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# tensor(ToricVectorBundle,ToricVectorBundle) -- the tensor product of two toric vector bundles

- Function: tensor
- Usage:
    `E = tensor(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 E1 and E2 are defined over the same fan and are in the same description, then tensor computes the tensor product of the two vector bundles 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 = tensor(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 1/3 0  0   |, | -1 0 -1 0 |)}
                   | 3  |     | 3  0   0  0   |
                              | 0  0   -1 1/3 |
                              | 0  0   3  0   |
                   | 0  | => (| 0  1 0  0 |, | -1 0 -1 0 |)
                   | -1 |     | -1 0 0  0 |
                              | 0  0 0  1 |
                              | 0  0 -1 0 |
                   | 0 | => (| 0 1 0 0 |, | -1 0 -1 0 |)
                   | 1 |     | 1 0 0 0 |
                             | 0 0 0 1 |
                             | 0 0 1 0 |
                   | 1 | => (| 1 0 0 0 |, | -1 0 -1 0 |)
                   | 0 |     | 0 1 0 0 |
                             | 0 0 1 0 |
                             | 0 0 0 1 |

    o4 : HashTable

## See also

- ToricVectorBundle ** ToricVectorBundle -- the tensor product of two toric vector bundles
- ToricVectorBundle ++ ToricVectorBundle -- the direct sum of two toric vector bundles
- exteriorPower(ZZ,ToricVectorBundle) -- the 'l'-th exterior power of a toric vector bundle
- symmetricPower(ZZ,ToricVectorBundle) -- the 'l'-th symmetric power of a toric vector bundle

## Ways to use this method:

- tensor(ToricVectorBundle,ToricVectorBundle) -- the tensor product of two toric vector bundles

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OldToricVectorBundles.m2:3653:0.