# base -- the basis matrices for the rays

• Usage:
b = base E
• Inputs:
• Outputs:
• b,

## Description

The basis of a toric vector bundle in Klyachko's description is given for each ray as a square matrix of rank $k$ of the bundle. The output is a HashTable where the keys are the rays of the fan given as one column matrices over ZZ, and for each ray a $k$ by $k$ matrix over QQ and $k$ is the rank of the bundle.

 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 : base E o2 = HashTable{| -1 | => | -1 1/3 |} | 3 | | 3 0 | | 0 | => | 0 1 | | -1 | | -1 0 | | 0 | => | 0 1 | | 1 | | 1 0 | | 1 | => | 1 0 | | 0 | | 0 1 | o2 : HashTable

## See also

• addBase -- changing the basis matrices of a toric vector bundle in Klyachko's description
• filtration -- the filtration matrices of the vector bundle
• isVectorBundle -- checks if the data does in fact define an equivariant toric vector bundle

## Ways to use base :

• "base(ToricVectorBundleKlyachko)"

## For the programmer

The object base is .