lift kocykli do drw zrobiony z drobnymi bledami

2023-02-24 16:57:49 +00:00 · 2023-02-24 16:57:49 +00:00 · e1a000f7a5
commit e1a000f7a5
parent 22872e266b
5 changed files with 524 additions and 5 deletions
--- a/sage/.run.term-0.term
+++ b/sage/.run.term-0.term
@ -39866,3 +39866,437 @@ Untracked files:
 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$ git add sage/drqa[K[Kafty/second_patch.sage 
 ]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 commit -m ""r"o"z"n"i"c"z"k"o"w"a"n"i"e" "f"o"r"m" "d"r"w" "z"r"o"b"i"o"n"e" "("?")"[C
 [master 22872e2] rozniczkowanie form drw zrobione (?)
 6 files changed, 1514 insertions(+), 117 deletions(-)
 create mode 100644 sage/drafty/second_patch.sage
 rewrite sage/drafty/superelliptic_drw.sage (68%)
 ]0;~/Research/2021 De Rham/DeRhamComputation[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': 
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Counting objects: 100% (19/19), done.
 Delta compression using up to 4 threads
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Writing objects: 100% (11/11), 18.02 KiB | 271.00 KiB/s, done.
 Total 11 (delta 6), reused 0 (delta 0)
 remote: . Processing 1 references[K
 remote: Processed 1 references in total[K
 To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
   856d742..22872e2  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')[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;241m.y.teichmuller().diffn()[24D[?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[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241my.teichmuller().diffn()[23D[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;241mx == C.dx[0m[K[9D[?7h[0m[?12l[?25h[?25l[?7l[0me[0;38;5;241m_rham_basis()[13D[?7h[0m[?12l[?25h[?25l[?7l[0m_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;1m0[?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[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?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.de_rham_basis()[[0;38;5;20;1m0[0m][20D[?7h[0m[?12l[?25h[?25l[?7l[0m C.de_rham_basis()[[0;38;5;20;1m0[0m][20D[?7h[0m[?12l[?25h[?25l[?7l[0m=C.de_rham_basis()[[0;38;5;20;1m0[0m][20D[?7h[0m[?12l[?25h[?25l[?7l[0m C.de_rham_basis()[[0;38;5;20;1m0[0m][20D[?7h[0m[?12l[?25h[?25l[?7l[10D[0m[J[0;94msage: [0ma = C.de_rham_basis()[[0;38;5;20;1m0[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[0ma[0;38;5;241m = C.de_rham_basis()[0][23D[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mdiffn()[0m[K[7D[?7h[0m[?12l[?25h[?25l[?7l[8D[0;94msage: [0ma.[0;38;5;241mdiffn()[0m
 [8C[0;38;5;16;48;5;250m a.coordinates  a.frobenius    a.omega8      [0m
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 [8C[0;38;5;16;48;5;250m a.f            a.omega0                     [0m
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 [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.verschiebung()[18D[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241m.verschiebung()[0m[K[15D[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mt[C[0;38;5;241michmuller()*C.y.teichmuller()[30D[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mh[?7h[0m[?12l[?25h[?25l[?7l[0mn[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0ml[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mr[?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;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[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[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[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.dx.verschiebung()[18D[?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[0mC.dx.verschiebung[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[17D[0mx.verschiebung[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[18D[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[?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[0mC.dx.verschiebung[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[25D[0m[J[0;94msage: [0mC.dx.verschiebung()[25D[0m
 [J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mV(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[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 [9][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>:7[0;36m[0m
 [0;31m    for a in[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[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;241m.dx.verschiebung()[18D[?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[0md[0;38;5;241miffn(C.y.teichmuller())[23D[?7h[0m[?12l[?25h[?25l[?7l[0me[0;38;5;241mnominator(((C.y)^(-1[C*C.dx).form) == y[38D[?7h[0m[?12l[?25h[?25l[?7l[0mc[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mm[?7h[0m[?12l[?25h[?25l[?7l[11D[0;94msage: [0mdecomposition[0m
 [19C[0;38;5;16;48;5;250m decomposition              [0m
 [19C[0;38;5;16;48;5;250m decomposition_g0_g8        [0m
 [19C[0;38;5;16;48;5;250m decomposition_omega0_omega8[0m
 [0m [5A[19C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m
 [19C[0;38;5;231;48;5;102m decomposition              [0m
 [19C[0;38;5;16;48;5;248m <unknown> [4A[11D[?7h[0m[?12l[?25h[?25l[?7l[0m_g0_g8[0m
 [19C[0;38;5;16;48;5;250m decomposition              [0m
 [19C[0;38;5;231;48;5;102m decomposition_g0_g8        [2A[22D[?7h[0m[?12l[?25h[?25l[?7l[0m
 [C[0m[K[0m
 [C[0m[K[0m
 [C[0m[K[0m
 [C[0m[K[4A[24C[?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[34D[0m[J[0;94msage: [0mdecomposition_g0_g8(C.y/C.x)[34D[0m
 [J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
 [0;31mAttributeError[0m                            Traceback (most recent call last)
 Input [0;32mIn [11][0m, in [0;36m<cell line: 1>[0;34m()[0m
 [0;32m----> 1[0m [43mdecomposition_g0_g8[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<string>:6[0m, in [0;36mdecomposition_g0_g8[0;34m(fct)[0m
