#  Copyright (c) 1997-2010
#  Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Darmstadt, Germany)
#  http://www.polymake.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: help.rules 9502 2010-02-24 00:26:29Z gawrilow $

# @topic functions/Producing from scratch
# With these clients you can create polytopes belonging to various parameterized
# families which occur frequently in polytope theory, as well as random
# polytopes with different models of randomness.


# @topic functions/Producing a new polyhedron from others
# Another important way of constructing polytopes is to modify an 
# already existing polytope.
#
# Actually, these function don't alter the input polytope
# (it is forbidden in polymake), but create a new polytope object.
#
# Many functions can at your choice either calculate the vertex or facet coordinates,
# or constrain themselves on the purely combinatorial description of the
# resulting polytope.


# @topic functions/Transforming a polyhedron
# These functions take a realized polytope and produce a new one by applying a
# suitable affine or projective transformation in order to obtain some special
# coordinate description but preserve the combinatorial type.
#
# For example, before you can polarize an arbitrary polyhedron, it
# must be transformed to a combinatorially equivalent bounded polytope with the
# origin as a relatively interior point. It is achieved with the sequence
# orthantify - bound - center - polarize.


# Local Variables:
# mode: perl
# c-basic-offset:3
# End:
