lift kocykli do drw zrobiony z drobnymi bledami

This commit is contained in:
jgarnek 2023-02-24 16:57:49 +00:00
parent 22872e266b
commit e1a000f7a5
5 changed files with 524 additions and 5 deletions

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@ -39866,3 +39866,437 @@ Untracked files:
no changes added to commit (use "git add" and/or "git commit -a") no changes added to commit (use "git add" and/or "git commit -a")
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add sage/drqaafty/second_patch.sage ]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add sage/drqaafty/second_patch.sage
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u ]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m ""r"o"z"n"i"c"z"k"o"w"a"n"i"e" "f"o"r"m" "d"r"w" "z"r"o"b"i"o"n"e" "("?")"
[master 22872e2] rozniczkowanie form drw zrobione (?)
6 files changed, 1514 insertions(+), 117 deletions(-)
create mode 100644 sage/drafty/second_patch.sage
rewrite sage/drafty/superelliptic_drw.sage (68%)
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push
Username for 'https://git.wmi.amu.edu.pl': jgarnek
Password for 'https://jgarnek@git.wmi.amu.edu.pl':
Enumerating objects: 19, done.
Counting objects: 5% (1/19) Counting objects: 10% (2/19) Counting objects: 15% (3/19) Counting objects: 21% (4/19) Counting objects: 26% (5/19) Counting objects: 31% (6/19) Counting objects: 36% (7/19) Counting objects: 42% (8/19) Counting objects: 47% (9/19) Counting objects: 52% (10/19) Counting objects: 57% (11/19) Counting objects: 63% (12/19) Counting objects: 68% (13/19) Counting objects: 73% (14/19) Counting objects: 78% (15/19) Counting objects: 84% (16/19) Counting objects: 89% (17/19) Counting objects: 94% (18/19) Counting objects: 100% (19/19) Counting objects: 100% (19/19), done.
Delta compression using up to 4 threads
Compressing objects: 9% (1/11) Compressing objects: 18% (2/11) Compressing objects: 27% (3/11) Compressing objects: 36% (4/11) Compressing objects: 45% (5/11) Compressing objects: 54% (6/11) Compressing objects: 63% (7/11) Compressing objects: 72% (8/11) Compressing objects: 81% (9/11) Compressing objects: 90% (10/11) Compressing objects: 100% (11/11) Compressing objects: 100% (11/11), done.
Writing objects: 9% (1/11) Writing objects: 18% (2/11) Writing objects: 27% (3/11) Writing objects: 36% (4/11) Writing objects: 45% (5/11) Writing objects: 54% (6/11) Writing objects: 63% (7/11) Writing objects: 72% (8/11) Writing objects: 81% (9/11) Writing objects: 90% (10/11) Writing objects: 100% (11/11) Writing objects: 100% (11/11), 18.02 KiB | 271.00 KiB/s, done.
Total 11 (delta 6), reused 0 (delta 0)
remote: . Processing 1 references
remote: Processed 1 references in total
To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
856d742..22872e2 master -> master
]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.7, Release Date: 2022-09-19 │
│ Using Python 3.10.5. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: C
[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7ldx == C.dx[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laC.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l=C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: a = C.de_rham_basis()[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lsage: a.diffn()
 a.coordinates a.frobenius a.omega8 
 a.curve a.is_cocycle a.verschiebung
 a.f a.omega0 
 [?7h[?12l[?25h[?25l[?7l