 File [0;32m<string>:101[0m, in [0;36mcoordinates[0;34m(self, basis, basis_holo, prec)[0m
 [0;31mAttributeError[0m: 'superelliptic' object has no attribute 'basis_of_cohomology'
 [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[0mdecomposition_g0_g8[0;38;5;16;48;5;152m([0mC.y/C.x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[34D[0m[J[0;94msage: [0mdecomposition_g0_g8(C.y/C.x)[34D[0m
 [J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
 [0;31mNameError[0m                                 Traceback (most recent call last)
 Input [0;32mIn [13][0m, in [0;36m<cell line: 1>[0;34m()[0m
 [0;32m----> 1[0m [43mdecomposition_g0_g8[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<string>:8[0m, in [0;36mdecomposition_g0_g8[0;34m(fct)[0m
 [0;31mNameError[0m: name 'enumeratate' 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[0mdecomposition_g0_g8[0;38;5;16;48;5;152m([0mC.y/C.x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[28D[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[?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[0mdecomposition_g0_g8[0;38;5;16;48;5;152m([0mC.y/C.x[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[34D[0m[J[0;94msage: [0mdecomposition_g0_g8(C.y/C.x)[34D[0m
 [J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(0, 0, 1/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.verschiebung()[18D[?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[0mC[0;38;5;241m.dx.verschiebung()[18D[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0me[0;38;5;241m_rham_basis()[0m[K[13D[?7h[0m[?12l[?25h[?25l[?7l[0m_rham_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mC.de_rham_basis()[23D[0m
 [J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[((1/y) dx, 0, (1/y) dx), ((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[0mC.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;1m0[?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[17D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mxC.de_rham_basis()[[0;38;5;20;1m0[0m][20D[?7h[0m[?12l[?25h[?25l[?7l[0miC.de_rham_basis()[[0;38;5;20;1m0[0m][20D[?7h[0m[?12l[?25h[?25l[?7l[0m C.de_rham_basis()[[0;38;5;20;1m0[0m][20D[?7h[0m[?12l[?25h[?25l[?7l[0m=C.de_rham_basis()[[0;38;5;20;1m0[0m][20D[?7h[0m[?12l[?25h[?25l[?7l[0m C.de_rham_basis()[[0;38;5;20;1m0[0m][20D[?7h[0m[?12l[?25h[?25l[?7l[11D[0m[J[0;94msage: [0mxi = C.de_rham_basis()[[0;38;5;20;1m0[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(omega)[21D[?7h[0m[?12l[?25h[?25l[?7l[8D[0;94msage: [0mli[0;38;5;241mft_form_to_drw(omega)[0m
 [8C[0;38;5;16;48;5;250m  li                                lie                               lift_form_to_drw                  line                              linear_relation                   list                               [0m
 [8C[0;38;5;16;48;5;250m  libgap                            lie_algebras                      lift_to_sl2z                      line2d                            linear_representation_polynomials list_plot                          [0m
 [8C[0;38;5;16;48;5;250m  libgiac                           lie_conformal_algebras            lim                               line3d                            linear_transformation             list_plot3d                       >[0m
 [8C[0;38;5;16;48;5;250m  license                           lift                              limit                             linear_program                    lisp                              list_plot_loglog                   [0m
 [0m [5A[8C[?7h[0m[?12l[?25h[?25l[?7l[0mft_form_to_drw[0;38;5;16;48;5;152m([0momega[0;38;5;16;48;5;152m)[0m
 [C[0m[K[0m
 [C[0m[K[0m
 [C[0m[K[0m
 [C[0m[K[4A[28C[?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[0mx[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[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[26D[0m[J[0;94msage: [0mlift_form_to_drw(xi)[26D[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 [43mlift_form_to_drw[49m[43m([49m[43mxi[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_g0_g8(C.y/C.x)[27D[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0m_[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mh[?7h[0m[?12l[?25h[?25l[?7l[0mam_witt_lift[?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[0mx[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;16;48;5;152m([2C)[?7h[0m[?12l[?25h[?25l[?7l[27D[0m[J[0;94msage: [0mde_rham_witt_lift(xi)[27D[0m
 [J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
 [0;31mTypeError[0m                                 Traceback (most recent call last)
 Input [0;32mIn [19][0m, in [0;36m<cell line: 1>[0;34m()[0m
 [0;32m----> 1[0m [43mde_rham_witt_lift[49m[43m([49m[43mxi[49m[43m)[49m
 File [0;32m<string>:270[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
 File [0;32m<string>:88[0m, in [0;36mdiffn[0;34m(self)[0m
 [0;31mTypeError[0m: unsupported operand type(s) for -: 'superelliptic_drw_form' and 'superelliptic_drw_form'
 [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(xi)[19D[?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[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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[27D[0m[J[0;94msage: [0mde_rham_witt_lift(xi)[27D[0m
 [J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
 [0;31mAttributeError[0m                            Traceback (most recent call last)
 Input [0;32mIn [21][0m, in [0;36m<cell line: 1>[0;34m()[0m
 [0;32m----> 1[0m [43mde_rham_witt_lift[49m[43m([49m[43mxi[49m[43m)[49m
 File [0;32m<string>:269[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
 File [0;32m<string>:5[0m, in [0;36mregular_form[0;34m(omega)[0m
 [0;31mAttributeError[0m: 'NoneType' object has no attribute 'curve'
