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D.16.2.27 maximalFace
Syntax:
Polymake::maximalFace( polytope p, intvec v )
Assume:
- v lies in the negative 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 maximal.
Note:
- The 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. Hence the maximal 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::maximalFace(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
==>
==> 1,1,0,
==> 1,0,1
v = -5,1,1;
Polymake::maximalFace(p,v);
==> 1,1,0,
==> 1,0,1
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