf = superelliptic_function(C, ff)[33D[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0m*[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m/[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[12D[0m[J[0;94msage: [0mff/C.y[12D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m((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
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mff/C.y[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2C[0mf/C.y[6D[?7h[0m[?12l[?25h[?25l[?7l[2C[0mf/C.y[6D[?7h[0m[?12l[?25h[?25l[?7l[0m [Cf/C.y[6D[?7h[0m[?12l[?25h[?25l[?7l[0m=[Cf/C.y[6D[?7h[0m[?12l[?25h[?25l[?7l[0m [Cf/C.y[6D[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[17D[0m[J[0;94msage: [0mff = ff/C.y[17D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mf[0;38;5;241mf = ff/C.y[10D[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mexpansion_at_infty()[20D[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mnsion_at_infty[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[29D[0m[J[0;94msage: [0mff.expansion_at_infty()[29D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mt^5 + t^9 + 2*t^11 + 2*t^13 + t^21 + 2*t^23 + O(t^25)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mff.expansion_at_infty[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mp[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0ma[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mc[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0me[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m=[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[37D[0m[J[0;94msage: [0mff.expansion_at_infty(place = [0;38;5;20;1m0[0m)[38D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mt^5 + t^9 + 2*t^11 + 2*t^13 + t^21 + 2*t^23 + O(t^25)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mff.expansion_at_infty[0;38;5;16;48;5;152m([0mplace = [0;38;5;20;1m0[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[37D[0m[J[0;94msage: [0mff.expansion_at_infty(place = [0;38;5;20;1m1[0m)[38D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mt^5 + t^9 + 2*t^11 + 2*t^13 + t^21 + 2*t^23 + O(t^25)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mf[0;38;5;241mf.expansion_at_infty(place = 1)[31D[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= ff/C.y[0m[K[8D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0m*[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[18D[0m[J[0;94msage: [0mff = ff*C.dx[18D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mf[0;38;5;241mf = ff*C.dx[11D[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mexpansion_at_infty(place = 1)[29D[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0mansion_at_infty[0;38;5;16;48;5;152m([0mplace = [0;38;5;20;1m1[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[38D[0m[J[0;94msage: [0mff.expansion_at_infty(place = [0;38;5;20;1m1[0m)[38D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mt^2 + t^8 + t^10 + O(t^12)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mff.expansion_at_infty[0;38;5;16;48;5;152m([0mplace = [0;38;5;20;1m1[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[37D[0m[J[0;94msage: [0mff.expansion_at_infty(place = [0;38;5;20;1m0[0m)[38D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mt^2 + t^8 + t^10 + O(t^12)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:706[0m, in [0;36mFractionField_generic._element_constructor_[0;34m(self, x, y, coerce)[0m
+[1;32m    705[0m [38;5;28;01mtry[39;00m:
+[0;32m--> 706[0m     x, y [38;5;241m=[39m [43mresolve_fractions[49m[43m([49m[43mx0[49m[43m,[49m[43m [49m[43my0[49m[43m)[49m
+[1;32m    707[0m [38;5;28;01mexcept[39;00m ([38;5;167;01mAttributeError[39;00m, [38;5;167;01mTypeError[39;00m):
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:683[0m, in [0;36mFractionField_generic._element_constructor_.<locals>.resolve_fractions[0;34m(x, y)[0m
+[1;32m    682[0m [38;5;28;01mdef[39;00m [38;5;21mresolve_fractions[39m(x, y):
+[0;32m--> 683[0m     xn [38;5;241m=[39m [43mx[49m[38;5;241;43m.[39;49m[43mnumerator[49m()
+[1;32m    684[0m     xd [38;5;241m=[39m x[38;5;241m.[39mdenominator()
+
+[0;31mAttributeError[0m: 'superelliptic_function' object has no attribute 'numerator'
+
+During handling of the above exception, another exception occurred:
+
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [21][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:27[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:9[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:51[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+File [0;32m<string>:216[0m, in [0;36mreduction[0;34m(C, g)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    159[0m             print(type(C), C)
+[1;32m    160[0m             print(type(C._element_constructor), C._element_constructor)
+[0;32m--> 161[0m         raise
+[1;32m    162[0m 
+[1;32m    163[0m cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    154[0m cdef Parent C = self._codomain
+[1;32m    155[0m try:
+[0;32m--> 156[0m     return C._element_constructor(x)
+[1;32m    157[0m except Exception:
+[1;32m    158[0m     if print_warnings:
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:708[0m, in [0;36mFractionField_generic._element_constructor_[0;34m(self, x, y, coerce)[0m
+[1;32m    706[0m     x, y [38;5;241m=[39m resolve_fractions(x0, y0)
+[1;32m    707[0m [38;5;28;01mexcept[39;00m ([38;5;167;01mAttributeError[39;00m, [38;5;167;01mTypeError[39;00m):
+[0;32m--> 708[0m     [38;5;28;01mraise[39;00m [38;5;167;01mTypeError[39;00m([38;5;124m"[39m[38;5;124mcannot convert [39m[38;5;132;01m{!r}[39;00m[38;5;124m/[39m[38;5;132;01m{!r}[39;00m[38;5;124m to an element of [39m[38;5;132;01m{}[39;00m[38;5;124m"[39m[38;5;241m.[39mformat(
+[1;32m    709[0m                     x0, y0, [38;5;28mself[39m))
+[1;32m    710[0m [38;5;28;01mtry[39;00m:
+[1;32m    711[0m     [38;5;28;01mreturn[39;00m [38;5;28mself[39m[38;5;241m.[39m_element_class([38;5;28mself[39m, x, y, coerce[38;5;241m=[39mcoerce)
+
+[0;31mTypeError[0m: 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
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mValueError[0m                                Traceback (most recent call last)
+Input [0;32mIn [22][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:27[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:9[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:60[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+[0;31mValueError[0m: 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
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m15[0m - x^[0;38;5;20;1m14[0m + x^[0;38;5;20;1m13[0m + x^[0;38;5;20;1m12[0m + x^[0;38;5;20;1m11[0m + x^[0;38;5;20;1m10[0m - x^[0;38;5;20;1m8[0;38;5;16;48;5;152m)[0;38;5;241m.quo_rem(x^6 + x^5 + x^4 - x^3 + x^2 + 1)[41D[?7h[0m[?12l[?25h[?25l[?7l[47D[0m([45C).quo_rem[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m6[0m + x^[0;38;5;20;1m5[0m + x^[0;38;5;20;1m4[0m - x^[0;38;5;20;1m3[0m + x^[0;38;5;20;1m2[0m + [0;38;5;20;1m1[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[94D[0m[J[0;94msage: [0m(x^[0;38;5;20;1m15[0m - x^[0;38;5;20;1m14[0m + x^[0;38;5;20;1m13[0m + x^[0;38;5;20;1m12[0m + x^[0;38;5;20;1m11[0m + x^[0;38;5;20;1m10[0m - x^[0;38;5;20;1m8[0m).quo_rem(x^[0;38;5;20;1m6[0m + x^[0;38;5;20;1m5[0m + x^[0;38;5;20;1m4[0m - x^[0;38;5;20;1m3[0m + x^[0;38;5;20;1m2[0m + [0;38;5;20;1m1[0m)[94D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(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)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m(x^[0;38;5;20;1m15[0m - x^[0;38;5;20;1m14[0m + x^[0;38;5;20;1m13[0m + x^[0;38;5;20;1m12[0m + x^[0;38;5;20;1m11[0m + x^[0;38;5;20;1m10[0m - x^[0;38;5;20;1m8[0m).quo_rem[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m6[0m + x^[0;38;5;20;1m5[0m + x^[0;38;5;20;1m4[0m - x^[0;38;5;20;1m3[0m + x^[0;38;5;20;1m2[0m + [0;38;5;20;1m1[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[88D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[17D[0mff.expansion_at_infty[0;38;5;16;48;5;152m([0mplace = [0;38;5;20;1m0[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;20;1m1[C[?7h[0m[?12l[?25h[?25l[?7l[30D[0m = ff*C.dx[0m[K[?7h[0m[?12l[?25h[?25l[?7l[10D[0m.expansion_at_infty[0;38;5;16;48;5;152m([0mplace = [0;38;5;20;1m1[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;20;1m0[C[?7h[0m[?12l[?25h[?25l[?7l[10D[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[21D[0m = ff/C.y[0m[K[?7h[0m[?12l[?25h[?25l[?7l[9D[0m/C.y[0m[K[?7h[0m[?12l[?25h[?25l[?7l[4D[0m = superelliptic_function[0;38;5;16;48;5;152m([0mC, ff[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[32D[0m/C.y[0m[K[?7h[0m[?12l[?25h[?25l[?7l[4D[0m = ff/C.y[?7h[0m[?12l[?25h[?25l[?7l[9D[0m.expansion_at_infty[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0mplace = [0;38;5;20;1m0[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;20;1m1[C[?7h[0m[?12l[?25h[?25l[?7l[30D[0m = ff*C.dx[0m[K[?7h[0m[?12l[?25h[?25l[?7l[10D[0m.expansion_at_infty[0;38;5;16;48;5;152m([0mplace = [0;38;5;20;1m1[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;20;1m0[C[?7h[0m[?12l[?25h[?25l[?7l[32D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[17D[0m(x^[0;38;5;20;1m15[0m - x^[0;38;5;20;1m14[0m + x^[0;38;5;20;1m13[0m + x^[0;38;5;20;1m12[0m + x^[0;38;5;20;1m11[0m + x^[0;38;5;20;1m10[0m - x^[0;38;5;20;1m8[0m).quo_rem[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m6[0m + x^[0;38;5;20;1m5[0m + x^[0;38;5;20;1m4[0m - x^[0;38;5;20;1m3[0m + x^[0;38;5;20;1m2[0m + [0;38;5;20;1m1[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[88D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ 
[K]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ 
[K]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+[22;0t]0;IPython: DeRhamComputation/sage[6n[?2004h[?1l[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mValueError[0m                                Traceback (most recent call last)
+Input [0;32mIn [1][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:27[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:9[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:60[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+[0;31mValueError[0m: 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
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.nb_of_pts_at_infty[19D[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mC[7D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mSuperelliptic curve with the equation y^2 = x^3 + 2*x + 1 over Finite Field of size 3
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mnb_of_pts_at_infty[18D[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;241mx.residue()[0m[K[11D[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mi[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mh[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mo[0;38;5;241mmega = C.holomorphic_differentials_basis()[0][45D[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= gg^8*gg.diffn()[0m[K[17D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mC[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[15D[0m[J[0;94msage: [0mom = C.dx[15D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mo[0;38;5;241mm = C.dx[8D[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mexpansion_at_infty(prec = 30)[29D[?7h[0m[?12l[?25h[?25l[?7l[0mi[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mh[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mom = C.dx[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m(C.dx[4D[?7h[0m[?12l[?25h[?25l[?7l[C[0mC.dx[4D[?7h[0m[?12l[?25h[?25l[?7l[0m.C.dx[4D[?7h[0m[?12l[?25h[?25l[?7l[0myC.dx[4D[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m([3C)[0mC.dx[4D[?7h[0m[?12l[?25h[?25l[?7l[5D[0m([3C)^C.dx[4D[?7h[0m[?12l[?25h[?25l[?7l[0m(C.dx[4D[?7h[0m[?12l[?25h[?25l[?7l[0m-C.dx[4D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[0mC.dx[4D[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;16;48;5;152m([2C)[0mC.dx[4D[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([2C)*C.dx[4D[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[26D[0m[J[0;94msage: [0mom = (C.y)^(-[0;38;5;20;1m1[0m)*C.dx[26D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mo[0;38;5;241mm = (C.y)^(-1)*C.dx[19D[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mexpansion_at_infty(prec = 30)[29D[?7h[0m[?12l[?25h[?25l[?7l[0mi[0m[K[?7h[0m[?12l[?25h[?25l[?7l[10D[0;94msage: [0mom.is_regular_on_U[0m

+[24C[0;38;5;16;48;5;250m om.is_regular_on_U0    [0m

+[24C[0;38;5;16;48;5;250m om.is_regular_on_Uinfty[0m

+

+

+[0m [5A[24C[?7h[0m[?12l[?25h[?25l[?7l[0m[K[0m

+[C[0m[K[0m

+[C[0m[K[2A[22C[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;28mis[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0mi[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m

+[9C[0;38;5;16;48;5;250m om.cartier               om.expansion_at_infty    om.is_regular_on_Uinfty  om.serre_duality_pairing[0m

+[9C[0;38;5;16;48;5;250m om.coordinates           om.form                  om.jth_component         om.verschiebung         [0m

