For a vector bundle in Kaneyama's description the graded ring is QQ with degree space the lattice of the underlying fan.
i1 : E = tangentBundle(projectiveSpaceFan 3,"Type" => "Kaneyama") o1 = {dimension of the variety => 3 } number of affine charts => 4 rank of the vector bundle => 3 o1 : ToricVectorBundleKaneyama |
i2 : ring E o2 = QQ[] o2 : PolynomialRing |
For a vector bundle in Klyachko's description the graded ring is QQ with degree space the lattice of the underlying fan.
i3 : E = toricVectorBundle(1,projectiveSpaceFan 2, toList(3:matrix{{1/2}}),toList(3:matrix{{-1}})) o3 = {dimension of the variety => 2 } number of affine charts => 3 number of rays => 3 rank of the vector bundle => 1 o3 : ToricVectorBundleKlyachko |
i4 : ring E o4 = QQ[] o4 : PolynomialRing |