#6812: Enumerate integer vectors modulo to the action of a Permutation Group
------------------------------------------------------------------+---------
Reporter: nborie |
Owner: nborie
Type: enhancement |
Status: needs_review
Priority: major |
Milestone: sage-5.1
Component: combinatorics |
Resolution:
Keywords: enumeration, integer, list, permutation, group | Work
issues: long time tests, information about listing infinite sets
Report Upstream: N/A |
Reviewers: Karl-Dieter Crisman, Simon King
Authors: Nicolas Borie | Merged
in:
Dependencies: |
Stopgaps:
------------------------------------------------------------------+---------
Comment (by SimonKing):
Replying to [comment:82 nborie]:
> Yes, this piece of code is horribly ugly... The point is that the orbit
method will work with any integer vector. v doesn't need to be canonical.
I don't have a use case but I was thinking it would be more convenient to
allow the user to use this method for any integer vector (canonical or
not).
Agreed. So, check=False should be fine.
But I do think that the orbit method should try to convert the input
vector from a different parent into self, and should certainly not return
"None".
> Anyway, the test is_canonical should be very very much faster than the
full expansion of an orbit
Of course. The algorithm for is_canonical looks almost the same as the
full expansion of an orbit, but if it is in fact non-canonical then the
function will return "False" before finishing the computation of the whole
orbit.
By the way, I made some further tweaks and am now down to
{{{
sage: TEST_generation_orbit_sum(TransitiveGroup(8,1), verbose=True)
For G be the transitive group number 1 of degree 8
Cardinality of G : 8
Cardinality of secondary invariants : 5040
Number of canonical monomials under staircase : 18297
Total time : 1.43067121506
-------------------------------------
(1.430671215057373, 18297, 8)
sage: TEST_generation_orbit_sum(TransitiveGroup(9,1), verbose=True)
For G be the transitive group number 1 of degree 9
Cardinality of G : 9
Cardinality of secondary invariants : 40320
Number of canonical monomials under staircase : 153974
Total time : 12.9384939671
-------------------------------------
(12.938493967056274, 153974, 9)
sage: TEST_generation_orbit_sum(TransitiveGroup(10,1), verbose=True)
For G be the transitive group number 1 of degree 10
Cardinality of G : 10
Cardinality of secondary invariants : 362880
Number of canonical monomials under staircase : 1452325
Total time : 134.613152981
-------------------------------------
(134.61315298080444, 1452325, 10)
sage: G = TransitiveGroup(15,28)
sage: S = IntegerVectorsModPermutationGroup(G, max_part=1)
sage: timeit('S._cardinality_from_iterator()')
5 loops, best of 3: 408 ms per loop
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6812#comment:83>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