[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
 [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lx^3 - C.x[?7h[?12l[?25h[?25l[?7l.teichmuller()*C.y.teichmuller()[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.verschiebung()
[?7h[?12l[?25h[?2004l[?7hV(x)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
 [?7h[?12l[?25h[?25l[?7lC.x.verschiebung()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldx.verschiebung()[?7h[?12l[?25h[?25l[?7lsage: C.dx.verschiebung()
[?7h[?12l[?25h[?2004l[?7h<repr(<__main__.superelliptic_drw_form at 0x7f09bae4bf10>) failed: AttributeError: 'superelliptic_form' object has no attribute 'function'>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.verschiebung()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ltichmuller()*C.y.teichmuller()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7lx.verschiebung()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7lsage: C.dx.verschiebung()
[?7h[?12l[?25h[?2004l[?7hV(1 dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004lTraceback (most recent call last):
File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
exec(code_obj, self.user_global_ns, self.user_ns)
Input In [9] in <cell line: 1>
load('init.sage')
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
File /ext/sage/9.7/src/sage/repl/load.py:272 in load
exec(preparse_file(f.read()) + "\n", globals)
File <string>:6 in <module>
File sage/misc/persist.pyx:175 in sage.misc.persist.load
sage.repl.load.load(filename, globals())
 File /ext/sage/9.7/src/sage/repl/load.py:272 in load
 exec(preparse_file(f.read()) + "\n", globals)
 File <string>:7
 for a in
 ^
SyntaxError: invalid syntax
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldiffn(C.y.teichmuller())[?7h[?12l[?25h[?25l[?7lenominator(((C.y)^(-1*C.dx).form) == y[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: decomposition
 decomposition 
 decomposition_g0_g8 
 decomposition_omega0_omega8
 [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l
 decomposition 
 <unknown> [?7h[?12l[?25h[?25l[?7l_g0_g8
 decomposition 
 decomposition_g0_g8 [?7h[?12l[?25h[?25l[?7l



[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(C.y/C.x)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [11], in <cell line: 1>()
----> 1 decomposition_g0_g8(C.y/C.x)
File <string>:6, in decomposition_g0_g8(fct)
File <string>:101, in coordinates(self, basis, basis_holo, prec)
AttributeError: 'superelliptic' object has no attribute 'basis_of_cohomology'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(C.y/C.x)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Input In [13], in <cell line: 1>()
----> 1 decomposition_g0_g8(C.y/C.x)
File <string>:8, in decomposition_g0_g8(fct)
NameError: name 'enumeratate' is not defined
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(C.y/C.x)
[?7h[?12l[?25h[?2004l[?7h(0, 0, 1/x*y)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.verschiebung()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()
[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxC.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7liC.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l=C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lift_form_to_drw(omega)[?7h[?12l[?25h[?25l[?7lsage: lift_form_to_drw(omega)
 li lie lift_form_to_drw line linear_relation list 
 libgap lie_algebras lift_to_sl2z line2d linear_representation_polynomials list_plot 
 libgiac lie_conformal_algebras lim line3d linear_transformation list_plot3d >
 license lift limit linear_program lisp list_plot_loglog 
 [?7h[?12l[?25h[?25l[?7lft_form_to_drw(omega)



