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.
i1 : P = stdSimplex 2
o1 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 3
number of rays => 0
number of vertices => 3
o1 : Polyhedron
|
i2 : hyperplanes P
o2 = (| 1 1 1 |, | 1 |)
o2 : Sequence
|
i3 : C = posHull matrix {{1,2,4},{2,3,5},{3,4,6}}
o3 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of the cone => 2
number of facets => 2
number of rays => 2
o3 : Cone
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i4 : hyperplanes C
o4 = | 1 -2 1 |
1 3
o4 : Matrix ZZ <-- ZZ
|