Equivalence of Genus One Models

IsEquivalent(model1, model2): ModelG1, ModelG1 -> BoolElt, TransG1

IsEquivalent(cubic1, cubic2): RngMPolElt, RngMPolElt -> BoolElt, TransG1

Return true if and only if the two given cubics (or genus one models of degree 3) are equivalent as genus one models. In other words, that there exists a linear transformation of the ambient projective space \({\mathbb{P}}_{{\mathbb{Q}}}^2\) which takes one cubic to the other, up to scaling. The algorithm is given in [Fisher, 2006].

When true, the transformation is also returned as a tuple (the syntax is explained in Section Transformations between Genus One Models, on transformations, below).