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D.13.2.42 maximalValue

Procedure from library polymake.lib (see polymake_lib).

Usage:
maximalValue(p,v); p polytope, v intvec

Assume:
v lies in the negative dual tail cone of p

Return:
intmat, vertices of the face of p on which the linear form v is maximal

Note:
first coordinate of v corresponds to a shift of the maximal value since p is considered as a polytope in the plane (first coordinate) = 1.

Example:
 
LIB "polymake.lib";
==> Welcome to polymake version
==> Copyright (c) 1997-2015
==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt)
==> http://www.polymake.org
intmat M[3][3]=
1,1,0,
1,0,1,
1,-1,-1;
intvec v = 0,1,1;
polytope p = polytopeViaPoints(M);
maximalValue(p,v);
==> polymake: used package ppl
==>   The Parma Polyhedra Library (PPL): A C++ library for convex polyhedra
==>   and other numerical abstractions.
==>   http://www.cs.unipr.it/ppl/
==> 
==> 1
intvec w = -5,1,1;
maximalValue(p,w);
==> -4