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

Synopsis

• Function: tensor

• Usage:

  E = tensor(E1,E2)

• Inputs:
  • E1, an instance of the type ToricVectorBundle
  • E2, an instance of the type ToricVectorBundle
• Optional inputs:
  • Constants (missing documentation) => ..., default value false,
  • DegreeLift => ..., default value null,
  • DegreeMap => ..., default value null,
  • DegreeRank => ..., default value null,
  • Degrees => ..., default value null,
  • Global => ..., default value true,
  • Heft => ..., default value null,
  • Inverses => ..., default value null,
  • Join => ..., default value null,
  • Local => ..., default value false,
  • MonomialOrder => ..., default value null,
  • MonomialSize => ..., default value 32,
  • SkewCommutative => ..., default value {},
  • VariableBaseName => ..., default value null,
  • Variables => ..., default value null,
  • Weights => ..., default value {},
  • WeylAlgebra => ..., default value {},
• 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