From b79484be4f94f93561a47787344c8a8e69c6714d Mon Sep 17 00:00:00 2001 From: jgarnek Date: Tue, 7 Mar 2023 12:41:20 +0000 Subject: [PATCH] przed dodaniem ekspansji w dowolnym punkcie --- sage/.run.term-0.term | 3037 ++++++++++++++++- sage/as_covers/as_form_class.sage | 14 +- sage/drafty/draft.sage | 8 +- sage/drafty/superelliptic_drw.sage | 3 +- sage/init.sage | 4 +- .../superelliptic_form_class.sage | 18 +- 6 files changed, 3072 insertions(+), 12 deletions(-) diff --git a/sage/.run.term-0.term b/sage/.run.term-0.term index 11e32c3..c122d07 100644 --- a/sage/.run.term-0.term +++ b/sage/.run.term-0.term @@ -43060,4 +43060,3039 @@ Untracked files: superelliptic_arbitrary_field.ipynb no changes added to commit (use "git add" and/or "git commit -a") -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ \ No newline at end of file +]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 ""p"o"p"r"a"w"i"o"n"e" """y" "r"o"z"k"l"a"d" "n"a" "o"m"e"g"a"0" "-" "o"m"e"g"a"8" +[master 7e8546b] poprawiony rozklad na omega0 - omega8 + 6 files changed, 2553 insertions(+), 29 deletions(-) +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push +Username for 'https://git.wmi.amu.edu.pl': jgarnek +Password for 'https://jgarnek@git.wmi.amu.edu.pl': +Enumerating objects: 21, done. +Counting objects: 4% (1/21) Counting objects: 9% (2/21) Counting objects: 14% (3/21) Counting objects: 19% (4/21) Counting objects: 23% (5/21) Counting objects: 28% (6/21) Counting objects: 33% (7/21) Counting objects: 38% (8/21) Counting objects: 42% (9/21) Counting objects: 47% (10/21) Counting objects: 52% (11/21) Counting objects: 57% (12/21) Counting objects: 61% (13/21) Counting objects: 66% (14/21) Counting objects: 71% (15/21) Counting objects: 76% (16/21) Counting objects: 80% (17/21) Counting objects: 85% (18/21) Counting objects: 90% (19/21) Counting objects: 95% (20/21) Counting objects: 100% (21/21) Counting objects: 100% (21/21), 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), 27.84 KiB | 293.00 KiB/s, done. +Total 11 (delta 9), reused 0 (delta 0) +remote: . Processing 1 references +remote: Processed 1 references in total +To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git + 8719e64..7e8546b 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('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('drafty/draft5.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lnit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') + in initial_seed install_scripts integer_floor integrate invariant_theory inverse_jacobi_cs inverse_jacobi_nc inverse_jacobi_sd  + infinity input installed_packages integral interacts inverse_jacobi inverse_jacobi_dc inverse_jacobi_nd inverse_jacobi_sn  + infix_operator install_dict int integral_closure interfaces inverse_jacobi_cd inverse_jacobi_dn inverse_jacobi_ns inverse_laplace  + init.sage install_doc integer_ceil integral_numerical interval inverse_jacobi_cn inverse_jacobi_ds inverse_jacobi_sc inverse_mod  + [?7h[?12l[?25h[?25l[?7l(it.sage') + + + +[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [1], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :13, in  + +File :18, in convert_super_into_AS(C) + +ValueError: This is not a polynomial of x^p - x! +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[Finite Field of size 3] +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [2], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :13, in  + +File :19, in convert_super_into_AS(C) + +ValueError: This is not a polynomial of x^p - x! +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: + z^3 - z = x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [4], in () +----> 1 AS + +NameError: name 'AS' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: + z^3 - z = x +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [5], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :15, in  + +File :36, in convert_super_fct_into_AS(fct) + +File :4, in adic_expansion(g, h) + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.fraction_field_FpT.FpTElement' object has no attribute 'degree' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: + z^3 - z = x +--------------------------------------------------------------------------- +NotImplementedError Traceback (most recent call last) +Input In [6], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :15, in  + +File :36, in convert_super_fct_into_AS(fct) + +File :4, in adic_expansion(g, h) + +File /ext/sage/9.7/src/sage/structure/element.pyx:4100, in sage.structure.element.EuclideanDomainElement.degree() + 4098 + 4099 def degree(self): +-> 4100 raise NotImplementedError + 4101 + 4102 def leading_coefficient(self): + +NotImplementedError: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: + z^3 - z = x +component.numerator(), component.denominator() x^4 + 2*x 1 +adic_expansion(component.numerator(), x^p - x) [x^2 - x, x] +component.numerator(), component.denominator() 0 1 +--------------------------------------------------------------------------- +NotImplementedError Traceback (most recent call last) +Input In [7], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :15, in  + +File :37, in convert_super_fct_into_AS(fct) + +File :4, in adic_expansion(g, h) + +File /ext/sage/9.7/src/sage/structure/element.pyx:4100, in sage.structure.element.EuclideanDomainElement.degree() + 4098 + 4099 def degree(self): +-> 4100 raise NotImplementedError + 4101 + 4102 def leading_coefficient(self): + +NotImplementedError: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: + z^3 - z = x +component.numerator(), component.denominator() x^4 + 2*x 1 +adic_expansion(component.numerator(), x^p - x) [x^2 - x, x] +component.numerator(), component.denominator() 0 1 +adic_expansion(component.numerator(), x^p - x) [0] +--------------------------------------------------------------------------- +NotImplementedError Traceback (most recent call last) +Input In [8], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :15, in  + +File :41, in convert_super_fct_into_AS(fct) + +File :6, in adic_expansion(g, h) + +File /ext/sage/9.7/src/sage/structure/element.pyx:4100, in sage.structure.element.EuclideanDomainElement.degree() + 4098 + 4099 def degree(self): +-> 4100 raise NotImplementedError + 4101 + 4102 def leading_coefficient(self): + +NotImplementedError: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: + z^3 - z = x +component.numerator(), component.denominator() x^4 + 2*x 1 +adic_expansion(component.numerator(), x^p - x) [x^2 + 2*x, x] +adic_expansion(Rx(component.denominator()), x^p - x) [1] +component.numerator(), component.denominator() 0 1 +adic_expansion(component.numerator(), x^p - x) [0] +adic_expansion(Rx(component.denominator()), x^p - x) [1] +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [9], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :15, in  + +File :48, in convert_super_fct_into_AS(fct) + +TypeError: 'sage.rings.integer.Integer' object is not callable +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: + z^3 - z = x +component.numerator(), component.denominator() x^4 + 2*x 1 +adic_expansion(component.numerator(), x^p - x) [x^2 + 2*x, x] +adic_expansion(Rx(component.denominator()), x^p - x) [1] +component.numerator(), component.denominator() 0 1 +adic_expansion(component.numerator(), x^p - x) [0] +adic_expansion(Rx(component.denominator()), x^p - x) [1] +x*z0 + z0^2 - z0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: + z^3 - z = x +component.numerator(), component.denominator() x^4 + 2*x^2 1 +adic_expansion(component.numerator(), x^p - x) [0, x] +adic_expansion(Rx(component.denominator()), x^p - x) [1] +component.numerator(), component.denominator() 0 1 +adic_expansion(component.numerator(), x^p - x) [0] +adic_expansion(Rx(component.denominator()), x^p - x) [1] +x*z0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: + z^3 - z = x +x*z0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lchang(b)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: con + %conda conjugate continue contour_plot converted  + cones constructions continued_fraction convert_super_fct_into_AS convolution  + %config continuant continued_fraction_list convert_super_into_AS conway_polynomial  + + [?7h[?12l[?25h[?25l[?7l%conda + %conda  + + + [?7h[?12l[?25h[?25l[?7lconjugate + %conda  conjugate [?7h[?12l[?25h[?25l[?7lcontinue + conjugate  continue [?7h[?12l[?25h[?25l[?7lcontour_plot + continue  contour_plot [?7h[?12l[?25h[?25l[?7lverted + contour_plot  converted [?7h[?12l[?25h[?25l[?7lolution + converted  + convolution [?7h[?12l[?25h[?25l[?7lert_super_fct_into_AS + + convert_super_fct_into_AS convolution [?7h[?12l[?25h[?25l[?7l + + + +[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.dx[?7h[?12l[?25h[?25l[?7l2C2.dx[?7h[?12l[?25h[?25l[?7l.C2.dx[?7h[?12l[?25h[?25l[?7lyC2.dx[?7h[?12l[?25h[?25l[?7l*C2.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.dx[?7h[?12l[?25h[?25l[?7l2C2.dx[?7h[?12l[?25h[?25l[?7l.C2.dx[?7h[?12l[?25h[?25l[?7lxC2.dx[?7h[?12l[?25h[?25l[?7l^C2.dx[?7h[?12l[?25h[?25l[?7l2C2.dx[?7h[?12l[?25h[?25l[?7l*C2.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(C2.y*C2.x^2*C2.dx) +[?7h[?12l[?25h[?2004l[?7h(y*z0^2) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: + z^3 - z = x +x*z0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: C2 +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^12 + 2*x^10 + 2*x^9 + 2*x^6 + x^4 + 2*x^3 + 2*x over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfff = ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + C.one)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C.y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lorain xi.coordinates():[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lV[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lline_cohomology_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: B = C2.crystalline_cohomology_basis() +[?7h[?12l[?25h[?2004l^C--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() + 379 try: +--> 380 z = integer_ring.Z(value) + 381 except (TypeError, ValueError): + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_() + 286 cdef Map m +--> 287 cdef Element e = method(C) + 288 if e is None: + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:832, in sage.rings.fraction_field_element.FractionFieldElement._conversion() + 831 self.reduce() +--> 832 num = R(self.__numerator) + 833 inv_den = R(self.__denominator).inverse_of_unit() + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + +File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_() + 1691 for f in self.__list: +-> 1692 x = f._call_(x) + 1693 return x + +File /ext/sage/9.7/src/sage/categories/map.pyx:1677, in sage.categories.map.FormalCompositeMap._call_() + 1676 +-> 1677 cpdef Element _call_(self, x): + 1678 """ + +File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_() + 1691 for f in self.__list: +-> 1692 x = f._call_(x) + 1693 return x + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1620, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() + 1619 +-> 1620 cpdef Element _call_(self, _x): + 1621 """ + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:1652, in sage.rings.fraction_field_FpT.FpT_Fp_section._call_() + 1651 if nmod_poly_degree(x._denom) != 0: +-> 1652 raise ValueError("not integral") + 1653 if nmod_poly_degree(x._numer) > 0: + +ValueError: not integral + +During handling of the above exception, another exception occurred: + +KeyboardInterrupt Traceback (most recent call last) +Input In [16], in () +----> 1 B = C2.crystalline_cohomology_basis() + +File :356, in crystalline_cohomology_basis(self, prec) + +File :340, in de_rham_witt_lift(cech_class, prec) + +File :65, in __mul__(self, other) + +File :23, in __sub__(self, other) + +File :7, in __init__(self, C, g) + +File :259, in reduction_form(C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:638, in FractionField_generic._element_constructor_(self, x, y, coerce) + 636 ring_one = self.ring().one() + 637 try: +--> 638 return self._element_class(self, x, ring_one, coerce=coerce) + 639 except (TypeError, ValueError): + 640 pass + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:114, in sage.rings.fraction_field_element.FractionFieldElement.__init__() + 112 FieldElement.__init__(self, parent) + 113 if coerce: +--> 114 self.__numerator = parent.ring()(numerator) + 115 self.__denominator = parent.ring()(denominator) + 116 else: + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx:1009, in sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular._element_constructor_() + 1007 try: + 1008 # now try calling the base ring's __call__ methods +-> 1009 element = self.base_ring()(element) + 1010 _p = p_NSet(sa2si(element,_ring), _ring) + 1011 return new_MP(self,_p) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x) + 1143 """ + 1144 TESTS:: + 1145 + (...) + 1182  True + 1183 """ + 1184 try: +-> 1185 return integer_mod.IntegerMod(self, x) + 1186 except (NotImplementedError, PariError): + 1187 raise TypeError("error coercing to finite field") + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod() + 199 return a + 200 t = modulus.element_class() +--> 201 return t(parent, value) + 202 + 203 + +File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:388, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() + 386 value = py_scalar_to_element(value) + 387 if isinstance(value, Element) and value.parent().is_exact(): +--> 388 value = sage.rings.rational_field.QQ(value) + 389 z = value % self.