 [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()[0][24D[?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[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[0mxi[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[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[K[?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[0mxi[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mlift_form_[Co[Cdrw[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[20D[0mx[C = C.de[Crham_bas[Cs()[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[31D[0m[J[0;94msage: [0mxi = C.de_rham_basis()[[0;38;5;20;1m0[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[0mxi = C.de_rham_basis()[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[25D[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[0mxi[0m[K[?7h[0m[?12l[?25h[?25l[?7l[2D[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[27D[0m[J[0;94msage: [0mde_rham_witt_lift(xi)[27D[0m
 [J[?7h[0m[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
 [0;31m---------------------------------------------------------------------------[0m
 [0;31mTypeError[0m                                 Traceback (most recent call last)
 Input [0;32mIn [25][0m, in [0;36m<cell line: 1>[0;34m()[0m
 [0;32m----> 1[0m [43mde_rham_witt_lift[49m[43m([49m[43mxi[49m[43m)[49m
 File [0;32m<string>:275[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
 [0;31mTypeError[0m: unsupported operand type(s) for -: 'tuple' and 'tuple'
 [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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[31D[0m[J[0;94msage: [0mxi = C.de_rham_basis()[[0;38;5;20;1m0[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[0mxi = C.de_rham_basis()[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[25D[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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[27D[0m[J[0;94msage: [0mde_rham_witt_lift(xi)[27D[0m
 [J[?7h[0m[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
 [0;31m---------------------------------------------------------------------------[0m
 [0;31mAttributeError[0m                            Traceback (most recent call last)
 Input [0;32mIn [28][0m, in [0;36m<cell line: 1>[0;34m()[0m
 [0;32m----> 1[0m [43mde_rham_witt_lift[49m[43m([49m[43mxi[49m[43m)[49m
 File [0;32m<string>:276[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
 [0;31mAttributeError[0m: 'superelliptic_function' object has no attribute 'decomposition_g0_g8'
 [6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[25D[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[?2004l0
 [6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?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[?7h[0m[?12l[?25h[?25l[?7l[17D[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[31D[0m[J[0;94msage: [0mxi = C.de_rham_basis()[[0;38;5;20;1m0[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[0mxi = C.de_rham_basis()[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[25D[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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[27D[0m[J[0;94msage: [0mde_rham_witt_lift(xi)[27D[0m
 [J[?7h[0m[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
 [0;31m---------------------------------------------------------------------------[0m
 [0;31mAttributeError[0m                            Traceback (most recent call last)
 Input [0;32mIn [31][0m, in [0;36m<cell line: 1>[0;34m()[0m
 [0;32m----> 1[0m [43mde_rham_witt_lift[49m[43m([49m[43mxi[49m[43m)[49m
 File [0;32m<string>:278[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
 [0;31mAttributeError[0m: 'superelliptic_form' object has no attribute 'decomposition_omega0_omega8'
 [6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[25D[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[?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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[31D[0m[J[0;94msage: [0mxi = C.de_rham_basis()[[0;38;5;20;1m0[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[0mxi = C.de_rham_basis()[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[25D[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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[27D[0m[J[0;94msage: [0mde_rham_witt_lift(xi)[27D[0m
 [J[?7h[0m[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
 [0m[?7h[0;91m[0m[0m<__main__.superelliptic_drw_cech object at 0x7f09ba3d4f40>
 [6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[25D[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[?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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[31D[0m[J[0;94msage: [0mxi = C.de_rham_basis()[[0;38;5;20;1m0[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[0mxi = C.de_rham_basis()[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[25D[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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[27D[0m[J[0;94msage: [0mde_rham_witt_lift(xi)[27D[0m
 [J[?7h[0m[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
 [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([(x^3/(x^2 + 2))*y]), [0], [0])
 <repr(<__main__.superelliptic_drw_cech at 0x7f09bad3fbe0>) failed: TypeError: __repr__ returned non-string (type NoneType)>
 [6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[25D[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[?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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[31D[0m[J[0;94msage: [0mxi = C.de_rham_basis()[[0;38;5;20;1m0[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[0mxi = C.de_rham_basis()[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[25D[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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[27D[0m[J[0;94msage: [0mde_rham_witt_lift(xi)[27D[0m
