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. Cheers, Bill.