#  Copyright (c) 1997-2015
#  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.
#-------------------------------------------------------------------------------


# n_polytopes, dimension, n_vertices (in each) => list of Polytope<Rational>
sub generate_random_spheres {
   my ($n, $d, $n_vert)=@_;

   map { rand_sphere($d, $n_vert) } 1..$n;
}

# list of polytopes => saves the polytope with the greatest number of facets in a file
sub save_max_facets {
   # construct the file name from the dimension and the number of vertices
   my $filename= "max_facets_" . $_[0]->DIM . "_" . $_[0]->N_VERTICES;

   my $p= -f "$filename.poly" ? load($filename) : shift;
   foreach (@_) {
      $p=$_ if $_->N_FACETS > $p->N_FACETS;
   }

   save($p, $filename);
   print "$filename has ", $p->N_FACETS, " facets\n";
}

# main
if (@ARGV != 3) {
   die "usage: polymake --script polytope::rand_polytopes n_polytopes dimension n_vertices\n";
}
my @p=generate_random_spheres(@ARGV);
save_max_facets(@p);


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