 [J[?7h[0m[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
 [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([(x^3/(x^2 + 2))*y]), [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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[25D[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[0mxi = C.de_rham_basis()[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[25D[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[21D[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[0mde_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).[?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[0m0[?7h[0m[?12l[?25h[?25l[?7l[0m
 [0;1mI-search:[9D[10C[?7h[0m[?12l[?25h[?25l[?7l[A[10D[0;94msage: [0mde_rham_witt_lift(xi).omega0[0m
 [0m [0m[K[A[33C[?7h[0m[?12l[?25h[?25l[?7l[34D[0m[J[0;94msage: [0mde_rham_witt_lift(xi).omega0[34D[0m
 [J[?7h[0m[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
 [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([(x^3/(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[0mde_rham_witt_lift(xi).omega0[?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[40D[0m[J[0;94msage: [0mde_rham_witt_lift(xi).omega0.omega[40D[0m
 [J[?7h[0m[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
 [0m[?7h[0;91m[0m[0m((x^7 - x^3 - x)/(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[0mde_rham_witt_lift(xi).omega0.omega[?7h[0m[?12l[?25h[?25l[?7l[5D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[6D[?7h[0m[?12l[?25h[?25l[?7l[5D[0;38;5;16;48;5;152m([2C[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)[21D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0made_rham_wi[Ct_lift(xi).omega0.omega[34D[?7h[0m[?12l[?25h[?25l[?7l[0m de_rham_wi[Ct_lift(xi).omega0.omega[34D[?7h[0m[?12l[?25h[?25l[?7l[0m=de_rham_wi[Ct_lift(xi).omega0.omega[34D[?7h[0m[?12l[?25h[?25l[?7l[0m de_rham_wi[Ct_lift(xi).omega0.omega[34D[?7h[0m[?12l[?25h[?25l[?7l[10D[0m[J[0;94msage: [0ma = de_rham_witt_lift(xi).omega0.omega[44D[0m
 [J[?7h[0m[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (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 = de_rham_witt_lift(xi).omega0.omega[37D[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mdiffn()[0m[K[7D[?7h[0m[?12l[?25h[?25l[?7l[8D[0;94msage: [0ma.[0;38;5;241mdiffn()[0m
 [8C[0;38;5;16;48;5;250m a.cartier               a.expansion_at_infty    a.is_regular_on_Uinfty  a.verschiebung         [0m
 [8C[0;38;5;16;48;5;250m a.coordinates           a.form                  a.jth_component                                [0m
 [8C[0;38;5;16;48;5;250m a.curve                 a.is_regular_on_U0      a.serre_duality_pairing                        [0m
 [0m [5A[8C[?7h[0m[?12l[?25h[?25l[?7l[0mcartier[0m
 [8C[0;38;5;231;48;5;102m a.cartier              [0m
 [8C[0;38;5;16;48;5;248m <unknown> [4A[4D[?7h[0m[?12l[?25h[?25l[?7l[6D[0moordinates[0m
 [8C[0;38;5;16;48;5;250m a.cartier              [0m
 [8C[0;38;5;231;48;5;102m a.coordinates          [2A[13D[?7h[0m[?12l[?25h[?25l[?7l[10D[0murve[0m[K[0m
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 [8C[0;38;5;231;48;5;102m a.curve                [3A[19D[?7h[0m[?12l[?25h[?25l[?7l[5D[0mis_r[Cgular_on_U0[0m
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 [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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[31D[0m[J[0;94msage: [0mxi = C.de_rham_basis()[[0;38;5;20;1m0[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[0mxi = C.de_rham_basis()[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[25D[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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[27D[0m[J[0;94msage: [0mde_rham_witt_lift(xi)[27D[0m
 [J[?7h[0m[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
 [(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
 [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([(x^3/(x^2 + 2))*y]), [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[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[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[?7h[0m[?12l[?25h[?25l[?7l[17D[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[31D[0m[J[0;94msage: [0mxi = C.de_rham_basis()[[0;38;5;20;1m0[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[0mxi = C.de_rham_basis()[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[25D[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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[27D[0m[J[0;94msage: [0mde_rham_witt_lift(xi)[27D[0m
 [J[?7h[0m[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
 0
 [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([(x^3/(x^2 + 2))*y]), [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[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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[31D[0m[J[0;94msage: [0mxi = C.de_rham_basis()[[0;38;5;20;1m0[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[0mxi = C.de_rham_basis()[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[25D[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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[27D[0m[J[0;94msage: [0mde_rham_witt_lift(xi)[27D[0m
 [J[?7h[0m[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
 [1]
