# dual(ToricVectorBundle) -- the dual bundle of a toric vector bundle

## Description

dual computes the dual vector bundle of a toric vector bundle.

 i1 : E = tangentBundle(pp1ProductFan 2,"Type" => "Kaneyama") o1 = {dimension of the variety => 2 } number of affine charts => 4 rank of the vector bundle => 2 o1 : ToricVectorBundleKaneyama i2 : Ed = dual E o2 = {dimension of the variety => 2 } number of affine charts => 4 rank of the vector bundle => 2 o2 : ToricVectorBundleKaneyama i3 : details Ed o3 = (HashTable{0 => (| 1 0 |, | 1 0 |) }, HashTable{(0, 1) => | 1 0 |}) | 0 1 | | 0 1 | | 0 -1 | 1 => (| 1 0 |, | 1 0 |) (0, 2) => | -1 0 | | 0 -1 | | 0 -1 | | 0 1 | 2 => (| -1 0 |, | -1 0 |) (1, 3) => | -1 0 | | 0 1 | | 0 1 | | 0 1 | 3 => (| -1 0 |, | -1 0 |) (2, 3) => | 1 0 | | 0 -1 | | 0 -1 | | 0 -1 | o3 : Sequence i4 : Ed == cotangentBundle(pp1ProductFan 2,"Type" => "Kaneyama") o4 = false
 i5 : E = tangentBundle projectiveSpaceFan 2 o5 = {dimension of the variety => 2 } number of affine charts => 3 number of rays => 3 rank of the vector bundle => 2 o5 : ToricVectorBundleKlyachko i6 : Ed = dual E o6 = {dimension of the variety => 2 } number of affine charts => 3 number of rays => 3 rank of the vector bundle => 2 o6 : ToricVectorBundleKlyachko i7 : details Ed o7 = HashTable{| -1 | => (| 0 -1 |, | 1 0 |)} | -1 | | -1 1 | | 0 | => (| 0 1 |, | 1 0 |) | 1 | | 1 0 | | 1 | => (| 1 0 |, | 1 0 |) | 0 | | 0 1 | o7 : HashTable i8 : Ed == cotangentBundle projectiveSpaceFan 2 o8 = false