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

[Bors Alexander]

Dear Forum, dear Alexander and Bill,

Thank you both for your messages and your helpfulness. Unlike Bill, I was able to access Alexander's link and read his function in.

Bill, could you please send me the details of the PARI/GP algorithm which you mentioned?

Best wishes,
Alexander

________________________________________
Von: forum-bounces at gap-system.org [forum-bounces at gap-system.org]" im Auftrag von "Bill Allombert [Bill.Allombert at math.u-bordeaux.fr]
Gesendet: Donnerstag, 4. Mai 2017 11:35
An: forum at gap-system.org
Betreff: Re: [GAP Forum] Frobenius normal form (explicit change of basis)

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.

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