| #### 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 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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