deltaE -- the polytope of possible degrees that give non zero cohomology

Description

For a toric vector bundle over a complete toric variety there is a finite set of degrees $u$ such that the degree $u$ part of the cohomology of the vector bundle is non-zero. This function computes a polytope $\Delta_E$, such that these degrees are contained in this polytope. If the underlying toric variety is not complete then an error is returned.

 i1 : E = toricVectorBundle(2,pp1ProductFan 2, "Type" => "Kaneyama") o1 = {dimension of the variety => 2 } number of affine charts => 4 rank of the vector bundle => 2 o1 : ToricVectorBundleKaneyama i2 : P = deltaE E o2 = {ambient dimension => 2 } dimension of lineality space => 0 dimension of polyhedron => 0 number of facets => 0 number of rays => 0 number of vertices => 1 o2 : Polyhedron i3 : vertices P o3 = 0 2 1 o3 : Matrix QQ <--- QQ i4 : E1 = tangentBundle projectiveSpaceFan 2 o4 = {dimension of the variety => 2 } number of affine charts => 3 number of rays => 3 rank of the vector bundle => 2 o4 : ToricVectorBundleKlyachko i5 : P1 = deltaE E1 o5 = {ambient dimension => 2 } dimension of lineality space => 0 dimension of polyhedron => 2 number of facets => 6 number of rays => 0 number of vertices => 6 o5 : Polyhedron i6 : vertices P1 o6 = | -1 1 0 1 0 -1 | | 0 0 -1 -1 1 1 | 2 6 o6 : Matrix QQ <--- QQ