[with patch] permutation group element (dict method, acting on lists)

[jason]

It would be nice to get permutation elements as dictionaries as well as lists. If g is a permutation group element, then something like

  sage: g.dict()
{1:2, 2:1}

It would also be nice if we could have permutation elements act on lists to switch the order according to the permutation.

  sage: g.action(range(3))
[0,2,1]

Are these things possible already?

[boothby]

Added a patch to implement something similar to the second. With this patch, one may do the following:

sage: G = SymmetricGroup(4)
sage: g = G((1,2,3,4))
sage: sage: g('abcd')
'bcda'
sage: sage: g([0,1,2,3])
[1, 2, 3, 0]
sage: sage: g(('foo','bar','baz','what'))
('bar', 'baz', 'what', 'foo')

However, I can see absolutely no reason for one to want a dict rather than a list. Do you have an example of where this might be useful?

[boothby]

Robert Miller convinced me that there are good reasons to want a dict, so I implemented this, too.

[boothby]

Includes .dict() code.

[boothby]

fixes bugs from previous edition / ready for 2.8.11