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

[Hulpke,Alexander]

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,
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