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PositivityToricBundles :: parliament

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

Synopsis

Description

Given a toric vector bundle in Klyachko's description, parliament computes its parliament of polytopes as introduced in [RJS, Section 3].
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
If the toric variety is two-dimensional, then the result can be visualised using drawParliament2Dtikz. parliament calles internally the method groundSet.

See also

Ways to use parliament :

For the programmer

The object parliament is a method function with options.