double cosets in Sage

asked 2012-09-07 11:57:16 -0600

Sydahmad
11 ●3

Suppose G is a group and H and I are two subgroup of it how can I compute the double cosets I\G/H?

answered 2012-09-12 11:23:55 -0600

benjaminfjones
2715 ●7 ●42 ●76 http://bfj7.com/

The DoubleCoset function in GAP has not been wrapped yet, so this is currently "not implemented". But, you can always ask GAP to compute (double) cosets from within Sage:

sage: gap.eval('g:=Group((1,2,3,4),(1,2));;')
sage: gap.eval('u:=Subgroup(g,[(1,2,3),(1,2)]);;')
sage: gap.eval('v:=Subgroup(g,[(3,4)]);;')
sage: gap.eval('c:=DoubleCoset(u,(2,4),v);')
'DoubleCoset(Group( [ (1,2,3), (1,2) ] ),(2,4),Group( [ (3,4) ] ))'
sage: gap.eval('List(c);')
'[ (2,3,4), (1,4,2), (1,3)(2,4), (2,4), (1,4,2,3), (1,3,4,2) ]'

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I guess these wouldn't be translatable to Sage... yet.

kcrisman ( 2012-09-13 15:49:45 -0600 )edit

I think this could be easily wrapped, the return type is a list of tuples. It's just that no one has done it yet.

benjaminfjones ( 2012-09-13 15:53:44 -0600 )edit

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