+[9C[0;38;5;16;48;5;250m om.curve                 om.is_regular_on_U0      om.residue                                       [3A[100D[?7h[0m[?12l[?25h[?25l[?7l[0mcartier[0m

+[9C[0;38;5;231;48;5;102m om.cartier              [0m

+

+

+[9C[0;38;5;16;48;5;248m <unknown> [4A[4D[?7h[0m[?12l[?25h[?25l[?7l[6D[0moordinates[0m

+[9C[0;38;5;16;48;5;250m om.cartier              [0m

+[9C[0;38;5;231;48;5;102m om.coordinates          [2A[14D[?7h[0m[?12l[?25h[?25l[?7l[11D[0mf[Crm[0m[K[0m

+

+[9C[0;38;5;16;48;5;250m om.coordinates          [0;38;5;231;48;5;102m om.form                 [2A[46D[?7h[0m[?12l[?25h[?25l[?7l[4D[0mjth_component[0m

+

+[34C[0;38;5;16;48;5;250m om.form                 [0;38;5;231;48;5;102m om.jth_component        [2A[62D[?7h[0m[?12l[?25h[?25l[?7l[13D[0mvers[Chiebung[0m[K[0m

+

+[59C[0;38;5;16;48;5;250m om.jth_component        [0;38;5;231;48;5;102m om.verschiebung         [2A[88D[?7h[0m[?12l[?25h[?25l[?7l[12D[0mjth_[Component[0m

+

+[59C[0;38;5;231;48;5;102m om.jth_component        [0;38;5;16;48;5;250m om.verschiebung         [2A[87D[?7h[0m[?12l[?25h[?25l[?7l[0m

