On Wed, May 03, 2017 at 05:40:14PM +0000, Hulpke,Alexander wrote: > Dear Forum, Dear Alexander > > > I am looking for a function that takes as input a square matrix M over a > > finite field k and outputs a regular matrix T over k, of the same dimension > > as M, such that TMT^(-1) is in Frobenius normal form (aka rational > > canonical form). Is there a simple way to construct such a function from > > GAP's built-in functions? > > As long as only basic (not guaranteed to be particular efficient) > functionality is required, this can be added reasonably easily to GAP. > > In name-based favoritism, I have put together such a routine > > RationalCanonicalFormTransform (which will return the transforming matrix T > such that T^-1MT is RCF), it is located at > > https://www.dropbox.com/s/xm5713mdif00gyd/rcft.g?dl=0
I did not manage to access this link. For what it is worth, PARI/GP has a similar function (matfrobenius) which implement a fast algorithm. I can send you the detail of the algorithm used to port it to GAP. It is not very long. Cheers, Bill. _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
