Description
This function computes the regular cell decomposition of
P given by the weight vector
w. This is computed by placing the i-th lattice point of
P on height
w_i in n+1 space, taking the convexHull of these with the ray (0,...,0,1), and projecting the compact faces into n space. Note that the polyhedron must be compact, i.e. a polytope and the length of the weight vector must be the number of lattice points.
i1 : P = crossPolytope 3
o1 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 3
number of facets => 8
number of rays => 0
number of vertices => 6
o1 : Polyhedron
|
i2 : w = matrix {{1,2,2,2,2,2,1}}
o2 = | 1 2 2 2 2 2 1 |
1 7
o2 : Matrix ZZ <-- ZZ
|
i3 : L = cellDecompose(P,w)
o3 = {{ambient dimension => 3 }, {ambient dimension => 3
dimension of lineality space => 0 dimension of lineality space =>
dimension of polyhedron => 3 dimension of polyhedron => 3
number of facets => 4 number of facets => 4
number of rays => 0 number of rays => 0
number of vertices => 4 number of vertices => 4
------------------------------------------------------------------------
}, {ambient dimension => 3 }, {ambient dimension => 3
0 dimension of lineality space => 0 dimension of lineality space
dimension of polyhedron => 3 dimension of polyhedron => 3
number of facets => 4 number of facets => 4
number of rays => 0 number of rays => 0
number of vertices => 4 number of vertices => 4
------------------------------------------------------------------------
}}
=> 0
o3 : List
|
i4 : apply(L,vertices)
o4 = {| -1 1 0 0 |, | -1 1 0 0 |, | -1 1 0 0 |, | -1 1 0 0 |}
| 0 0 -1 0 | | 0 0 1 0 | | 0 0 -1 0 | | 0 0 1 0 |
| 0 0 0 -1 | | 0 0 0 -1 | | 0 0 0 1 | | 0 0 0 1 |
o4 : List
|