__modulus.sageInteger + 390 else: + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() + 536 """ + 537 if x is not None: +--> 538 self.__set_value(x, base) + 539 + 540 def __reduce__(self): + +File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value() + 624 + 625 elif hasattr(x, "_rational_"): +--> 626 set_from_Rational(self, x._rational_()) + 627 + 628 elif isinstance(x, tuple) and len(x) == 2: + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:784, in sage.rings.fraction_field_element.FractionFieldElement._rational_() + 782 1/2 + 783 """ +--> 784 return self._conversion(QQ) + 785 + 786 def _conversion(self, R): + +File /ext/sage/9.7/src/sage/rings/fraction_field_element.pyx:832, in sage.rings.fraction_field_element.FractionFieldElement._conversion() + 830 else: + 831 self.reduce() +--> 832 num = R(self.__numerator) + 833 inv_den = R(self.__denominator).inverse_of_unit() + 834 return num * inv_den + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() + 536 """ + 537 if x is not None: +--> 538 self.__set_value(x, base) + 539 + 540 def __reduce__(self): + +File /ext/sage/9.7/src/sage/rings/rational.pyx:626, in sage.rings.rational.Rational.__set_value() + 624 + 625 elif hasattr(x, "_rational_"): +--> 626 set_from_Rational(self, x._rational_()) + 627 + 628 elif isinstance(x, tuple) and len(x) == 2: + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1446, in sage.rings.polynomial.polynomial_element.Polynomial._rational_() + 1444 TypeError: not a constant polynomial + 1445 """ +-> 1446 return self._scalar_conversion(sage.rings.rational.Rational) + 1447 + 1448 def _symbolic_(self, R): + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1391, in sage.rings.polynomial.polynomial_element.Polynomial._scalar_conversion() + 1389 if self.degree() > 0: + 1390 raise TypeError("cannot convert nonconstant polynomial") +-> 1391 return R(self.get_coeff_c(0)) + 1392 + 1393 _real_double_ = _scalar_conversion + +File /ext/sage/9.7/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() + 536 """ + 537 if x is not None: +--> 538 self.__set_value(x, base) + 539 + 540 def __reduce__(self): + +File /ext/sage/9.7/src/sage/rings/rational.pyx:691, in sage.rings.rational.Rational.__set_value() + 689 + 690 else: +--> 691 raise TypeError("unable to convert {!r} to a rational".format(x)) + 692 + 693 cdef void set_from_mpq(Rational self, mpq_t value): + +File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() + 192 except AttributeError: + 193 return super().__repr__() +--> 194 result = reprfunc() + 195 if isinstance(result, str): + 196 return result + +File /ext/sage/9.7/src/sage/rings/fraction_field_FpT.pyx:340, in sage.rings.fraction_field_FpT.FpTElement._repr_() + 338 return repr(self.numer()) + 339 else: +--> 340 numer_s = repr(self.numer()) + 341 denom_s = repr(self.denom()) + 342 if '-' in numer_s or '+' in numer_s: + +File /ext/sage/9.7/src/sage/structure/sage_object.pyx:194, in sage.structure.sage_object.SageObject.__repr__() + 192 except AttributeError: + 193 return super().__repr__() +--> 194 result = reprfunc() + 195 if isinstance(result, str): + 196 return result + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2690, in sage.rings.polynomial.polynomial_element.Polynomial._repr_() + 2688 NotImplementedError: object does not support renaming: x^3 + 2/3*x^2 - 5/3 + 2689 """ +-> 2690 return self._repr() + 2691 + 2692 def _latex_(self, name=None): + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2662, in sage.rings.polynomial.polynomial_element.Polynomial._repr() + 2660 x = "(%s)"%x + 2661 if n > 1: +-> 2662 var = "*%s^%s"%(name,n) + 2663 elif n==1: + 2664 var = "*%s"%name + +File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt() + +KeyboardInterrupt: +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C2.crystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B = C2.crystalline_cohomology_basis(prec = 100) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +IndexError Traceback (most recent call last) +Input In [17], in () +----> 1 B = C2.crystalline_cohomology_basis(prec = Integer(100)) + +File :356, in crystalline_cohomology_basis(self, prec) + +File :347, in de_rham_witt_lift(cech_class, prec) + +File :6, in decomposition_g0_g8(fct, prec) + +File :107, in coordinates(self, basis, basis_holo, prec) + +File :77, in serre_duality_pairing(self, fct, prec) + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__() + 542 return type(self)(self._parent, f, self.__n) + 543 +--> 544 return self.__u[i - self.__n] + 545 + 546 def __iter__(self): + +File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__() + 451 return self.base_ring().zero() + 452 else: +--> 453 raise IndexError("coefficient not known") + 454 return self.__f[n] + 455 + +IndexError: coefficient not known +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB = C2.crystalline_cohomology_basis(prec = 100)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: A = C2.de + C2.de_rham_basis C2.degrees_de_rham1  + C2.degrees_de_rham0 C2.degrees_holomorphic_differentials + + + [?7h[?12l[?25h[?25l[?7l_rham_basis + C2.de_rham_basis  + + [?7h[?12l[?25h[?25l[?7l + + +[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A = C2.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + [?7h[?12l[?25h[?25l[?7lA = C2.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: A +[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), + ((x/y) dx, 0, (x/y) dx), + ((x^2/y) dx, 0, (x^2/y) dx), + ((x^3/y) dx, 0, (x^3/y) dx), + ((x^4/y) dx, 0, (x^4/y) dx), + (((x^10 + x^8 - x^7 - x^4 - x^2 - x)/y) dx, 2/x*y, ((-1)/(x*y)) dx), + (((-x^9 + x^6 + x^3 + 1)/y) dx, 2/x^2*y, 0 dx), + (((-x^6 + 1)/y) dx, 2/x^3*y, (1/(x^3*y)) dx), + (((x^7 + x^5 - x^4 - x)/y) dx, 2/x^4*y, ((x^3 + x^2 - 1)/(x^4*y)) dx), + (((-x^6 + x^3 + 1)/y) dx, 2/x^5*y, ((-1)/(x^3*y)) dx)] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laA[2][?7h[?12l[?25h[?25l[?7l A[2][?7h[?12l[?25h[?25l[?7l=A[2][?7h[?12l[?25h[?25l[?7l A[2][?7h[?12l[?25h[?25l[?7ldA[2][?7h[?12l[?25h[?25l[?7lA[2][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7l_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lade_rham_wit_lift(A[2])[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(A[2])[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift(A[2])[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(A[2])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: a = de_rham_witt_lift(A[2]) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lsage: a +[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(C2.y*C2.x^2*C2.dx)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lrt_super_fct_into_AS(C2.y*C2.x^2*C2.dx)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7la)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(a) +[?7h[?12l[?25h[?2004l[?7h((y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), + ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, + (x^15*y*z0^2 + x^15*y*z0 + x^14*y*z0^2 - x^15*y - x^13*y*z0^2 - x^13*y*z0 + x^12*y*z0^2 + x^13*y + x^11*y*z0^2 + x^12*y + x^11*y*z0 + x^10*y*z0^2 + x^10*y*z0 - x^9*y*z0^2 + x^10*y - x^9*y*z0 - x^9*y - x^8*y*z0 + x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^6*y + x^4*y - x^2*y*z0^2 + x^3*y + x^2*y*z0 - x*y*z0^2 - x*y - y*z0)/(x^7*z0 - x^6*z0^2 + x^6*z0 - x^5*z0^2 + x^6 + x^5*z0 - x^4*z0^2 + x^5 - x^4*z0 + x^3*z0^2 + x^4 + x^3*z0 - x^2*z0^2 - x^3 + x^2 + x*z0 - z0^2 + 1)), + (0, (-x*y*z0 - y)/(x*z0^2 + x + z0)), + (y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), + ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, + (x^17*y*z0 + x^16*y*z0^2 + x^17*y - x^15*y*z0 - x^14*y*z0^2 - x^13*y*z0^2 + x^13*y*z0 - x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^12*y - x^11*y*z0 + x^10*y*z0^2 + x^11*y - x^9*y*z0^2 - x^9*y*z0 + x^9*y + x^8*y*z0 - x^7*y*z0^2 + x^8*y - x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^5*y*z0^2 + x^5*y*z0 + x^4*y*z0^2 - x^4*y*z0 - x^3*y*z0^2 - x^4*y + x^2*y*z0^2 + x^3*y - x^2*y*z0 + y*z0^2 + y)/(x^9 + x^8*z0 + x^8 + x^7*z0 + x^7 + x^6*z0 - x^6 - x^5*z0 + x^5 + x^4*z0 + x^3 + x^2*z0))) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a +[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.omega0[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lduce[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.reduce() +[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.reduce()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.r() +[?7h[?12l[?25h[?2004l[?7h((x^2/y) dx, 0, (x^2/y) dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: + z^3 - z = x +x*z0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.r()[?7h[?12l[?25h[?25l[?7leduce()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lsage: a = de_rham_witt_lift(A[2]) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [27], in () +----> 1 a = de_rham_witt_lift(A[Integer(2)]) + +File :341, in de_rham_witt_lift(cech_class, prec) + +File :5, in regular_form(omega) + +AttributeError: 'NoneType' object has no attribute 'curve' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.r()[?7h[?12l[?25h[?25l[?7leduce()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l = C2.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: A = C2.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C2.de_rham_basis()[?7h[?12l[?25h[?25l[?7lade_rham_witt_lft(A[2])[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lsage: a = de_rham_witt_lift(A[2]) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(a) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [30], in () +----> 1 de_rham_witt_lift(a) + +File :339, in de_rham_witt_lift(cech_class, prec) + +File :10, in regular_form(omega) + +AttributeError: 'superelliptic_drw_form' object has no attribute 'form' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lsage: a +[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lrt_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(a) +[?7h[?12l[?25h[?2004l[?7h((y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), + ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, + (x^15*y*z0^2 + x^15*y*z0 + x^14*y*z0^2 - x^15*y - x^13*y*z0^2 - x^13*y*z0 + x^12*y*z0^2 + x^13*y + x^11*y*z0^2 + x^12*y + x^11*y*z0 + x^10*y*z0^2 + x^10*y*z0 - x^9*y*z0^2 + x^10*y - x^9*y*z0 - x^9*y - x^8*y*z0 + x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^6*y + x^4*y - x^2*y*z0^2 + x^3*y + x^2*y*z0 - x*y*z0^2 - x*y - y*z0)/(x^7*z0 - x^6*z0^2 + x^6*z0 - x^5*z0^2 + x^6 + x^5*z0 - x^4*z0^2 + x^5 - x^4*z0 + x^3*z0^2 + x^4 + x^3*z0 - x^2*z0^2 - x^3 + x^2 + x*z0 - z0^2 + 1)), + (0, (-x*y*z0 - y)/(x*z0^2 + x + z0)), + (y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), + ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, + (x^17*y*z0 + x^16*y*z0^2 + x^17*y - x^15*y*z0 - x^14*y*z0^2 - x^13*y*z0^2 + x^13*y*z0 - x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^12*y - x^11*y*z0 + x^10*y*z0^2 + x^11*y - x^9*y*z0^2 - x^9*y*z0 + x^9*y + x^8*y*z0 - x^7*y*z0^2 + x^8*y - x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^5*y*z0^2 + x^5*y*z0 + x^4*y*z0^2 - x^4*y*z0 - x^3*y*z0^2 - x^4*y + x^2*y*z0^2 + x^3*y - x^2*y*z0 + y*z0^2 + y)/(x^9 + x^8*z0 + x^8 + x^7*z0 + x^7 + x^6*z0 - x^6 - x^5*z0 + x^5 + x^4*z0 + x^3 + x^2*z0))) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.r()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.r() +[?7h[?12l[?25h[?2004l[?7h((x^2/y) dx, 0, (x^2/y) dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.r()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega0[?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[?7lh[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: a.omega0.h1 +[?7h[?12l[?25h[?2004l[?7h(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0.h1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?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[?7l0[?7h[?12l[?25h[?25l[?7lsage: a.omega0.h1 == a.r().omega0 +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [35], in () +----> 1 a.omega0.h1 == a.r().omega0 + +File :18, in __eq__(self, other) + +AttributeError: 'superelliptic_form' object has no attribute 'function' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0.h1 == a.r().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[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7lform[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsa.omega0.form[?7h[?12l[?25h[?25l[?7lua.omega0.form[?7h[?12l[?25h[?25l[?7lpa.omega0.form[?7h[?12l[?25h[?25l[?7lea.omega0.form[?7h[?12l[?25h[?25l[?7lra.omega0.form[?7h[?12l[?25h[?25l[?7lea.omega0.form[?7h[?12l[?25h[?25l[?7lla.omega0.form[?7h[?12l[?25h[?25l[?7lla.omega0.form[?7h[?12l[?25h[?25l[?7lia.omega0.form[?7h[?12l[?25h[?25l[?7lta.omega0.form[?7h[?12l[?25h[?25l[?7lpa.omega0.form[?7h[?12l[?25h[?25l[?7la.omega0.form[?7h[?12l[?25h[?25l[?7la.omega0.form[?7h[?12l[?25h[?25l[?7lpa.omega0.form[?7h[?12l[?25h[?25l[?7lta.omega0.form[?7h[?12l[?25h[?25l[?7lia.omega0.form[?7h[?12l[?25h[?25l[?7lca.omega0.form[?7h[?12l[?25h[?25l[?7l_a.omega0.form[?7h[?12l[?25h[?25l[?7lfa.omega0.form[?7h[?12l[?25h[?25l[?7lua.omega0.form[?7h[?12l[?25h[?25l[?7lna.omega0.form[?7h[?12l[?25h[?25l[?7lca.omega0.form[?7h[?12l[?25h[?25l[?7lta.omega0.form[?7h[?12l[?25h[?25l[?7lia.omega0.form[?7h[?12l[?25h[?25l[?7loa.omega0.form[?7h[?12l[?25h[?25l[?7lna.omega0.form[?7h[?12l[?25h[?25l[?7l(a.omega0.form[?7h[?12l[?25h[?25l[?7lCa.omega0.form[?7h[?12l[?25h[?25l[?7l2a.omega0.form[?7h[?12l[?25h[?25l[?7l,a.omega0.form[?7h[?12l[?25h[?25l[?7l a.omega0.form[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: superelliptic_function(C2, a.omega0.form) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [36], in () +----> 1 superelliptic_function(C2, a.omega0.form) + +AttributeError: 'superelliptic_drw_form' object has no attribute 'form' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C2, a.omega0.form)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lfor)[?7h[?12l[?25h[?25l[?7lfo)[?