#11598: Congruence testing for odd modular subgroups
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Reporter: davidloeffler | Owner: craigcitro
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.7.2
Component: modular forms | Keywords: modular congruence subgroup
Work_issues: | Upstream: N/A
Reviewer: Vincent Delecroix | Author: David Loeffler
Merged: | Dependencies: #11422
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Changes (by davidloeffler):
* status: needs_work => needs_review
Old description:
> The new functionality added in ticket #11422 makes it possible to
> manipulate arbitrary finite index (not necessarily congruence) subgroups
> of SL2Z. This massively extends my old code which only worked for
> subgroups containing -1.
>
> The "is_congruence" method in the new code, though, *defines* a subgroup
> to be congruence if its image modulo -1 is a congruence subgroup of
> PSL2Z. This is not the same as the conventional definition of a
> congruence subgroup of SL2Z. The patch below modifies the algorithm so it
> uses the conventional notion of "congruence".
New description:
The new functionality added in ticket #11422 makes it possible to
manipulate arbitrary finite index (not necessarily congruence) subgroups
of SL2Z. This massively extends my old code which only worked for
subgroups containing -1.
The "is_congruence" method in the new code, though, *defines* a subgroup
to be congruence if its image modulo -1 is a congruence subgroup of PSL2Z.
This is not the same as the conventional definition of a congruence
subgroup of SL2Z. The patch below modifies the algorithm so it uses the
conventional notion of "congruence". It also adds functionality for
enumerating all the liftings of a projective modular subgroup.
--
Comment:
Here's a new patch, which:
- implements a congruence test for odd subgroups, using only calculations
in finite matrix groups (much faster than the previous version);
- implements enumeration of the index 2 odd subgroups of an even subgroup;
- corrects a few typos etc in the documentation.
There are probably far better ways of doing the congruence test, as you
suggest; but I'd rather get something that works in quickly, rather than
having to release a Sage version that uses a different definition and then
change it back to the conventional definition later.
I haven't implemented congruence closure yet, because I'm working on a
patch that will introduce a new class for generic congruence subgroups
defined by a finite group of matrices in {{{ SL(2, Z / N) }}}, and I'll
include congruence closure in that.
Thanks Vincent for the helpful feedback on my previous patch!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11598#comment:5>
Sage <http://www.sagemath.org>
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