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use application "polytope";
sub lpclosure
{
my $p = shift;
my $d = $p->AMBIENT_DIM;
my $q = new Polytope<Rational>($p);
for (my $k = 0; $k < $d; $k = $k+1)
{
if ( $q->DIM == -1 ) # can stop as soon as $q is empty
{
return $q;
}
# create reversed opposite inequalities of 0/1-cube and corresponding polyhedra
my $v1 = new Vector<Rational>(0 | -unit_vector($d, $k));
my $v2 = new Vector<Rational>(-1 | unit_vector($d, $k));
# create intersection of corresponding polyhedra with iterated polyhedron $q
my $b1 = new Polytope<Rational>(INEQUALITIES => $v1 / $q->FACETS);
my $b2 = new Polytope<Rational>(INEQUALITIES => $v2 / $q->FACETS);
if ( ($b1->DIM > -1) && ($b2->DIM > -1) )
{
my $c = conv($b1, $b2);
$q = intersection($q, $c);
}
elsif ( ($b1->DIM > -1) && ($b2->DIM == -1) )
{
$q = intersection($q, $b1);
}
elsif ( ($b1->DIM == -1) && ($b2->DIM > -1) )
{
$q = intersection($q, $b2);
}
}
return $q;
}
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