+[C[0m[K[0m

+[C[0m[K[0m

+[C[0m[K[0m

+[C[0m[K[4A[21C[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[24D[0m[J[0;94msage: [0mom.jth_component()[24D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [5][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mom[49m[38;5;241;43m.[39;49m[43mjth_component[49m[43m([49m[43m)[49m
+
+[0;31mTypeError[0m: superelliptic_form.jth_component() missing 1 required positional argument: 'j'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mom.jth_component[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[24D[0m[J[0;94msage: [0mom.jth_component([0;38;5;20;1m1[0m)[25D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m1
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mom.jth_component[0;38;5;16;48;5;152m([0;38;5;20;1m1[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[16D[0m = (C.y)^(-[0;38;5;20;1m1[0m)*C.dx[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[C[0mC.dx[4D[?7h[0m[?12l[?25h[?25l[?7l[0m.C.dx[4D[?7h[0m[?12l[?25h[?25l[?7l[0mxC.dx[4D[?7h[0m[?12l[?25h[?25l[?7l[0m*C.dx[4D[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[30D[0m[J[0;94msage: [0mom = (C.y)^(-[0;38;5;20;1m1[0m)*C.x*C.dx[30D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mom = (C.y)^(-[0;38;5;20;1m1[0m)*C.x*C.dx[?7h[0m[?12l[?25h[?25l[?7l[22D[0m.jth_component[0;38;5;16;48;5;152m([0;38;5;20;1m1[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[25D[0m[J[0;94msage: [0mom.jth_component([0;38;5;20;1m1[0m)[25D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mx
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mnb_of_pts_at_infty[18D[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;241mx.residue()[0m[K[11D[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mv[C[0;38;5;241mrschiebung()[13D[?7h[0m[?12l[?25h[?25l[?7l[0ma[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[22D[0m[J[0;94msage: [0mC.dx.valuation()[22D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [9][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mC[49m[38;5;241;43m.[39;49m[43mdx[49m[38;5;241;43m.[39;49m[43mvaluation[49m()
+
+[0;31mAttributeError[0m: 'superelliptic_form' object has no attribute 'valuation'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [10][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:27[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:9[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:81[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+File [0;32m<string>:105[0m, in [0;36mjth_component[0;34m(self, j)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/categories/map.pyx:788[0m, in [0;36msage.categories.map.Map._call_[0;34m()[0m
+[1;32m    786[0m     return self._call_with_args(x, args, kwds)
+[1;32m    787[0m 
+[0;32m--> 788[0m cpdef Element _call_(self, x):
+[1;32m    789[0m     """
+[1;32m    790[0m     Call method with a single argument, not implemented in the base class.
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:1254[0m, in [0;36mFractionFieldEmbeddingSection._call_[0;34m(self, x, check)[0m
+[1;32m   1249[0m     [38;5;28;01mreturn[39;00m num
+[1;32m   1250[0m [38;5;28;01mif[39;00m check [38;5;129;01mand[39;00m [38;5;129;01mnot[39;00m den[38;5;241m.[39mis_unit():
+[1;32m   1251[0m     [38;5;66;03m# This should probably be a ValueError.[39;00m
+[1;32m   1252[0m     [38;5;66;03m# However, too much existing code is expecting this to throw a[39;00m
+[1;32m   1253[0m     [38;5;66;03m# TypeError, so we decided to keep it for the time being.[39;00m
+[0;32m-> 1254[0m     [38;5;28;01mraise[39;00m [38;5;167;01mTypeError[39;00m([38;5;124m"[39m[38;5;124mfraction must have unit denominator[39m[38;5;124m"[39m)
+[1;32m   1255[0m [38;5;28;01mreturn[39;00m num [38;5;241m*[39m den[38;5;241m.[39minverse_of_unit()
+
+[0;31mTypeError[0m: fraction must have unit denominator
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [11][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:27[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:9[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:81[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+File [0;32m<string>:105[0m, in [0;36mjth_component[0;34m(self, j)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/categories/map.pyx:788[0m, in [0;36msage.categories.map.Map._call_[0;34m()[0m
+[1;32m    786[0m     return self._call_with_args(x, args, kwds)
+[1;32m    787[0m 
+[0;32m--> 788[0m cpdef Element _call_(self, x):
+[1;32m    789[0m     """
+[1;32m    790[0m     Call method with a single argument, not implemented in the base class.
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:1254[0m, in [0;36mFractionFieldEmbeddingSection._call_[0;34m(self, x, check)[0m
+[1;32m   1249[0m     [38;5;28;01mreturn[39;00m num
+[1;32m   1250[0m [38;5;28;01mif[39;00m check [38;5;129;01mand[39;00m [38;5;129;01mnot[39;00m den[38;5;241m.[39mis_unit():
+[1;32m   1251[0m     [38;5;66;03m# This should probably be a ValueError.[39;00m
+[1;32m   1252[0m     [38;5;66;03m# However, too much existing code is expecting this to throw a[39;00m
+[1;32m   1253[0m     [38;5;66;03m# TypeError, so we decided to keep it for the time being.[39;00m
+[0;32m-> 1254[0m     [38;5;28;01mraise[39;00m [38;5;167;01mTypeError[39;00m([38;5;124m"[39m[38;5;124mfraction must have unit denominator[39m[38;5;124m"[39m)
+[1;32m   1255[0m [38;5;28;01mreturn[39;00m num [38;5;241m*[39m den[38;5;241m.[39minverse_of_unit()
+
+[0;31mTypeError[0m: fraction must have unit denominator
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [12][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:27[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:9[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:81[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+File [0;32m<string>:105[0m, in [0;36mjth_component[0;34m(self, j)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/categories/map.pyx:788[0m, in [0;36msage.categories.map.Map._call_[0;34m()[0m
+[1;32m    786[0m     return self._call_with_args(x, args, kwds)
+[1;32m    787[0m 
+[0;32m--> 788[0m cpdef Element _call_(self, x):
+[1;32m    789[0m     """
+[1;32m    790[0m     Call method with a single argument, not implemented in the base class.
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:1254[0m, in [0;36mFractionFieldEmbeddingSection._call_[0;34m(self, x, check)[0m
+[1;32m   1249[0m     [38;5;28;01mreturn[39;00m num
+[1;32m   1250[0m [38;5;28;01mif[39;00m check [38;5;129;01mand[39;00m [38;5;129;01mnot[39;00m den[38;5;241m.[39mis_unit():
+[1;32m   1251[0m     [38;5;66;03m# This should probably be a ValueError.[39;00m
+[1;32m   1252[0m     [38;5;66;03m# However, too much existing code is expecting this to throw a[39;00m
+[1;32m   1253[0m     [38;5;66;03m# TypeError, so we decided to keep it for the time being.[39;00m
+[0;32m-> 1254[0m     [38;5;28;01mraise[39;00m [38;5;167;01mTypeError[39;00m([38;5;124m"[39m[38;5;124mfraction must have unit denominator[39m[38;5;124m"[39m)
+[1;32m   1255[0m [38;5;28;01mreturn[39;00m num [38;5;241m*[39m den[38;5;241m.[39minverse_of_unit()
+
+[0;31mTypeError[0m: fraction must have unit denominator
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?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
+[0;31m---------------------------------------------------------------------------[0m
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [13][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:27[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:9[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:81[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+File [0;32m<string>:106[0m, in [0;36mjth_component[0;34m(self, j)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/categories/map.pyx:788[0m, in [0;36msage.categories.map.Map._call_[0;34m()[0m
+[1;32m    786[0m     return self._call_with_args(x, args, kwds)
+[1;32m    787[0m 
+[0;32m--> 788[0m cpdef Element _call_(self, x):
+[1;32m    789[0m     """
+[1;32m    790[0m     Call method with a single argument, not implemented in the base class.
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:1254[0m, in [0;36mFractionFieldEmbeddingSection._call_[0;34m(self, x, check)[0m
+[1;32m   1249[0m     [38;5;28;01mreturn[39;00m num
+[1;32m   1250[0m [38;5;28;01mif[39;00m check [38;5;129;01mand[39;00m [38;5;129;01mnot[39;00m den[38;5;241m.[39mis_unit():
+[1;32m   1251[0m     [38;5;66;03m# This should probably be a ValueError.[39;00m
+[1;32m   1252[0m     [38;5;66;03m# However, too much existing code is expecting this to throw a[39;00m
+[1;32m   1253[0m     [38;5;66;03m# TypeError, so we decided to keep it for the time being.[39;00m
+[0;32m-> 1254[0m     [38;5;28;01mraise[39;00m [38;5;167;01mTypeError[39;00m([38;5;124m"[39m[38;5;124mfraction must have unit denominator[39m[38;5;124m"[39m)
+[1;32m   1255[0m [38;5;28;01mreturn[39;00m num [38;5;241m*[39m den[38;5;241m.[39minverse_of_unit()
+
+[0;31mTypeError[0m: fraction must have unit denominator
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?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
+[0;31m---------------------------------------------------------------------------[0m
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [14][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:27[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:9[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:81[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+File [0;32m<string>:107[0m, in [0;36mjth_component[0;34m(self, j)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/categories/map.pyx:788[0m, in [0;36msage.categories.map.Map._call_[0;34m()[0m
+[1;32m    786[0m     return self._call_with_args(x, args, kwds)
+[1;32m    787[0m 
+[0;32m--> 788[0m cpdef Element _call_(self, x):
+[1;32m    789[0m     """
+[1;32m    790[0m     Call method with a single argument, not implemented in the base class.
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:1254[0m, in [0;36mFractionFieldEmbeddingSection._call_[0;34m(self, x, check)[0m
+[1;32m   1249[0m     [38;5;28;01mreturn[39;00m num
+[1;32m   1250[0m [38;5;28;01mif[39;00m check [38;5;129;01mand[39;00m [38;5;129;01mnot[39;00m den[38;5;241m.[39mis_unit():
+[1;32m   1251[0m     [38;5;66;03m# This should probably be a ValueError.[39;00m
+[1;32m   1252[0m     [38;5;66;03m# However, too much existing code is expecting this to throw a[39;00m
+[1;32m   1253[0m     [38;5;66;03m# TypeError, so we decided to keep it for the time being.[39;00m
+[0;32m-> 1254[0m     [38;5;28;01mraise[39;00m [38;5;167;01mTypeError[39;00m([38;5;124m"[39m[38;5;124mfraction must have unit denominator[39m[38;5;124m"[39m)
+[1;32m   1255[0m [38;5;28;01mreturn[39;00m num [38;5;241m*[39m den[38;5;241m.[39minverse_of_unit()
+
+[0;31mTypeError[0m: fraction must have unit denominator
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?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'>
+[0;31m---------------------------------------------------------------------------[0m
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [15][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:27[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:9[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:81[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+File [0;32m<string>:107[0m, in [0;36mjth_component[0;34m(self, j)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/categories/map.pyx:788[0m, in [0;36msage.categories.map.Map._call_[0;34m()[0m
+[1;32m    786[0m     return self._call_with_args(x, args, kwds)
+[1;32m    787[0m 
+[0;32m--> 788[0m cpdef Element _call_(self, x):
+[1;32m    789[0m     """
+[1;32m    790[0m     Call method with a single argument, not implemented in the base class.
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:1254[0m, in [0;36mFractionFieldEmbeddingSection._call_[0;34m(self, x, check)[0m
+[1;32m   1249[0m     [38;5;28;01mreturn[39;00m num
+[1;32m   1250[0m [38;5;28;01mif[39;00m check [38;5;129;01mand[39;00m [38;5;129;01mnot[39;00m den[38;5;241m.[39mis_unit():
+[1;32m   1251[0m     [38;5;66;03m# This should probably be a ValueError.[39;00m
+[1;32m   1252[0m     [38;5;66;03m# However, too much existing code is expecting this to throw a[39;00m
+[1;32m   1253[0m     [38;5;66;03m# TypeError, so we decided to keep it for the time being.[39;00m
+[0;32m-> 1254[0m     [38;5;28;01mraise[39;00m [38;5;167;01mTypeError[39;00m([38;5;124m"[39m[38;5;124mfraction must have unit denominator[39m[38;5;124m"[39m)
+[1;32m   1255[0m [38;5;28;01mreturn[39;00m num [38;5;241m*[39m den[38;5;241m.[39minverse_of_unit()
+
+[0;31mTypeError[0m: fraction must have unit denominator
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?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
+[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [16][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:27[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:9[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:81[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+File [0;32m<string>:105[0m, in [0;36mjth_component[0;34m(self, j)[0m
+
+File [0;32m<string>:140[0m, in [0;36mcoff[0;34m(f, d)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/element.pyx:494[0m, in [0;36msage.structure.element.Element.__getattr__[0;34m()[0m
+[1;32m    492[0m         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+[1;32m    493[0m     """
+[0;32m--> 494[0m     return self.getattr_from_category(name)
+[1;32m    495[0m 
+[1;32m    496[0m cdef getattr_from_category(self, name):
+
+File [0;32m/ext/sage/9.7/src/sage/structure/element.pyx:507[0m, in [0;36msage.structure.element.Element.getattr_from_category[0;34m()[0m
+[1;32m    505[0m     else:
+[1;32m    506[0m         cls = P._abstract_element_class
+[0;32m--> 507[0m     return getattr_from_other_class(self, cls, name)
+[1;32m    508[0m 
+[1;32m    509[0m def __dir__(self):
+
+File [0;32m/ext/sage/9.7/src/sage/cpython/getattr.pyx:361[0m, in [0;36msage.cpython.getattr.getattr_from_other_class[0;34m()[0m
+[1;32m    359[0m     dummy_error_message.cls = type(self)
+[1;32m    360[0m     dummy_error_message.name = name
+[0;32m--> 361[0m     raise AttributeError(dummy_error_message)
+[1;32m    362[0m attribute = <object>attr
+[1;32m    363[0m # Check for a descriptor (__get__ in Python)
+
+[0;31mAttributeError[0m: 'sage.rings.fraction_field_element.FractionFieldElement_1poly_field' object has no attribute 'coefficients'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?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
+[0;31m---------------------------------------------------------------------------[0m
+[0;31mNameError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [17][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:27[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:9[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:83[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+[0;31mNameError[0m: name 'quo_rem' is not defined
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?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]))]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m([0;38;5;241mx^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)[87D[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.x*C.d[C).form[0m[K[13D[?7h[0m[?12l[?25h[?25l[?7l[0m.x*C.dx).form[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;28;1mfor[0m[K[?7h[0m[?12l[?25h[?25l[?7l[3D[0mfo[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mj[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mh[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m_[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[32D[0m[J[0;94msage: [0m(C.x*C.dx).jth_component([0;38;5;20;1m1[0m)[33D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m0
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+[J[?7h[0m[?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
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+[([(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]))]
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+[J[?7h[0m[?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
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+[([(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]))]
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+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?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]))]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mR[0;38;5;241mx.<x> = PolynomialRing(GF(2))[29D[?7h[0m[?12l[?25h[?25l[?7l[0mx.<x> = PolynomialRing[0;38;5;16;48;5;152m([0mGF([0;38;5;20;1m2[0m)[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[7D[0m([2C[0;38;5;16;48;5;152m([C[0;38;5;210;48;5;88m)[0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m)[0m[K[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m3[0;38;5;210;48;5;88m)[0m)[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[0m([C)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([C[0;38;5;16;48;5;152m)[3D[?7h[0m[?12l[?25h[?25l[?7l[0m([C)[5D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([5C[0;38;5;16;48;5;152m)[7D[?7h[0m[?12l[?25h[?25l[?7l[0m([5C)[21D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[15C[0;38;5;210;48;5;88m([5C[0;38;5;16;48;5;152m)[7D[?7h[0m[?12l[?25h[?25l[?7l[0m([2C[0;38;5;210;48;5;88m([C[0;38;5;16;48;5;152m)[0m)[4D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[5D[0;38;5;16;48;5;152m([2C[0m([C)[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[36D[0m[J[0;94msage: [0mRx.<x> = PolynomialRing(GF([0;38;5;20;1m3[0m))[36D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mF[0;38;5;241mxy[2D[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mF[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mF[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mR[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;16;48;5;152m([2C)[?7h[0m[?12l[?25h[?25l[?7l[28D[0m[J[0;94msage: [0mFx = FractionField(Rx)[28D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mF[0;38;5;241mx = FractionField(Rx)[21D[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0mR[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0m<[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[0m>[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mP[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0mR[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mF[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;16;48;5;152m([2C)[?7h[0m[?12l[?25h[?25l[?7l[35D[0m[J[0;94msage: [0mFxRy.<y> = PolynomialRing(Fx)[35D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mg[0;38;5;241mroup_action_matrices_dR(AS)[27D[?7h[0m[?12l[?25h[?25l[?7l[0mg[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mF[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0mR[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[0m/[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[8D[0;38;5;16;48;5;152m([7C)[?7h[0m[?12l[?25h[?25l[?7l[25D[0m[J[0;94msage: [0mggg = FxRy(C.y/C.x)[25D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:706[0m, in [0;36mFractionField_generic._element_constructor_[0;34m(self, x, y, coerce)[0m
+[1;32m    705[0m [38;5;28;01mtry[39;00m:
+[0;32m--> 706[0m     x, y [38;5;241m=[39m [43mresolve_fractions[49m[43m([49m[43mx0[49m[43m,[49m[43m [49m[43my0[49m[43m)[49m
+[1;32m    707[0m [38;5;28;01mexcept[39;00m ([38;5;167;01mAttributeError[39;00m, [38;5;167;01mTypeError[39;00m):
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:683[0m, in [0;36mFractionField_generic._element_constructor_.<locals>.resolve_fractions[0;34m(x, y)[0m
+[1;32m    682[0m [38;5;28;01mdef[39;00m [38;5;21mresolve_fractions[39m(x, y):
+[0;32m--> 683[0m     xn [38;5;241m=[39m [43mx[49m[38;5;241;43m.[39;49m[43mnumerator[49m()
+[1;32m    684[0m     xd [38;5;241m=[39m x[38;5;241m.[39mdenominator()
+
+[0;31mAttributeError[0m: 'superelliptic_function' object has no attribute 'numerator'
+
+During handling of the above exception, another exception occurred:
+
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [30][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m ggg [38;5;241m=[39m [43mFxRy[49m[43m([49m[43mC[49m[38;5;241;43m.[39;49m[43my[49m[38;5;241;43m/[39;49m[43mC[49m[38;5;241;43m.[39;49m[43mx[49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    159[0m             print(type(C), C)
+[1;32m    160[0m             print(type(C._element_constructor), C._element_constructor)
+[0;32m--> 161[0m         raise
+[1;32m    162[0m 
+[1;32m    163[0m cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    154[0m cdef Parent C = self._codomain
+[1;32m    155[0m try:
+[0;32m--> 156[0m     return C._element_constructor(x)
+[1;32m    157[0m except Exception:
+[1;32m    158[0m     if print_warnings:
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:469[0m, in [0;36mPolynomialRing_general._element_constructor_[0;34m(self, x, check, is_gen, construct, **kwds)[0m
+[1;32m    467[0m [38;5;28;01melif[39;00m [38;5;28misinstance[39m(x, sage[38;5;241m.[39mrings[38;5;241m.[39mpower_series_ring_element[38;5;241m.[39mPowerSeries):
+[1;32m    468[0m     x [38;5;241m=[39m x[38;5;241m.[39mtruncate()
+[0;32m--> 469[0m [38;5;28;01mreturn[39;00m [43mC[49m[43m([49m[38;5;28;43mself[39;49m[43m,[49m[43m [49m[43mx[49m[43m,[49m[43m [49m[43mcheck[49m[43m,[49m[43m [49m[43mis_gen[49m[43m,[49m[43m [49m[43mconstruct[49m[38;5;241;43m=[39;49m[43mconstruct[49m[43m,[49m[43m [49m[38;5;241;43m*[39;49m[38;5;241;43m*[39;49m[43mkwds[49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_element_generic.py:1083[0m, in [0;36mPolynomial_generic_dense_field.__init__[0;34m(self, parent, x, check, is_gen, construct)[0m
+[1;32m   1082[0m [38;5;28;01mdef[39;00m [38;5;21m__init__[39m([38;5;28mself[39m, parent, x[38;5;241m=[39m[38;5;28;01mNone[39;00m, check[38;5;241m=[39m[38;5;28;01mTrue[39;00m, is_gen [38;5;241m=[39m [38;5;28;01mFalse[39;00m, construct[38;5;241m=[39m[38;5;28;01mFalse[39;00m):
+[0;32m-> 1083[0m     [43mPolynomial_generic_dense[49m[38;5;241;43m.[39;49m[38;5;21;43m__init__[39;49m[43m([49m[38;5;28;43mself[39;49m[43m,[49m[43m [49m[43mparent[49m[43m,[49m[43m [49m[43mx[49m[43m,[49m[43m [49m[43mcheck[49m[43m,[49m[43m [49m[43mis_gen[49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:11222[0m, in [0;36msage.rings.polynomial.polynomial_element.Polynomial_generic_dense.__init__[0;34m()[0m
+[1;32m  11220[0m #                x = []    # zero polynomial
+[1;32m  11221[0m         if check:
+[0;32m> 11222[0m             self.__coeffs = [R(z, **kwds) for z in x]
+[1;32m  11223[0m             self.__normalize()
+[1;32m  11224[0m         else:
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    159[0m             print(type(C), C)
+[1;32m    160[0m             print(type(C._element_constructor), C._element_constructor)
+[0;32m--> 161[0m         raise
+[1;32m    162[0m 
+[1;32m    163[0m cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    154[0m cdef Parent C = self._codomain
+[1;32m    155[0m try:
+[0;32m--> 156[0m     return C._element_constructor(x)
+[1;32m    157[0m except Exception:
+[1;32m    158[0m     if print_warnings:
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field.py:708[0m, in [0;36mFractionField_generic._element_constructor_[0;34m(self, x, y, coerce)[0m
+[1;32m    706[0m     x, y [38;5;241m=[39m resolve_fractions(x0, y0)
+[1;32m    707[0m [38;5;28;01mexcept[39;00m ([38;5;167;01mAttributeError[39;00m, [38;5;167;01mTypeError[39;00m):
+[0;32m--> 708[0m     [38;5;28;01mraise[39;00m [38;5;167;01mTypeError[39;00m([38;5;124m"[39m[38;5;124mcannot convert [39m[38;5;132;01m{!r}[39;00m[38;5;124m/[39m[38;5;132;01m{!r}[39;00m[38;5;124m to an element of [39m[38;5;132;01m{}[39;00m[38;5;124m"[39m[38;5;241m.[39mformat(
+[1;32m    709[0m                     x0, y0, [38;5;28mself[39m))
+[1;32m    710[0m [38;5;28;01mtry[39;00m:
+[1;32m    711[0m     [38;5;28;01mreturn[39;00m [38;5;28mself[39m[38;5;241m.[39m_element_class([38;5;28mself[39m, x, y, coerce[38;5;241m=[39mcoerce)
+
+[0;31mTypeError[0m: cannot convert 1/x*y/1 to an element of Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mggg = FxRy[0;38;5;16;48;5;152m([0mC.y/C.x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[19D[0mFxRy.<y> = PolynomialRing[0;38;5;16;48;5;152m([0mFx[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([2C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mF[0;38;5;241mxRy.<y> = PolynomialRing(Fx)[28D[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0mR[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[10D[0m[J[0;94msage: [0mFxRy[10D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mUnivariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 3
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mFxRy[?7h[0m[?12l[?25h[?25l[?7l[4D[0mggg = FxRy[0;38;5;16;48;5;152m([0mC.y/C.x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[19D[0mFxRy.<y> = PolynomialRing[0;38;5;16;48;5;152m([0mFx[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[29D[0mggg = FxRy[0;38;5;16;48;5;152m([0mC.y/C.x[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0my[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m/[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0m[J[0;94msage: [0mggg = FxRy(y/x)[21D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mg[0;38;5;241mgg = FxRy(y/x)[14D[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0m.[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0micients[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m([C)[?7h[0m[?12l[?25h[?25l[?7l[24D[0m[J[0;94msage: [0mggg.coefficient(y)[24D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [33][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mggg[49m[38;5;241;43m.[39;49m[43mcoefficient[49m(y)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/element.pyx:494[0m, in [0;36msage.structure.element.Element.__getattr__[0;34m()[0m
+[1;32m    492[0m         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+[1;32m    493[0m     """
+[0;32m--> 494[0m     return self.getattr_from_category(name)
+[1;32m    495[0m 
+[1;32m    496[0m cdef getattr_from_category(self, name):
+
+File [0;32m/ext/sage/9.7/src/sage/structure/element.pyx:507[0m, in [0;36msage.structure.element.Element.getattr_from_category[0;34m()[0m
+[1;32m    505[0m     else:
+[1;32m    506[0m         cls = P._abstract_element_class
+[0;32m--> 507[0m     return getattr_from_other_class(self, cls, name)
+[1;32m    508[0m 
+[1;32m    509[0m def __dir__(self):
+
+File [0;32m/ext/sage/9.7/src/sage/cpython/getattr.pyx:356[0m, in [0;36msage.cpython.getattr.getattr_from_other_class[0;34m()[0m
+[1;32m    354[0m     dummy_error_message.cls = type(self)
+[1;32m    355[0m     dummy_error_message.name = name
+[0;32m--> 356[0m     raise AttributeError(dummy_error_message)
+[1;32m    357[0m cdef PyObject* attr = instance_getattr(cls, name)
+[1;32m    358[0m if attr is NULL:
+
+[0;31mAttributeError[0m: 'PolynomialRing_field_with_category.element_class' object has no attribute 'coefficient'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mggg.coefficient[0;38;5;16;48;5;152m([0my[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[2D[0m([C)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([C[0;38;5;16;48;5;152m)[3D[?7h[0m[?12l[?25h[?25l[?7l[0m([C)[14D[?7h[0m[?12l[?25h[?25l[?7l[0mmcoe[Cficient(y)[14D[?7h[0m[?12l[?25h[?25l[?7l[0mocoe[Cficient(y)[14D[?7h[0m[?12l[?25h[?25l[?7l[0mncoe[Cficient(y)[14D[?7h[0m[?12l[?25h[?25l[?7l[0mocoe[Cficient(y)[14D[?7h[0m[?12l[?25h[?25l[?7l[0mmcoe[Cficient(y)[14D[?7h[0m[?12l[?25h[?25l[?7l[0micoe[Cficient(y)[14D[?7h[0m[?12l[?25h[?25l[?7l[0macoe[Cficient(y)[14D[?7h[0m[?12l[?25h[?25l[?7l[0mlcoe[Cficient(y)[14D[?7h[0m[?12l[?25h[?25l[?7l[0m_coe[Cficient(y)[14D[?7h[0m[?12l[?25h[?25l[?7l[11C[0;38;5;210;48;5;88m([C[0;38;5;16;48;5;152m)[3D[?7h[0m[?12l[?25h[?25l[?7l[0m([C)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[33D[0m[J[0;94msage: [0mggg.monomial_coefficient(y)[33D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m1/x
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?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]))]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[17D[0mggg.monomial_coefficient[0;38;5;16;48;5;152m([0my[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0mc[Ceff[Ccient[0;38;5;16;48;5;152m([0my[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[15D[0m = FxRy[0;38;5;16;48;5;152m([0my/x[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[15D[0mFxRy[0m[K[?7h[0m[?12l[?25h[?25l[?7l[4D[0mggg = FxRy[0;38;5;16;48;5;152m([0my/x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[15D[0mFxRy[0m[K[?7h[0m[?12l[?25h[?25l[?7l[4D[0mggg = FxRy[0;38;5;16;48;5;152m([0mC.y/C.x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[19D[0mFxRy.<y> = PolynomialRing[0;38;5;16;48;5;152m([0mFx[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[27D[0m = FractionField[0;38;5;16;48;5;152m([0mRx[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[22D[0mR[C.<x> = Polynomial[Cing[0;38;5;16;48;5;152m([0mGF([0;38;5;20;1m3[0m)[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[30D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[17D[0m((C.x)^(-[0;38;5;20;1m1[0m)*C.dx).jth_component[0;38;5;16;48;5;152m([0;38;5;20;1m1[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[40D[0m[J[0;94msage: [0m((C.x)^(-[0;38;5;20;1m1[0m)*C.dx).jth_component([0;38;5;20;1m1[0m)[40D[0m