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: superelliptic_function(C2, a.omega0.h1) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce) + 705 try: +--> 706 x, y = resolve_fractions(x0, y0) + 707 except (AttributeError, TypeError): + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_..resolve_fractions(x, y) + 682 def resolve_fractions(x, y): +--> 683 xn = x.numerator() + 684 xd = x.denominator() + +AttributeError: 'superelliptic_function' object has no attribute 'numerator' + +During handling of the above exception, another exception occurred: + +TypeError Traceback (most recent call last) +Input In [37], in () +----> 1 superelliptic_function(C2, a.omega0.h1) + +File :14, in __init__(self, C, g) + +File :216, in reduction(C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 159 print(type(C), C) + 160 print(type(C._element_constructor), C._element_constructor) +--> 161 raise + 162 + 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce) + 706 x, y = resolve_fractions(x0, y0) + 707 except (AttributeError, TypeError): +--> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( + 709 x0, y0, self)) + 710 try: + 711 return self._element_class(self, x, y, coerce=coerce) + +TypeError: cannot convert (x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C2, a.omega0.h1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: superelliptic_function(C2, a.omega0.h1.function) +[?7h[?12l[?25h[?2004l[?7h(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: C2.polynomial +[?7h[?12l[?25h[?2004l[?7hx^12 + 2*x^10 + 2*x^9 + 2*x^6 + x^4 + 2*x^3 + 2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 with the equation: + z^3 - z = x +x*z0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC2.polynomial[?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C2, a.omega0.h1.function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lform)[?7h[?12l[?25h[?25l[?7la.omega0.h1 == a.r().omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lAC2.de_rham_bass()[?7h[?12l[?25h[?25l[?7lade_rham_witt_lft(A[2])[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.r()[?7h[?12l[?25h[?25l[?7leduce()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l = C2.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: A = C2.de_rham_basis() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C2.de_rham_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC2.polynomial[?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C2, a.omega0.h1.function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lform)[?7h[?12l[?25h[?25l[?7la.omega0.h1 == a.r().omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(a)[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lsage: a = de_rham_witt_lift(A[2]) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lAC2.de_rham_bass()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC2.polynomial[?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C2, a.omega0.h1.function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lform)[?7h[?12l[?25h[?25l[?7la.omega0.h1 == a.r().omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr()[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(a) +[?7h[?12l[?25h[?2004l[?7h((y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), + ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, + (x^15*y*z0^2 + x^15*y*z0 + x^14*y*z0^2 - x^15*y - x^13*y*z0^2 - x^13*y*z0 + x^12*y*z0^2 + x^13*y + x^11*y*z0^2 + x^12*y + x^11*y*z0 + x^10*y*z0^2 + x^10*y*z0 - x^9*y*z0^2 + x^10*y - x^9*y*z0 - x^9*y - x^8*y*z0 + x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^6*y + x^4*y - x^2*y*z0^2 + x^3*y + x^2*y*z0 - x*y*z0^2 - x*y - y*z0)/(x^7*z0 - x^6*z0^2 + x^6*z0 - x^5*z0^2 + x^6 + x^5*z0 - x^4*z0^2 + x^5 - x^4*z0 + x^3*z0^2 + x^4 + x^3*z0 - x^2*z0^2 - x^3 + x^2 + x*z0 - z0^2 + 1)), + (0, (-x*y*z0 - y)/(x*z0^2 + x + z0)), + (y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), + ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, + (x^17*y*z0 + x^16*y*z0^2 + x^17*y - x^15*y*z0 - x^14*y*z0^2 - x^13*y*z0^2 + x^13*y*z0 - x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^12*y - x^11*y*z0 + x^10*y*z0^2 + x^11*y - x^9*y*z0^2 - x^9*y*z0 + x^9*y + x^8*y*z0 - x^7*y*z0^2 + x^8*y - x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^5*y*z0^2 + x^5*y*z0 + x^4*y*z0^2 - x^4*y*z0 - x^3*y*z0^2 - x^4*y + x^2*y*z0^2 + x^3*y - x^2*y*z0 + y*z0^2 + y)/(x^9 + x^8*z0 + x^8 + x^7*z0 + x^7 + x^6*z0 - x^6 - x^5*z0 + x^5 + x^4*z0 + x^3 + x^2*z0))) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = de_rham_witt_lift(A[2])[?7h[?12l[?25h[?25l[?7lsage: a +[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.omega0.h1 == a.r().omega0[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: a.omega0 +[?7h[?12l[?25h[?2004l[?7h[(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7l.h1 == a.r().omega0[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: a.omega0.h1 +[?7h[?12l[?25h[?2004l[?7h(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0.h1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lra.omega0[?7h[?12l[?25h[?25l[?7lea.omega0[?7h[?12l[?25h[?25l[?7lda.omega0[?7h[?12l[?25h[?25l[?7lua.omega0[?7h[?12l[?25h[?25l[?7lca.omega0[?7h[?12l[?25h[?25l[?7lea.omega0[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lra.omega0[?7h[?12l[?25h[?25l[?7lea.omega0[?7h[?12l[?25h[?25l[?7lda.omega0[?7h[?12l[?25h[?25l[?7lua.omega0[?7h[?12l[?25h[?25l[?7lca.omega0[?7h[?12l[?25h[?25l[?7lta.omega0[?7h[?12l[?25h[?25l[?7lia.omega0[?7h[?12l[?25h[?25l[?7loa.omega0[?7h[?12l[?25h[?25l[?7lna.omega0[?7h[?12l[?25h[?25l[?7lCa.omega0[?7h[?12l[?25h[?25l[?7l2a.omega0[?7h[?12l[?25h[?25l[?7l,a.omega0[?7h[?12l[?25h[?25l[?7l 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[?7l[?7h[?12l[?25h[?25l[?7l(C2, 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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lya.omega0.h1)[?7h[?12l[?25h[?25l[?7l^a.omega0.h1)[?7h[?12l[?25h[?25l[?7l2a.omega0.h1)[?7h[?12l[?25h[?25l[?7l*a.omega0.h1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: reduction(C2, y^2*a.omega0.h1)/y^2 +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [47], in () +----> 1 reduction(C2, y**Integer(2)*a.omega0.h1)/y**Integer(2) + +NameError: name 'y' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7ly. = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l<[?7h[?12l[?25h[?25l[?7l>[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?7lP[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,> = Poi[?7h[?12l[?25h[?25l[?7l > = Poi[?7h[?12l[?25h[?25l[?7ly> = Poi[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7llRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7lsage: Rxy. = PolynomialRing(GF(3), 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxy. = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7lreduction(C2, y^2*a.omega0.h1)/y^2[?7h[?12l[?25h[?25l[?7lsage: reduction(C2, y^2*a.omega0.h1)/y^2 +[?7h[?12l[?25h[?2004l[?7hx^2/y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lvert_super_fct_into_AS(a)[?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(a) +[?7h[?12l[?25h[?2004l[?7h((y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), + ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, + (x^15*y*z0^2 + x^15*y*z0 + x^14*y*z0^2 - x^15*y - x^13*y*z0^2 - x^13*y*z0 + x^12*y*z0^2 + x^13*y + x^11*y*z0^2 + x^12*y + x^11*y*z0 + x^10*y*z0^2 + x^10*y*z0 - x^9*y*z0^2 + x^10*y - x^9*y*z0 - x^9*y - x^8*y*z0 + x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^6*y + x^4*y - x^2*y*z0^2 + x^3*y + x^2*y*z0 - x*y*z0^2 - x*y - y*z0)/(x^7*z0 - x^6*z0^2 + x^6*z0 - x^5*z0^2 + x^6 + x^5*z0 - x^4*z0^2 + x^5 - x^4*z0 + x^3*z0^2 + x^4 + x^3*z0 - x^2*z0^2 - x^3 + x^2 + x*z0 - z0^2 + 1)), + (0, (-x*y*z0 - y)/(x*z0^2 + x + z0)), + (y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), + ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, + (x^17*y*z0 + x^16*y*z0^2 + x^17*y - x^15*y*z0 - x^14*y*z0^2 - x^13*y*z0^2 + x^13*y*z0 - x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^12*y - x^11*y*z0 + x^10*y*z0^2 + x^11*y - x^9*y*z0^2 - x^9*y*z0 + x^9*y + x^8*y*z0 - x^7*y*z0^2 + x^8*y - x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^5*y*z0^2 + x^5*y*z0 + x^4*y*z0^2 - x^4*y*z0 - x^3*y*z0^2 - x^4*y + x^2*y*z0^2 + x^3*y - x^2*y*z0 + y*z0^2 + y)/(x^9 + x^8*z0 + x^8 + x^7*z0 + x^7 + x^6*z0 - x^6 - x^5*z0 + x^5 + x^4*z0 + x^3 + x^2*z0))) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[?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[?7lsage: convert_super_fct_into_AS(a).omega0 +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [51], in () +----> 1 convert_super_fct_into_AS(a).omega0 + +AttributeError: 'tuple' object has no attribute 'omega0' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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.omega0.h1[?7h[?12l[?25h[?25l[?7lsage: a +[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: a[1] +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [53], in () +----> 1 a[Integer(1)] + +TypeError: 'superelliptic_drw_cech' object is not subscriptable +[?2004h[?25l[?7lsage: [?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[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(a)[1] +[?7h[?12l[?25h[?2004l[?7h(0, (-x*y*z0 - y)/(x*z0^2 + x + z0)) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(a)[0] +[?7h[?12l[?25h[?2004l[?7h(y*z0/(x^3*z0^2 - x^2*z0^2 - x^3 + x^2 + z0^2 - 1), + ((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx, + (x^15*y*z0^2 + x^15*y*z0 + x^14*y*z0^2 - x^15*y - x^13*y*z0^2 - x^13*y*z0 + x^12*y*z0^2 + x^13*y + x^11*y*z0^2 + x^12*y + x^11*y*z0 + x^10*y*z0^2 + x^10*y*z0 - x^9*y*z0^2 + x^10*y - x^9*y*z0 - x^9*y - x^8*y*z0 + x^7*y*z0 - x^6*y*z0^2 - x^6*y*z0 - x^6*y + x^4*y - x^2*y*z0^2 + x^3*y + x^2*y*z0 - x*y*z0^2 - x*y - y*z0)/(x^7*z0 - x^6*z0^2 + x^6*z0 - x^5*z0^2 + x^6 + x^5*z0 - x^4*z0^2 + x^5 - x^4*z0 + x^3*z0^2 + x^4 + x^3*z0 - x^2*z0^2 - x^3 + x^2 + x*z0 - z0^2 + 1)) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[0][?7h[?12l[?25h[?25l[?7l[][[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: convert_super_fct_into_AS(a)[0][1] +[?7h[?12l[?25h[?2004l[?7h((-x^20*y + x^18*y*z0^2 - x^19*y - x^18*y - x^16*y*z0 - x^15*y*z0^2 - x^15*y*z0 + x^13*y*z0^2 + x^13*y*z0 + x^12*y*z0^2 - x^12*y*z0 + x^11*y*z0^2 - x^11*y*z0 - x^11*y + x^10*y*z0 - x^9*y*z0^2 - x^10*y - x^9*y*z0 - x^8*y*z0^2 - x^8*y*z0 - x^7*y*z0^2 + x^8*y + x^7*y*z0 - x^6*y*z0^2 - x^7*y - x^6*y*z0 + x^5*y*z0^2 + x^5*y - x^4*y*z0 + x^3*y*z0^2 + x^3*y*z0 + x^2*y*z0^2 + x^3*y - x*y*z0^2 - x^2*y - x*y*z0 - y*z0^2 + x*y - y*z0 + y)/(x^11*z0 - x^10*z0^2 + x^10 - x^8*z0 + x^7*z0^2 - x^7 + x^2*z0 - x*z0^2 + x)) * dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3*a.omega0 - mult_by_p(C.x*C.y.diffn())[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 3*a +[?7h[?12l[?25h[?2004l[?7h(V((x^7/(x^11*y - x^9*y - x^8*y - x^5*y + x^3*y - x^2*y - y)) dx), [0], V((x^7/(x^11*y - x^9*y - x^8*y - x^5*y + x^3*y - x^2*y - y)) dx)) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)*C.dx).jth_component(0)[?7h[?12l[?25h[?25l[?7l3*a).reduce()[?7h[?12l[?25h[?25l[?7l3.[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*a).reduce()[?7h[?12l[?25h[?25l[?7la[?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[?7l0[?7h[?12l[?25h[?25l[?7lsage: (3*a).omega0 +[?7h[?12l[?25h[?2004l[?7hV((x^7/(x^11*y - x^9*y - x^8*y - x^5*y + x^3*y - x^2*y - y)) dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*a).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: (3*a).omega0.omega +[?7h[?12l[?25h[?2004l[?7h(x^7/(x^11*y - x^9*y - x^8*y - x^5*y + x^3*y - x^2*y - y)) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*a).omega0.omega[?