# symmetricPower(ZZ,ToricVectorBundle) -- the 'l'-th symmetric power of a toric vector bundle

## Description

symmetricPower computes the $l$-th symmetric power of a toric vector bundle in each description. The resulting bundle will be given in the same description as the original bundle. $l$ must be strictly positive.

 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 : details E o2 = HashTable{| -1 | => (| -1 1/3 |, | -1 0 |)} | 3 | | 3 0 | | 0 | => (| 0 1 |, | -1 0 |) | -1 | | -1 0 | | 0 | => (| 0 1 |, | -1 0 |) | 1 | | 1 0 | | 1 | => (| 1 0 |, | -1 0 |) | 0 | | 0 1 | o2 : HashTable i3 : Es = symmetricPower(2,E) o3 = {dimension of the variety => 2 } number of affine charts => 4 number of rays => 4 rank of the vector bundle => 3 o3 : ToricVectorBundleKlyachko i4 : details Es o4 = HashTable{| -1 | => (| 1 -1/3 1/9 |, | -2 -1 0 |)} | 3 | | -6 1 0 | | 9 0 0 | | 0 | => (| 0 0 1 |, | -2 -1 0 |) | -1 | | 0 -1 0 | | 1 0 0 | | 0 | => (| 0 0 1 |, | -2 -1 0 |) | 1 | | 0 1 0 | | 1 0 0 | | 1 | => (| 1 0 0 |, | -2 -1 0 |) | 0 | | 0 1 0 | | 0 0 1 | o4 : HashTable