# double cosets in Sage

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

double cosets in Sage

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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2

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) ]'
```

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.

Asked: **
2012-09-07 11:57:16 -0500
**

Seen: **425 times**

Last updated: **Sep 12 '12**

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