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 halfspaces.
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 halfspaces.
Please see
V and Hrepresentation 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
