1. you can coerce the coefficients to GF(3) 2. You can try G1 = gap(G) and G2 = gap(SymmetricGroup(4)) and G1.IsomorphismGroups(G2):
sage: s1 = [-1, 0, 0] sage: s1 = matrix([[-1, 0, 0], [1, 1, 0], [0, 0, 1]]) sage: s2 = matrix([[1, 1, 0], [0, -1, 0], [0, 1, 1]]) sage: s3 = matrix([[1, 0, 0], [0, 1, 1], [0, 0, -1]]) sage: G = MatrixGroup([s1,s2,s3]) sage: G1 = gap(G) sage: G2 = gap(SymmetricGroup(4)) sage: G1.IsomorphismGroups(G2) CompositionMapping( GroupGeneralMappingByImages( SymmetricGroup( [ 1 .. 4 ] ), SymmetricGroup( [ 1 .. 4 ] ), [ (1,3,2,4), (1,2,3,4) ], [ (1,2,3,4), (1,4,2,3) ] ), <action isomorphism> ) On Tue, May 19, 2009 at 12:21 PM, javier <[email protected]> wrote: > > Hi there, > > just playing around this time, tried to use SAGE to compute the Weyl > group associated to the Cartan matrix > [2, -1, 0] > [-1, 2, 0] > [0, -1, 2] > > that should be the usual permutation group S_4. > > After obtaining the generators > > s1= [-1 0 0] > [ 1 1 0] > [ 0 0 1], > > s2 = [ 1 1 0] > [ 0 -1 0] > [ 0 1 1], > > s3 = [ 1 0 0] > [ 0 1 1] > [ 0 0 -1] > > I create the group with the order > > G = MatrixGroup([s1,s2,s3]) > > It is easy to check that the order is indeed 24: > > sage: G.order() > 24 > > but how can I check that G is actually isomorphic to S_4? Direct > comparison > G == SymmetricGroup(4) > fails because G is a matrix group and not a permutation group, so I > tried converting it with > G.as_permutation_group() > but I get the error message "NotImplementedError: Base ring must be > finite." > > Is there any other way of checking the isomorphism? > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
