Bill Allombert on Tue, 09 Jun 2015 17:46:03 +0200

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Re: qfisom over Q

On Tue, Jun 09, 2015 at 04:02:42PM +0200, Jeroen Demeyer wrote:
> Dear pari-users,
> In qfisom, I am guessing that the isomorphism is supposed to be
> defined over Z,

Yes, it is a isomorphism of lattices.

>  i.e. the transformation matrix is unimodular. 

This is a consequence of defined over Z, but not the other way round.

> Is there any way to do this computation over Q, i.e. allowing the
> transformation matrix to be any non-singular rational matrix?

So given two (symmetric, positive definite) matrices M and N, you are looking
for P such that P~ * M * P = N ?

You can use qfgaussred() to reduce the problem to diagonal matrices.
Then you need to find a permutation s such that m_{i,i}/n_{s(i),s(i)} is a square
for all i.