 [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([(x^3/(x^2 + 2))*y]), [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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[25D[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[?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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[31D[0m[J[0;94msage: [0mxi = C.de_rham_basis()[[0;38;5;20;1m0[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[0mxi = C.de_rham_basis()[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[25D[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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[27D[0m[J[0;94msage: [0mde_rham_witt_lift(xi)[27D[0m
 [J[?7h[0m[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
 [1]
 [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([(x^3/(x^2 + 2))*y]), [0], [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]))
 [6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[25D[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[0mxi = C.de_rham_basis()[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[25D[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[21D[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;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[25D[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[?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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[31D[0m[J[0;94msage: [0mxi = C.de_rham_basis()[[0;38;5;20;1m0[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[0mxi = C.de_rham_basis()[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[25D[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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[27D[0m[J[0;94msage: [0mde_rham_witt_lift(xi)[27D[0m
 [J[?7h[0m[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
 aux V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
 [1]
 [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([(x^3/(x^2 + 2))*y]), [0], [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]))
 [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.de_rham_basis()[16D[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241m.verschiebung()[15D[?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[0mx[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mx[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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[25D[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[?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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mxi = C.de_rham_basis()[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[31D[0m[J[0;94msage: [0mxi = C.de_rham_basis()[[0;38;5;20;1m0[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[0mxi = C.de_rham_basis()[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[25D[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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[27D[0m[J[0;94msage: [0mde_rham_witt_lift(xi)[27D[0m
 [J[?7h[0m[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
 aux V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
 [0m[?7h[0;91m[0m[0mV(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
 [6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mde_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)[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)[21D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?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(xi)[21D[?7h[0m[?12l[?25h[?25l[?7l[0mude_rham_wi[Ct_lift(xi)[21D[?7h[0m[?12l[?25h[?25l[?7l[0mxde_rham_wi[Ct_lift(xi)[21D[?7h[0m[?12l[?25h[?25l[?7l[0m de_rham_wi[Ct_lift(xi)[21D[?7h[0m[?12l[?25h[?25l[?7l[0m=de_rham_wi[Ct_lift(xi)[21D[?7h[0m[?12l[?25h[?25l[?7l[0m de_rham_wi[Ct_lift(xi)[21D[?7h[0m[?12l[?25h[?25l[?7l[17C[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[32D[0m[J[0;94msage: [0maux = de_rham_witt_lift(xi)[33D[0m
 [J[?7h[0m[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
 aux V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
 [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;241me_rham_witt_lift(xi)[20D[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0mc[0;38;5;241momposition_omega0_omega8(a)[1].expansion_at_infty()[51D[?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[0ms[?7h[0m[?12l[?25h[?25l[?7l[0mi[?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[0mg[0;38;5;241m0_[C8(C.y/C.x)[0m[K[13D[?7h[0m[?12l[?25h[?25l[?7l[0m0_g8[0;38;5;16;48;5;152m([0mC.y/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[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[0ma[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mu[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[29D[0m[J[0;94msage: [0mdecomposition_g0_g8(aux)[30D[0m
 [J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
 [0;31mAttributeError[0m                            Traceback (most recent call last)
 Input [0;32mIn [73][0m, in [0;36m<cell line: 1>[0;34m()[0m
 [0;32m----> 1[0m [43mdecomposition_g0_g8[49m[43m([49m[43maux[49m[43m)[49m
 File [0;32m<string>:6[0m, in [0;36mdecomposition_g0_g8[0;34m(fct)[0m
 [0;31mAttributeError[0m: 'superelliptic_drw_form' 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[0mdecomposition_g0_g8[0;38;5;16;48;5;152m([0maux[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[0mh[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m1[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: [0mdecomposition_g0_g8(aux.h1)[33D[0m
 [J[?7h[0m[?12l[?25h[?2004l[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[0ma[0;38;5;241mux = de_rham_witt_lift(xi)[26D[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0m.[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mh[?7h[0m[?12l[?25h[?25l[?7l[0m1[?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[26D[0m[J[0;94msage: [0maux.h1.coordinates()[26D[0m
 [J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[0]
