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

Synopsis

Operator: ++
Usage:

E = E1 ++ E2
Inputs:
- E1, an instance of the type ToricVectorBundle
- E2, an instance of the type ToricVectorBundle
Outputs:
- E, an instance of the type ToricVectorBundle

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

Ways to use this method: