# 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 $(a,b,c)$.