 [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;241mux.h1.coordinates()[19D[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mh[?7h[0m[?12l[?25h[?25l[?7l[0m1[?7h[0m[?12l[?25h[?25l[?7l[12D[0m[J[0;94msage: [0maux.h1[12D[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[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241mi = C.de_rham_basis()[0][24D[?7h[0m[?12l[?25h[?25l[?7l[0mu[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[0ma[0;38;5;241mux.h1[5D[?7h[0m[?12l[?25h[?25l[?7l[0mu[?7h[0m[?12l[?25h[?25l[?7l[0mx[?7h[0m[?12l[?25h[?25l[?7l[9D[0m[J[0;94msage: [0maux[9D[0m
 [J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mV(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*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[0maux[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mh1[2D[?7h[0m[?12l[?25h[?25l[?7l[0mh[?7h[0m[?12l[?25h[?25l[?7l[0m2[?7h[0m[?12l[?25h[?25l[?7l[12D[0m[J[0;94msage: [0maux.h2[12D[0m
 [J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m((x^4 + x^2 + 1)/x^3)*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[0maux.h2[?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[26D[0m[J[0;94msage: [0maux.h2.coordinates()[26D[0m
 [J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[2]
 [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[13D[0m([11C);[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mxi = C.de_rham_basis()[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[3D[0m[[C];[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[73D[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]; de_rham_witt_lift(xi)[73D[0m
 [J[?7h[0m[?12l[?25h[?2004l0
 (1/y) dx ((-1)/y) dx (0, 1)
 aux V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
 [1]
 [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]))
 [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]; 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[67D[0maux.h2.coordinates[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[20D[0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m0[0m]; 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[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; de_rham_wit[C_lift(xi)[0m[K[24D[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m1[0;38;5;210;48;5;88m][0m; de_rham_wi[Ct_lift(xi)[24D[?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[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[0;38;5;210;48;5;88m([2C[0;38;5;16;48;5;152m)[4D[?7h[0m[?12l[?25h[?25l[?7l[0m([2C)[3D[?7h[0m[?12l[?25h[?25l[?7l[C[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m([2C[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[73D[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]; de_rham_witt_lift(xi)[73D[0m
 [J[?7h[0m[?12l[?25h[?2004l0
 (x/y) dx ((-1)/(x*y)) dx None
 [0;31m---------------------------------------------------------------------------[0m
 [0;31mTypeError[0m                                 Traceback (most recent call last)
 Input [0;32mIn [81][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); xi [38;5;241m=[39m C[38;5;241m.[39mde_rham_basis()[Integer([38;5;241m1[39m)]; [43mde_rham_witt_lift[49m[43m([49m[43mxi[49m[43m)[49m
 File [0;32m<string>:304[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
 [0;31mTypeError[0m: 'NoneType' 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[0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m]; 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[73D[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]; de_rham_witt_lift(xi)[73D[0m
 [J[?7h[0m[?12l[?25h[?2004l0
 (x/y) dx ((-1)/(x*y)) dx None
 None
 [0;31m---------------------------------------------------------------------------[0m
 [0;31mTypeError[0m                                 Traceback (most recent call last)
 Input [0;32mIn [82][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); xi [38;5;241m=[39m C[38;5;241m.[39mde_rham_basis()[Integer([38;5;241m1[39m)]; [43mde_rham_witt_lift[49m[43m([49m[43mxi[49m[43m)[49m
 File [0;32m<string>:305[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
 [0;31mTypeError[0m: 'NoneType' 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[0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m]; 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[73D[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]; de_rham_witt_lift(xi)[73D[0m
 [J[?7h[0m[?12l[?25h[?2004l0
 omega8_re None
 [0;31m---------------------------------------------------------------------------[0m
 [0;31mTypeError[0m                                 Traceback (most recent call last)
 Input [0;32mIn [83][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); xi [38;5;241m=[39m C[38;5;241m.[39mde_rham_basis()[Integer([38;5;241m1[39m)]; [43mde_rham_witt_lift[49m[43m([49m[43mxi[49m[43m)[49m
 File [0;32m<string>:304[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
 [0;31mTypeError[0m: 'NoneType' 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[0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m]; 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[25D[0;38;5;20;1m0[24C[?7h[0m[?12l[?25h[?25l[?7l[67D[0maux.h2.coordinates[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[20D[0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m0[0m]; 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[25D[0;38;5;20;1m1[24C[?7h[0m[?12l[?25h[?25l[?7l[73D[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]; de_rham_witt_lift(xi)[73D[0m
 [J[?7h[0m[?12l[?25h[?2004l0
 omega8_re None
 [0;31m---------------------------------------------------------------------------[0m
 [0;31mTypeError[0m                                 Traceback (most recent call last)
