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ToricVectorBundles :: ToricVectorBundle ++ ToricVectorBundle

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

Synopsis

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

See also