Re: qfisom over Q

[Jeroen Demeyer <jdemeyer@cage.ugent.be>]

On 2015-06-09 17:45, Bill Allombert wrote:
> So given two (symmetric, positive definite) matrices M and N, you are looking
> for P such that P~ * M * P = N ?
Well, I would prefer if the "positive definite" was not required. But 
yes, essentially I'm looking for that.

> You can use qfgaussred() to reduce the problem to diagonal matrices.
Agreed.

> Then you need to find a permutation s such that m_{i,i}/n_{s(i),s(i)} is a square
> for all i.
That condition is too strong. Example:

gp> A=[1,-2;2,1]; A~ * matid(2) * A
%12 =
[5 0]

[0 5]

Then %12 and matid(2) are two isomorphic quadratic forms but they do not 
satisfy your condition.