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
|
i4 : P112 = ccRefinement transpose matrix {{1,0},{0,1},{-1,-2}};
|
i5 : D = {1,0,0};
|
i6 : L = toricVectorBundle(1, P112, toList(3: matrix{{1_QQ}}), apply( D, i-> matrix{{-i}}));
|
i7 : details L
o7 = HashTable{| -1 | => (| 1 |, | -1 |)}
| -2 |
| 0 | => (| 1 |, 0)
| 1 |
| 1 | => (| 1 |, 0)
| 0 |
o7 : HashTable
|
i8 : apply(values parliament L, vertices)
o8 = {| 0 1 0 |}
| 0 0 1/2 |
o8 : List
|
If the toric variety is two-dimensional, then the result can be visualised using
drawParliament2Dtikz.
parliament calls internally the method
groundSet.