#12043: Hecke series for overconvergent modular forms
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Reporter: lauder | Owner: craigcitro
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-4.8
Component: modular forms | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author: lauder
Merged: | Dependencies:
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Comment(by lauder):
Dear David
Thanks for your message.
On integral_generators, ideally I would like (b).
Regarding the algorithm terminating, I thought very briefly about bounding
the number of random q-series
generated during the attempt to construct the complementary spaces modulo
p, with the algorithm then extending the
low weight bases if this was exceeded. This would of course guarantee
eventual termination! The funny thing is though that if you get the code
to print the rank "rk" when generating the bases modulo p, you will see it
looks rather uneven, with the routine getting "stuck" in certain subspaces
and then whizzing off again. This didn't fit with my heuristic idea of how
the rank
should be increasing. So in short, since I couldn't think of a
mathematically elegant bound on how many series to generate, and coding it
up this way looked a bit fiddly, I didn't bother. Probably it is better to
wait and see what we do with integral_generators.
I followed your suggestion, and cut row_reduced_form altogether, replacing
the list of q-series modulo p with a matrix. This
is much better, but in larger examples doesn't give such a dramatic speed-
up. (The same idea applied to the magma implementation doubled the speed
though!) I have not applied this to your patch yet though, just my old
sage copy.
Best wishes
Alan.
Replying to [comment:9 davidloeffler]:
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12043#comment:10>
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