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[?7l2[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (3*a).omega0.omega.reduce2() +[?7h[?12l[?25h[?2004l[?7h(x^7/(x^11*y - x^9*y - x^8*y - x^5*y + x^3*y - x^2*y - y)) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*a).omega0.omega.reduce2()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.polynomial[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: C2.polynomial +[?7h[?12l[?25h[?2004l[?7hx^12 + 2*x^10 + 2*x^9 + 2*x^6 + x^4 + 2*x^3 + 2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[1][?7h[?12l[?25h[?25l[?7lsage: a +[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a +[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.omega0.h1[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmega0.h1[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lga0.h1[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lsage: a.omega0 +[?7h[?12l[?25h[?2004l[?7h[(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0[?7h[?12l[?25h[?25l[?7l.h1[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: a.omega0.frobenius +[?7h[?12l[?25h[?2004l[?7h +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0.frobenius[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.omega0.frobenius() +[?7h[?12l[?25h[?2004l[?7h((x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7)/(x^9*y - x^6*y - x^4*y - x^3*y - x^2*y + y)) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(3*a).omega0.omega.reduce2()[?7h[?12l[?25h[?25l[?7lx^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lsage: (x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7).quo_rem(x^9*y - x^6*y - x^4*y - x^3*y - x^2*y + y +....: [?7h[?12l[?25h[?25l[?7l( +)[?7h[?12l[?25h[?25l[?7lsage: (x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7).quo_rem(x^9*y - x^6*y - x^4*y - x^3*y - x^2*y + y +....: ) +[?7h[?12l[?25h[?2004l[?7h(0, + x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7).quo_rem(x^9*y - x^6*y - x^4*y - x^3*y - x^2*y + y +....: )[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l( +)[?7h[?12l[?25h[?25l[?7l ( +)[?7h[?12l[?25h[?25l[?7l) +[?7h[?12l[?25h[?25l[?7l 1 +)[?7h[?12l[?25h[?25l[?7l( +)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l + 1 ) +[?7h[?12l[?25h[?25l[?7l + 1)  + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - x^2 + 1)[?7h[?12l[?25h[?25l[?7l - x^2 + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - x^3 - x^2 + 1)[?7h[?12l[?25h[?25l[?7l - x^3 - x^2 + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - x^4 - x^3 - x^2 + 1)[?7h[?12l[?25h[?25l[?7l - x^4 - x^3 - x^2 + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l - x^6 - x^4 - x^3 - x^2 + 1)[?7h[?12l[?25h[?25l[?7l - x^6 - x^4 - x^3 - x^2 + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7).quo_rem(x^9 - x^6 - x^4 - x^3 - x^2 + 1) +[?7h[?12l[?25h[?2004l[?7h(x^36 - x^34 - x^33 - x^32 - x^30 - x^29 - x^28 - x^27 + x^26 - x^25 - x^24 - x^22 - x^18 + x^17 - x^15 + x^14 + x^13 + x^12 - x^11 - x^10 + x^7 - x^6 + x^2 + x, + -x^7 - x^6 - x^5 - x^4 + x^3 - x^2 - x) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7).quo_rem(x^9 - x^6 - x^4 - x^3 - x^2 + 1)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7).quo_rem(C2.polynomial) +[?7h[?12l[?25h[?2004l[?7h(x^33 - x^30 - x^29 - x^28 + x^27 + x^26 + x^23 - x^22 - x^20 - x^19 - x^18 - x^17 - x^16 + x^15 + x^13 - x^12 - x^11 - x^8 - x^7 - x^6 - x^5 + x^3 + x, + -x^11 + x^10 + x^8 + x^7 - x^5 - x^4 + x^2) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7).quo_rem(C2.polynomial)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^3 + x^32 + x^30 + x^28 + x^26 + x^2 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^1 - x^7).quo_rem(C2.polynomial)[?7h[?12l[?25h[?25l[?7l*(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^3 + x^32 + x^30 + x^28 + x^26 + x^2 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^1 - x^7).quo_rem(C2.polynomial)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x*(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^3 + x^32 + x^30 + x^28 + x^26 + x^2 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^1 - x^7).quo_rem(C2.polynomial)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).quo_rem(C2.polynomial)[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (x*(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7)).quo_rem(C2.polynomial) +[?7h[?12l[?25h[?2004l[?7h(x^34 - x^31 - x^30 - x^29 + x^28 + x^27 + x^24 - x^23 - x^21 - x^20 - x^19 - x^18 - x^17 + x^16 + x^14 - x^13 - x^12 - x^9 - x^8 - x^7 - x^6 + x^4 + x^2 - 1, + x^11 - x^10 + x^8 + x^6 - x^5 + x^4 - x) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.polynomial[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lsage: C2.polynomial +[?7h[?12l[?25h[?2004l[?7hx^12 + 2*x^10 + 2*x^9 + 2*x^6 + x^4 + 2*x^3 + 2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.polynomial[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x*(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7)).quo_rem(C2.polynomial)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^*(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^3 + x^32 + x^30 + x^28 + x^26 + x^2 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^1 - x^7).quo_rem(C2.polynomial)[?7h[?12l[?25h[?25l[?7l2*(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^3 + x^32 + x^30 + x^28 + x^26 + x^2 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^1 - x^7).quo_rem(C2.polynomial)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (x^2*(x^45 - x^43 + x^42 - x^41 - x^39 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^30 + x^28 + x^26 + x^22 - x^21 + x^20 + x^19 + x^18 + x^17 - x^16 - x^14 - x^13 - x^11 - x^7)).quo_rem(C2.polynomial) +[?7h[?12l[?25h[?2004l[?7h(x^35 - x^32 - x^31 - x^30 + x^29 + x^28 + x^25 - x^24 - x^22 - x^21 - x^20 - x^19 - x^18 + x^17 + x^15 - x^14 - x^13 - x^10 - x^9 - x^8 - x^7 + x^5 + x^3 - x + 1, + -x^11 + x^10 - x^9 + x^7 + x^5 - x^4 + x^3 - x^2 + x) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.omega0.frobenius()[?7h[?12l[?25h[?25l[?7lsage: a +[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.omega0.frobenius()[?7h[?12l[?25h[?25l[?7lfrobenius()[?7h[?12l[?25h[?25l[?7lsage: a.f +[?7h[?12l[?25h[?2004l[?7hV(((2*x^4 + x^2 + 2)/x^5)*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lconvert_super_fct_into_AS(a)[0][1][?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lvert_super_fct_into_AS(a)[0][1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lf)[?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: convert_super_fct_into_AS(a.f) +[?7h[?12l[?25h[?2004l[?7h(0, (-x*y*z0 - y)/(x*z0^2 + x + z0)) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC2.polynomial[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: C1 +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^4 + 2*x^3 + x over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.polynomial[?7h[?12l[?25h[?25l[?7lcrystalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lalline_cohomology_basis()[?7h[?12l[?25h[?25l[?7llline_cohomology_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C2.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: A +[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), + ((x/y) dx, 0, (x/y) dx), + ((x^2/y) dx, 0, (x^2/y) dx), + ((x^3/y) dx, 0, (x^3/y) dx), + ((x^4/y) dx, 0, (x^4/y) dx), + (((x^10 + x^8 - x^7 - x^4 - x^2 - x)/y) dx, 2/x*y, ((-1)/(x*y)) dx), + (((-x^9 + x^6 + x^3 + 1)/y) dx, 2/x^2*y, 0 dx), + (((-x^6 + 1)/y) dx, 2/x^3*y, (1/(x^3*y)) dx), + (((x^7 + x^5 - x^4 - x)/y) dx, 2/x^4*y, ((x^3 + x^2 - 1)/(x^4*y)) dx), + (((-x^6 + x^3 + 1)/y) dx, 2/x^5*y, ((-1)/(x^3*y)) dx)] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.polynomial[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: C1.de + C1.de_rham_basis C1.degrees_de_rham1  + C1.degrees_de_rham0 C1.degrees_holomorphic_differentials + + + [?7h[?12l[?25h[?25l[?7l_rham_basis + C1.de_rham_basis  + + [?7h[?12l[?25h[?25l[?7l + + +[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.de_rham_basis() +[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), (((-x^2 - x)/y) dx, 2/x*y, (1/(x*y)) dx)] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lC1.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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7leC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l_C1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lrC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lhC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7laC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lmC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l_C1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lwC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7liC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7ltC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7ltC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l_C1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7llC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7liC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7lfC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7ltC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l)C1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l(C1.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: de_rham_witt_lift(C1.de_rham_basis()[0]) +[?7h[?12l[?25h[?2004l[?7h([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lde_rham_witt_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCde_rham_wit_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l1de_rham_wit_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7lde_rham_wit_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7lrde_rham_wit_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7lwde_rham_wit_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l=de_rham_wit_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l de_rham_wit_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C1drw = de_rham_witt_lift(C1.de_rham_basis()[0]) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1drw = de_rham_witt_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lw[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldrw.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: C1drw.f +[?7h[?12l[?25h[?2004l[?7h[0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1drw.f[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7lpolynoial[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lk[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C1.p_rank() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [82], in () +----> 1 C1.p_rank() + +File :176, in p_rank(self) + +File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.py:1889, in HyperellipticCurve_finite_field.p_rank(self) + 1855 r""" + 1856 INPUT: + 1857 + (...) + 1880  0 + 1881 """ + 1882 #We use caching here since Hasse Witt is needed to compute p_rank. So if the Hasse Witt + 1883 #is already computed it is stored in list A. If it was not cached (i.e. A is empty), we simply + 1884 #compute it. If it is cached then we need to make sure that we have the correct one. So check + (...) + 1887 # However, it seems a waste of time to manually analyse the cache + 1888 # -- See Trac Ticket #11115 +-> 1889 N, E = self._Hasse_Witt_cached() + 1890 if E != self: + 1891 self._Hasse_Witt_cached.clear_cache() + +File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__() + 2297 if self.cache is None: + 2298 f = self.f +-> 2299 self.cache = f(self._instance) + 2300 return self.cache + 2301 + +File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.py:1727, in HyperellipticCurve_finite_field._Hasse_Witt_cached(self) + 1647 r""" + 1648 This is where Hasse_Witt is actually computed. + 1649 + (...) + 1712  0 + 1713 """ + 1714 # If Cartier Matrix is already cached for this curve, use that or evaluate it to get M, + 1715 #Coeffs, genus, Fq=base field of self, p=char(Fq). This is so we have one less matrix to + 1716 #compute. + (...) + 1725 #that don't accept arguments. Anyway, the easiest is to call + 1726 #the cached method and simply see whether the data belong to self. +-> 1727 M, Coeffs, g, Fq, p, E = self._Cartier_matrix_cached() + 1728 if E != self: + 1729 self._Cartier_matrix_cached.clear_cache() + +File /ext/sage/9.7/src/sage/misc/cachefunc.pyx:2299, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__() + 2297 if self.cache is None: + 2298 f = self.f +-> 2299 self.cache = f(self._instance) + 2300 return self.cache + 2301 + +File /ext/sage/9.7/src/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.py:1523, in HyperellipticCurve_finite_field._Cartier_matrix_cached(self) + 1521 #this implementation is for odd degree only, even degree will be handled later. + 1522 if d%2 == 0: +-> 1523 raise ValueError("In this implementation the degree of f must be odd") + 1524 #Compute resultant to make sure no repeated roots + 1525 df=f.derivative() + +ValueError: In this implementation the degree of f must be odd +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.p_rank()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.p_rank()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1drw.f[?7h[?12l[?25h[?25l[?7l = de_rham_witt_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7lde_ham_witt_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7lC1dw = de_rham_witt_lift(C1.de_rham_basis()[0])[?7h[?12l[?25h[?25l[?7l([][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lw.f[?7h[?12l[?25h[?25l[?7lsage: C1drw +[?7h[?12l[?25h[?2004l[?7h([(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y]), [0], [(1/(x^4 + 2*x^3 + x))*y] d[x] + V(((-x^15 + x^14 - x^13 - x^12 - x^11 + x^10 + x^9 - x^8 - x^7 - x^5 + x^4 + x + 1)/(x^6*y + x^5*y + x^4*y - x^3*y + x^2*y + y)) dx) + dV([((2*x^12 + x^11 + x^10 + 2*x^9 + x^4 + 2*x^3)/(x^6 + x^5 + x^4 + 2*x^3 + x^2 + 1))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.f[?7h[?12l[?25h[?25l[?7lsage: a +[?7h[?12l[?25h[?2004l[?7h([(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^47 + x^46 + 2*x^45 + x^44 + x^42 + x^40 + x^39 + x^38 + 2*x^37 + 2*x^34 + x^33 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^21 + 2*x^19 + 2*x^18 + 2*x^17 + 2*x^16 + x^15 + x^14 + x^13 + x^11 + 2*x^10 + x^9)/(x^22 + x^20 + x^19 + x^18 + 2*x^17 + 2*x^16 + x^14 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 1))*y]), V(((2*x^4 + x^2 + 2)/x^5)*y), [(x/(x^11 + 2*x^9 + 2*x^8 + 2*x^5 + x^3 + 2*x^2 + 2))*y] d[x] + V(((-x^60 - x^58 - x^57 + x^55 - x^54 - x^49 - x^46 - x^43 - x^42 + x^41 - x^40 + x^39 - x^37 - x^36 + x^33 - x^32 + x^30 + x^28 - x^26 - x^24 - x^21 + x^20 - x^19 - x^18 - x^17 + x^16 - x^14 + x^13 - x^12 - x^10 + x^9 - x^7 - x^5 + x^4 + x^3 - x^2 + x + 1)/(x^22*y + x^20*y + x^19*y + x^18*y - x^17*y - x^16*y + x^14*y + x^12*y + x^11*y - x^9*y - x^7*y + x^6*y + x^4*y + x^3*y - x^2*y + y)) dx) + dV([((x^52 + x^51 + 2*x^50 + x^49 + x^47 + x^45 + x^44 + x^43 + 2*x^42 + 2*x^39 + x^38 + 2*x^31 + 2*x^30 + 2*x^29 + 2*x^28 + 2*x^26 + 2*x^24 + x^18 + 2*x^17 + x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^6 + 2*x^5 + x^3 + x^2 + 1)/(x^27 + x^25 + x^24 + x^23 + 2*x^22 + 2*x^21 + x^19 + x^17 + x^16 + 2*x^14 + 2*x^12 + x^11 + x^9 + x^8 + 2*x^7 + x^5))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.f[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: a.f +[?7h[?12l[?25h[?2004l[?7hV(((2*x^4 + x^2 + 2)/x^5)*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [1], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :6, in  + +NameError: name 'C' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lIncrease precision. +Increase precision. +--------------------------------------------------------------------------- +IndexError Traceback (most recent call last) +Input In [2], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :7, in  + +File :389, in de_rham_basis(self, threshold) + +File :342, in cohomology_of_structure_sheaf_basis(self, threshold) + +File :342, in (.0) + +File :109, in serre_duality_pairing(self, fct) + +File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds) + 583 return expression.sum(*args, **kwds) + 584 elif max(len(args),len(kwds)) <= 1: +--> 585 return sum(expression, *args, **kwds) + 586 else: + 587 from sage.symbolic.ring import SR + +File :109, in (.0) + +File :102, in residue(self, place) + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:618, in sage.rings.laurent_series_ring_element.LaurentSeries.residue() + 616 Integer Ring + 617 """ +--> 618 return self[-1] + 619 + 620 def exponents(self): + +File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__() + 542 return type(self)(self._parent, f, self.