# yAction -- defines a vector bundle on E

## Synopsis

• Usage:
M = V.yAction
• Outputs:
• M, , a square matrix on PP^1, representing the action of y

## Description

A matrix representing the action of y for the hyperelliptic curve E with equation y^2 - (-1)^g * f.

 i1 : kk = ZZ/101; i2 : R = kk[s,t]; i3 : f = (s+2*t)*(s+t)*(s-t)*(s-2*t); i4 : L0 = randomLineBundle(0,f) o4 = VectorBundleOnE{...1...} o4 : VectorBundleOnE i5 : M = L0.yAction o5 = {-1} | -29s2+19st+19t2 38s2+9st+47t2 | {-1} | 47s2-22st+t2 29s2-19st-19t2 | 2 2 o5 : Matrix R <--- R i6 : M^2 - f*id_(source M) o6 = 0 2 2 o6 : Matrix R <--- R

• randomLineBundle -- a random line bundle on the hyperelliptic curve
• randomExtension -- a random extension of a vector bundle on E by another vector bundle
• vectorBundleOnE -- creates a VectorBundleOnE, represented as a matrix factorization
• VectorBundleOnE -- vector bundle on a hyperelliptic curve E
• degOnE -- degree of a vector bundle on E
• orderInPic -- order of a line bundle of degree 0 in Pic(E)
• tensorProduct -- tensor product of sheaves on the elliptic curve or sheaf times CliffordModule

## For the programmer

The object yAction is .