parliament -- computes the parliament of polytopes to a toric vector bundle

Synopsis

• Usage:

  p = parliament E

• Inputs:
  • E, a vector bundle on a toric variety (Klyachko's description)
  • g, a list, containing elements of ground set as one column matrices
• Outputs:
  • p, a hash table, whose keys are elements of the ground set and the value of a key is a Polyhedron
• Consequences:

  • The result of parliament will be stored as a cacheValue in E.cache#parliament. It will be used by other methods.

Description

i1 : E = tangentBundle(projectiveSpaceFan 2)

o1 = {dimension of the variety => 2 }
      number of affine charts => 3
      number of rays => 3
      rank of the vector bundle => 2

o1 : ToricVectorBundleKlyachko

i2 : p = parliament E

o2 = HashTable{| 0 | => Polyhedron{...1...}}
               | 1 |
               | 1 | => Polyhedron{...1...}
               | 0 |
               | 1 | => Polyhedron{...1...}
               | 1 |

o2 : HashTable

i3 : applyValues(p, vertices)

o3 = HashTable{| 0 | => | 0 0  1  |}
               | 1 |    | 0 -1 -1 |
               | 1 | => | 0 -1 -1 |
               | 0 |    | 0 0  1  |
               | 1 | => | 0 1 0 |
               | 1 |    | 0 0 1 |

o3 : HashTable

See also

• ToricVectorBundleKlyachko -- the class of all toric vector bundles in Klyachko's description
• groundSet -- computes the ground set of a matroid associated to a toric vector bundle
• drawParliament2Dtikz -- visualises the parliament of polytopes for a vector bundle on a toric surface using TikZ