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D.13.2.47 minimalValue
Procedure from library polymake.lib (see polymake_lib).
- Usage:
- minimalValue(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 minimal
- Note:
- 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.
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);
minimalValue(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
==>
==> 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;
minimalValue(p,w);
==> 4
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