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:
Well, I would prefer if the "positive definite" was not required. But yes, essentially I'm looking for that.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.
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.