Problem 18

Compute the tropical convex hull of the Hilbert matrix, for various :math::n.

Solution

In Polymake:

sub Hilbert{
  my $n = $_[0];
  my $h = new Matrix(zero_matrix($n,$n));
  for(my $i=0; $i<$n; $i++){
    for(my $j=0; $j<$n; $j++){
      $h->elem($i,$j)=new Rational(1,($i+$j+1));
    }
  }
  return new tropical::Polytope<Min>(POINTS=>$h);
}