ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 30 Dec 2012 12:58:09 +0100Unitary matrices over finite fieldshttps://ask.sagemath.org/question/9667/unitary-matrices-over-finite-fields/Hi everyone
I was delighted to see that the SAGE team had implemented the unitary groups GU(n,q) and SU(n,q), since they are such peculiar objects; however the implementation does not seem to include many matrix functions (eg det, trace, transpose etc.).
Let S be a (small) subset of GF(q^2). Let G=GU(n,q) and define a subset D_S of G (ie D_S is NOT a vector subspace or subgroup or anything) to be the matrices whose entries may only be chosen from this particular subset S. Let U, V in D_S. I need to check the matrix products (U^t)V for membership of D_S, where U^t denotes U.transpose() acted on by Frobenius in the usual way, and ideally I would like to store the set of pairs P = {(U,V) satisfying (U^t)V in D_S}, or even better to store some "generators" for P.
I have two questions:
(1) which matrix operations are available for elements of GU(n,q)?
(2) is there an easy way of specifying a sub-SET like D_S so that such a search may be performed? Needless to say once q and/or n gets any bigger than 3, holding any of these subsets naively in memory becomes prohibitively costly!
Many thanks for any help.
PS I can find generators for these groups using G.gens(); how please do I find relations between the gens?GaryMakSun, 30 Dec 2012 12:58:09 +0100https://ask.sagemath.org/question/9667/