# Jacobians

The Jacobian of a hyperelliptic curve is implemented as the divisor class group of the curve. In particular, no equations giving the Jacobian as a variety ever appear. The Jacobian of any hyperelliptic curve can be created, but most of the interesting functionality is over finite fields, or for genus $2$ over number fields or ${\mathbb{Q}}$.

## Creation of a Jacobian

### `Jacobian(C): CrvHyp -> JacHyp`

The Jacobian of the hyperelliptic curve $C$.

## Access Operations

### `Curve(J): JacHyp -> CrvHyp`

The hyperelliptic curve from which the Jacobian $J$ was constructed.

### `Dimension(J): JacHyp -> RngIntElt`

The dimension of the Jacobian $J$ as an algebraic variety, equal to the genus of the curve $C$ of which $J$ is the Jacobian.

## Base Ring

### `BaseField(J): JacHyp -> Fld`

### `BaseRing(J): JacHyp -> Rng`

### `CoefficientRing(J): JacHyp -> Rng`

The base field of the Jacobian $J$.

## Changing the Base Ring

### `BaseChange(J, F): JacHyp, Rng -> JacHyp`

### `BaseExtend(J, F): JacHyp, Rng -> JacHyp`

The base extension of the Jacobian $J$ to the field $F$.

### `BaseChange(J, j): JacHyp, Map -> JacHyp`

### `BaseExtend(J, j): JacHyp, Map -> JacHyp`

The base extension of the Jacobian $J$ obtained by the map $j$, where $j$ is a ring homomorphism with the base field of $C$ as its domain.

### `BaseChange(J, n): JacHyp, RngIntElt -> JacHyp`

### `BaseExtend(J, n): JacHyp, RngIntElt -> JacHyp`

The base extension of the Jacobian $J$ over a finite field to its degree $n$ extension.