On Sun, 07 Jan 2007 22:30:22 -0800, David Kohel <[EMAIL PROTECTED]> wrote:
Hi David J et al.,
There are two "natural" representations for permutations, cycles, and
enumerated
lists of images (or indices). In addition to this constructor:
sage: G = SymmetricGroup(14)
sage: G = SymmetricGroup(4)
sage: g = G("(1,2,3,4)")
sage: g(1)
2
sage: [ g(i+1) for i in range(4) ]
[2, 3, 4, 1]
it would be nice to be able to go
sage: G([2,3,4,1])
(1,2,3,4)
This representation at least can be represented in Python syntax,
whereas the other
constructor for permutations must be passed to GAP as a string. Does
GAP have a
similar constructor and conversions between cycle and image notation?
You don't have to use strings for creating permutations. You
can use lists of tuples (or a single tuple for a cyclic permutation).
sage: G = SymmetricGroup(14)
sage: G = SymmetricGroup(4)
sage: G((1,2,3,4))
(1,2,3,4)
sage: G([(1,2), (3,4)])
(1,2)(3,4)
The GAP function PermList described here:
http://wwwmaths.anu.edu.au/research.groups/aat/GAP/www/Manual/C020S009.htm
does the sort of thing you want. I've incorporated it into SAGE, so now the
following works:
sage: G([1,2,4,3])
(3,4)
sage: G([2,3,4,1])
(1,2,3,4)
This will be in sage-1.6 (to be released soon). Also, you can get
it by doing hg_sage.pull(), though probably be sure to do
a "sage -upgrade" first as always.
I also added going the other way:
sage: G = SymmetricGroup(4)
sage: x = G([2,1,4,3]); x
(1,2)(3,4)
sage: v = x.list(); v
[2, 1, 4, 3]
sage: type(v[0])
<type 'int'>
William
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to sage-devel@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/
-~----------~----~----~----~------~----~------~--~---
