use Math::Polynomial::Solve qw!poly_derivative poly_roots!;

my %haystack;

my $rep = int 5; # $rep means right endpoint of the interval [0, $rep]

foreach ( $a = 1; $a <= $rep; $a++ ) {
	foreach ( $b = 1; $b <= $rep; $b++ ) {
		foreach ( $c = 1; $c <= $rep; $c++ ) {
			if ( $a == $b || $b == $c || $c == $a ){
				next;
				} else {

                # expanded form of (x^2)*(x - a)*(x - b)*(x - c)
                # coeffs are in an array

				my @quintic = (1, -$a - $b - $c, $a*$b + $a*$c + $b*$c, -$a*$b*$c, 0, 0); 
				my @derivative = poly_derivative(@quintic);
				my @zeros = poly_roots(@derivative);	
							
				$haystack{@quintic}{@derivative} =  @zeros;
			}
		}
	}
}