#  Copyright (c) 1997-2004
#  Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
#  http://www.math.tu-berlin.de/polymake,  mailto:polymake@math.tu-berlin.de
#
#  This program is free software; you can redistribute it and/or modify it
#  under the terms of the GNU General Public License as published by the
#  Free Software Foundation; either version 2, or (at your option) any
#  later version: http://www.gnu.org/licenses/gpl.txt.
#
#  This program is distributed in the hope that it will be useful,
#  but WITHOUT ANY WARRANTY; without even the implied warranty of
#  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#  GNU General Public License for more details.
#-----------------------------------------------------------------------------
#  $Project: polymake $$Id: polarize.rules 7567 2007-01-17 15:19:17Z joswig $

object Polytope;

# category: Polarization
# Relatively interior point of the polyhedron.

property REL_INT_POINT
$type="vector";


# category: Polarization
# Valid strict inequality for all affine points of the polyhedron.

property FAR_HYPERPLANE
$type="vector";


REL_INT_POINT : AMBIENT_DIM
PRECONDITION: CENTERED
   $this->CENTERED
WEIGHT 0.10
   $this->REL_INT_POINT= "1".(" 0" x $this->AMBIENT_DIM);

FAR_HYPERPLANE : AMBIENT_DIM
PRECONDITION: BOUNDED
   $this->BOUNDED
WEIGHT 0.10
   $this->FAR_HYPERPLANE= "1".(" 0" x $this->AMBIENT_DIM);

REL_INT_POINT : VERTEX_BARYCENTER
WEIGHT 0.10
   $this->REL_INT_POINT=$this->VERTEX_BARYCENTER;

REL_INT_POINT : VERTICES | POINTS
   client("inner_point", $this, "VERTICES | POINTS", "REL_INT_POINT")

FAR_HYPERPLANE : FACETS | INEQUALITIES
   client("inner_point", $this, "FACETS | INEQUALITIES", "FAR_HYPERPLANE")


DIM, REL_INT_POINT, AFFINE_HULL : FACETS | INEQUALITIES, ONE_VERTEX
PRECONDITION: BOUNDED
   $this->BOUNDED
WEIGHT 3.30
   client("rel_int_point", $this);

DIM, REL_INT_POINT : FACETS | INEQUALITIES, AFFINE_HULL, ONE_VERTEX
PRECONDITION: BOUNDED, AFFINE_HULL
   defined($this->AFFINE_HULL)&&$this->BOUNDED
WEIGHT 3.25
   client("rel_int_point", $this,"-affinehull");

DIM, REL_INT_POINT : FACETS | INEQUALITIES, AFFINE_HULL, ONE_VERTEX
PRECONDITION: AFFINE_HULL
   defined($this->AFFINE_HULL)
WEIGHT 3.35
   client("rel_int_point", $this,"-unbounded","-affinehull");

DIM, REL_INT_POINT, AFFINE_HULL : FACETS | INEQUALITIES, ONE_VERTEX
WEIGHT 3.40
   client("rel_int_point", $this,"-unbounded");

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