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D.13.2.43 minimalFace
Procedure from library polymake.lib (see polymake_lib).
- Usage:
- minimalFace(p,v); p polytope, v intvec
- Assume:
- v lies in the dual tail cone of p
- Return:
- intmat, vertices of the face of p on which the linear form v is minimal
- Note:
- the minimal face is independent of the first coordinate of v
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);
minimalFace(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/
==>
==> 1,1,0,
==> 1,0,1
intvec w = 5,-1,-1;
minimalFace(p,w);
==> 1,1,0,
==> 1,0,1
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