degOnE -- degree of a vector bundle on E

Synopsis

• Usage:

  d = degOnE(L)

  d = degOnE(phi)

• Inputs:
  • L, an instance of the type VectorBundleOnE, a vector bundle on E
  • phi, a matrix, a matrix which is the yAction of some VectorBundleOnE
• Outputs:
  • d, an integer, the degree of L

Description

i1 : kk=ZZ/101;

i2 : g=1;

i3 : rNP=randNicePencil(kk,g);

i4 : f=(cliffordModule(rNP.matFact1,rNP.matFact2,rNP.baseRing)).hyperellipticBranchEquation;

i5 : L0=randomLineBundle(0,f)

o5 = VectorBundleOnE{...1...}

o5 : VectorBundleOnE

i6 : degOnE L0

o6 = 0

i7 : L1=randomLineBundle(1,f)

o7 = VectorBundleOnE{...1...}

o7 : VectorBundleOnE

i8 : degOnE L1

o8 = 1

i9 : Lm1=randomLineBundle(-1,f)

o9 = VectorBundleOnE{...1...}

o9 : VectorBundleOnE

i10 : degOnE Lm1

o10 = -1

See also

• randomLineBundle -- a random line bundle on the hyperelliptic curve
• vectorBundleOnE -- creates a VectorBundleOnE, represented as a matrix factorization
• VectorBundleOnE -- vector bundle on a hyperelliptic curve E
• yAction -- defines a vector bundle on E
• degOnE -- degree of a vector bundle on E