# objectiveVector -- computes an objective vector of a face of a polyhedron

## Synopsis

• Usage:
v = objectiveVector(P,Q)
• Inputs:
• Q, , which must be a face of P
• Outputs:
• v, , one column vector over QQ representing a vector

## Description

An objective vector v of a face Q of a polyhedron P is vector such that Q = {p in P | v*p = max over P} i.e. it is the face on which v attains its maximum.

 i1 : P = hypercube 3 o1 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => 3 number of facets => 6 number of rays => 0 number of vertices => 8 o1 : Polyhedron i2 : Q = convexHull matrix {{1,1,-1,-1},{1,-1,1,-1},{1,1,1,1}} o2 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => 2 number of facets => 4 number of rays => 0 number of vertices => 4 o2 : Polyhedron i3 : v = objectiveVector(P,Q) o3 = | 0 | | 0 | | 1 | 3 1 o3 : Matrix ZZ <--- ZZ

Since it is the face on which v attains its maximum it can be recovered with maxFace:

 i4 : Q == maxFace(v,P) o4 = true

## Ways to use objectiveVector :

• "objectiveVector(Polyhedron,Polyhedron)"

## For the programmer

The object objectiveVector is .