+[J[?7h[0m[?12l[?25h[?2004lg 1/x
+g2 1/x*y^2
+[0m[?7h[0;91m[0m[0m0
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m((C.x)^(-[0;38;5;20;1m1[0m)*C.dx).jth_component[0;38;5;16;48;5;152m([0;38;5;20;1m1[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[40D[0m[J[0;94msage: [0m((C.x)^(-[0;38;5;20;1m1[0m)*C.dx).jth_component([0;38;5;20;1m0[0m)[40D[0m

+[J[?7h[0m[?12l[?25h[?2004lg 1/x
+g2 1/x*y^2
+[0m[?7h[0;91m[0m[0m1/x
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m((C.x)^(-[0;38;5;20;1m1[0m)*C.dx).jth_component[0;38;5;16;48;5;152m([0;38;5;20;1m0[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;20;1m1[C[?7h[0m[?12l[?25h[?25l[?7l[34D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?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]))]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mr[0;38;5;241mes.reduce()[11D[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;241muc[C(xi)[0m[K[7D[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mC[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m,[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[?7h[0m[?12l[?25h[?25l[?7l[0m/[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[7D[0;38;5;16;48;5;152m([6C)[?7h[0m[?12l[?25h[?25l[?7l[20D[0m[J[0;94msage: [0mreduce(C, [0;38;5;20;1m1[0m/y)[20D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [39][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mreduce[49m[43m([49m[43mC[49m[43m,[49m[43m [49m[43mInteger[49m[43m([49m[38;5;241;43m1[39;49m[43m)[49m[38;5;241;43m/[39;49m[43my[49m[43m)[49m
+
+[0;31mTypeError[0m: reduce() arg 2 must support iteration
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mreduce[0;38;5;16;48;5;152m([0mC, [0;38;5;20;1m1[0m/y[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[7D[0m([6C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([6C[0;38;5;16;48;5;152m)[8D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0mC, [0;38;5;20;1m1[0m/y[0;38;5;16;48;5;152m)[0m[K[8D[?7h[0m[?12l[?25h[?25l[?7l[0mt[0;38;5;210;48;5;88m([0mC, [0;38;5;20;1m1[0m/y[0;38;5;16;48;5;152m)[8D[?7h[0m[?12l[?25h[?25l[?7l[0mi[0;38;5;210;48;5;88m([0mC, [0;38;5;20;1m1[0m/y[0;38;5;16;48;5;152m)[8D[?7h[0m[?12l[?25h[?25l[?7l[0mo[0;38;5;210;48;5;88m([0mC, [0;38;5;20;1m1[0m/y[0;38;5;16;48;5;152m)[8D[?7h[0m[?12l[?25h[?25l[?7l[0mn[0;38;5;210;48;5;88m([0mC, [0;38;5;20;1m1[0m/y[0;38;5;16;48;5;152m)[8D[?7h[0m[?12l[?25h[?25l[?7l[0m([6C)[6D[?7h[0m[?12l[?25h[?25l[?7l[3C[?7h[0m[?12l[?25h[?25l[?7l[5D[0;38;5;16;48;5;152m([6C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mreduction(C, [0;38;5;20;1m1[0m/y)[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(1/(x^3 + 2*x + 1))*y
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?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
+[0;31m---------------------------------------------------------------------------[0m
+[0;31mValueError[0m                                Traceback (most recent call last)
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009[0m, in [0;36msage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_[0;34m()[0m
+[1;32m   1008[0m # now try calling the base ring's __call__ methods
+[0;32m-> 1009[0m element = self.base_ring()(element)
+[1;32m   1010[0m _p = p_NSet(sa2si(element,_ring), _ring)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    896[0m if no_extra_args:
+[0;32m--> 897[0m     return mor._call_(x)
+[1;32m    898[0m else:
+
+File [0;32m/ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1652[0m, in [0;36msage.rings.fraction_field_FpT.FpT_Fp_section._call_[0;34m()[0m
+[1;32m   1651[0m if nmod_poly_degree(x._denom) != 0:
+[0;32m-> 1652[0m     raise ValueError("not integral")
+[1;32m   1653[0m if nmod_poly_degree(x._numer) > 0:
+
+[0;31mValueError[0m: not integral
+
+During handling of the above exception, another exception occurred:
+
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [41][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mload[49m[43m([49m[38;5;124;43m'[39;49m[38;5;124;43minit.sage[39;49m[38;5;124;43m'[39;49m[43m)[49m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:27[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/persist.pyx:175[0m, in [0;36msage.misc.persist.load[0;34m()[0m
+[1;32m    173[0m 
+[1;32m    174[0m     if sage.repl.load.is_loadable_filename(filename):
+[0;32m--> 175[0m         sage.repl.load.load(filename, globals())
+[1;32m    176[0m         return
+[1;32m    177[0m 
+
+File [0;32m/ext/sage/9.7/src/sage/repl/load.py:272[0m, in [0;36mload[0;34m(filename, globals, attach)[0m
+[1;32m    270[0m             add_attached_file(fpath)
+[1;32m    271[0m         [38;5;28;01mwith[39;00m [38;5;28mopen[39m(fpath) [38;5;28;01mas[39;00m f:
+[0;32m--> 272[0m             [43mexec[49m[43m([49m[43mpreparse_file[49m[43m([49m[43mf[49m[38;5;241;43m.[39;49m[43mread[49m[43m([49m[43m)[49m[43m)[49m[43m [49m[38;5;241;43m+[39;49m[43m [49m[38;5;124;43m"[39;49m[38;5;130;43;01m\n[39;49;00m[38;5;124;43m"[39;49m[43m,[49m[43m [49m[38;5;28;43mglobals[39;49m[43m)[49m
+[1;32m    273[0m [38;5;28;01melif[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.spyx[39m[38;5;124m'[39m [38;5;129;01mor[39;00m ext [38;5;241m==[39m [38;5;124m'[39m[38;5;124m.pyx[39m[38;5;124m'[39m:
+[1;32m    274[0m     [38;5;28;01mif[39;00m attach:
+
+File [0;32m<string>:9[0m, in [0;36m<module>[0;34m[0m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:87[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/structure/parent.pyx:897[0m, in [0;36msage.structure.parent.Parent.__call__[0;34m()[0m
+[1;32m    895[0m if mor is not None:
+[1;32m    896[0m     if no_extra_args:
+[0;32m--> 897[0m         return mor._call_(x)
+[1;32m    898[0m     else:
+[1;32m    899[0m         return mor._call_with_args(x, args, kwds)
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    159[0m             print(type(C), C)
+[1;32m    160[0m             print(type(C._element_constructor), C._element_constructor)
+[0;32m--> 161[0m         raise
+[1;32m    162[0m 
+[1;32m    163[0m cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File [0;32m/ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156[0m, in [0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_[0;34m()[0m
+[1;32m    154[0m cdef Parent C = self._codomain
+[1;32m    155[0m try:
+[0;32m--> 156[0m     return C._element_constructor(x)
+[1;32m    157[0m except Exception:
+[1;32m    158[0m     if print_warnings:
+
+File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1013[0m, in [0;36msage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_[0;34m()[0m
+[1;32m   1011[0m         return new_MP(self,_p)
+[1;32m   1012[0m     except (TypeError, ValueError):
+[0;32m-> 1013[0m         raise TypeError("Could not find a mapping of the passed element to this ring.")
+[1;32m   1014[0m 
+[1;32m   1015[0m def _repr_(self):
+
+[0;31mTypeError[0m: Could not find a mapping of the passed element to this ring.
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?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]))]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?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]))]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.dx.valuation()[15D[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mC[7D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mSuperelliptic curve with the equation y^2 = x^3 + 2*x + 1 over Finite Field of size 3
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([0m(C.x^[0;38;5;20;1m17[0m - C.x^[0;38;5;20;1m16[0m + C.x^[0;38;5;20;1m15[0m + C.x^[0;38;5;20;1m14[0m + C.x^[0;38;5;20;1m13[0m + C.x^[0;38;5;20;1m12[0m - C.x^[0;38;5;20;1m10[0m + C.x^[0;38;5;20;1m7[0m + C.x^[0;38;5;20;1m6[0m - C.x^[0;38;5;20;1m5[0m - C.x^[0;38;5;20;1m4[0m + C.x^[0;38;5;20;1m2[0m - C.x + [0;38;5;20;1m1[0m)/(C.x^[0;38;5;20;1m8[0m*C.y + C.x^[0;38;5;20;1m7[0m*C.y + C.x^[0;38;5;20;1m6[0m*C.y - C.x^[0;38;5;20;1m5[0m*C.y + C.x^[0;38;5;20;1m4[0m*C.y + 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C.x^[0;38;5;20;1m2[0m*C.y[C)*C.dx[79D[?7h[0m[?12l[?25h[?25l[?7l[115D[0m([114C)[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[3C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[4C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[68D[0;38;5;16;48;5;152m([69C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[70D[0m([69C)[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[207D[0m[J[0;94msage: [0mfff = ((C.x^[0;38;5;20;1m17[0m - C.x^[0;38;5;20;1m16[0m + C.x^[0;38;5;20;1m15[0m + C.x^[0;38;5;20;1m14[0m + C.x^[0;38;5;20;1m13[0m + C.x^[0;38;5;20;1m12[0m - C.x^[0;38;5;20;1m10[0m + C.x^[0;38;5;20;1m7[0m + C.x^[0;38;5;20;1m6[0m - C.x^[0;38;5;20;1m5[0m - C.x^[0;38;5;20;1m4[0m + C.x^[0;38;5;20;1m2[0m - C.x + C.one)/(C.x^[0;38;5;20;1m8[0m*C.y + C.x^[0;38;5;20;1m7[0m*C.y + C.x^[0;38;5;20;1m6[0m*C.y - C.x^[0;38;5;20;1m5[0m*C.y + C.x^[0;38;5;20;1m4[0m*C.y + C.x^[0;38;5;20;1m2[0m*C.y))*C.dx[207D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mf[0;38;5;241mff = ((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[200D[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[9D[0m[J[0;94msage: [0mfff[9D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m((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
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;241mef chang(a):[12D[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mc[0;38;5;241momposition_g0_g8((3*a).f)[25D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0mposition_g0_g8[0;38;5;16;48;5;152m([0m([0;38;5;20;1m3[0m*a).f[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[9D[0m([7C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;16;48;5;152m([3C)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[5D[0m([3C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mo[0;38;5;241mmega0_omega8(a)[1].expansion_at_infty()[39D[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[23D[0;94msage: [0mdecomposition_omega0_omega8[0;38;5;241m(a)[1].expansion_at_infty()[0m

