Function Field

Function Field and Polynomial Ring

FunctionField(C): Sch -> FldFunG

The function field of the hyperelliptic curve \(C\).

DefiningPolynomial(C): Sch -> RngMPolElt

A weighted homogeneous polynomial for the hyperelliptic curve \(C\).

EvaluatePolynomial(C, a, b, c): CrvHyp, RngElt, RngElt, RngElt -> RngElt

EvaluatePolynomial(C, [a, b, c]): CrvHyp, [RngElt] -> RngElt

Evaluates the homogeneous defining polynomial of the hyperelliptic curve \(C\) at the point \((a,b,c)\).