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# HH^ZZ(ToricVectorBundle,Matrix) -- the i-th cohomology of a toric vector bundle in a given degree

- Function: cohomology
- Usage:
    `c = HH_i^E u`
- Inputs:
  - i, an integer
  - E, an instance of the type ToricVectorBundle
  - u, a matrix, over ZZ with just one column, giving a weight in the lattice
- Optional inputs:
  - Degree => ..., default value 0,
- Outputs:
  - c, a module

## Description

"Computes the $i$-th cohomology group of the toric vector bundle $E$ of degree $u$ where $u$ must be a one-column matrix giving a point in the lattice of the fan over which $E$ is defined and $i$ must be between $0$ and the dimension of the underlying toric variety."

    i1 : E = tangentBundle hirzebruchFan 3

    o1 = {dimension of the variety => 2 }
          number of affine charts => 4
          number of rays => 4
          rank of the vector bundle => 2

    o1 : ToricVectorBundleKlyachko

    i2 : HH^0 (E,matrix{{1},{0}})

               1
    o2 = (QQ[])

    o2 : QQ[]-module, free, degrees {{1, 0}}

## See also

- ring(ToricVectorBundle) -- the graded ring of the bundle
- deltaE -- the polytope of possible degrees that give non zero cohomology
- HH^ZZ ToricVectorBundle -- the i-th cohomology group of a toric vector bundle
- HH^ZZ(ToricVectorBundle,List) -- the i-th cohomology of a toric vector bundle for a given list of degrees
- hh^ZZ ToricVectorBundle
- eulerChi -- the Euler characteristic of a toric vector bundle

## Ways to use this method:

- HH^ZZ(ToricVectorBundle,Matrix) -- the i-th cohomology of a toric vector bundle in a given degree

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OldToricVectorBundles.m2:2601:0.