+[33C[0;38;5;16;48;5;250m decomposition_omega0_omega8 [0m

+[33C[0;38;5;16;48;5;250m decomposition_omega0_omega82[0m

+[33C[0;38;5;16;48;5;250m dec…omega0_omega8_old       [0m

+

+[0m [5A[33C[?7h[0m[?12l[?25h[?25l[?7l[0m([0m

+[C[0m[K[0m

+[C[0m[K[0m

+[C[0m[K[3A[33C[?7h[0m[?12l[?25h[?25l[?7l[0mf[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m([3C)[?7h[0m[?12l[?25h[?25l[?7l[38D[0m[J[0;94msage: [0mdecomposition_omega0_omega8(fff)[38D[0m

+[J[?7h[0m[?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
+[0m[?7h[0;91m[0m[0m(((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)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[6D[0;94msage: [0m

+[0m [A[6C[?7h[0m[?12l[?25h[?25l[?7l[0mdecomposition_omega0_omega8[0;38;5;16;48;5;152m([0mfff[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([3C)[4D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([3C[0;38;5;16;48;5;152m)[5D[?7h[0m[?12l[?25h[?25l[?7l[0m([3C)[32D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mldecomposition_omega0_omega8([2Cf)[32D[?7h[0m[?12l[?25h[?25l[?7l[0medecomposition_omega0_omega8([2Cf)[32D[?7h[0m[?12l[?25h[?25l[?7l[0mndecomposition_omega0_omega8([2Cf)[32D[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;24mlen[0m(decomposition_omega0_omega8([2Cf)[32D[?7h[0m[?12l[?25h[?25l[?7l[27C[0;38;5;210;48;5;88m([3C[0;38;5;16;48;5;152m)[5D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([3C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[33D[0;38;5;16;48;5;152m([27C[0m([3C)[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[43D[0m[J[0;94msage: [0;38;5;24mlen[0m(decomposition_omega0_omega8(fff))[43D[0m

+[J[?7h[0m[?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
+[0m[?7h[0;91m[0m[0m2
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;24mlen[0;38;5;16;48;5;152m([0mdecomposition_omega0_omega8(fff)[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[43D[0m[J[0;94msage: [0;38;5;24mlen[0m(decomposition_omega0_omega8(fff))[43D[0m

+[J[?7h[0m[?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
+[0m[?7h[0;91m[0m[0m2
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;24mlen[0;38;5;16;48;5;152m([0mdecomposition_omega0_omega8(fff)[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[34D[0m([27C[0;38;5;16;48;5;152m([3C)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([3C)[4D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([3C[0;38;5;16;48;5;152m)[5D[?7h[0m[?12l[?25h[?25l[?7l[0m([3C)[32D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[3D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[4D[0mlendecomposition_omega0_omega8(f[2C)[0m[K[32D[?7h[0m[?12l[?25h[?25l[?7l[0mdecomposition_omega0_omega8(f[2C)[0m[K[32D[?7h[0m[?12l[?25h[?25l[?7l[0mdecomposition_omega0_omega8(f[2C)[0m[K[32D[?7h[0m[?12l[?25h[?25l[?7l[0mdecomposition_omega0_omega8(f[2C)[0m[K[32D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[6D[0m[J[0;94msage: [0mdecomposition_omega0_omega8(fff)[38D[0m

+[J[?7h[0m[?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
+[0m[?7h[0;91m[0m[0m(((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)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241men(decomposition_omega0_omega8(fff))[36D[?7h[0m[?12l[?25h[?25l[?7l[0mo[0;38;5;241mad('init.[Cage')[0m[K[15D[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?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]))]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?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]))]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[17D[0mdecomposition_omega0_omega8[0;38;5;16;48;5;152m([0mfff[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[32D[0;38;5;24mlen[0;38;5;16;48;5;152m([0mdecomposition_omega0_omega8(fff)[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[37D[0mdecomposition_omega0_omega8[0;38;5;16;48;5;152m([0mfff[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[32D[0mfff[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m = ((C.x^[0;38;5;20;1m17[0m - C.x^[0;38;5;20;1m16[0m + C.x^[0;38;5;20;1m15[0m + C.x^[0;38;5;20;1m14[0m + C.x^[0;38;5;20;1m13[0m + C.x^[0;38;5;20;1m12[0m - C.x^[0;38;5;20;1m10[0m + C.x^[0;38;5;20;1m7[0m + C.x^[0;38;5;20;1m6[0m - C.x^[0;38;5;20;1m5[0m - C.x^[0;38;5;20;1m4[0m + C.x^[0;38;5;20;1m2[0m - C.x + C.one)/(C.x^[0;38;5;20;1m8[0m*C.y + C.x^[0;38;5;20;1m7[0m*C.y + C.x^[0;38;5;20;1m6[0m*C.y - C.x^[0;38;5;20;1m5[0m*C.y + C.x^[0;38;5;20;1m4[0m*C.y + C.x^[0;38;5;20;1m2[0m*C.y))*C.dx[?7h[0m[?12l[?25h[?25l[?7l[201D[0mC[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[17D[0mC[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mfff = ((C.x^[0;38;5;20;1m17[0m - C.x^[0;38;5;20;1m16[0m + C.x^[0;38;5;20;1m15[0m + C.x^[0;38;5;20;1m14[0m + C.x^[0;38;5;20;1m13[0m + C.x^[0;38;5;20;1m12[0m - C.x^[0;38;5;20;1m10[0m + C.x^[0;38;5;20;1m7[0m + C.x^[0;38;5;20;1m6[0m - C.x^[0;38;5;20;1m5[0m - C.x^[0;38;5;20;1m4[0m + C.x^[0;38;5;20;1m2[0m - C.x + C.one)/(C.x^[0;38;5;20;1m8[0m*C.y + C.x^[0;38;5;20;1m7[0m*C.y + C.x^[0;38;5;20;1m6[0m*C.y - C.x^[0;38;5;20;1m5[0m*C.y + C.x^[0;38;5;20;1m4[0m*C.y + C.x^[0;38;5;20;1m2[0m*C.y))*C.dx[?7h[0m[?12l[?25h[?25l[?7l[207D[0m[J[0;94msage: [0mfff = ((C.x^[0;38;5;20;1m17[0m - C.x^[0;38;5;20;1m16[0m + C.x^[0;38;5;20;1m15[0m + C.x^[0;38;5;20;1m14[0m + C.x^[0;38;5;20;1m13[0m + C.x^[0;38;5;20;1m12[0m - C.x^[0;38;5;20;1m10[0m + C.x^[0;38;5;20;1m7[0m + C.x^[0;38;5;20;1m6[0m - C.x^[0;38;5;20;1m5[0m - C.x^[0;38;5;20;1m4[0m + C.x^[0;38;5;20;1m2[0m - C.x + C.one)/(C.x^[0;38;5;20;1m8[0m*C.y + C.x^[0;38;5;20;1m7[0m*C.y + C.x^[0;38;5;20;1m6[0m*C.y - C.x^[0;38;5;20;1m5[0m*C.y + C.x^[0;38;5;20;1m4[0m*C.y + C.x^[0;38;5;20;1m2[0m*C.y))*C.dx[207D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mfff = ((C.x^[0;38;5;20;1m17[0m - C.x^[0;38;5;20;1m16[0m + C.x^[0;38;5;20;1m15[0m + C.x^[0;38;5;20;1m14[0m + C.x^[0;38;5;20;1m13[0m + C.x^[0;38;5;20;1m12[0m - C.x^[0;38;5;20;1m10[0m + C.x^[0;38;5;20;1m7[0m + C.x^[0;38;5;20;1m6[0m - C.x^[0;38;5;20;1m5[0m - C.x^[0;38;5;20;1m4[0m + C.x^[0;38;5;20;1m2[0m - C.x + C.one)/(C.x^[0;38;5;20;1m8[0m*C.y + C.x^[0;38;5;20;1m7[0m*C.y + C.x^[0;38;5;20;1m6[0m*C.y - C.x^[0;38;5;20;1m5[0m*C.y + C.x^[0;38;5;20;1m4[0m*C.y + C.x^[0;38;5;20;1m2[0m*C.y))*C.dx[?7h[0m[?12l[?25h[?25l[?7l[201D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[17D[0mdecomposition_omega0_omega8[0;38;5;16;48;5;152m([0mfff[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[32D[0;38;5;24mlen[0;38;5;16;48;5;152m([0mdecomposition_omega0_omega8(fff)[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[37D[0mdecomposition_omega0_omega8[0;38;5;16;48;5;152m([0mfff[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[32D[0;38;5;24mlen[0;38;5;16;48;5;152m([0mdecomposition_omega0_omega8(fff)[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[37D[0mdecomposition_omega0_omega8[0;38;5;16;48;5;152m([0mfff[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[38D[0m[J[0;94msage: [0mdecomposition_omega0_omega8(fff)[38D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(((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)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mdecomposition_omega0_omega8[0;38;5;16;48;5;152m([0mfff[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[5D[0m([3C)[[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C][C[?7h[0m[?12l[?25h[?25l[?7l[0m-[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[44D[0;94msage: [0mdecomposition_omega0_omega8(fff)[[0;38;5;20;1m0[0m] - [0;38;5;16;48;5;152m([0m(C.x^[0;38;5;20;1m17[0m - C.x^[0;38;5;20;1m16[0m + C.x^[0;38;5;20;1m15[0m + C.x^[0;38;5;20;1m14[0m + C.x^[0;38;5;20;1m13[0m + C.x^[0;38;5;20;1m12[0m - C.x^[0;38;5;20;1m10[0m + C.x^[0;38;5;20;1m7[0m + C.x^[0;38;5;20;1m6[0m - C.x^[0;38;5;20;1m5[0m - C.x^[0;38;5;20;1m4[0m + C.x^[0;38;5;20;1m2[0m - C.x + [0;38;5;20;1m1[0m)/(C.x^[0;38;5;20;1m8[0m*C.y + C.x^[0;38;5;20;1m7[0m*C.y + C.x^[0;38;5;20;1m6[0m*C.y - C.x^[0;38;5;20;1m5[0m*C.y + C.x^[0;38;5;20;1m4[0m*C.y + C.x^[0;38;5;20;1m2[0m*C.y
[228C)[0m

