#  Copyright (c) 1997-2021
#  Ewgenij Gawrilow, Michael Joswig, and the polymake team
#  Technische Universität Berlin, Germany
#  https://polymake.org
#
#  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.
#-------------------------------------------------------------------------------

declare object SlackIdeal : ideal::Ideal {

   property NON_SATURATED : ideal::Ideal;

   rule N_VARIABLES = NON_SATURATED.N_VARIABLES;

}

object Polytope {

# @category Geometry
# The slack ideal of the polytope as described in
# > João Gouveia, Antonio Macchia, Rekha R. Thomas, Amy Wiebe:
# > The Slack Realization Space of a Polytope
# > (https://arxiv.org/abs/1708.04739)
#
# Since saturation is computationally expensive, a non-saturated version of the
# ideal is stored in the property [[NON_SATURATED]]. Asking for [[GENERATORS]]
# will do the saturation.
#
# @example [nocompare][require bundled:singular]
# > $c = cube(2,1,0);
# > $I = $c->SLACK_IDEAL;
# > $I->properties;
# | type: SlackIdeal
# | 
# | NON_SATURATED
# | type: Ideal
# | 
# > $I->NON_SATURATED->properties;
# | type: Ideal
# | 
# | N_VARIABLES
# | 8
# | 
# | GENERATORS
# | x_0*x_3*x_5*x_6 - x_1*x_2*x_4*x_7
# | 
# > print $I->GENERATORS;
# | x_0*x_3*x_5*x_6 - x_1*x_2*x_4*x_7
# | 
# @depends singular
property SLACK_IDEAL : SlackIdeal;

}
