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

Synopsis

Function: symmetricPower
Usage:

Es = symmetricPower(l,E)
Inputs:
- l, an integer, strictly positive
- E, an instance of the type ToricVectorBundle
Outputs:
- Es, an instance of the type ToricVectorBundle

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

Ways to use this method: