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# Copyright (c) 1997-2024
# 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.
#-------------------------------------------------------------------------------
# @topic application
# This application deals with polyhedral fans. You can define a fan, e.g. via its [[RAYS]] and [[MAXIMAL_CONES]]
# and compute several properties like [[HASSE_DIAGRAM]] and [[F_VECTOR]].
IMPORT polytope
USE ideal
file_suffix fan
HELP help.rules
# @category Geometry
# A polyhedral fan.
# The current restriction is that each cone in the fan has to be pointed. This will be relaxed later.
# If a fan is specified via [[INPUT_RAYS]] and [[INPUT_CONES]] each input cone must list all the input rays incident.
#
# Once non-trivial linealities are allowed the following will apply:
# The [[RAYS]] always lie in a linear subspace which is complementary to the [[LINEALITY_SPACE]].
# @tparam Scalar numeric data type used for the coordinates, must be an ordered field. Default is [[Rational]].
# @example A typical example is the normal fan of a convex polytope.
# > $f=normal_fan(polytope::cube(3));
# > print $f->F_VECTOR;
# | 6 12 8
declare object PolyhedralFan<Scalar=Rational> [ is_ordered_field(Scalar) ];
# @category Geometry
# A hyperplane arrangement.
# The hyperplane arrangement is given by a matrix [[HYPERPLANES]] whose rows
# are the linear equations of the hyperplanes and an optional support cone. The
# support cone defaults to being the whole space. Duplicate hyperplanes are
# ignored, as well as hyperplanes that intersect the support cone trivially.
# The support cone is subdivided by the hyperplanes resulting in a fan
# [[CHAMBER_DECOMPOSITION]].
# @tparam Scalar numeric data type used for the coordinates, must be an ordered field. Default is [[Rational]].
# @example Take the 2-dimensional positive orthant and slice it along the ray through (1,1)
# > $HA = new HyperplaneArrangement(HYPERPLANES=>[[-1,1]], "SUPPORT.INPUT_RAYS"=>[[1,0],[0,1]]);
# > $CD = $HA->CHAMBER_DECOMPOSITION;
# > print $CD->RAYS;
# | 0 1
# | 1 0
# | 1 1
# > print $CD->MAXIMAL_CONES;
# | {1 2}
# | {0 2}
#
# @example Coxeter hyperplane arrangement of type E8.
# > $E8 = new HyperplaneArrangement(HYPERPLANES=>root_system("E8")->VECTORS->minor(All,~[0]));
# Note that the roots lie "at infinity", which is why the leading zero column of the root vectors is eliminated.
declare object HyperplaneArrangement<Scalar=Rational> [ is_ordered_field(Scalar) ] : VectorConfiguration<Scalar> ;
# @category Geometry
# A polyhedral complex. The derivation from [[PolyhedralFan]] works like the derivation of [[Polytope]] from [[Cone]].
# @example The following defines a subdivision of a square in the plane into two triangles.
# > $c=new PolyhedralComplex(VERTICES=>[[1,0,0],[1,1,0],[1,0,1],[1,1,1]],MAXIMAL_POLYTOPES=>[[0,1,2],[1,2,3]]);
declare object PolyhedralComplex<Scalar=Rational> [ is_ordered_field(Scalar) ] : PolyhedralFan<Scalar>;
# @category Geometry
# A special big object class devoted to planar unfoldings of 3-polytopes. Its main functionality is the visualization.
# @example [require bundled:cdd] To visualize a planar net of some Johnson solid (with flaps, such that you can print, cut and glue):
# > planar_net(polytope::johnson_solid(52))->VISUAL->FLAPS;
declare object PlanarNet<Scalar=Rational> : PolyhedralComplex<Float>;
# @category Geometry
# A subdivision of vectors, in contrast to [[PolyhedralFan]] this allows cells with interior points.
# Similar to the distinction between [[Cone]] and [[VectorConfiguration]].
# @tparam Scalar default: [[Rational]]
declare object SubdivisionOfVectors<Scalar=Rational> [ is_ordered_field(Scalar) ];
# @category Geometry
# The inhomogeneous variant of [[SubdivisionOfVectors]], similar to the derivation of [[PointConfiguration]] from [[VectorConfiguration]].
# @tparam Scalar default: [[Rational]]
# @example [require bundled:cdd] [prefer cdd] To produce a regular subdivision of the vertices of a square:
# > $c=new SubdivisionOfPoints(POINTS=>polytope::cube(2)->VERTICES,WEIGHTS=>[0,0,0,1]);
# > print $c->MAXIMAL_CELLS;
# | {0 1 2}
# | {1 2 3}
declare object SubdivisionOfPoints<Scalar=Rational> [ is_ordered_field(Scalar) ] : SubdivisionOfVectors<Scalar>;
INCLUDE
fan_properties.rules
initial.rules
polyhedral_complex_properties.rules
subdivision_properties.rules
common.rules
incidence_perm.rules
polyhedral_complex.rules
planar_net.rules
bounded_complex.rules
bounded_complex_visual_graph.rules
subdivision.rules
visual.rules
lattice.rules
gfan.rules
splitstree.rules
action.rules
symmetric_fan.rules
voronoi.rules
visual_voronoi.rules
hyperplane_arrangement.rules
compactification.rules
stacky_fan.rules
# Local Variables:
# mode: perl
# cperl-indent-level:3
# indent-tabs-mode:nil
# End:
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