Jeroen Demeyer on Tue, 09 Jun 2015 19:29:54 +0200

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Re: qfisom over Q

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.

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.