yAction -- defines a vector bundle on E

Synopsis

• Usage:

  M = V.yAction

• Outputs:
  • M, a matrix, a square matrix on PP^1, representing the action of y

Description

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

See also

• 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