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double cosets in Sage

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

Sydahmad gravatar image

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

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

benjaminfjones gravatar image

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 gravatar imagekcrisman ( 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 gravatar imagebenjaminfjones ( 2012-09-13 15:53:44 -0600 )edit

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

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Last updated: Sep 12 '12