__n) + 543 +--> 544 return self.__u[i - self.__n] + 545 + 546 def __iter__(self): + +File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__() + 451 return self.base_ring().zero() + 452 else: +--> 453 raise IndexError("coefficient not known") + 454 return self.__f[n] + 455 + +IndexError: coefficient not known +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^3*z0 + x*z1) * dx, z0*z1/x ), ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^3 +z1^2 - z1 = x^5 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.z[0]/AS.x[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[1]/AS.x)/expansion_at_infty() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [5], in () +----> 1 (AS.z[Integer(1)]/AS.x)/expansion_at_infty() + +NameError: name 'expansion_at_infty' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x)/expansion_at_infty()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()expansion_at_infty()[?7h[?12l[?25h[?25l[?7l().expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[1]/AS.x).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-6 + t^-3 + t^-2 + t + t^2 + t^3 + t^4 + t^6 + t^7 + t^8 + t^9 + t^12 + t^13 + t^14 + t^15 + t^16 + t^17 + t^19 + t^21 + t^22 + t^24 + t^26 + t^27 + t^28 + t^29 + t^30 + t^35 + t^36 + t^41 + t^43 + t^44 + t^47 + t^49 + t^50 + t^51 + t^55 + t^57 + t^58 + t^59 + t^63 + t^64 + t^65 + t^66 + t^67 + t^70 + t^73 + t^76 + t^77 + t^79 + t^83 + t^86 + t^88 + t^89 + t^91 + O(t^94) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l^).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[1]/AS.x^2).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-2 + t + t^2 + t^4 + t^5 + t^8 + t^9 + t^12 + t^13 + t^14 + t^16 + t^17 + t^19 + t^20 + t^22 + t^24 + t^25 + t^26 + t^27 + t^29 + t^30 + t^32 + t^33 + t^36 + t^38 + t^40 + t^41 + t^45 + t^47 + t^54 + t^56 + t^57 + t^58 + t^61 + t^65 + t^68 + t^70 + t^75 + t^76 + t^77 + t^81 + t^82 + t^86 + t^89 + t^91 + t^94 + t^96 + t^97 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[1]/AS.x^3).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^2 + t^5 + t^6 + t^9 + t^10 + t^11 + t^12 + t^15 + t^16 + t^20 + t^21 + t^25 + t^26 + t^27 + t^28 + t^29 + t^30 + t^31 + t^32 + t^34 + t^37 + t^39 + t^41 + t^43 + t^44 + t^46 + t^47 + t^49 + t^50 + t^53 + t^54 + t^56 + t^58 + t^59 + t^61 + t^63 + t^64 + t^67 + t^72 + t^75 + t^76 + t^78 + t^79 + t^80 + t^82 + t^83 + t^87 + t^88 + t^89 + t^93 + t^94 + t^99 + t^100 + t^101 + O(t^102) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^3 +z1^2 - z1 = x^5 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]/AS.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l0]/AS.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]/AS.x).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^-2 + t^2 + t^5 + t^8 + t^9 + t^10 + t^16 + t^17 + t^19 + t^20 + t^22 + t^24 + t^29 + t^30 + t^33 + t^36 + t^37 + t^38 + t^41 + t^43 + t^44 + t^45 + t^46 + t^47 + t^51 + t^52 + t^53 + t^57 + t^58 + t^60 + t^61 + t^64 + t^65 + t^67 + t^72 + t^75 + t^79 + t^89 + t^90 + t^92 + t^94 + t^95 + t^96 + t^97 + O(t^98) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]/AS.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l(AS.x).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l^).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]/(AS.x)^2).expansion_at_infty() +[?7h[?12l[?25h[?2004l[?7ht^2 + t^6 + t^8 + t^9 + t^10 + t^12 + t^13 + t^16 + t^17 + t^18 + t^22 + t^24 + t^25 + t^26 + t^27 + t^29 + t^32 + t^38 + t^40 + t^41 + t^43 + t^44 + t^45 + t^52 + t^54 + t^58 + t^60 + t^62 + t^66 + t^69 + t^70 + t^73 + t^77 + t^80 + t^81 + t^83 + t^84 + t^86 + t^90 + t^91 + t^92 + t^94 + t^96 + t^101 + O(t^102) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.z[0]/AS.x[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() +[?7h[?12l[?25h[?2004l[?7h5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^3 +z1^2 - z1 = x^5 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lonent_of_different_prim()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim() +[?7h[?12l[?25h[?2004l[?7h13 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x^3*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^2*z0) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^4) * dx, 0 ), ( (x^7) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^7*z0 + x*z1) * dx, z0*z1/x ), ( (x^6) * dx, z1/x^2 ), ( (x^6*z0 + z1) * dx, z0*z1/x^2 ), ( (x^5) * dx, z1/x^3 ), ( (x^5*z0) * dx, z0*z1/x^3 ), ( (x^4*z0) * dx, z0*z1/x^4 ), ( (x^3*z0) * dx, z0*z1/x^5 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^3*z0 + x*z1) * dx, z0*z1/x ), ( (x^2*z0 + z1) * dx, z0*z1/x^2 ), ( (x*z0) * dx, z0*z1/x^3 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (x^5*z0 + z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^2*z0) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^3*z0) * dx, 0 ), ( (x^4) * dx, 0 ), ( (x^4*z0) * dx, 0 ), ( (x^5) * dx, 0 ), ( (x^6) * dx, 0 ), ( (x^11) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^11*z0 + x*z1) * dx, z0*z1/x ), ( (x^10) * dx, z1/x^2 ), ( (x^10*z0 + z1) * dx, z0*z1/x^2 ), ( (x^9) * dx, z1/x^3 ), ( (x^9*z0) * dx, z0*z1/x^3 ), ( (x^8) * dx, z1/x^4 ), ( (x^8*z0) * dx, z0*z1/x^4 ), ( (x^7) * dx, z1/x^5 ), ( (x^7*z0) * dx, z0*z1/x^5 ), ( (x^6*z0) * dx, z0*z1/x^6 ), ( (x^5*z0) * dx, z0*z1/x^7 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^2*z0 + x*z1) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^5) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^5*z0 + x^4 + x^3*z1) * dx, z0*z1/x ), ( (x^4) * dx, z1/x^2 ), ( (x^2) * dx, z0/x^2 ), ( (x^4*z0 + x^2*z1) * dx, z0*z1/x^2 ), ( (x^3*z0 + x^2*z0) * dx, z0*z1/x^3 ), ( (x^2*z0 + z1) * dx, z0*z1/x^4 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^5 +z1^2 - z1 = x^7 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^5*z0 + x*z1) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^2*z0) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^3*z0) * dx, 0 ), ( (x^4) * dx, 0 ), ( (x^4*z0) * dx, 0 ), ( (x^5) * dx, 0 ), ( (x^6) * dx, 0 ), ( (x^11) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^11*z0 + x^7 + x^3*z1) * dx, z0*z1/x ), ( (x^10) * dx, z1/x^2 ), ( (x^2) * dx, z0/x^2 ), ( (x^10*z0 + x^2*z1) * dx, z0*z1/x^2 ), ( (x^9) * dx, z1/x^3 ), ( (x^9*z0 + x^5*z0) * dx, z0*z1/x^3 ), ( (x^8) * dx, z1/x^4 ), ( (x^8*z0 + z1) * dx, z0*z1/x^4 ), ( (x^7) * dx, z1/x^5 ), ( (x^7*z0) * dx, z0*z1/x^5 ), ( (x^6*z0) * dx, z0*z1/x^6 ), ( (x^5*z0) * dx, z0*z1/x^7 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7le_ring[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS. + AS.a_number AS.cartier_matrix AS.dx AS.fct_field AS.height  + AS.at_most_poles AS.characteristic AS.dx_series AS.functions AS.holomorphic_differentials_basis  + AS.at_most_poles_forms AS.cohomology_of_structure_sheaf_basis AS.exponent_of_different AS.genus AS.ith_ramification_gp > + AS.base_ring AS.de_rham_basis AS.exponent_of_different_prim AS.group AS.jumps  + [?7h[?12l[?25h[?25l[?7la_number + AS.a_number  + + + + [?7h[?12l[?25h[?25l[?7lcartier_matrix + AS.a_number  AS.cartier_matrix [?7h[?12l[?25h[?25l[?7ldx + AS.cartier_matrix  AS.dx [?7h[?12l[?25h[?25l[?7lcartier_matrix + AS.cartier_matrix  AS.dx [?7h[?12l[?25h[?25l[?7lharacteristc + AS.cartier_matrix  + AS.characteristic [?7h[?12l[?25h[?25l[?7lohomology_of_structure_sheaf_basis + + AS.characteristic  + AS.cohomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7l + + + + +[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.cohomology_of_structure_sheaf_basis() +[?7h[?12l[?25h[?2004l[?7h[z1/x, + z0/x, + z0*z1/x, + z1/x^2, + z0/x^2, + z0*z1/x^2, + z1/x^3, + z0*z1/x^3, + z1/x^4, + z0*z1/x^4, + z1/x^5, + z0*z1/x^5, + z0*z1/x^6, + z0*z1/x^7] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^5 +z1^2 - z1 = x^13 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[( (1) * dx, 0 ), ( (z1) * dx, 0 ), ( (z0) * dx, 0 ), ( (x) * dx, 0 ), ( (x^6*z0 + x*z1) * dx, 0 ), ( (x*z0) * dx, 0 ), ( (x^2) * dx, 0 ), ( (x^2*z0) * dx, 0 ), ( (x^3) * dx, 0 ), ( (x^3*z0) * dx, 0 ), ( (x^4) * dx, 0 ), ( (x^4*z0) * dx, 0 ), ( (x^5) * dx, 0 ), ( (x^5*z0) * dx, 0 ), ( (x^6) * dx, 0 ), ( (x^7) * dx, 0 ), ( (x^13) * dx, z1/x ), ( (0) * dx, z0/x ), ( (x^13*z0 + x^8 + x^3*z1) * dx, z0*z1/x ), ( (x^12) * dx, z1/x^2 ), ( (x^2) * dx, z0/x^2 ), ( (x^12*z0 + x^2*z1) * dx, z0*z1/x^2 ), ( (x^11) * dx, z1/x^3 ), ( (x^11*z0 + x^6*z0) * dx, z0*z1/x^3 ), ( (x^10) * dx, z1/x^4 ), ( (x^10*z0 + z1) * dx, z0*z1/x^4 ), ( (x^9) * dx, z1/x^5 ), ( (x^9*z0) * dx, z0*z1/x^5 ), ( (x^8) * dx, z1/x^6 ), ( (x^8*z0) * dx, z0*z1/x^6 ), ( (x^7*z0) * dx, z0*z1/x^7 ), ( (x^6*z0) * dx, z0*z1/x^8 )] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.cohomology_of_structure_sheaf_basis() +[?7h[?12l[?25h[?2004l[?7h[z1/x, + z0/x, + z0*z1/x, + z1/x^2, + z0/x^2, + z0*z1/x^2, + z1/x^3, + z0*z1/x^3, + z1/x^4, + z0*z1/x^4, + z1/x^5, + z0*z1/x^5, + z1/x^6, + z0*z1/x^6, + z0*z1/x^7, + z0*z1/x^8] +[?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[?2004lI haven't found all forms. +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [25], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :7, in  + +File :316, in cohomology_of_structure_sheaf_basis(self, threshold) + +File :145, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?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[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lI haven't found all forms. +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [26], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :7, in  + +File :316, in cohomology_of_structure_sheaf_basis(self, threshold) + +File :145, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lI haven't found all forms. +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [27], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :7, in  + +File :316, in cohomology_of_structure_sheaf_basis(self, threshold) + +File :145, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^7 +z1^2 - z1 = x^11 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0*z1/x^2, z1/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^3 +z1^2 - z1 = x^11 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^3 +z1^2 - z1 = x^11 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0*z1/x^2, z1/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z1/x^5, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^3 +z1^2 - z1 = x^13 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/2 in QQ[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: 13 -1 + 1 +[?7h[?12l[?25h[?2004l[?7h13 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.cohomology_of_structure_sheaf_basis()[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lnu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() +[?7h[?12l[?25h[?2004l[?7h13 +[?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[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z1/x^5, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() +[?7h[?12l[?25h[?2004l[?7h14 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7l13 -1 + 1[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.genus()[?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[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^7 +z1^2 - z1 = x^11 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lnus()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() +[?7h[?12l[?25h[?2004l[?7h13 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7, z0*z1/x^8] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^7 +z1^2 - z1 = x^13 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() +[?7h[?12l[?25h[?2004l[?7h15 +[?