[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: lift_form_to_drw(xi)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [18], in <cell line: 1>()
----> 1 lift_form_to_drw(xi)
File <string>:29, in lift_form_to_drw(omega)
File <string>:10, in regular_form(omega)
AttributeError: 'superelliptic_cech' object has no attribute 'form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lam_witt_lift[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [19], in <cell line: 1>()
----> 1 de_rham_witt_lift(xi)
File <string>:270, in de_rham_witt_lift(cech_class)
File <string>:88, in diffn(self)
TypeError: unsupported operand type(s) for -: 'superelliptic_drw_form' and 'superelliptic_drw_form'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llift_form_to_drw(xi)[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [21], in <cell line: 1>()
----> 1 de_rham_witt_lift(xi)
File <string>:269, in de_rham_witt_lift(cech_class)
File <string>:5, in regular_form(omega)
AttributeError: 'NoneType' object has no attribute 'curve'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: xi
[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7llift_form_odrw(xi)[?7h[?12l[?25h[?25l[?7lx = C.derham_bass()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [25], in <cell line: 1>()
----> 1 de_rham_witt_lift(xi)
File <string>:275, in de_rham_witt_lift(cech_class)
TypeError: unsupported operand type(s) for -: 'tuple' and 'tuple'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [28], in <cell line: 1>()
----> 1 de_rham_witt_lift(xi)
File <string>:276, in de_rham_witt_lift(cech_class)
AttributeError: 'superelliptic_function' object has no attribute 'decomposition_g0_g8'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [31], in <cell line: 1>()
----> 1 de_rham_witt_lift(xi)
File <string>:278, in de_rham_witt_lift(cech_class)
AttributeError: 'superelliptic_form' object has no attribute 'decomposition_omega0_omega8'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
[?7h<__main__.superelliptic_drw_cech object at 0x7f09ba3d4f40>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), [0], [0])
<repr(<__main__.superelliptic_drw_cech at 0x7f09bad3fbe0>) failed: TypeError: __repr__ returned non-string (type NoneType)>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), [0], [0])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l
I-search:[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi).omega0
 [?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi).omega0
[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi).omega0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi).omega0.omega
[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
[?7h((x^7 - x^3 - x)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lade_rham_wit_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7lsage: a = de_rham_witt_lift(xi).omega0.omega
[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lsage: a.diffn()
 a.cartier a.expansion_at_infty a.is_regular_on_Uinfty a.verschiebung 
 a.coordinates a.form a.jth_component 
 a.curve a.is_regular_on_U0 a.serre_duality_pairing 
 [?7h[?12l[?25h[?25l[?7lcartier
 a.cartier 
 <unknown> [?7h[?12l[?25h[?25l[?7loordinates
 a.cartier 
 a.coordinates [?7h[?12l[?25h[?25l[?7lurve
 a.coordinates 
 a.curve [?7h[?12l[?25h[?25l[?7lis_rgular_on_U0
 a.curve  a.is_regular_on_U0 [?7h[?12l[?25h[?25l[?7l



