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# Copyright (c) 1997-2018
# Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
# http://www.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.
#-------------------------------------------------------------------------------
# @topic application
# This application concentrates on [[Hypersurface|tropical hypersurfaces]] and [[Polytope|tropical polytopes]].
# It provides the functionality for the computation of basic properties. Visualization and various constructions are possible.
IMPORT common graph
USE polytope fan graph matroid
file_suffix trop
HELP help.rules
##################################################################################
declare property_type CovectorDecoration : c++ (include=>"polymake/tropical/covectors.h");
# A tropical polytope is the tropical convex hull of finitely many points in tropical projective space.
# It should always be defined via [[POINTS]] instead of [[VERTICES]], as those define the combinatorics
# of the induced subdivision.
# @tparam Addition Either [[Min]] or [[Max]]. There is NO default for this, you have to choose!
# @tparam Scalar Rational by default. The underlying type of ordered group.
declare object Polytope<Addition, Scalar=Rational> [ is_ordered_field_with_unlimited_precision(Scalar) ];
# A tropical cycle is a weighted, balanced, pure polyhedral complex.
# It is given as a polyhedral complex in tropical projective coordinates.
# To be precise: Each row of [[VERTICES]] and [[LINEALITY_SPACE]]
# has a leading 1 or 0, depending on whether it is a vertex or a ray.
# The remaining n coordinates are interpreted as an element of
# R<sup>n</sup> modulo (1,..,1).
# IMPORTANT NOTE: VERTICES are assumed to be normalized such that the first coordinate (i.e.
# column index 1) is 0. If your input is not of that form, use [[PROJECTIVE_VERTICES]].
# Note that there is a convenience method [[thomog]], which converts affine coordinates
# into projective coordinates.
# @tparam Addition The tropical addition. Warning: There is NO default for this, you have to choose either [[Max]] or [[Min]].
declare object Cycle<Addition> : fan::PolyhedralComplex<Rational>;
# This is a special instance of a Cycle: It is the tropical locus of a
# polynomial over the tropical numbers.
declare object Hypersurface<Addition> : Cycle<Addition>;
INCLUDE
cycle.rules
hypersurface.rules
covector_lattice.rules
cone_properties.rules
cone.rules
gfan.rules
#FIXME Add connection to tplib again?
#tplib.rules
visual.rules
visual_covector.rules
# Local Variables:
# mode: perl
# cperl-indent-level: 3
# indent-tabs-mode:nil
# End:
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