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[?2004lI haven't found all forms. +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [45], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :7, in  + +File :316, in cohomology_of_structure_sheaf_basis(self, threshold) + +File :145, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() +[?7h[?12l[?25h[?2004l[?7h17 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lI haven't found all forms. +--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [47], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :7, in  + +File :316, in cohomology_of_structure_sheaf_basis(self, threshold) + +File :145, in holomorphic_differentials_basis(self, threshold) + +NameError: name 'holomorphic_differentials_basis' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z0/x^4, z0*z1/x^4, z0/x^5, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7, z0*z1/x^8, z0*z1/x^9] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z1/x^5, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7, z0*z1/x^8] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus() +[?7h[?12l[?25h[?2004l[?7h15 +[?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[?2004l\[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6] +[?2004h[?25l[?7lsage: [?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[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0*z1/x, z0*z1/x^2] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in z2 of size 2^2 with the equations: +z0^2 - z0 = x^3 +z1^2 - z1 = z2*x^3 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lquo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() +[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ s + age +┌────────────────────────────────────────────────────────────────────┐ +│ 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]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0*z1/x, z0*z1/x^2] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0*z1/x^2, z0*z1/x^3] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0*z1/x^2, z1/x^3, z0*z1/x^3, z0*z1/x^4, z0*z1/x^5] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z1/x^5, z0*z1/x^5, z1/x^6, z0*z1/x^6, z0*z1/x^7, z0*z1/x^8, z0*z1/x^9] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z0/x^3, z0*z1/x^3, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] +False +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] +z0/x^4 False +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] +z1/x^4 False +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[z1/x, z0/x, z0*z1/x, z1/x^2, z0/x^2, z0*z1/x^2, z1/x^3, z0/x^3, z0*z1/x^3, z1/x^4, z0*z1/x^4, z0*z1/x^5, z0*z1/x^6, z0*z1/x^7] +z1/x^4 False +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].coordinates(basis = b)[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lti[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: bbb[0].function +[?7h[?12l[?25h[?2004l[?7hz1/x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].function[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: bbb[0].function.exponents() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [7], in () +----> 1 bbb[Integer(0)].function.exponents() + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.fraction_field_element.FractionFieldElement' object has no attribute 'exponents' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].function.exponents()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldb[0].function.exponents()[?7h[?12l[?25h[?25l[?7leb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lnb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lob[0].function.exponents()[?7h[?12l[?25h[?25l[?7lmb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lib[0].function.exponents()[?7h[?12l[?25h[?25l[?7lnb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lab[0].function.exponents()[?7h[?12l[?25h[?25l[?7ltb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lob[0].function.exponents()[?7h[?12l[?25h[?25l[?7lrb[0].function.exponents()[?7h[?12l[?25h[?25l[?7l(b[0].function.exponents()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lbbb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lbbb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lb[0].function.exponents()[?7h[?12l[?25h[?25l[?7lb[0].function.exponents()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldexponents()[?7h[?12l[?25h[?25l[?7lexponents()[?7h[?12l[?25h[?25l[?7lnexponents()[?7h[?12l[?25h[?25l[?7loexponents()[?7h[?12l[?25h[?25l[?7lmexponents()[?7h[?12l[?25h[?25l[?7liexponents()[?7h[?12l[?25h[?25l[?7lnexponents()[?7h[?12l[?25h[?25l[?7laexponents()[?7h[?12l[?25h[?25l[?7ltexponents()[?7h[?12l[?25h[?25l[?7loexponents()[?7h[?12l[?25h[?25l[?7lrexponents()[?7h[?12l[?25h[?25l[?7l(exponents()[?7h[?12l[?25h[?25l[?7l()exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l exponents()[?7h[?12l[?25h[?25l[?7lsage: bbb[0].function.denominator(). exponents() +[?7h[?12l[?25h[?2004l[?7h[(1, 0, 0, 0)] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].function.denominator(). exponents()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lexponents()[?7h[?12l[?25h[?25l[?7l[?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: bbb[0].function.denominator().exponents() +[?7h[?12l[?25h[?2004l[?7h[(1, 0, 0, 0)] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].function.denominator().exponents()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7l().exponents()[?7h[?12l[?25h[?25l[?7ln().exponents()[?7h[?12l[?25h[?25l[?7lu().exponents()[?7h[?12l[?25h[?25l[?7lm().exponents()[?7h[?12l[?25h[?25l[?7le().exponents()[?7h[?12l[?25h[?25l[?7lr().exponents()[?7h[?12l[?25h[?25l[?7la().exponents()[?7h[?12l[?25h[?25l[?7lt().exponents()[?7h[?12l[?25h[?25l[?7lo().exponents()[?7h[?12l[?25h[?25l[?7lr().exponents()[?7h[?12l[?25h[?25l[?7lsage: bbb[0].function.numerator().exponents() +[?7h[?12l[?25h[?2004l[?7h[(0, 0, 0, 1)] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].function.numerator().exponents()[?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[?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 [11] in  + 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 :28 in  + + 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 :14 + if a.function.numerator().exponents()[_sage_const_3 :] = (_sage_const_1 , _sage_const_1 ): + ^ +SyntaxError: cannot assign to subscript here. Maybe you meant '==' instead of '='? + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l;[?7h[?12l[?25h[?25l[?7lp[?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[?7lsage: lo +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [12], in () +----> 1 lo + +NameError: name 'lo' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[] +[] +[] +[] +[] +[] +[] +[] +[] +[] +[] +[] +[] +[] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[(0, 0, 0, 1)] +[(0, 0, 1, 0)] +[(0, 0, 1, 1)] +[(0, 0, 0, 1)] +[(0, 0, 1, 0)] +[(0, 0, 1, 1)] +[(0, 0, 0, 1)] +[(0, 0, 1, 0)] +[(0, 0, 1, 1)] +[(0, 0, 0, 1)] +[(0, 0, 1, 1)] +[(0, 0, 1, 1)] +[(0, 0, 1, 1)] +[(0, 0, 1, 1)] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [18], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :14, in  + +TypeError: Argument 'other' has incorrect type (expected sage.rings.polynomial.polydict.ETuple, got list) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [19], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :14, in  + +TypeError: Argument 'other' has incorrect type (expected sage.rings.polynomial.polydict.ETuple, got tuple) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [20], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :14, in  + +TypeError: Argument 'other' has incorrect type (expected sage.rings.polynomial.polydict.ETuple, got 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[?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 [21] in  + 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 :28 in  + + 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 :14 + print(a.function.numerator().exponents())[_sage_const_0 ][_sage_const_2 :]) + ^ +SyntaxError: unmatched ')' + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l(0, 1) +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [22], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :15, in  + +TypeError: Argument 'other' has incorrect type (expected sage.rings.polynomial.polydict.ETuple, got tuple) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [23], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :14, in  + +TypeError: Argument 'other' has incorrect type (expected sage.rings.polynomial.polydict.ETuple, got tuple) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [24], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :14, in  + +TypeError: Argument 'other' has incorrect type (expected sage.rings.polynomial.polydict.ETuple, got 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[?2004lz1/x (0, 0, 0, 1) +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [25], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :15, in  + +TypeError: Argument 'other' has incorrect type (expected sage.rings.polynomial.polydict.ETuple, got tuple) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lz1/x [0, 0, 0, 1] +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [26], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :15, in  + +TypeError: Argument 'other' has incorrect type (expected sage.rings.polynomial.polydict.ETuple, got 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[?2004l--------------------------------------------------------------------------- +IndexError Traceback (most recent call last) +Input In [27], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :20, in  + +IndexError: list index out of range +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +IndexError Traceback (most recent call last) +Input In [28], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :20, in  + +IndexError: list index out of range +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[0, 1] +[1, 0] +[1, 1] +z0*z1/x +[0, 1] +[1, 0] +[1, 1] +z0*z1/x^2 +[0, 1] +[1, 0] +[1, 1] +z0*z1/x^3 +[0, 1] +[1, 1] +z0*z1/x^4 +[1, 1] +z0*z1/x^5 +[1, 1] +z0*z1/x^6 +[1, 1] +z0*z1/x^7 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [30], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :27, in  + +TypeError: 'int' object is not iterable +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: z0z1 +[?7h[?12l[?25h[?2004l[?7h[] +[?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[?2004l[0, 0, 0, 1] [1, 0, 0, 0] +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [32], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +TypeError: 'int' object is not iterable +[?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[?2004l7 3 4 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lM, m 11 9 +7 3 4 +4 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lM, m 11 5 +6 4 2 +2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lM, m 11 5 +6 4 2 +8 ? 2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lM, m 11 3 +6 4 1 +8 ? 1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lM, m 11 1 +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Input In [38], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :28, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :30, in  + +ValueError: max() arg is an empty sequence +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lz0z1[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lM, m 11 1 +5 5 0 +8 ? 0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lM, m 11 1 +5 5 0 +8 ? 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[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7ldrafty/draft5.sage')[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l(afty/draft5.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l.sage')[?7h[?12l[?25h[?25l[?7l2.sage')[?7h[?12l[?25h[?25l[?7lg.sage')[?7h[?12l[?25h[?25l[?7lp.sage')[?7h[?12l[?25h[?25l[?7lc.sage')[?7h[?12l[?25h[?25l[?7lo.sage')[?7h[?12l[?25h[?25l[?7lv.sage')[?7h[?12l[?25h[?25l[?7le.sage')[?7h[?12l[?25h[?25l[?7lr.sage')[?7h[?12l[?25h[?25l[?7ls.sage')[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: load('drafty/2gpcovers.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [2], in () +----> 1 load('drafty/2gpcovers.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :7, in  + +File :36, in __init__(self, C, list_of_fcts, prec) + +File :135, in expansion_at_infty(self, place, prec) + +TypeError: unsupported operand type(s) for ** or pow(): 'NoneType' and 'int' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/2gpcovers.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [3], in () +----> 1 load('drafty/2gpcovers.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :7, in  + +File :36, in __init__(self, C, list_of_fcts, prec) + +File :135, in expansion_at_infty(self, place, prec) + +TypeError: unsupported operand type(s) for ** or pow(): 'NoneType' and 'int' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1drw[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^3 = x^3 + 1 over Finite Field of size 2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.polynomial[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth() +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations: +z0^2 - z0 = x^11 +z1^2 - z1 = x + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/2gpcovers.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [7], in () +----> 1 load('drafty/2gpcovers.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :7, in  + +File :36, in __init__(self, C, list_of_fcts, prec) + +File :135, in expansion_at_infty(self, place, prec) + +TypeError: unsupported operand type(s) for ** or pow(): 'NoneType' and 'int' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l.