+[0;94m....: [0;38;5;16;48;5;152m)[7D[7C[?7h[0m[?12l[?25h[?25l[?7l[A[37C[0m([113C[0;38;5;16;48;5;152m([69C)[0m

+[6C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[A[152C[0m([69C[0m[K[0m

+[0m [0m[K[A[227C[?7h[0m[?12l[?25h[?25l[?7l
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+[0m                                                         [0;38;5;16;48;5;250m decomposition                   decomposition_omega0_omega82   [0m

+[57C[0;38;5;16;48;5;250m decomposition_g0_g8             decomposition_omega0_omega8_old[0m

+[57C[0;38;5;16;48;5;250m decomposition_omega0_omega8                                    [0m

+

+[0m [5A[57C[?7h[0m[?12l[?25h[?25l[?7l[0m

+[57C[0;38;5;231;48;5;102m decomposition                  [0m

+

+

+[57C[0;38;5;16;48;5;248m <unknown> [4A[11D[?7h[0m[?12l[?25h[?25l[?7l[0m_g0_g8[0m

+[57C[0;38;5;16;48;5;250m decomposition                  [0m

+[57C[0;38;5;231;48;5;102m decomposition_g0_g8            [2A[26D[?7h[0m[?12l[?25h[?25l[?7l[5D[0mome[Ca0_omega8[0m

+

+[57C[0;38;5;16;48;5;250m decomposition_g0_g8            [0m

+[57C[0;38;5;231;48;5;102m decomposition_omega0_omega8    [3A[18D[?7h[0m[?12l[?25h[?25l[?7l[0m

+[C[0m[K[0m

+[C[0m[K[0m

+[C[0m[K[0m

+[C[0m[K[4A[70C[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m([3C)[?7h[0m[?12l[?25h[?25l[?7l[5D[0m([3C)[[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C][C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[86D[0m[J[0;94msage: [0mdecomposition_omega0_omega8(fff)[[0;38;5;20;1m0[0m] - decomposition_omega0_omega8(fff)[[0;38;5;20;1m1[0m] == fff[86D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mFalse
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[6D[0;94msage: [0m

+

+

+[0m [3A[6C[?7h[0m[?12l[?25h[?25l[?7l[6D[0m[J[0;94msage: [6D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[6D[0;94msage: [0m

+

+[0m [2A[6C[?7h[0m[?12l[?25h[?25l[?7l[0mdecomposition_omega0_omega8(fff)[[0;38;5;20;1m0[0m] - decomposition_omega0_omega8(fff)[[0;38;5;20;1m1[0m] == fff[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m f[2C[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0m f[2C[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C][C[0mf[2C[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C], [2Cf[4D[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[84D[0m[J[0;94msage: [0mdecomposition_omega0_omega8(fff)[[0;38;5;20;1m0[0m] - decomposition_omega0_omega8(fff)[[0;38;5;20;1m1[0m], fff[84D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(((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)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mdecomposition_omega0_omega8(fff)[[0;38;5;20;1m0[0m] - decomposition_omega0_omega8(fff)[[0;38;5;20;1m1[0m], fff[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C]), [2Cf[5D[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;16;48;5;152m([3C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([3C)[4D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([3C[0;38;5;16;48;5;152m)[5D[?7h[0m[?12l[?25h[?25l[?7l[0m([3C)[32D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;16;48;5;152m([3C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([3C)[4D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([3C[0;38;5;16;48;5;152m)[5D[?7h[0m[?12l[?25h[?25l[?7l[0m([3C)[32D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m(decomposition_omega0_omega8([2Cf)[[0;38;5;20;1m0[0m] - decomposition_omega0_omega8([2Cf)[[0;38;5;20;1m1[0m]), [2Cf[79D[?7h[0m[?12l[?25h[?25l[?7l[27C[0;38;5;210;48;5;88m([3C[0;38;5;16;48;5;152m)[5D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([3C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([3C)[C[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C][2C[?7h[0m[?12l[?25h[?25l[?7l[28C[0;38;5;210;48;5;88m([3C[0;38;5;16;48;5;152m)[5D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([3C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([3C)[C[?7h[0m[?12l[?25h[?25l[?7l[4C[?7h[0m[?12l[?25h[?25l[?7l[4C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[3D[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;16;48;5;152m[[C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[73D[0;38;5;16;48;5;152m([70C[0m[[C][0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[75D[0m([73C)., [2Cf[5D[?7h[0m[?12l[?25h[?25l[?7l[0mf, [2Cf[5D[?7h[0m[?12l[?25h[?25l[?7l[0mo, [2Cf[5D[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;28;1mfor[0m, [2Cf[5D[?7h[0m[?12l[?25h[?25l[?7l[3D[0mform, [2Cf[5D[?7h[0m[?12l[?25h[?25l[?7l[4D[?7h[0m[?12l[?25h[?25l[?7l[5D[0;38;5;16;48;5;152m[[C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;16;48;5;152m([3C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([3C)[4D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([3C[0;38;5;16;48;5;152m)[5D[?7h[0m[?12l[?25h[?25l[?7l[0m([3C)[32D[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;16;48;5;152m([3C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([3C)[4D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([3C[0;38;5;16;48;5;152m)[5D[?7h[0m[?12l[?25h[?25l[?7l[0m([3C)[32D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([73C[0;38;5;16;48;5;152m)[75D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mr[0;38;5;210;48;5;88m([0mdecomposition_omega0_omega8([2Cf)[[0;38;5;20;1m0[0m] - decomposition_omega0_omega8([2Cf)[[0;38;5;20;1m1[0m][0;38;5;16;48;5;152m)[0m.form, [2Cf[85D[?7h[0m[?12l[?25h[?25l[?7l[0me[0;38;5;210;48;5;88m([0mdecomposition_omega0_omega8([2Cf)[[0;38;5;20;1m0[0m] - decomposition_omega0_omega8([2Cf)[[0;38;5;20;1m1[0m][0;38;5;16;48;5;152m)[0m.form, [2Cf[85D[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;210;48;5;88m([0mdecomposition_omega0_omega8([2Cf)[[0;38;5;20;1m0[0m] - decomposition_omega0_omega8([2Cf)[[0;38;5;20;1m1[0m][0;38;5;16;48;5;152m)[0m.form, [2Cf[85D[?7h[0m[?12l[?25h[?25l[?7l[0mu[0;38;5;210;48;5;88m([0mdecomposition_omega0_omega8([2Cf)[[0;38;5;20;1m0[0m] - decomposition_omega0_omega8([2Cf)[[0;38;5;20;1m1[0m][0;38;5;16;48;5;152m)[0m.form, [2Cf[85D[?7h[0m[?12l[?25h[?25l[?7l[0mc[0;38;5;210;48;5;88m([0mdecomposition_omega0_omega8([2Cf)[[0;38;5;20;1m0[0m] - decomposition_omega0_omega8([2Cf)[[0;38;5;20;1m1[0m][0;38;5;16;48;5;152m)[0m.form, [2Cf[85D[?7h[0m[?12l[?25h[?25l[?7l[0me[0;38;5;210;48;5;88m([0mdecomposition_omega0_omega8([2Cf)[[0;38;5;20;1m0[0m] - decomposition_omega0_omega8([2Cf)[[0;38;5;20;1m1[0m][0;38;5;16;48;5;152m)[0m.form, [2Cf[85D[?7h[0m[?12l[?25h[?25l[?7l[0m([0;38;5;210;48;5;88m([0mdecomposition_omega0_omega8([2Cf)[[0;38;5;20;1m0[0m] - decomposition_omega0_omega8([2Cf)[[0;38;5;20;1m1[0m][0;38;5;16;48;5;152m)[0m.form, [2Cf[85D[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;210;48;5;88m([0mdecomposition_omega0_omega8([2Cf)[[0;38;5;20;1m0[0m] - decomposition_omega0_omega8([2Cf)[[0;38;5;20;1m1[0m][0;38;5;16;48;5;152m)[0m.form, [2Cf[85D[?7h[0m[?12l[?25h[?25l[?7l[0m,[0;38;5;210;48;5;88m([0mdecomposition_omega0_omega8([2Cf)[[0;38;5;20;1m0[0m] - decomposition_omega0_omega8([2Cf)[[0;38;5;20;1m1[0m][0;38;5;16;48;5;152m)[0m.form, [2Cf[85D[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m([0mdecomposition_omega0_omega8([2Cf)[[0;38;5;20;1m0[0m] - decomposition_omega0_omega8([2Cf)[[0;38;5;20;1m1[0m][0;38;5;16;48;5;152m)[0m.form, [2Cf[85D[?7h[0m[?12l[?25h[?25l[?7l[0m([27C[0;38;5;210;48;5;88m([3C[0;38;5;16;48;5;152m)[41C[0m)[47D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([3C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([3C)[C[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C][2C[?7h[0m[?12l[?25h[?25l[?7l[28C[0;38;5;210;48;5;88m([3C[0;38;5;16;48;5;152m)[5D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([3C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[4D[0m([3C)[C[?7h[0m[?12l[?25h[?25l[?7l[4C[?7h[0m[?12l[?25h[?25l[?7l[4C[?7h[0m[?12l[?25h[?25l[?7l[5C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m f[2C[0m[K[4D[?7h[0m[?12l[?25h[?25l[?7l[0m- [2Cf[4D[?7h[0m[?12l[?25h[?25l[?7l[4C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;28;1mfor[?7h[0m[?12l[?25h[?25l[?7l[3D[0mform[?7h[0m[?12l[?25h[?25l[?7l[94D[0;38;5;16;48;5;152m([93C)[?7h[0m[?12l[?25h[?25l[?7l[107D[0m[J[0;94msage: [0mreduce(C, (decomposition_omega0_omega8(fff)[[0;38;5;20;1m0[0m] - decomposition_omega0_omega8(fff)[[0;38;5;20;1m1[0m]).form- fff.form)[107D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mTypeError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [57][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mreduce[49m[43m([49m[43mC[49m[43m,[49m[43m [49m[43m([49m[43mdecomposition_omega0_omega8[49m[43m([49m[43mfff[49m[43m)[49m[43m[[49m[43mInteger[49m[43m([49m[38;5;241;43m0[39;49m[43m)[49m[43m][49m[43m [49m[38;5;241;43m-[39;49m[43m [49m[43mdecomposition_omega0_omega8[49m[43m([49m[43mfff[49m[43m)[49m[43m[[49m[43mInteger[49m[43m([49m[38;5;241;43m1[39;49m[43m)[49m[43m][49m[43m)[49m[38;5;241;43m.[39;49m[43mform[49m[38;5;241;43m-[39;49m[43m [49m[43mfff[49m[38;5;241;43m.[39;49m[43mform[49m[43m)[49m
+
+[0;31mTypeError[0m: reduce() arg 2 must support iteration
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decomposition_omega0_omega8(fff)[[0;38;5;20;1m1[0m]).form- fff.form)[110D[0m

