Description
halfspaces returns the defining affine half-spaces. For a polyhedron
P the output is
(M,v), where the source of
M has the dimension of the ambient space of
P and
v is a one column matrix in the target space of
M such that
P = {p in H | M*p =< v} where
H is the intersection of the defining affine hyperplanes.
For a cone
C the output is the matrix
M that is the same matrix as before but
v is omitted since it is 0, so
C = {c in H | M*c =< 0} and
H is the intersection of the defining linear hyperplanes.
i1 : R = matrix {{1,1,2,2},{2,3,1,3},{3,2,3,1}};
3 4
o1 : Matrix ZZ <-- ZZ
|
i2 : V = matrix {{1,-1},{0,0},{0,0}};
3 2
o2 : Matrix ZZ <-- ZZ
|
i3 : C = posHull R
o3 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of the cone => 3
number of facets => 4
number of rays => 4
o3 : Cone
|
i4 : halfspaces C
o4 = | -2 1 1 |
| 1 -1 1 |
| 1 1 -1 |
| 5 -1 -1 |
4 3
o4 : Matrix ZZ <-- ZZ
|
Now we take this cone over a line and get a polyhedron.
i5 : P = convexHull(V,R)
o5 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 3
number of facets => 6
number of rays => 4
number of vertices => 2
o5 : Polyhedron
|
i6 : halfspaces P
o6 = (| 0 1 -3 |, | 0 |)
| 2 -1 -1 | | 2 |
| -1 1 -1 | | 1 |
| 0 -3 1 | | 0 |
| -1 -1 1 | | 1 |
| -5 1 1 | | 5 |
o6 : Sequence
|