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Polyhedra :: hyperplanes

hyperplanes -- computes the defining hyperplanes of a Cone or a Polyhedron

Synopsis

Description

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

Ways to use hyperplanes :