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+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mt^2 + t^6 + t^10 + O(t^12)
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mdx.valuation()[14D[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mC[7D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mSuperelliptic curve with the equation y^2 = x^3 + 2*x + 1 over Finite Field of size 3
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m,[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mdx.valuation()[14D[?7h[0m[?12l[?25h[?25l[?7l[0mc[0;38;5;241mrystalline_cohomology_basis()[29D[?7h[0m[?12l[?25h[?25l[?7l[0mrystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[38D[0m[J[0;94msage: [0mC.crystalline_cohomology_basis()[38D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[([(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]))]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m()[3D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mpC.crysta[Cline_cohomology_basis()[32D[?7h[0m[?12l[?25h[?25l[?7l[0maC.crysta[Cline_cohomology_basis()[32D[?7h[0m[?12l[?25h[?25l[?7l[0mtC.crysta[Cline_cohomology_basis()[32D[?7h[0m[?12l[?25h[?25l[?7l[0mcC.crysta[Cline_cohomology_basis()[32D[?7h[0m[?12l[?25h[?25l[?7l[0mhC.crysta[Cline_cohomology_basis()[32D[?7h[0m[?12l[?25h[?25l[?7l[0m(C.crysta[Cline_cohomology_basis()[32D[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m([C)[0m.crysta[Cline_cohomology_basis()[31D[?7h[0m[?12l[?25h[?25l[?7l[3D[0m([C)[29C[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[45D[0m[J[0;94msage: [0mpatch(C).crystalline_cohomology_basis()[45D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[([(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]))]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ 
[K]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ 
[K]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+[22;0t]0;IPython: DeRhamComputation/sage[6n[?2004h[?1l[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?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]))]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[13D[0m([11C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.crystalline_cohomology_basis()[31D[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mC[7D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mSuperelliptic curve with the equation y^2 = x^3 + 2*x + 1 over Finite Field of size 3
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m1[0;38;5;241m.crystalline_cohomology_basis()[31D[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= pa[Cch(C)[0m[K[10D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mpatch[0;38;5;16;48;5;152m([0mC[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[19D[0m[J[0;94msage: [0mC1 = patch(C)[19D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m1 = patch(C)[12D[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mcrystalline_cohomology_basis()[30D[?7h[0m[?12l[?25h[?25l[?7l[0mp[0;38;5;241m_rank()[0m[K[7D[?7h[0m[?12l[?25h[?25l[?7l[0mo[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[18D[0m[J[0;94msage: [0mC.polynomial[18D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mx^3 + 2*x + 1
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.polynomial[11D[?7h[0m[?12l[?25h[?25l[?7l[0m1[0;38;5;241m = patch(C)[11D[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mcrys[Calline_cohomology_basis()[30D[?7h[0m[?12l[?25h[?25l[?7l[0mp[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[19D[0m[J[0;94msage: [0mC1.polynomial[19D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mx^4 + 2*x^3 + x
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mR[0;38;5;241mx.<x> = PolynomialRing(GF(3))[29D[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[8D[0m[J[0;94msage: [0mRx[8D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mUnivariate Polynomial Ring in x over Finite Field of size 3
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mRx[?7h[0m[?12l[?25h[?25l[?7l[2D[0mC1.polynomial[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mgC1.polynomial[13D[?7h[0m[?12l[?25h[?25l[?7l[0m C1.polynomial[13D[?7h[0m[?12l[?25h[?25l[?7l[0m=C1.polynomial[13D[?7h[0m[?12l[?25h[?25l[?7l[0m C1.polynomial[13D[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[11C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mg = C1.polynomial[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mg[0;38;5;241m = C1.polynomial[16D[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mg[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0m^[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m3[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m-[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[8D[0;38;5;16;48;5;152m([7C)[?7h[0m[?12l[?25h[?25l[?7l[20D[0m[J[0;94msage: [0mg = g(x^[0;38;5;20;1m3[0m - x)[20D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mg[0;38;5;241m = g(x^3 - x)[13D[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mg[7D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mx^12 + 2*x^10 + 2*x^9 + 2*x^6 + x^4 + 2*x^3 + 2*x
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m1.polynomial[12D[?7h[0m[?12l[?25h[?25l[?7l[0m2[0m[K[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;24msuper[?7h[0m[?12l[?25h[?25l[?7l[5D[0msupere[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m([C)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m,[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m2[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[30D[0m[J[0;94msage: [0mC2 = superelliptic(g, [0;38;5;20;1m2[0m)[30D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m2 = superelliptic(g, 2)[23D[?7h[0m[?12l[?25h[?25l[?7l[0m2[?7h[0m[?12l[?25h[?25l[?7l[8D[0m[J[0;94msage: [0mC2[8D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mSuperelliptic 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
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m2[?7h[0m[?12l[?25h[?25l[?7l[0m2[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[16D[0m[J[0;94msage: [0mC2.genus()[16D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m5
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m2.genus()[9D[?7h[0m[?12l[?25h[?25l[?7l[0m2[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mc[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0malline_cohomology_basis[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[39D[0m[J[0;94msage: [0mC2.crystalline_cohomology_basis()[39D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mIndexError[0m                                Traceback (most recent call last)
+Input [0;32mIn [13][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mC2[49m[38;5;241;43m.[39;49m[43mcrystalline_cohomology_basis[49m[43m([49m[43m)[49m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self)[0m
+
+File [0;32m<string>:349[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
+
+File [0;32m<string>:69[0m, in [0;36mdecomposition_omega0_omega8[0;34m(omega, prec)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/misc/functional.py:585[0m, in [0;36msymbolic_sum[0;34m(expression, *args, **kwds)[0m
+[1;32m    583[0m     [38;5;28;01mreturn[39;00m expression[38;5;241m.[39msum([38;5;241m*[39margs, [38;5;241m*[39m[38;5;241m*[39mkwds)
+[1;32m    584[0m [38;5;28;01melif[39;00m [38;5;28mmax[39m([38;5;28mlen[39m(args),[38;5;28mlen[39m(kwds)) [38;5;241m<[39m[38;5;241m=[39m [38;5;241m1[39m:
+[0;32m--> 585[0m     [38;5;28;01mreturn[39;00m [38;5;28;43msum[39;49m[43m([49m[43mexpression[49m[43m,[49m[43m [49m[38;5;241;43m*[39;49m[43margs[49m[43m,[49m[43m [49m[38;5;241;43m*[39;49m[38;5;241;43m*[39;49m[43mkwds[49m[43m)[49m
+[1;32m    586[0m [38;5;28;01melse[39;00m:
+[1;32m    587[0m     [38;5;28;01mfrom[39;00m [38;5;21;01msage[39;00m[38;5;21;01m.[39;00m[38;5;21;01msymbolic[39;00m[38;5;21;01m.[39;00m[38;5;21;01mring[39;00m [38;5;28;01mimport[39;00m SR
+
+File [0;32m<string>:69[0m, in [0;36m<genexpr>[0;34m(.0)[0m
+
+File [0;32m<string>:143[0m, in [0;36mresidue[0;34m(self, place, prec)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544[0m, in [0;36msage.rings.laurent_series_ring_element.LaurentSeries.__getitem__[0;34m()[0m
+[1;32m    542[0m         return type(self)(self._parent, f, self.__n)
+[1;32m    543[0m 
+[0;32m--> 544[0m     return self.__u[i - self.__n]
+[1;32m    545[0m 
+[1;32m    546[0m def __iter__(self):
+
+File [0;32m/ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453[0m, in [0;36msage.rings.power_series_poly.PowerSeries_poly.__getitem__[0;34m()[0m
+[1;32m    451[0m         return self.base_ring().zero()
+[1;32m    452[0m     else:
+[0;32m--> 453[0m         raise IndexError("coefficient not known")
+[1;32m    454[0m return self.__f[n]
+[1;32m    455[0m 
+
+[0;31mIndexError[0m: coefficient not known
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC2.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[33D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[13D[0m([11C);[0;38;5;241m xi = C.de_rham_basis()[1];xi.coordinates()[43D[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mC2 = superelliptic[0;38;5;16;48;5;152m([0mg, [0;38;5;20;1m2[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[6D[0m([4C);[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m2[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mne_cohomology_basis[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mp[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mr[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0me[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mc[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m=[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[94D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m); C2 = superelliptic(g, [0;38;5;20;1m2[0m); C2.crystalline_cohomology_basis(prec = [0;38;5;20;1m100[0m)[94D[0m

+[J[?7h[0m[?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]))]
+[0;31m---------------------------------------------------------------------------[0m
+[0;31mIndexError[0m                                Traceback (most recent call last)
+Input [0;32mIn [14][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m load([38;5;124m'[39m[38;5;124minit.sage[39m[38;5;124m'[39m); C2 [38;5;241m=[39m superelliptic(g, Integer([38;5;241m2[39m)); [43mC2[49m[38;5;241;43m.[39;49m[43mcrystalline_cohomology_basis[49m[43m([49m[43mprec[49m[43m [49m[38;5;241;43m=[39;49m[43m [49m[43mInteger[49m[43m([49m[38;5;241;43m100[39;49m[43m)[49m[43m)[49m
+
+File [0;32m<string>:355[0m, in [0;36mcrystalline_cohomology_basis[0;34m(self, prec)[0m
+
+File [0;32m<string>:347[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class, prec)[0m
+
+File [0;32m<string>:6[0m, in [0;36mdecomposition_g0_g8[0;34m(fct)[0m
+
+File [0;32m<string>:107[0m, in [0;36mcoordinates[0;34m(self, basis, basis_holo, prec)[0m
+
+File [0;32m<string>:77[0m, in [0;36mserre_duality_pairing[0;34m(self, fct, prec)[0m
+
+File [0;32m/ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544[0m, in [0;36msage.rings.laurent_series_ring_element.LaurentSeries.__getitem__[0;34m()[0m
+[1;32m    542[0m         return type(self)(self._parent, f, self.__n)
+[1;32m    543[0m 
+[0;32m--> 544[0m     return self.__u[i - self.__n]
+[1;32m    545[0m 
+[1;32m    546[0m def __iter__(self):
+
+File [0;32m/ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453[0m, in [0;36msage.rings.power_series_poly.PowerSeries_poly.__getitem__[0;34m()[0m
+[1;32m    451[0m         return self.base_ring().zero()
+[1;32m    452[0m     else:
+[0;32m--> 453[0m         raise IndexError("coefficient not known")
+[1;32m    454[0m return self.__f[n]
+[1;32m    455[0m 
+
+[0;31mIndexError[0m: coefficient not known
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage'); C2 = superelliptic(g, 2); C2.crystalline_cohomology_basis(prec = 100)[87D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0m([0;38;5;160;48;5;231m'init.sage'[0m); C2 = superelliptic(g, [0;38;5;20;1m2[0m); C2.crystalline_cohomology_basis[0;38;5;16;48;5;152m([0mprec = [0;38;5;20;1m100[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[12D[0m([10C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[7D[0;38;5;16;48;5;152m([4C)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[6D[0m([4C[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;24msuper[0m[K[?7h[0m[?12l[?25h[?25l[?7l[5D[0msupe[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[14D[0;38;5;16;48;5;152m([11C)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m

+[J[?7h[0m[?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]))]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m2.crystalline_cohomology_basis()[32D[?7h[0m[?12l[?25h[?25l[?7l[0m2[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= superelliptic(g, 2)[0m[K[21D[?7h[0m[?12l[?25h[?25l[?7l[0m= superelliptic[0;38;5;16;48;5;152m([0mg, [0;38;5;20;1m2[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[30D[0m[J[0;94msage: [0mC2 = superelliptic(g, [0;38;5;20;1m2[0m)[30D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m2 = superelliptic(g, 2)[23D[?7h[0m[?12l[?25h[?25l[?7l[0m2[?7h[0m[?12l[?25h[?25l[?7l[8D[0m[J[0;94msage: [0mC2[8D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mSuperelliptic 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
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m2[?7h[0m[?12l[?25h[?25l[?7l[0m2[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mcrystalline_cohomology_basis()[30D[?7h[0m[?12l[?25h[?25l[?7l[0md[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0m_[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mh[?7h[0m[?12l[?25h[?25l[?7l[0mam_basis[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[24D[0m[J[0;94msage: [0mC2.de_rham_basis()[24D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[((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)]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC2.de_rham_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[2D[0m()[[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m2[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m()[15D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0maC2.de_rham_basis()[[0;38;5;20;1m2[0m][21D[?7h[0m[?12l[?25h[?25l[?7l[0m C2.de_rham_basis()[[0;38;5;20;1m2[0m][21D[?7h[0m[?12l[?25h[?25l[?7l[0m=C2.de_rham_basis()[[0;38;5;20;1m2[0m][21D[?7h[0m[?12l[?25h[?25l[?7l[0m C2.de_rham_basis()[[0;38;5;20;1m2[0m][21D[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[14C[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m()[C[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[31D[0m[J[0;94msage: [0ma = C2.de_rham_basis()[[0;38;5;20;1m2[0m][31D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mi[0;38;5;241mft_form_to_drw(xi)[18D[?7h[0m[?12l[?25h[?25l[?7l[0mft_form_to_drw[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0ma[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[25D[0m[J[0;94msage: [0mlift_form_to_drw(a)[25D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mAttributeError[0m                            Traceback (most recent call last)
+Input [0;32mIn [20][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43mlift_form_to_drw[49m[43m([49m[43ma[49m[43m)[49m
+
+File [0;32m<string>:29[0m, in [0;36mlift_form_to_drw[0;34m(omega)[0m
+
+File [0;32m<string>:10[0m, in [0;36mregular_form[0;34m(omega)[0m
+
+[0;31mAttributeError[0m: 'superelliptic_cech' object has no attribute 'form'
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;241mecomposition_omega0_omega8(fff)[1].expansion_at_infty()[55D[?7h[0m[?12l[?25h[?25l[?7l[0mr[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mw[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mde_rham_witt_lift[0;38;5;241m(xi)[4D[?7h[0m[?12l[?25h[?25l[?7l[0ma[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m)[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m([0;38;5;241mxi)[3D[?7h[0m[?12l[?25h[?25l[?7l[0ma[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m([C)[?7h[0m[?12l[?25h[?25l[?7l[26D[0m[J[0;94msage: [0mde_rham_witt_lift(a)[26D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m([(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]))
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ma[0;38;5;241m = C2.de_rham_basis()[2][24D[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;241mic_expansion(gg, x^3 - x)[25D[?7h[0m[?12l[?25h[?25l[?7l[0mic_expansion[0;38;5;16;48;5;152m([0mgg, x^[0;38;5;20;1m3[0m - x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[12D[0m([11C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([11C[0;38;5;16;48;5;152m)[13D[?7h[0m[?12l[?25h[?25l[?7l[0m([11C)[12D[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0m, x^[0;38;5;20;1m3[0m - x)[0m[K[10D[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[10D[0;38;5;16;48;5;152m([10C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[32D[0m[J[0;94msage: [0madic_expansion(g, x^[0;38;5;20;1m3[0m - x)[32D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
+[0;31mNameError[0m                                 Traceback (most recent call last)
+Input [0;32mIn [22][0m, in [0;36m<cell line: 1>[0;34m()[0m
+[0;32m----> 1[0m [43madic_expansion[49m(g, x[38;5;241m*[39m[38;5;241m*[39mInteger([38;5;241m3[39m) [38;5;241m-[39m x)
+
+[0;31mNameError[0m: name 'adic_expansion' is not defined
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241mift_form_to_drw(a)[18D[?7h[0m[?12l[?25h[?25l[?7l[0mo[0;38;5;241mad('init.sage')[0m[K[15D[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231m'[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231md[0;38;5;241mrafty/draft.sage')[18D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231mr[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m([3C[0;38;5;160;48;5;231mafty/draft.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[20D[0m([19C)[2D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;160;48;5;231m5.sage'[0m)[7D[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[20D[0;38;5;16;48;5;152m([20C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[32D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'drafty/draft5.sage'[0m)[32D[0m

