Macaulay2 » Documentation
Packages » PencilsOfQuadrics :: degOnE
next | previous | forward | backward | up | index | toc

# degOnE -- degree of a vector bundle on E

- 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

Computes the degree of a vector bundle L on the hyperelliptic curve E.

    i1 : kk=ZZ/101;

    i2 : setRandomSeed 0
     -- setting random seed to 0

    o2 = 0

    i3 : g=1;

    i4 : rNP=randNicePencil(kk,g);

    i5 : f=(cliffordModule(rNP.matFact1,rNP.matFact2,rNP.baseRing)).hyperellipticBranchEquation;

    i6 : L0=randomLineBundle(0,f)

    o6 = VectorBundleOnE{...1...}

    o6 : VectorBundleOnE

    i7 : degOnE L0

    o7 = 0

    i8 : L1=randomLineBundle(1,f)

    o8 = VectorBundleOnE{...1...}

    o8 : VectorBundleOnE

    i9 : degOnE L1

    o9 = 1

    i10 : Lm1=randomLineBundle(-1,f)

    o10 = VectorBundleOnE{...1...}

    o10 : VectorBundleOnE

    i11 : degOnE Lm1

    o11 = -1

## See also

- randomLineBundle -- a random balanced 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

## Ways to use degOnE:

- `degOnE(Matrix)`
- `degOnE(VectorBundleOnE)`

## For the programmer

The object degOnE is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/PencilsOfQuadrics.m2:2990:0.