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 twodimensional, then the result can be visualised using
drawParliament2Dtikz.
parliament calls internally the method
groundSet.