+[J[?7h[0m[?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]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ma[0;38;5;241mdic_expansion(g, x^3 - x)[25D[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mc_expansion[0;38;5;16;48;5;152m([0mg, x^[0;38;5;20;1m3[0m - x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[32D[0m[J[0;94msage: [0madic_expansion(g, x^[0;38;5;20;1m3[0m - x)[32D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[2, 1, x^2 + 2*x + 2, 2*x^2 + 2*x + 1, x^2 + 1, x^2 + x + 2, 2*x]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0madic_expansion[0;38;5;16;48;5;152m([0mg, x^[0;38;5;20;1m3[0m - x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[26D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'drafty/draft5.sage'[C[?7h[0m[?12l[?25h[?25l[?7l[26D[0madic_expansion[0;38;5;16;48;5;152m([0mg, x^[0;38;5;20;1m3[0m - x[C[?7h[0m[?12l[?25h[?25l[?7l[26D[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0ma[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[20D[0mlift_form_[Co[Cdrw[0;38;5;16;48;5;152m([0ma[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[19D[0ma = C2.de[Crham_basis()[0;38;5;16;48;5;152m[[0;38;5;20;1m2[0;38;5;16;48;5;152m][?7h[0m[?12l[?25h[?25l[?7l[25D[0mC2.de_rham_b[Csis[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[16D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mR[0;38;5;241mx[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[8D[0m[J[0;94msage: [0mRx[8D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mUnivariate Polynomial Ring in x over Finite Field of size 3
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mRx[?7h[0m[?12l[?25h[?25l[?7l[2D[0madic_expansion[0;38;5;16;48;5;152m([0mg, x^[0;38;5;20;1m3[0m - x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[26D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'drafty/draft5.sage'[C[?7h[0m[?12l[?25h[?25l[?7l[26D[0madic_expansion[0;38;5;16;48;5;152m([0mg, x^[0;38;5;20;1m3[0m - x[C[?7h[0m[?12l[?25h[?25l[?7l[26D[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0ma[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[20D[0mlift_form_[Co[Cdrw[0;38;5;16;48;5;152m([0ma[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[19D[0ma = C2.de[Crham_basis()[0;38;5;16;48;5;152m[[0;38;5;20;1m2[0;38;5;16;48;5;152m][?7h[0m[?12l[?25h[?25l[?7l[25D[0mC2.de_rham_b[Csis[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[16D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m = superelliptic[0;38;5;16;48;5;152m([0mg, [0;38;5;20;1m2[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[24D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[13D[0m([11C); C2 = superelliptic(g, [0;38;5;20;1m2[0m); C2.crystalline_cohomology_basis[0;38;5;16;48;5;152m([0mprec = [0;38;5;20;1m100[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[88D[0mC2.crystalline_cohomology_basis[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[30D[0mgenus[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[8D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m = superelliptic[0;38;5;16;48;5;152m([0mg, [0;38;5;20;1m2[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[24D[0mg[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m = g[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m3[0m - x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[10D[0mC1.polynomial[?7h[0m[?12l[?25h[?25l[?7l[17D[0mRx[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0mC1.polynomial[?7h[0m[?12l[?25h[?25l[?7l[12D[0m.polynomial[0m[K[?7h[0m[?12l[?25h[?25l[?7l[11D[0m1 = patch[0;38;5;16;48;5;152m([0mC[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[12D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[17D[0mC[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m1 = patch[0;38;5;16;48;5;152m([0mC[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[12D[0m.polynomial[0m[K[?7h[0m[?12l[?25h[?25l[?7l[11D[0m1.polynomial[?7h[0m[?12l[?25h[?25l[?7l[13D[0mRx[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0mg = C1.polynomial[?7h[0m[?12l[?25h[?25l[?7l[13D[0mg[0;38;5;16;48;5;152m([0mx^[0;38;5;20;1m3[0m - x[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[13D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mC2 = superelliptic[0;38;5;16;48;5;152m([0mg, [0;38;5;20;1m2[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[22D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m.genus[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[7D[0mcrystalline_cohomology_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[33D[0mload([0;38;5;160;48;5;231m'init.sage'[0m); C2 = superelliptic(g, [0;38;5;20;1m2[0m); C2.crystalline_cohomology_basis[0;38;5;16;48;5;152m([0mprec = [0;38;5;20;1m100[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[84D[0;38;5;16;48;5;152m([11C)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[17D[0mC2 = superelliptic[0;38;5;16;48;5;152m([0mg, [0;38;5;20;1m2[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[22D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m.de_rham_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[18D[0ma = C2.de_rh[Cm_basis()[0;38;5;16;48;5;152m[[0;38;5;20;1m2[0;38;5;16;48;5;152m][?7h[0m[?12l[?25h[?25l[?7l[25D[0mlift_form[Cto_drw[0;38;5;16;48;5;152m([0ma[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[19D[0mde_rham_wi[Ct[Clift[0;38;5;16;48;5;152m([0ma[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[20D[0madic_expansion[0;38;5;16;48;5;152m([0mg, x^[0;38;5;20;1m3[0m - x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[26D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'drafty/draft5.sage'[C[?7h[0m[?12l[?25h[?25l[?7l[26D[0madic_expansion[0;38;5;16;48;5;152m([0mg, x^[0;38;5;20;1m3[0m - x[C[?7h[0m[?12l[?25h[?25l[?7l[26D[0mRx[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m2.de_rham_basis()[17D[?7h[0m[?12l[?25h[?25l[?7l[0m2[?7h[0m[?12l[?25h[?25l[?7l[8D[0m[J[0;94msage: [0mC2[8D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mSuperelliptic 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
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mg[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= g(x^3 - x)[12D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m1.polynomial[12D[?7h[0m[?12l[?25h[?25l[?7l[0m2[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0my[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mg = C2.polynomial[23D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ma[0;38;5;241mdic_expansion(g, x^3 - x)[25D[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mc_expansion[0;38;5;16;48;5;152m([0mg, x^[0;38;5;20;1m3[0m - x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[32D[0m[J[0;94msage: [0madic_expansion(g, x^[0;38;5;20;1m3[0m - x)[32D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[1, 2, 0, 1, 0]
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0madic_expansion[0;38;5;16;48;5;152m([0mg, x^[0;38;5;20;1m3[0m - x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[26D[0mg = C2.[Colyn[Cmial[0m[K[?7h[0m[?12l[?25h[?25l[?7l[17D[0mC2[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0mRx[?7h[0m[?12l[?25h[?25l[?7l[2D[0madic_expansion[0;38;5;16;48;5;152m([0mg, x^[0;38;5;20;1m3[0m - x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[26D[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'drafty/draft5.sage'[C[?7h[0m[?12l[?25h[?25l[?7l[26D[0madic_expansion[0;38;5;16;48;5;152m([0mg, x^[0;38;5;20;1m3[0m - x[C[?7h[0m[?12l[?25h[?25l[?7l[26D[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0ma[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[20D[0mlift_form_[Co[Cdrw[0;38;5;16;48;5;152m([0ma[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[19D[0mde_rham_wi[Ct[Clift[0;38;5;16;48;5;152m([0ma[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[2D[0m([C)[2D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m([C[0;38;5;16;48;5;152m)[3D[?7h[0m[?12l[?25h[?25l[?7l[0m([C)[4D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0made_rham_wi[Ct_lift(a)[20D[?7h[0m[?12l[?25h[?25l[?7l[0m1de_rham_wi[Ct_lift(a)[20D[?7h[0m[?12l[?25h[?25l[?7l[0m de_rham_wi[Ct_lift(a)[20D[?7h[0m[?12l[?25h[?25l[?7l[0m=de_rham_wi[Ct_lift(a)[20D[?7h[0m[?12l[?25h[?25l[?7l[0m de_rham_wi[Ct_lift(a)[20D[?7h[0m[?12l[?25h[?25l[?7l[17C[0;38;5;210;48;5;88m([C[0;38;5;16;48;5;152m)[3D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m([C[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[31D[0m[J[0;94msage: [0ma1 = de_rham_witt_lift(a)[31D[0m

+[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mp[0;38;5;241match(C).crystalline_cohomology_basis()[38D[?7h[0m[?12l[?25h[?25l[?7l[0m*[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0m1[?7h[0m[?12l[?25h[?25l[?7l[10D[0m[J[0;94msage: [0mp*a1[10D[0m

+[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(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))
+[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mq[0;38;5;241muo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1)[39D[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mi[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[12D[0m[J[0;94msage: [0mquit()[12D[0m

+[J[?7h[0m[?12l[?25h[?2004l[23;0t]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ cd ..
+]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ 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)
+	[31mmodified:   sage/.run.term-0.term[m
+	[31mmodified:   sage/drafty/draft.sage[m
+	[31mmodified:   sage/drafty/superelliptic_drw.sage[m
+	[31mmodified:   sage/superelliptic/decomposition_into_g0_g8.sage[m
+	[31mmodified:   sage/superelliptic/superelliptic_cech_class.sage[m
+	[31mmodified:   sage/superelliptic/superelliptic_form_class.sage[m
+
+Untracked files:
+  (use "git add <file>..." to include in what will be committed)
+	[31m.crystalline_p2.ipynb.sage-jupyter2[m
+	[31m.deRhamComputation.ipynb.sage-jupyter2[m
+	[31m.elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2[m
+	[31m.git.x11-0.term[m
+	[31m.superelliptic.ipynb.sage-jupyter2[m
+	[31m.superelliptic_alpha.ipynb.sage-jupyter2[m
+	[31m.superelliptic_arbitrary_field.ipynb.sage-jupyter2[m
+	[31mgit.x11[m
+	[31msage/as_covers/tests/cartier_test.sage[m
+	[31msage/drafty/as_cartier.sage[m
+	[31msage/drafty/better_trace.sage[m
+	[31msage/drafty/cartier_image_representation.sage[m
+	[31msage/drafty/draft4.sage[m
+	[31msage/drafty/draft5.sage[m
+	[31msage/drafty/draft6.sage[m
+	[31msage/drafty/draft7.sage[m
+	[31msage/drafty/lift_to_de_rham.sage[m
+	[31msage/drafty/pole_numbers.sage[m
+	[31msage/drafty/regular_on_U0.sage[m
+	[31msage/superelliptic/frobenius_kernel.sage[m
+	[31msage/superelliptic/tests/[m
+	[31msuperelliptic_arbitrary_field.ipynb[m
+
+no changes added to commit (use "git add" and/or "git commit -a")
+]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ 
\ 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
