#12949: Better congruence testing for odd arithmetic subgroups
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Reporter: davidloeffler | Owner: craigcitro
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.1
Component: modular forms | Keywords:
Work issues: | Report Upstream: N/A
Reviewers: | Authors: David Loeffler
Merged in: | Dependencies:
Stopgaps: |
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This patch relates to the {{{ is_congruence() }}} method of arithmetic
subgroups of SL2Z (described in terms of permutations, cf. {{{
sage.modular.arithgroup.arithgroup_perm}}}). For even subgroups
(containing -1), there is a very fast algorithm due to Tim Hsu, but for
odd subgroups we were using a much, much slower brute-force algorithm.
My student Thomas Hamilton checked in his MMath thesis that Hsu's
algorithm also works for odd subgroups with minor modifications. This
patch implements this generalized Hsu algorithm, resulting in a speedup of
about three orders of magnitude in all the examples I tried.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12949>
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