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D.16.2.29 minimalFace

Syntax:
Polymake::minimalFace( polytope p, intvec v )
Assume:
v lies in the dual tail cone of p.
Type:
intmat
Purpose:
intmat, whose rows are the vertices of the face of p on which the linear form v is minimal.
Note:
The first coordinate of v corresponds to a shift of the minimal value since p is considered as a polytope in the plane (first coordinate) = 1. Hence the minimal face is independent of the first coordinate of v.
Example:
 
  LIB"polymake.lib";
==> Welcome to polymake
==> Copyright (c) 1997-2012
==> 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);
  Polymake::maximalValue(p,v);
==> polymake: used package cddlib
==>   Implementation of the double description method of Motzkin et al.
==>   Copyright by Komei Fukuda.
==>   http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html
==> 
==> 1
  v = -5,1,1;
  Polymake::maximalValue(p,v);
==> -4