 Input [0;32mIn [84][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); xi [38;5;241m=[39m C[38;5;241m.[39mde_rham_basis()[Integer([38;5;241m1[39m)]; [43mde_rham_witt_lift[49m[43m([49m[43mxi[49m[43m)[49m
 File [0;32m<string>:304[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
 [0;31mTypeError[0m: 'NoneType' 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[0ml[0;38;5;241moad('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[66D[?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]; 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[73D[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]; de_rham_witt_lift(xi)[73D[0m
 [J[?7h[0m[?12l[?25h[?2004l0
 second_patch(omega0) ((-1)/(x*y)) dx
 [0;31m---------------------------------------------------------------------------[0m
 [0;31mTypeError[0m                                 Traceback (most recent call last)
 Input [0;32mIn [85][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); xi [38;5;241m=[39m C[38;5;241m.[39mde_rham_basis()[Integer([38;5;241m1[39m)]; [43mde_rham_witt_lift[49m[43m([49m[43mxi[49m[43m)[49m
 File [0;32m<string>:304[0m, in [0;36mde_rham_witt_lift[0;34m(cech_class)[0m
 [0;31mTypeError[0m: 'NoneType' 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[0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m]; 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[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[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[4D[0;38;5;16;48;5;152m[[C][0m[K[?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C].[?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[0m9[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m8[?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[0me[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0m_[?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[0mx[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;16;48;5;152m([2C)[?7h[0m[?12l[?25h[?25l[?7l[75D[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].omega8; second_patch(xi)[75D[0m
 [J[?7h[0m[?12l[?25h[?2004l0
 [0m[?7h[0;91m[0m[0m(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[0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m].omega8; second_patch[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[25D[0m; d[C_rham_witt_lif[C[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[25D[0;38;5;20;1m0[24C[?7h[0m[?12l[?25h[?25l[?7l[67D[0maux.h2.coordinates[0;38;5;16;48;5;152m()[0m[K[?7h[0m[?12l[?25h[?25l[?7l[20D[0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m0[0m]; 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[25D[0;38;5;20;1m1[24C[?7h[0m[?12l[?25h[?25l[?7l[73D[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]; de_rham_witt_lift(xi)[73D[0m
 [J[?7h[0m[?12l[?25h[?2004l0
 second_patch(omega0) ((-1)/(x*y)) dx
 g0, g8 ((-x^8 + x^6)/y) dx ((-1)/(x^2*y - y)) dx
 [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[0md[0;38;5;241mecomposition_g0_g8(aux.h1)[26D[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0m_[0;38;5;241mrham_witt_lift(xi)[0m[K[18D[?7h[0m[?12l[?25h[?25l[?7l[0mrham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[27D[0m[J[0;94msage: [0mde_rham_witt_lift(xi)[27D[0m
 [J[?7h[0m[?12l[?25h[?2004lsecond_patch(omega0) ((-1)/(x*y)) dx
 g0, g8 ((-x^8 + x^6)/y) dx ((-1)/(x^2*y - y)) dx
 [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[0mde_rham_witt_lift[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[21D[0mload([0;38;5;160;48;5;231m'init.sage'[0m); xi = C.de_rham_basis()[[0;38;5;20;1m1[0m]; 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[23D[0m.om[Cga8; second_pa[Cch[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[25D[0m; d[C_rham_witt_lif[C[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[23D[0m.om[Cga8; second_pa[Cch[0;38;5;16;48;5;152m([0mxi[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[25D[0m; d[C_rham_witt_lif[C[0;38;5;16;48;5;152m([0mxi[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[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)[21D[?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[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[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[13C[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[C[?7h[0m[?12l[?25h[?25l[?7l[0made_rham_wi[Ct_lift(xi)[21D[?7h[0m[?12l[?25h[?25l[?7l[0m de_rham_wi[Ct_lift(xi)[21D[?7h[0m[?12l[?25h[?25l[?7l[0m=de_rham_wi[Ct_lift(xi)[21D[?7h[0m[?12l[?25h[?25l[?7l[0m de_rham_wi[Ct_lift(xi)[21D[?7h[0m[?12l[?25h[?25l[?7l[56D[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[0ma[0;38;5;241mux.h2.coordinates()[19D[?7h[0m[?12l[?25h[?25l[?7l[0m+[0;38;5;241ma[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0m+[0;38;5;241ma[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[11D[0m[J[0;94msage: [0ma+a+a[11D[0m
 [J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(V((x^4/(x^2*y - y)) dx), V(((2*x^2 + 1)/x^2)*y), V((x^4/(x^2*y - y)) dx) + dV([((x^2 + 2)/x^2)*y]))
 [6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ma+a+a[?7h[0m[?12l[?25h[?25l[?7l[5D[0mlo[Cd([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[0m([0;38;5;241mC.y.teichmuller()).diffn().frobenius() == C.y^2*C.y.diffn()[59D[?7h[0m[?12l[?25h[?25l[?7l[0ma[0m[K[?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[0ma[?7h[0m[?12l[?25h[?25l[?7l[6D[0;38;5;16;48;5;152m([5C)[?7h[0m[?12l[?25h[?25l[?7l[7D[0m([5C).[?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[22D[0m[J[0;94msage: [0m(a+a+a).reduce()[22D[0m
 [J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m(dV([y]), [0], dV([y]))
 [6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mq[?7h[0m[?12l[?25h
--- a/sage/drafty/superelliptic_drw.sage
+++ b/sage/drafty/superelliptic_drw.sage
