while (my ($x, $y, $z) = @{ $iter->next // [] }) {
	    
	push @wants,
	map { { join(', ', $x, $y, $z) => $_ } }
	grep { is_approximately_an_integer( @$_ ) } [
		poly_roots(
			poly_derivative(
                            
			# expanded form of x*(x - $x)*(x - $y)*(x - $z)
			1, -$x - $y - $z, $x*$y + $x*$z + $y*$z, -$x*$y*$z, 0
			)
		)       
	];
}

##</code><code>##

my @cnt;
my $seq= 0;
my $x = $cnt[0];
my $y = $cnt[1];
my $z = $cnt[2];

while(  @cnt = $iter->()  ) {
    #printf "%d) %s\n", ++$seq, join ' + ', @cnt
	map { { join(', ', $x, $y, $z) => $_ } }
	grep { is_approximately_an_integer( @$_ ) } [
		poly_roots(
			poly_derivative(
                            
			# expanded form of x*(x - $x)*(x - $y)*(x - $z)
			1, -$x - $y - $z, $x*$y + $x*$z + $y*$z, -$x*$y*$z, 0
			)
		)       
	];
}