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 -~----------~----~----~----~------~----~------~--~---
