Description
A must be a matrix from the ambient space of the polyhedron
P to some other target space and
v must be a vector in that target space, i.e. the number of columns of
A must equal the ambient dimension of
P and
A and
v must have the same number of rows. Then
affineImage computes the polyhedron
{(A*p)+v  p in P} where
v is set to 0 if omitted and
A is the identity if omitted.
For example, consider the following two dimensional polytope:
i1 : P = convexHull matrix {{2,0,2,4},{8,2,2,8}}
o1 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 4
number of rays => 0
number of vertices => 4
o1 : Polyhedron

This polytope is the affine image of the square:
i2 : A = matrix {{5,2},{3,1}}
o2 =  5 2 
 3 1 
2 2
o2 : Matrix ZZ < ZZ

i3 : v = matrix {{5},{3}}
o3 =  5 
 3 
2 1
o3 : Matrix ZZ < ZZ

i4 : Q = affineImage(A,P,v)
o4 = {ambient dimension => 2 }
dimension of lineality space => 0
dimension of polyhedron => 2
number of facets => 4
number of rays => 0
number of vertices => 4
o4 : Polyhedron

i5 : vertices Q
o5 =  1 1 1 1 
 1 1 1 1 
2 4
o5 : Matrix QQ < QQ
