On Fri, Jul 31, 2009 at 6:47 PM, javier<vengor...@gmail.com> wrote:
> If that you want are the cosets you can get them simply using
>
> cosets = Set([Set([h*g for h in H]) for g in G])
>
> or if you want to get a representative of each coset you can then use
>
> reps = [x[0] for x in cosets]
This will force you to enumerate the elements of the group G, and
that's not always a quick thing to do (e.g. what if you're working in
the Alternating group on 10 points?).
Gap provides RightCosets, CanonicalRightCosetElement and
Representative for working with cosets efficiently:
########################
G = gap.AlternatingGroup(4)
g = '(1,2,3)'
H = gap.Subgroup(G, [g])
rc = gap.RightCosets(G, H)
print "Canonical representatives:"
for x in gap.List(G):
print "H" + str(x) + ":", gap.CanonicalRightCosetElement(H, x)
print
print "Representatives:"
for C in gap.List(rc):
print C, ":", gap.Representative(C)
########################
Canonical representatives:
H(): ()
H(1,2)(3,4): (2,4,3)
H(1,3)(2,4): (2,3,4)
H(1,4)(2,3): (1,2,4)
H(2,3,4): (2,3,4)
H(1,2,4): (1,2,4)
H(1,3,2): ()
H(1,4,3): (2,4,3)
H(2,4,3): (2,4,3)
H(1,2,3): ()
H(1,3,4): (1,2,4)
H(1,4,2): (2,3,4)
Representatives:
RightCoset(Group( [ (1,2,3) ] ),()) : ()
RightCoset(Group( [ (1,2,3) ] ),(1,2)(3,4)) : (1,2)(3,4)
RightCoset(Group( [ (1,2,3) ] ),(1,3)(2,4)) : (1,3)(2,4)
RightCoset(Group( [ (1,2,3) ] ),(1,4)(2,3)) : (1,4)(2,3)
--
Carlo Hamalainen
http://carlo-hamalainen.net
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send an email to sage-devel@googlegroups.com
To unsubscribe from this group, send an email to
sage-devel-unsubscr...@googlegroups.com
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://www.sagemath.org
-~----------~----~----~----~------~----~------~--~---