[?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.function[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9C.x)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x)^2[?7h[?12l[?25h[?25l[?7l(C.x)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (C.x)^2 +[?7h[?12l[?25h[?2004l[?7hx^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/2gpcovers.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [9], in () +----> 1 load('drafty/2gpcovers.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :7, in  + +File :36, in __init__(self, C, list_of_fcts, prec) + +File :135, in expansion_at_infty(self, place, prec) + +TypeError: unsupported operand type(s) for ** or pow(): 'NoneType' and 'int' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/2gpcovers.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [10], in () +----> 1 load('drafty/2gpcovers.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :7, in  + +File :36, in __init__(self, C, list_of_fcts, prec) + +File :135, in expansion_at_infty(self, place, prec) + +TypeError: unsupported operand type(s) for ** or pow(): 'NoneType' and 'int' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lsage: load('drafty/2gpcovers.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^3 = x^3 + 1 over Finite Field in a of size 2^2 with the equation: + z^2 - z = x^3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: AS.a + AS.a_number  + AS.at_most_poles  + AS.at_most_poles_forms + + [?7h[?12l[?25h[?25l[?7l_number + AS.a_number  + + + [?7h[?12l[?25h[?25l[?7l + + + +[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.a_number() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [13], in () +----> 1 AS.a_number() + +File :313, in a_number(self) + +File :154, in cartier_matrix(self, prec) + +File :140, in holomorphic_differentials_basis(self, threshold) + +File :140, in (.0) + +TypeError: as_form.expansion_at_infty() got an unexpected keyword argument 'place' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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('drafty/2gpcovers.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7linit.sage')[?7h[?12l[?25h[?25l[?7l(nit.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.a_number()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7la_number()[?7h[?12l[?25h[?25l[?7lsage: AS.a_number() +[?7h[?12l[?25h[?2004l[?7h3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.a_number()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.a_number()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: ASP1. + ASP1.a_number ASP1.cartier_matrix ASP1.dx  + ASP1.at_most_poles ASP1.characteristic ASP1.dx_series  + ASP1.at_most_poles_forms ASP1.cohomology_of_structure_sheaf_basis ASP1.exponent_of_different > + ASP1.base_ring ASP1.de_rham_basis ASP1.exponent_of_different_prim  + [?7h[?12l[?25h[?25l[?7la + + + +[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: ASP1.a_number() +[?7h[?12l[?25h[?2004l[?7h3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + [?7h[?12l[?25h[?25l[?7lASP1.a_number()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS +[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^3 = x^5 + 1 over Finite Field in a of size 2^2 with the equation: + z^2 - z = x^3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.a_number()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_number()[?7h[?12l[?25h[?25l[?7lsage: AS.a_number() +[?7h[?12l[?25h[?2004l[?7h4 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x^3 + x over Finite Field in a of size 2^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth() +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x^3 + x over Finite Field in a of size 2^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth() +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l1 1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l1 1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.a_number()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lnb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lsage: AS.nb_of_pts_at_infty +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lof_pts_at_infty[?7h[?12l[?25h[?25l[?7lsage: AS3.nb_of_pts_at_infty +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: fff = ((C.x^17 - C.x^16 + C.x^15 + C.x^14 + C.x^13 + C.x^12 - C.x^10 + C.x^7 + C.x^6 - C.x^5 - C.x^4 + C.x^2 - C.x + C.one)/(C.x^8*C.y + C.x^7*C.y + C.x^6*C . +....: y - C.x^5*C.y + C.x^4*C.y + C.x^2*C.y))*C.dx[?7h[?12l[?25h[?25l[?7lsage: f +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [31], in () +----> 1 f + +NameError: name 'f' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l = x^5 - x^4 + 2*x[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3+2*x-1[?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[?7lx[?7h[?12l[?25h[?25l[?7lsage: f = x^3 - x +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = x^3 - x[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.derivative()(1) +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.derivative()(1)[?7h[?12l[?25h[?25l[?7l = x^3 - x[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f = (x+1)/(x-1) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = (x+1)/(x-1)[?7h[?12l[?25h[?25l[?7l.derivative()(1)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?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: f.poles() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [35], in () +----> 1 f.poles() + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.fraction_field_element.FractionFieldElement_1poly_field' object has no attribute 'poles' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.poles()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lderivative()(1)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.denominator().roots() +[?7h[?12l[?25h[?2004l[?7h[] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.denominator().roots()[?7h[?12l[?25h[?25l[?7lsage: f +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lTraceback (most recent call last): + + File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code + exec(code_obj, self.user_global_ns, self.user_ns) + + Input In [38] in  + 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 :29 in  + + 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 :12 + def expansion(fct, (x0, y0)): + ^ +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[?2004l1 1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRxy. = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l. = PolynmialRng(GF(3))[?7h[?12l[?25h[?25l[?7l = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7lsage: Rx. = PolynomialRing(GF(3)) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l = superelliptic(x, 1)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x, 1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^, 2)[?7h[?12l[?25h[?25l[?7l3, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l+, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + 1, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_smooth[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth() +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + x, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + x, 2)[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + x over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lRx. = PoynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l5))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: Rx. = PolynomialRing(GF(5)) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(GF(5))[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + 1, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l1 1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lexcept:[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: expan + expand  + expansion + + + [?7h[?12l[?25h[?25l[?7l + +[?7h[?12l[?25h[?25l[?7l[?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 = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(GF(5))[?7h[?12l[?25h[?25l[?7lx. = PolynomialRing(GF(5))[?7h[?12l[?25h[?25l[?7lsage: Rx. = PolynomialRing(GF(5)) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + [?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + 1, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_smooth[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth +[?7h[?12l[?25h[?2004l[?7h +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lC.is_smooth[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth() +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)^2[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^(-1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?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((C.x)^(-1))[?7h[?12l[?25h[?25l[?7lp((C.x)^(-1))[?7h[?12l[?25h[?25l[?7la((C.x)^(-1))[?7h[?12l[?25h[?25l[?7ln((C.x)^(-1))[?7h[?12l[?25h[?25l[?7l((C.x)^(-1))[?7h[?12l[?25h[?25l[?7l((C.x)^(-1))[?7h[?12l[?25h[?25l[?7l((C.x)^(-1))[?7h[?12l[?25h[?25l[?7lx((C.x)^(-1))[?7h[?12l[?25h[?25l[?7lp((C.x)^(-1))[?7h[?12l[?25h[?25l[?7la((C.x)^(-1))[?7h[?12l[?25h[?25l[?7ln((C.x)^(-1))[?7h[?12l[?25h[?25l[?7ls((C.x)^(-1))[?7h[?12l[?25h[?25l[?7li((C.x)^(-1))[?7h[?12l[?25h[?25l[?7lo((C.x)^(-1))[?7h[?12l[?25h[?25l[?7ln((C.x)^(-1))[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: expansion((C.x)^(-1), 0, 1) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +UnboundLocalError Traceback (most recent call last) +Input In [6], in () +----> 1 expansion((C.x)**(-Integer(1)), Integer(0), Integer(1)) + +File :22, in expansion(fct, x0, y0) + +UnboundLocalError: local variable 't' referenced before assignment +[?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[?2004l1 1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lexpansion((C.x)^(-1), 0, 1)[?7h[?12l[?25h[?25l[?7lC.is_moth()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lRx. = PoynomialRing(GF(5))[?7h[?12l[?25h[?25l[?7lsage: Rx. = PolynomialRing(GF(5)) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lRx. = PolynomialRing(GF(5))[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lexpansion((C.x)^(-1), 0, 1)[?7h[?12l[?25h[?25l[?7lC.is_moth()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + 1, 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lRx. = PoynomialRing(GF(5))[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lexpansion((C.x)^(-1), 0, 1)[?7h[?12l[?25h[?25l[?7lsage: expansion((C.x)^(-1), 0, 1) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [10], in () +----> 1 expansion((C.x)**(-Integer(1)), Integer(0), Integer(1)) + +File :23, in expansion(fct, x0, y0, prec) + +NameError: name 'y' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l1 1 +[?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[?2004l1 1 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [12], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :29, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File :25, in expansion(fct, x0, y0, prec) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:428, in sage.rings.polynomial.polynomial_element.Polynomial.subs() + 426 g = self._parent.gen() + 427 if g in x[0]: +--> 428 return self(x[0][g]) + 429 elif len(x[0]) > 0: + 430 raise TypeError("keys do not match self's parent") + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:870, in sage.rings.polynomial.polynomial_element.Polynomial.__call__() + 868 # This can save lots of coercions when the common parent is the + 869 # polynomial's base ring (e.g., for evaluations at integers). +--> 870 cst, aa = coercion_model.canonical_coercion(cst, a) + 871 # Use fast multiplication actions like matrix × scalar. + 872 # If there is no action, replace a by an element of the + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1393, in sage.structure.coerce.CoercionModel.canonical_coercion() + 1391 self._record_exception() + 1392 +-> 1393 raise TypeError("no common canonical parent for objects with parents: '%s' and '%s'"%(xp, yp)) + 1394 + 1395 + +TypeError: no common canonical parent for objects with parents: 'Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5' and 'Laurent Series Ring in t over Finite Field of size 5' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l1 1 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [13], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :29, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :32, in  + +File :25, in expansion(fct, x0, y0, prec) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:428, in sage.rings.polynomial.polynomial_element.Polynomial.subs() + 426 g = self._parent.gen() + 427 if g in x[0]: +--> 428 return self(x[0][g]) + 429 elif len(x[0]) > 0: + 430 raise TypeError("keys do not match self's parent") + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:870, in sage.rings.polynomial.polynomial_element.Polynomial.__call__() + 868 # This can save lots of coercions when the common parent is the + 869 # polynomial's base ring (e.g., for evaluations at integers). +--> 870 cst, aa = coercion_model.canonical_coercion(cst, a) + 871 # Use fast multiplication actions like matrix × scalar. + 872 # If there is no action, replace a by an element of the + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1393, in sage.structure.coerce.CoercionModel.canonical_coercion() + 1391 self._record_exception() + 1392 +-> 1393 raise TypeError("no common canonical parent for objects with parents: '%s' and '%s'"%(xp, yp)) + 1394 + 1395 + +TypeError: no common canonical parent for objects with parents: 'Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5' and 'Laurent Series Ring in t over Finite Field of size 5' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l1 1 +t^-1 +[?