# ToricVectorBundle ** ToricVectorBundle -- the tensor product of two toric vector bundles

## Description

If $E_1$ and $E_2$ are defined over the same fan and in the same description, then tensor computes the tensor product of the two vector bundles in this description

 i1 : E1 = toricVectorBundle(2,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 : E2 = tangentBundle hirzebruchFan 3 o2 = {dimension of the variety => 2 } number of affine charts => 4 number of rays => 4 rank of the vector bundle => 2 o2 : ToricVectorBundleKlyachko i3 : E = E1 ** E2 o3 = {dimension of the variety => 2 } number of affine charts => 4 number of rays => 4 rank of the vector bundle => 4 o3 : ToricVectorBundleKlyachko i4 : details E o4 = HashTable{| -1 | => (| -1 1/3 0 0 |, | -1 0 -1 0 |)} | 3 | | 3 0 0 0 | | 0 0 -1 1/3 | | 0 0 3 0 | | 0 | => (| 0 1 0 0 |, | -1 0 -1 0 |) | -1 | | -1 0 0 0 | | 0 0 0 1 | | 0 0 -1 0 | | 0 | => (| 0 1 0 0 |, | -1 0 -1 0 |) | 1 | | 1 0 0 0 | | 0 0 0 1 | | 0 0 1 0 | | 1 | => (| 1 0 0 0 |, | -1 0 -1 0 |) | 0 | | 0 1 0 0 | | 0 0 1 0 | | 0 0 0 1 | o4 : HashTable
 i5 : E1 = toricVectorBundle(2,hirzebruchFan 3,"Type" => "Kaneyama") o5 = {dimension of the variety => 2 } number of affine charts => 4 rank of the vector bundle => 2 o5 : ToricVectorBundleKaneyama i6 : E2 = tangentBundle(hirzebruchFan 3,"Type" => "Kaneyama") o6 = {dimension of the variety => 2 } number of affine charts => 4 rank of the vector bundle => 2 o6 : ToricVectorBundleKaneyama i7 : E = E1 ** E2 o7 = {dimension of the variety => 2 } number of affine charts => 4 rank of the vector bundle => 4 o7 : ToricVectorBundleKaneyama i8 : details E o8 = (HashTable{0 => (| 0 -1 |, | 1 1 -3 -3 |) }, HashTable{(0, 1) => | | 1 3 | | 0 0 -1 -1 | | 1 => (| 0 -1 |, | 1 1 3 3 |) | | -1 3 | | 0 0 1 1 | | 2 => (| 1 0 |, | -1 -1 0 0 |) (0, 2) => | | 0 1 | | 0 0 -1 -1 | | 3 => (| 1 0 |, | -1 -1 0 0 |) | | 0 -1 | | 0 0 1 1 | | (1, 3) => | | | | (2, 3) => | | | | ------------------------------------------------------------------------ 1 0 0 0 |}) 0 1 0 0 | 0 0 -1 0 | 0 0 0 -1 | -1 0 0 0 | 0 -1 0 0 | 3 0 1 0 | 0 3 0 1 | -1 0 0 0 | 0 -1 0 0 | -3 0 1 0 | 0 -3 0 1 | 1 0 0 0 | 0 1 0 0 | 0 0 -1 0 | 0 0 0 -1 | o8 : Sequence