This is a tutorial about how to use Perl within polymake, which was presented at the polymake-Workshop at Darmstadt, in March 2011. A short introduction to Perl in polymake can be found at “polymake for the Perl Newbie”.

The Perl programming language originally provides three different data structures, scalars($), arrays(@), and hashes(%). The user always has to specify the type of a variable using the appropriate symbol ''$, @, or %. If you forget to do so, you will receive the following error message: <code> polytope > i=5; polymake: ERROR: Unquoted string “i” may clash with future reserved word. </code>
Here are some simple commands illustrating how to use the different data structures: * Scalars <code> $i=5; $j=6; $sum=$i+$j; print $sum; </code> * Arrays <code> @array=(“a”,“b”,“c”); print scalar(@array); push(@array,“d”); print “@array”; $first_entry=$array[0]; print $first_entry; print join(“\n”,@array); @array2=(3,1,4,2); print sort(@array2); </code> * Hashes <code> %hash=(); $hash{“zero”}=0; $hash{“four”}=4; print keys %hash; print join(“, ”,keys %hash); print join(“, ”,values %hash); %hash=(“one”,1,“two”,2); %hash=(“one”⇒1,“two”⇒2); </code>
===“Small objects”: Data structures inherited from C++=== In addition to the three standard data structures, the enriched version of Perl used in polymake also provides special data structures that are inherited from the C++-side of polymake''.

$arr1=new Array<String>(\@array); print $arr1;
$arr2=new Array<Int>([3,2,5]); print $arr2; 
$arr3=new Array<Int>(0,1,2,3); print $arr3; 
$arr4=new Array<Int>(0..4); print $arr4;
@arr4=@{$arr4};
print $arr2;
$set=new Set<Int>(3,2,5); print $set;
$mat=new Matrix<Rational>([[2,1,4,0,0],[3,1,5,2,1],[1,0,4,0,6]]); print $mat;
$mat->row(1)->[1]=7; print $mat;
$mat->(1,2)=8; print $mat;
print 4*unit_matrix<Rational>(3);
$m_rat=new Matrix<Rational>(3/5*unit_matrix<Rational>(5)); print $m_rat; 
$m2=$mat/$m_rat; print $m2;
$m_int=new Matrix<Int>(unit_matrix<Rational>(5)); print $m_int;
$m3=$m_rat/$m_int;
$m3=$m_rat/(convert_to<Rational>($m_int)); print $m3;
$z_vec=zero_vector<Int>($m_int->rows);
$extended_matrix=($z_vec|$m_int); print $extended_matrix;
$template_Ex=new Array<Set<Int>>((new Set<Int>(5,2,6)),$set); print
$template_Ex;

$p=new Polytope<Rational>(POINTS=>cube(4)->VERTICES);
$lp=new LinearProgram<Rational>(LINEAR_OBJECTIVE=>[0,1,1,1,1]);
$p->LP=$lp;
print $p->LP->MAXIMAL_VALUE;

points.demo

open(INPUT, "< /home/katrin/polymake/demo/Workshop2011/points.demo");
$matrix=new Matrix<Rational>(<INPUT>);
close(INPUT);
print $matrix;

$p=new Polytope<Rational>(POINTS=>$matrix);
print $p->FACETS;
print $p->DIM;
print $p->VERTEX_SIZES;
;### choose "simple" vertices
for(my $i=0;$i<scalar(@{$p->VERTEX_SIZES});$i++){
    if($p->VERTEX_SIZES->[$i]==$p->DIM){
	print $i.": ".$p->VERTICES->row($i)."\n";
    }
}
$s=new Set<Int>();
for(my $i=0;$i<scalar(@{$p->VERTEX_SIZES});$i++){
    if($p->VERTEX_SIZES->[$i]==$p->DIM){
	$s+=$i;
    }
}
$special_points=$p->VERTICES->minor($s,All); print $special_points;
;
foreach(@{$s}){
    print $p->VERTICES->row($_)."\n";
}
foreach my $index(@{$s}){
    print $p->VERTICES->row($index)."\n";
}

Scripting