hyperplanes returns the defining affine hyperplanes for a polyhedron P. The output is (N,w), where the source of N has the dimension of the ambient space of P and w is a one column matrix in the target space of N such that P = {p in H | N*p = w} where H is the intersection of the defining affine half-spaces.
For a cone C the output is the matrix N, that is the same matrix as before but w is omitted since it is 0, so C = {c in H | N*c = 0} and H is the intersection of the defining linear half-spaces.
Please see V- and H-representation on the conventions we use for cones and polyhedra.
i1 : P = stdSimplex 2 o1 = P o1 : Polyhedron |
i2 : hyperplanes P o2 = (| 1 1 1 |, | 1 |) o2 : Sequence |
i3 : C = coneFromVData matrix {{1,2,4},{2,3,5},{3,4,6}} o3 = C o3 : Cone |
i4 : hyperplanes C o4 = | -1 2 -1 | 1 3 o4 : Matrix ZZ <--- ZZ |
The object hyperplanes is a method function.