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# VectorBundleOnE -- vector bundle on a hyperelliptic curve E

## Description

If the curve has equation y^2 +/- f, then the bundle is represented by a vector bundle on PP^1 and a matrix representing the action of y. the only key is yAction

## See also

- vectorBundleOnE -- creates a VectorBundleOnE, represented as a matrix factorization
- degOnE -- degree of a vector bundle on E
- orderInPic -- order of a line bundle of degree 0 in Pic(E)
- randomLineBundle -- a random balanced line bundle on the hyperelliptic curve
- randomExtension -- a random extension of a vector bundle on E by another vector bundle
- yAction -- defines a vector bundle on E

## Methods that use an object of class VectorBundleOnE:

- `degOnE(VectorBundleOnE)` -- see degOnE -- degree of a vector bundle on E
- `orderInPic(VectorBundleOnE)` -- see orderInPic -- order of a line bundle of degree 0 in Pic(E)
- `randomExtension(VectorBundleOnE,VectorBundleOnE)` -- see randomExtension -- a random extension of a vector bundle on E by another vector bundle
- `tensorProduct(CliffordModule,VectorBundleOnE)` -- see tensorProduct -- tensor product of sheaves on the elliptic curve or sheaf times CliffordModule
- `tensorProduct(VectorBundleOnE,VectorBundleOnE)` -- see tensorProduct -- tensor product of sheaves on the elliptic curve or sheaf times CliffordModule
- `translateIsotropicSubspace(CliffordModule,VectorBundleOnE,PolynomialRing)` -- see translateIsotropicSubspace -- choose a random isotropic subspace

## For the programmer

The object VectorBundleOnE is a type, with ancestor classes MutableHashTable < HashTable < Thing.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/PencilsOfQuadrics.m2:2649:0.