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Macaulay2 / M2

The primary source code repository for Macaulay2, a system for computing in commutative algebra, algebraic geometry and related fields.
https://macaulay2.com
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diagonalization of symmetric bilinear forms #1496

Open tbach01 opened 3 years ago

tbach01 commented 3 years ago

Given a symmetric matrix with entries in a field of characteristic not 2, there is a straigtforward procedure to find a new basis in which the associated bilinear form becomes diagonal. Is there a method in M2 to perform this process, and in particular to get the diagonal entries? We need this for things like finite fields, not just RR and CC.

DanGrayson commented 3 years ago

I don't think so. If you end up implementing it, it would be good to introduce a new type called something "BilinearForm" whose instances would serve as containers for those matrices.