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Predicates on Genus One Models

IsGenusOneModel(f) : RngMPolElt -> BoolElt, ModelG1
IsGenusOneModel(seq) : [ RngMPolElt ] -> BoolElt, ModelG1
IsGenusOneModel(mat) : Mtrx -> BoolElt, ModelG1
Returns true if and only if the given polynomial, sequence of polynomials, or matrix determines a "genus one model" in the sense described in the introduction to this chapter. When true, the model is also returned.

Important note: This does not imply that the associated scheme is a curve of genus 1, as degenerate cases are allowed!

IsEquivalent(model1, model2) : ModelG1, ModelG1 -> BoolElt, Tup
IsEquivalent(cubic1, cubic2) : RngMPolElt, RngMPolElt -> BoolElt, Tup
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 PQ2 which takes one cubic to the other, up to scaling. The algorithm is given in [Fis06].

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

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Version: V2.19 of Mon Dec 17 14:40:36 EST 2012