[GAP Forum] Frobenius normal form (explicit change of basis)

[Bill Allombert]

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.