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 and needs to be read in with `Reread` as it overwrites a library function. It implements the basic algorithm (as described in chapter 12.2 of Dummit&Foote) and will thus not be as efficient as it could be theoretically. Hope this helps, Alexander -- Colorado State University, Department of Mathematics, Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA email: hul...@colostate.edu, Phone: ++1-970-4914288 http://www.math.colostate.edu/~hulpke _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
