use application 'polytope';


sub ct_invariant {
 my ($P, $t) = @_;
 my $v = $P->VERTICES;
 my $hd = $P->HASSE_DIAGRAM;
 my $sign = 1;
 my $c = new Integer(0);

 for (my $d = $P->DIM; $d > 0; --$d) {
  foreach (@{$hd->nodes_of_dim($d)}) {
   my $F = new Polytope(VERTICES=>
              $v->minor($hd->FACES->[$_],All));
   my $vol = $F->LATTICE_VOLUME;
   $c += $sign*fac($d+$t)/fac($d)*$vol;
  }

  $sign = -$sign;
 }

 $c += $sign*fac($t)*$P->N_VERTICES;
 return $c;
}

sub f_poly_coeff {
 my ($P) = @_;
 my $d = $P->DIM;
 my $v = $P->VERTICES;
 my $hd = $P->HASSE_DIAGRAM;
 my $sign = 1;
 my $f = new Vector<Integer>($d+1);

 for (my $k = $d;  $k > 0; --$k) {
  foreach (@{$hd->nodes_of_dim($k)}) {
   my $q = new Polytope(VERTICES=>
              $v->minor($hd->FACES->[$_],All));
   my $h = (zero_vector<Rational>($d-$k))
                 |$q->EHRHART_POLYNOMIAL_COEFF;
   $f += $sign*fac($k+1)*$h;
  }
  $sign = -$sign;
 }

 $f += $sign*$P->N_VERTICES
                 *unit_vector<Rational>($d+1,$d);
 return $f; 
}


sub r_fold_pyr {
 my ($P, $r) = @_;
 for (; $r>0; --$r) {
  $P = lattice_pyramid($P);
 }
 return $P;
}