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[?2004l1 1 +3*t^-3 + 2 + 2*t^3 + 4*t^6 + 3*t^12 + 4*t^15 + 4*t^18 + 3*t^21 + 4*t^27 + 2*t^30 + 2*t^33 + 4*t^36 + O(t^47) +[?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[?2004l1 1 +1 + 4*t + 2*t^2 + 3*t^3 + 4*t^4 + t^5 + 3*t^6 + 2*t^7 + t^8 + 4*t^9 + O(t^10) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l'1 1 +1 + 4*t^2 + 2*t^3 + 2*t^4 + t^5 + 3*t^7 + 2*t^8 + 4*t^9 + t^10 + t^12 + 4*t^14 + 2*t^15 + 2*t^16 + t^17 + 3*t^19 + 2*t^20 + 4*t^21 + t^22 + t^24 + 4*t^26 + 2*t^27 + 2*t^28 + t^29 + 3*t^31 + 2*t^32 + 4*t^33 + t^34 + t^36 + 4*t^38 + 2*t^39 + 2*t^40 + t^41 + 3*t^43 + 2*t^44 + 4*t^45 + t^46 + t^48 + O(t^50) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?2004l1 1 +t^2 + 4*t^4 + 4*t^6 + 4*t^8 + 4*t^10 + 4*t^12 + 4*t^14 + 4*t^16 + 4*t^18 + 4*t^20 + 4*t^22 + 4*t^24 + 4*t^26 + 4*t^28 + 4*t^30 + 4*t^32 + 4*t^34 + 4*t^36 + 4*t^38 + 4*t^40 + 4*t^42 + 4*t^44 + 4*t^46 + 4*t^48 + 4*t^50 + 4*t^52 + 4*t^54 + 4*t^56 + 4*t^58 + 4*t^60 + 4*t^62 + 4*t^64 + 4*t^66 + 4*t^68 + 4*t^70 + 4*t^72 + 4*t^74 + 4*t^76 + 4*t^78 + 4*t^80 + 4*t^82 + 4*t^84 + 4*t^86 + 4*t^88 + 4*t^90 + 4*t^92 + 4*t^94 + 4*t^96 + 4*t^98 + 4*t^100 +[?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[?2004l1 1 +x_series t + 4*t^2 + 4*t^3 + 4*t^4 + 4*t^5 + 4*t^6 + 4*t^7 + 4*t^8 + 4*t^9 + 4*t^10 + 4*t^11 + 4*t^12 + 4*t^13 + 4*t^14 + 4*t^15 + 4*t^16 + 4*t^17 + 4*t^18 + 4*t^19 + 4*t^20 + 4*t^21 + 4*t^22 + 4*t^23 + 4*t^24 + 4*t^25 + 4*t^26 + 4*t^27 + 4*t^28 + 4*t^29 + 4*t^30 + 4*t^31 + 4*t^32 + 4*t^33 + 4*t^34 + 4*t^35 + 4*t^36 + 4*t^37 + 4*t^38 + 4*t^39 + 4*t^40 + 4*t^41 + 4*t^42 + 4*t^43 + 4*t^44 + 4*t^45 + 4*t^46 + 4*t^47 + 4*t^48 + 4*t^49 + 4*t^50 +t^2 + 4*t^4 + 4*t^6 + 4*t^8 + 4*t^10 + 4*t^12 + 4*t^14 + 4*t^16 + 4*t^18 + 4*t^20 + 4*t^22 + 4*t^24 + 4*t^26 + 4*t^28 + 4*t^30 + 4*t^32 + 4*t^34 + 4*t^36 + 4*t^38 + 4*t^40 + 4*t^42 + 4*t^44 + 4*t^46 + 4*t^48 + 4*t^50 + 4*t^52 + 4*t^54 + 4*t^56 + 4*t^58 + 4*t^60 + 4*t^62 + 4*t^64 + 4*t^66 + 4*t^68 + 4*t^70 + 4*t^72 + 4*t^74 + 4*t^76 + 4*t^78 + 4*t^80 + 4*t^82 + 4*t^84 + 4*t^86 + 4*t^88 + 4*t^90 + 4*t^92 + 4*t^94 + 4*t^96 + 4*t^98 + 4*t^100 +[?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[?2004l1 1 +x_series t + t^2 + t^3 + t^4 + t^5 + t^6 + t^7 + t^8 + t^9 + t^10 + t^11 + t^12 + t^13 + t^14 + t^15 + t^16 + t^17 + t^18 + t^19 + t^20 + t^21 + t^22 + t^23 + t^24 + t^25 + t^26 + t^27 + t^28 + t^29 + t^30 + t^31 + t^32 + t^33 + t^34 + t^35 + t^36 + t^37 + t^38 + t^39 + t^40 + t^41 + t^42 + t^43 + t^44 + t^45 + t^46 + t^47 + t^48 + t^49 + t^50 +4*t^50 + 3*t^52 + 4*t^54 + 2*t^56 + t^58 + 3*t^60 + 4*t^62 + 2*t^64 + t^66 + 3*t^68 + 4*t^70 + 2*t^72 + t^74 + 3*t^76 + 4*t^78 + 2*t^80 + t^82 + 3*t^84 + 4*t^86 + 2*t^88 + t^90 + 3*t^92 + 4*t^94 + 2*t^96 + t^98 + t^100 +[?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[?2004l1 1 +x_series 4*t^50 + 3*t^52 + 4*t^54 + 2*t^56 + t^58 + 3*t^60 + 4*t^62 + 2*t^64 + t^66 + 3*t^68 + 4*t^70 + 2*t^72 + t^74 + 3*t^76 + 4*t^78 + 2*t^80 + t^82 + 3*t^84 + 4*t^86 + 2*t^88 + t^90 + 3*t^92 + 4*t^94 + 2*t^96 + t^98 + t^100 +4*t^50 + 3*t^52 + 4*t^54 + 2*t^56 + t^58 + 3*t^60 + 4*t^62 + 2*t^64 + t^66 + 3*t^68 + 4*t^70 + 2*t^72 + t^74 + 3*t^76 + 4*t^78 + 2*t^80 + t^82 + 3*t^84 + 4*t^86 + 2*t^88 + t^90 + 3*t^92 + 4*t^94 + 2*t^96 + t^98 + t^100 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: f +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [22], in () +----> 1 f + +NameError: name 'f' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l1 1 +x_series 2 + 4*t^2 + 4*t^4 + t^10 + 4*t^12 + 4*t^14 + 2*t^20 + 3*t^22 + 3*t^24 + 3*t^30 + 2*t^32 + 2*t^34 + 2*t^50 + 3*t^52 + 3*t^54 + 2*t^60 + 3*t^62 + 3*t^64 + 4*t^70 + t^72 + t^74 + t^80 + 4*t^82 + 4*t^84 +2 + 4*t^2 + 4*t^4 + t^10 + 4*t^12 + 4*t^14 + 2*t^20 + 3*t^22 + 3*t^24 + 3*t^30 + 2*t^32 + 2*t^34 + 2*t^50 + 3*t^52 + 3*t^54 + 2*t^60 + 3*t^62 + 3*t^64 + 4*t^70 + t^72 + t^74 + t^80 + 4*t^82 + 4*t^84 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 1 over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.is_smooth()[?7h[?12l[?25h[?25l[?7lnbof_ps_at_infty[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l_of_pts_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.nb_of_pts_at_infty +[?7h[?12l[?25h[?2004l[?7h1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: C.nb_of_pts_at_infty = 3 +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty = 3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.nb_of_pts_at_infty +[?7h[?12l[?25h[?2004l[?7h3 +[?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[?2004l1 1 +x_series 4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 +4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x)^2[?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[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l2.[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.y)^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?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((C.y)^2)[?7h[?12l[?25h[?25l[?7lx((C.y)^2)[?7h[?12l[?25h[?25l[?7lp((C.y)^2)[?7h[?12l[?25h[?25l[?7la((C.y)^2)[?7h[?12l[?25h[?25l[?7ln((C.y)^2)[?7h[?12l[?25h[?25l[?7ls((C.y)^2)[?7h[?12l[?25h[?25l[?7li((C.y)^2)[?7h[?12l[?25h[?25l[?7lo((C.y)^2)[?7h[?12l[?25h[?25l[?7ln((C.y)^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?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[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: expansion((C.y)^2, -1, 0, prec=100) +[?7h[?12l[?25h[?2004lx_series 4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 +[?7ht^2 + t^250 + 4*t^252 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lexpansion((C.y)^2, -1, 0, prec=100)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l1 1 +4 + 2*t^2 + 4*t^4 + 3*t^10 + 4*t^12 + 3*t^14 + 2*t^20 + t^22 + 2*t^24 + t^30 + 3*t^32 + t^34 + t^50 + 3*t^52 + t^54 + 2*t^60 + t^62 + 2*t^64 + 3*t^70 + 4*t^72 + 3*t^74 + 4*t^80 + 2*t^82 + 4*t^84 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lexpansion((C.y)^2, -1, 0, prec=100)[?7h[?12l[?25h[?25l[?7lsage: expansion((C.y)^2, -1, 0, prec=100) +[?7h[?12l[?25h[?2004l[?7ht^2 + t^250 + 4*t^252 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lexpansion((C.y)^2, -1, 0, prec=100)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lexpansion((C.y)^2, -1, 0, prec=100)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 1 over Finite Field of size 5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lexpansion((C.y)^2, -1, 0, prec=100)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)^2, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7lx)^2, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7l3, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7l , -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7l+, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7l , -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7lC, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7l., -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7lo, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7ln, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7le, -1, 0, prec=10)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: expansion((C.x)^3 + C.one, -1, 0, prec=100) +[?7h[?12l[?25h[?2004l[?7ht^2 + t^250 + 4*t^252 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lquo_rem(x^10 + x^8 + x^6 - x^4, x^2 - 1)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit() +[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd .. +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ cdgit status +On branch master +Your branch is up to date with 'origin/master'. + +Changes not staged for commit: + (use "git add ..." to update what will be committed) + (use "git restore ..." to discard changes in working directory) + modified: sage/.run.term-0.term + modified: sage/as_covers/as_form_class.sage + modified: sage/drafty/draft.sage + modified: sage/drafty/superelliptic_drw.sage + modified: sage/init.sage + modified: sage/superelliptic/superelliptic_form_class.sage + +Untracked files: + (use "git add ..." to include in what will be committed) + .crystalline_p2.ipynb.sage-jupyter2 + .deRhamComputation.ipynb.sage-jupyter2 + .elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2 + .git.x11-0.term + .superelliptic.ipynb.sage-jupyter2 + .superelliptic_alpha.ipynb.sage-jupyter2 + .superelliptic_arbitrary_field.ipynb.sage-jupyter2 + git.x11 + sage/as_covers/tests/cartier_test.sage + sage/drafty/.2023-03-06-file-1.ipynb.sage-jupyter2 + sage/drafty/2gpcovers.sage + sage/drafty/as_cartier.sage + sage/drafty/better_trace.sage + sage/drafty/cartier_image_representation.sage + sage/drafty/convert_superelliptic_into_AS.sage + sage/drafty/draft4.sage + sage/drafty/draft5.sage + sage/drafty/draft6.sage + sage/drafty/draft7.sage + sage/drafty/draft8.sage + sage/drafty/draft_klein_covers.sage + sage/drafty/lift_to_de_rham.sage + sage/drafty/pole_numbers.sage + sage/drafty/regular_on_U0.sage + sage/superelliptic/frobenius_kernel.sage + sage/superelliptic/tests/ + superelliptic_arbitrary_field.ipynb + +no changes added to commit (use "git add" and/or "git commit -a") +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ gigit add - \ No newline at end of file diff --git a/sage/as_covers/as_form_class.sage b/sage/as_covers/as_form_class.sage index 99c1e80..14207c5 100644 --- a/sage/as_covers/as_form_class.sage +++ b/sage/as_covers/as_form_class.sage @@ -15,14 +15,14 @@ class as_form: def __repr__(self): return "(" + str(self.form)+") * dx" - def expansion_at_infty(self, i = 0): + def expansion_at_infty(self, place = 0): C = self.curve delta = C.nb_of_pts_at_infty F = C.base_ring - x_series = C.x_series[i] - y_series = C.y_series[i] - z_series = C.z_series[i] - dx_series = C.dx_series[i] + x_series = C.x_series[place] + y_series = C.y_series[place] + z_series = C.z_series[place] + dx_series = C.dx_series[place] n = C.height variable_names = 'x, y' for j in range(n): @@ -98,10 +98,10 @@ class as_form: return superelliptic_form(C_super, Qxy(result)) def residue(self, place=0): - return self.expansion_at_infty(i = place).residue() + return self.expansion_at_infty(place = place).residue() def valuation(self, place=0): - return self.expansion_at_infty(i = place).valuation() + return self.expansion_at_infty(place = place).valuation() def serre_duality_pairing(self, fct): AS = self.curve diff --git a/sage/drafty/draft.sage b/sage/drafty/draft.sage index 4834464..9ca00d8 100644 --- a/sage/drafty/draft.sage +++ b/sage/drafty/draft.sage @@ -5,4 +5,10 @@ Rx. = PolynomialRing(F) f = x^3 - x + 1 C = superelliptic(f, m) C1 = patch(C) -print(C1.crystalline_cohomology_basis()) \ No newline at end of file +#print(C1.crystalline_cohomology_basis()) +g1 = C1.polynomial +g_AS = g1(x^p - x) +C2 = superelliptic(g_AS, 2) +print(convert_super_into_AS(C2)) +converted = (C2.x)^4 - (C2.x)^2 +print(convert_super_fct_into_AS(converted)) \ No newline at end of file diff --git a/sage/drafty/superelliptic_drw.sage b/sage/drafty/superelliptic_drw.sage index 6d00826..a765a83 100644 --- a/sage/drafty/superelliptic_drw.sage +++ b/sage/drafty/superelliptic_drw.sage @@ -347,7 +347,8 @@ def de_rham_witt_lift(cech_class, prec = 50): aux_h2 = decom_aux_h2[0] aux_f = decom_aux_h2[2] aux_omega0 = decomposition_omega0_omega8(aux.omega, prec=prec)[0] - return superelliptic_drw_cech(omega0_lift + aux_h2.verschiebung().diffn() + aux_omega0.verschiebung(), fct.teichmuller() + aux_f.verschiebung()) + result = superelliptic_drw_cech(omega0_lift + aux_h2.verschiebung().diffn() + aux_omega0.verschiebung(), fct.teichmuller() + aux_f.verschiebung()) + return result.reduce() def crystalline_cohomology_basis(self, prec = 50): result = [] diff --git a/sage/init.sage b/sage/init.sage index 26843a6..f12681d 100644 --- a/sage/init.sage +++ b/sage/init.sage @@ -19,10 +19,12 @@ load('auxilliaries/hensel.sage') load('auxilliaries/linear_combination_polynomials.sage') ############## ############## +load('drafty/convert_superelliptic_into_AS.sage') load('drafty/second_patch.sage') load('drafty/regular_on_U0.sage') load('drafty/lift_to_de_rham.sage') #load('drafty/superelliptic_cohomology_class.sage') load('drafty/superelliptic_drw.sage') -load('drafty/draft.sage') +#load('drafty/draft_klein_covers.sage') +load('drafty/2gpcovers.sage') load('drafty/pole_numbers.sage') \ No newline at end of file diff --git a/sage/superelliptic/superelliptic_form_class.sage b/sage/superelliptic/superelliptic_form_class.sage index abbcc6a..f181e28 100644 --- a/sage/superelliptic/superelliptic_form_class.sage +++ b/sage/superelliptic/superelliptic_form_class.sage @@ -139,4 +139,20 @@ class superelliptic_form: return g*dx_series def residue(self, place = 0, prec=30): - return self.expansion_at_infty(place = place, prec=prec)[-1] \ No newline at end of file + return self.expansion_at_infty(place = place, prec=prec)[-1] + + def reduce(self): + fct = self.form + C = self.curve + fct = reduction(C, fct) + return superelliptic_form(C, fct) + + def reduce2(self): + fct = self.form + C = self.curve + m = C.exponent + F = C.base_ring + Rxy. = PolynomialRing(F, 2) + Fxy = FractionField(Rxy) + fct = reduction(C, Fxy(y^m*fct)) + return superelliptic_form(C, fct/y^m) \ No newline at end of file