#5080: [with patch, needs work] Bug in decomposing modular symbol subspace
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Reporter: robertwb | Owner: craigcitro
Type: defect | Status: new
Priority: major | Milestone: sage-4.0.1
Component: modular forms | Keywords:
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Comment(by davidloeffler):
Hi Craig,
It's a delicate thing. There are two potential first-approximation
algorithms for computing complements, or (equivalently) embedded duals:
either work on the dual side (cutting down to the smallest space on which
Hecke acts like it does on self) or work on the ambient side (cutting down
to the smallest space on which Hecke acts like it does on the quotient
ambient/self).
What we had before was one algorithm in {{{complement}}} and the other in
{{{dual_free_module}}}, never exploiting the fact that the two problems
are essentially equivalent. I standardised on the algorithm that
{{{complement}}} was using, largely because the code to handle the
pathological case (for which neither algorithm works) was already there in
the {{{complement}}} routine.
The classy fix is to heuristically choose which algorithm to use, because
(in non-pathological cases) the dual-side version is much quicker when the
given submodule is much smaller than the ambient space, and the ambient-
side version is much quicker when the given submodule is most of the
ambient space. This is (roughly) what is meant by the comment in
{{{submodule.py}}} saying:
{{{
# TODO: optimize in some cases by computing image of
# complementary factor instead of kernel...?
}}}
David
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5080#comment:12>
Sage <http://sagemath.org/>
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