[?7h[?12l[?25h[?25l[?7lsage: a.is_regular_on_U0
[?7h[?12l[?25h[?2004l[?7h<bound method superelliptic_form.is_regular_on_U0 of ((x^7 - x^3 - x)/(x^2*y - y)) dx>
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 
 [?7h[?12l[?25h[?25l[?7la.is_regular_on_U0[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.is_regular_on_U0()
[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 
 [?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.is_regular_on_U0()[?7h[?12l[?25h[?25l[?7lsage: a
[?7h[?12l[?25h[?2004l[?7h((x^7 - x^3 - x)/(x^2*y - y)) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_g0_g8(Cy/C.x)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lposition_g0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_g0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lga0_omega8[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(a)
[?7h[?12l[?25h[?2004l[?7h(((x^5 + x^3)/y) dx, ((-x)/(x^2*y - y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(a)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lg)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(xi.omega0)
[?7h[?12l[?25h[?2004l[?7h(0 dx, (1/y) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(xi.omega0)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(a)
[?7h[?12l[?25h[?2004l[?7h(((x^5 + x^3)/y) dx, ((-x)/(x^2*y - y)) dx)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(a)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: decomposition_omega0_omega8(a)[1].expansion_at_infty()
[?7h[?12l[?25h[?2004l[?7h2*t^2 + t^6 + O(t^12)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_omega0_omega8(a)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_witt_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7lrham_witt_lift(xi).omega0.omega[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
((-x^5 - x^3)/y) dx
[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), [0], [0])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y])
[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), [0], [0])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
0
[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), [0], [0])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
[1]
[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), [0], [0])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
[1]
[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), [0], [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
aux V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
[1]
[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]), [0], [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.verschiebung()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lsage: xi = C.de_rham_basis()[0]
[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
aux V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
[?7hV(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lade_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7lude_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7lxde_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: aux = de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l(1/y) dx ((-1)/y) dx (0, 1)
aux V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lcomposition_omega0_omega8(a)[1].expansion_at_infty()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lg0_8(C.y/C.x)[?7h[?12l[?25h[?25l[?7l0_g8(C.y/C.x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(aux)
[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Input In [73], in <cell line: 1>()
----> 1 decomposition_g0_g8(aux)
File <string>:6, in decomposition_g0_g8(fct)
AttributeError: 'superelliptic_drw_form' object has no attribute 'coordinates'
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: decomposition_g0_g8(aux.h1)
[?7h[?12l[?25h[?2004l[?7h(0, 0, 0)
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.h1.coordinates()
[?7h[?12l[?25h[?2004l[?7h[0]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.h1.coordinates()[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: aux.h1
[?7h[?12l[?25h[?2004l[?7h0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.h1[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: aux
[?7h[?12l[?25h[?2004l[?7hV(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux[?7h[?12l[?25h[?25l[?7l.h1[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: aux.h2
[?7h[?12l[?25h[?2004l[?7h((x^4 + x^2 + 1)/x^3)*y
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.h2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: aux.h2.coordinates()
[?7h[?12l[?25h[?2004l[?7h[2]
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = C.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l[];[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[0]; de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l0
(1/y) dx ((-1)/y) dx (0, 1)
aux V(((-x^6 - x^4 + 1)/(x*y)) dx) + dV([((x^4 + x^2 + 1)/x^3)*y])
[1]
[?7h([(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^3 + 2*x)/(x^2 + 2))*y]), V(1/x*y), [(1/(x^3 + 2*x))*y] d[x] + V(((x^7 - x^3 - x)/(x^2*y - y)) dx) + dV([((2*x^4 + x^2 + 1)/(x^3 + 2*x))*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7laux.h2.coordinates()[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]; de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l1]; de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l0
(x/y) dx ((-1)/(x*y)) dx None
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [81], in <cell line: 1>()
----> 1 load('init.sage'); xi = C.de_rham_basis()[Integer(1)]; de_rham_witt_lift(xi)
File <string>:304, in de_rham_witt_lift(cech_class)
TypeError: 'NoneType' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l0
(x/y) dx ((-1)/(x*y)) dx None
None
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [82], in <cell line: 1>()
----> 1 load('init.sage'); xi = C.de_rham_basis()[Integer(1)]; de_rham_witt_lift(xi)
File <string>:305, in de_rham_witt_lift(cech_class)
TypeError: 'NoneType' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l0
omega8_re None
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [83], in <cell line: 1>()
----> 1 load('init.sage'); xi = C.de_rham_basis()[Integer(1)]; de_rham_witt_lift(xi)
File <string>:304, in de_rham_witt_lift(cech_class)
TypeError: 'NoneType' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7laux.h2.coordinates()[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l0
omega8_re None
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [84], in <cell line: 1>()
----> 1 load('init.sage'); xi = C.de_rham_basis()[Integer(1)]; de_rham_witt_lift(xi)
File <string>:304, in de_rham_witt_lift(cech_class)
TypeError: 'NoneType' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l0
second_patch(omega0) ((-1)/(x*y)) dx
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
Input In [85], in <cell line: 1>()
----> 1 load('init.sage'); xi = C.de_rham_basis()[Integer(1)]; de_rham_witt_lift(xi)
File <string>:304, in de_rham_witt_lift(cech_class)
TypeError: 'NoneType' object is not subscriptable
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1].omega8; second_patch(xi)
[?7h[?12l[?25h[?2004l0
[?7h(x/y) dx
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1].omega8; second_patch(xi)[?7h[?12l[?25h[?25l[?7l; d_rham_witt_lif(xi)[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7laux.h2.coordinates()[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[0]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l0
second_patch(omega0) ((-1)/(x*y)) dx
g0, g8 ((-x^8 + x^6)/y) dx ((-1)/(x^2*y - y)) dx
[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^10 + x^8 + x^6 - x^4)/(x^2*y - y)) dx) + dV([(2*x^6/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((x^10 + x^8 + x^6 + x^4 - x^2 - 1)/(x^2*y - y)) dx) + dV([(2*x^4 + 2*x^2 + 2)*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldecomposition_g0_g8(aux.h1)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lrham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004lsecond_patch(omega0) ((-1)/(x*y)) dx
g0, g8 ((-x^8 + x^6)/y) dx ((-1)/(x^2*y - y)) dx
[?7h([(1/(x^2 + 2))*y] d[x] + V(((x^10 + x^8 + x^6 - x^4)/(x^2*y - y)) dx) + dV([(2*x^6/(x^2 + 2))*y]), [2/x*y], [(2/(x^4 + 2*x^2))*y] d[x] + V(((x^10 + x^8 + x^6 + x^4 - x^2 - 1)/(x^2*y - y)) dx) + dV([(2*x^4 + 2*x^2 + 2)*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lload('init.sage'); xi = C.de_rham_basis()[1]; de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7l.omga8; second_pach(xi)[?7h[?12l[?25h[?25l[?7l; d_rham_witt_lif(xi)[?7h[?12l[?25h[?25l[?7l.omga8; second_pach(xi)[?7h[?12l[?25h[?25l[?7l; d_rham_witt_lif(xi)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lade_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laux.h2.coordinates()[?7h[?12l[?25h[?25l[?7l+a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a+a+a
[?7h[?12l[?25h[?2004l[?7h(V((x^4/(x^2*y - y)) dx), V(((2*x^2 + 1)/x^2)*y), V((x^4/(x^2*y - y)) dx) + dV([((x^2 + 2)/x^2)*y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la+a+a[?7h[?12l[?25h[?25l[?7llod('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)[?7h[?12l[?25h[?25l[?7lsage: load('init.sage'); xi = C.de_rham_basis()[1]; a = de_rham_witt_lift(xi)
[?7h[?12l[?25h[?2004l0
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn().frobenius() == C.y^2*C.y.diffn()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (a+a+a).reduce()
[?7h[?12l[?25h[?2004l[?7h(dV([y]), [0], dV([y]))
[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h

