Equivalence

This section describes functionality to test equivalence of quadratic forms. Currently only implemented over the rationals.

IsRationallyEquivalent(X, Y): AlgMatElt, AlgMatElt -> BoolElt, AlgMatElt

Given two rational symmetric matrices \(X\) and \(Y\), determine if they are rationally equivalent, and if so, return \(T\) with \(Y=TXT^t\).

IsRationallyEquivalent(f, g): RngMPolElt, RngMPolElt -> BoolElt, AlgMatElt

Given two quadratic forms \(f\) and \(g\) over \({\mathbb{Q}}\), determine whether they are rationally equivalent, and if so, return a transform.

IsRationallySimilar(X, Y): AlgMatElt, AlgMatElt -> BoolElt, AlgMatElt, RngIntElt

Given two rational symmetric matrices \(X\) and \(Y\), determine if they are rationally similar, and if so, return \(T\) and \(s\) with \(s Y=TXT^t\).

IsRationallySimilar(f, g): RngMPolElt, RngMPolElt -> BoolElt, AlgMatElt, RngIntElt

Given two quadratic forms \(f\) and \(g\) over \({\mathbb{Q}}\), determine whether they are rationally similar, and if so, return a transform and a similarity factor.