#6925: Fast way of calculating cuspidal subgroup of J0(N)
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Reporter: syazdani | Owner: tbd
Type: enhancement | Status:
Priority: major | needs_work
Component: modular forms | Milestone:
Keywords: cuspidal subgroup, modular | sage-5.11
abelian variety | Resolution:
Authors: | Merged in:
Report Upstream: N/A | Reviewers:
Branch: | Work issues:
Stopgaps: | Dependencies:
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Old description:
> This is the first implementation of Ligozat's method of calculating the
> rational cuspidal subgroup of J_0(N). This is done by doing linear
> algebra in d(N)*d(N) matrices, which seems considerably faster than the
> modular symbol methods.
>
> This code is functional at this point. The problems with it are
> a) __cmp__ is not called.
> b) Hecke operators aren't defined yet.
> c) can't coerce specific degree zero cuspidal divisors in our group.
>
> Apply:
>
> * [attachment:6925-rationalcuspidal.patch]
New description:
This is the first implementation of Ligozat's method of calculating the
rational cuspidal subgroup of J_0(N). This is done by doing linear algebra
in d(N)*d(N) matrices, which seems considerably faster than the modular
symbol methods.
This code is functional at this point. The problems with it are
a) __cmp__ is not called.
b) Hecke operators aren't defined yet.
c) can't coerce specific degree zero cuspidal divisors in our group.
Apply:
* [attachment:6925-rationalcuspidal.patch]
* [attachment:trac_6925_addon1.patch]
--
Comment (by chapoton):
here is a first cleanup patch.
There is one failing doctest that needs a mathematical check.
--
Ticket URL: <http://trac.sagemath.org/ticket/6925#comment:9>
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