View File

@ -214,6 +214,9 @@ class superelliptic_drw_form:
omega = self.omega omega = self.omega
return superelliptic_drw_form(-h1, -omega, -h2) return superelliptic_drw_form(-h1, -omega, -h2)
def __sub__(self, other):
return self + (-other)
def __add__(self, other): def __add__(self, other):
C = self.curve C = self.curve
h1 = self.h1 h1 = self.h1
@ -243,3 +246,80 @@ def mult_by_p(omega):
result = superelliptic_drw_form(C, 0*C.dx, omega, 0*C.x) result = superelliptic_drw_form(C, 0*C.dx, omega, 0*C.x)
return result 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())

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@ -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.''' '''Writes fct as a difference g0 - g8, with g0 regular on the affine patch and g8 at the points in infinity.'''
C = fct.curve C = fct.curve
g = C.genus() 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]: if fct.coordinates() != g*[0]:
raise ValueError("The given function cannot be written as g0 - g8.") 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 g8 += num.monomial_coefficient(monomial)*aux/aux_den
else: else:
g0 += num.monomial_coefficient(monomial)*aux/aux_den g0 += num.monomial_coefficient(monomial)*aux/aux_den
return (g0, g8) return (g0, g8, nontrivial_part)
def decomposition_omega0_omega8(omega, prec=50): 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.''' '''Writes omega as a difference omega0 - omega8, with omega0 regular on the affine patch and omega8 at the points in infinity.'''

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@ -159,7 +159,7 @@ class superelliptic:
F = self.base_ring F = self.base_ring
p = F.characteristic() p = F.characteristic()
M = matrix(F, g, g) 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[i, :] = vector((f^p).coordinates(prec=prec))
M = M.transpose() M = M.transpose()
return M return M
@ -184,7 +184,7 @@ class superelliptic:
p = self.characteristic p = self.characteristic
return flag(Fr, V, p, test) 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).''' '''Basis of cohomology of structure sheaf H1(X, OX).'''
m = self.exponent m = self.exponent
f = self.polynomial f = self.polynomial

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@ -97,7 +97,7 @@ class superelliptic_function:
'''Find coordinates in H1(X, OX) in given basis basis with dual basis basis_holo.''' '''Find coordinates in H1(X, OX) in given basis basis with dual basis basis_holo.'''
C = self.curve C = self.curve
if basis == 0: if basis == 0:
basis = C.basis_of_cohomology() basis = C.cohomology_of_structure_sheaf_basis()
if basis_holo == 0: if basis_holo == 0:
basis_holo = C.holomorphic_differentials_basis() basis_holo = C.holomorphic_differentials_basis()
g = C.genus() g = C.genus()