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 cdd ==> 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