#10976: computing order of a certain subgroup of a permutation group is double
dog
slow (compared to Magma)
----------------------------+-----------------------------------------------
Reporter: was | Owner: swenson
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.0
Component: group theory | Keywords: sd32
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
----------------------------+-----------------------------------------------
Changes (by swenson):
* owner: joyner => swenson
Comment:
I have a workaround I am testing for this (patch coming soon) that
recognizes some subgroups of permutation groups (including stabilizer
subgroups of the symmetric group), and can compute the order very quickly
(~600 microseconds). The running time of foo(200) above is still about a
second, because GAP takes that long to construct the stabilizer group and
give us back the generators.
In the future, I can add some more cases, or try to develop a more general
theory for quickly computing these group orders (the special case I added
is based on a argument from graph theory).
{{{
sage: def foo(n):
....: G = SymmetricGroup(n)
....: H = G.stabilizer(n//2)
....: return H.order()
....:
sage: %timeit foo(200)
5 loops, best of 3: 935 ms per loop
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10976#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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