@ -214,6 +214,9 @@ class superelliptic_drw_form:
        omega = self.omega
        return superelliptic_drw_form(-h1, -omega, -h2)
    def __sub__(self, other):
        return self + (-other)
    def __add__(self, other):
        C = self.curve
        h1 = self.h1
@ -243,3 +246,80 @@ def mult_by_p(omega):
    result = superelliptic_drw_form(C, 0*C.dx, omega, 0*C.x)
    return result
 def verschiebung(elt):
    C = elt.curve
    if isinstance(elt, superelliptic_function):
        return superelliptic_witt(0*C.x, elt)
    if isinstance(elt, superelliptic_form):
        return superelliptic_drw_form(0*C.x, elt, 0*C.x)
 superelliptic_form.verschiebung = verschiebung
 superelliptic_function.verschiebung = verschiebung
 class superelliptic_drw_cech:
    def __init__(self, omega0, f):
        self.curve = omega0.curve
        self.omega0 = omega0
        self.omega8 = omega0 - f.diffn()
        self.f = f
    def reduce(self):
        C = self.curve
        fct = self.f
        f_first_comp = fct.t
        f_second_comp = fct.f
        decomp_first_comp = decomposition_g0_g8(f_first_comp)
        decomp_second_comp = decomposition_g0_g8(f_second_comp)
        new = superelliptic_drw_cech(0*C.dx.verschiebung(), 0*C.x.verschiebung())
        new.omega0 -= decomposition_g0_g8(f_first_comp)[0].teichmuller().diffn()
        new.omega0 -= decomposition_g0_g8(f_second_comp)[0].verschiebung().diffn()
        new.f = decomposition_g0_g8(f_first_comp)[2].teichmuller() + decomposition_g0_g8(f_second_comp)[2].verschiebung()
        new.omega8 = new.omega0 - new.f.diffn()
        return new
    def __repr__(self):
        return("(" + str(self.omega0) + ", "+ str(self.f) + ", " + str(self.omega8) + ")")
    def __add__(self, other):
        C = self.curve
        omega0 = self.omega0
        f = self.f
        omega0_1 = other.omega0
        f_1 = other.f
        return superelliptic_drw_cech(omega0 + omega0_1, f + f_1)
    def __sub__(self, other):
        C = self.curve
        omega0 = self.omega0
        f = self.f
        omega0_1 = other.omega0
        f_1 = other.f
        return superelliptic_drw_cech(omega0 - omega0_1, f - f_1)
    def __neg__(self):
        C = self.curve
        omega0 = self.omega0
        f = self.f
        return superelliptic_drw_cech(-omega0, -f)
 def de_rham_witt_lift(cech_class):
    C = cech_class.curve
    g = C.genus()
    omega0 = cech_class.omega0
    omega8 = cech_class.omega8
    fct = cech_class.f
    omega0_regular = regular_form(omega0)
    omega0_lift = omega0_regular[0].teichmuller()*(C.x.teichmuller().diffn()) + omega0_regular[1].teichmuller()*(C.y.teichmuller().diffn())
    omega8_regular = regular_form(second_patch(omega8))
    omega8_regular = (second_patch(omega8_regular[0]), second_patch(omega8_regular[1]))
    u = (C.x)^(-1)
    v = (C.y)/(C.x)^(g+1)
    omega8_lift = omega0_regular[0].teichmuller()*(u.teichmuller().diffn()) + omega0_regular[1].teichmuller()*(v.teichmuller().diffn())
    aux = omega0_lift - omega8_lift - fct.teichmuller().diffn()
    aux_h2 = decomposition_g0_g8(aux.h2)[0]
    aux_f = decomposition_g0_g8(aux.h2)[2] #do napisania - komponent od kohomologii
    aux_omega0 = decomposition_omega0_omega8(aux.omega)[0]
    return superelliptic_drw_cech(omega0_lift + aux_h2.verschiebung().diffn() + aux_omega0.verschiebung(), fct.teichmuller() + aux_f.verschiebung())
--- a/sage/superelliptic/decomposition_into_g0_g8.sage
+++ b/sage/superelliptic/decomposition_into_g0_g8.sage
@ -2,6 +2,11 @@ def decomposition_g0_g8(fct):
    '''Writes fct as a difference g0 - g8, with g0 regular on the affine patch and g8 at the points in infinity.'''
    C = fct.curve
    g = C.genus()
    coord = fct.coordinates()
    nontrivial_part = 0*C.x
    for i, a in enumerate(C.cohomology_of_structure_sheaf_basis()):
        nontrivial_part += coord[i]*a
    fct -= nontrivial_part
    if fct.coordinates() != g*[0]:
        raise ValueError("The given function cannot be written as g0 - g8.")
@ -18,7 +23,7 @@ def decomposition_g0_g8(fct):
            g8 += num.monomial_coefficient(monomial)*aux/aux_den
        else:
            g0 += num.monomial_coefficient(monomial)*aux/aux_den
-    return (g0, g8)
+    return (g0, g8, nontrivial_part)
 def decomposition_omega0_omega8(omega, prec=50):
    '''Writes omega as a difference omega0 - omega8, with omega0 regular on the affine patch and omega8 at the points in infinity.'''
--- a/sage/superelliptic/superelliptic_class.sage
+++ b/sage/superelliptic/superelliptic_class.sage
@ -159,7 +159,7 @@ class superelliptic:
        F = self.base_ring
        p = F.characteristic()
        M = matrix(F, g, g)
-        for i, f in enumerate(self.basis_of_cohomology()):
+        for i, f in enumerate(self.cohomology_of_structure_sheaf_basis()):
            M[i, :] = vector((f^p).coordinates(prec=prec))
        M = M.transpose()
        return M
@ -184,7 +184,7 @@ class superelliptic:
        p = self.characteristic
        return flag(Fr, V, p, test)
-    def basis_of_cohomology(self):
+    def cohomology_of_structure_sheaf_basis(self):
        '''Basis of cohomology of structure sheaf H1(X, OX).'''
        m = self.exponent
        f = self.polynomial
--- a/sage/superelliptic/superelliptic_function_class.sage
+++ b/sage/superelliptic/superelliptic_function_class.sage
@ -97,7 +97,7 @@ class superelliptic_function:
        '''Find coordinates in H1(X, OX) in given basis basis with dual basis basis_holo.'''
        C = self.curve
        if basis == 0:
-            basis = C.basis_of_cohomology()
+            basis = C.cohomology_of_structure_sheaf_basis()
        if basis_holo == 0:
            basis_holo = C.holomorphic_differentials_basis()
        g = C.genus()