ToricVectorBundle ++ ToricVectorBundle -- the direct sum of two toric vector bundles

Description

If $E_1$ and $E_2$ are defined over the same fan, then directSum computes the direct sum of the two vector bundles. The bundles must both be given in the same description and the resulting bundle will be 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 0 0 0 |, | 0 0 -1 0 |)} | 3 | | 0 1 0 0 | | 0 0 -1 1/3 | | 0 0 3 0 | | 0 | => (| 1 0 0 0 |, | 0 0 -1 0 |) | -1 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 -1 0 | | 0 | => (| 1 0 0 0 |, | 0 0 -1 0 |) | 1 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 1 0 | | 1 | => (| 1 0 0 0 |, | 0 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 |, | 0 0 1 -3 |)}, HashTable{(0, 1) => | 1 0 | 1 3 | | 0 0 0 -1 | | 0 1 1 => (| 0 -1 |, | 0 0 1 3 |) | 0 0 | -1 3 | | 0 0 0 1 | | 0 0 2 => (| 1 0 |, | 0 0 -1 0 |) (0, 2) => | 1 0 | 0 1 | | 0 0 0 -1 | | 0 1 3 => (| 1 0 |, | 0 0 -1 0 |) | 0 0 | 0 -1 | | 0 0 0 1 | | 0 0 (1, 3) => | 1 0 | 0 1 | 0 0 | 0 0 (2, 3) => | 1 0 | 0 1 | 0 0 | 0 0 ------------------------------------------------------------------------ 0 0 |}) 0 0 | 1 0 | 0 -1 | 0 0 | 0 0 | -1 0 | 3 1 | 0 0 | 0 0 | -1 0 | -3 1 | 0 0 | 0 0 | 1 0 | 0 -1 | o8 : Sequence