#!/usr/bin/perl -w
#use strict;
use warnings;
use Data::Dumper;
use Math::Polynomial::Solve qw! poly_derivative poly_roots !;
use Math::Round qw! round !;
use Devel::Size qw! size total_size !;
use Scalar::Util qw! weaken isweak !;
use Test::Memory::Cycle;
use Test::LeakTrace;

my %haystack;

# $rep means right endpoint of the interval [0, $rep]
my $rep = int 3;

foreach my $x (3 .. $rep ) {
    foreach my $y (2 .. $x-1 ) {
        foreach my $z (1 .. $y-1 ) {
            # expanded form of x*(x - $x)*(x - $y)*(x - $z)
            # coeffs are in an array
            
            $haystack{"$x, $y, $z"} =  [
                poly_roots(
                    poly_derivative(
                        1, -$x - $y - $z, $x*$y + $x*$z + $y*$z, -$x*$
+y*$z, 0
                    )
                )
            ];
        }
    }
}

# for each zero in @zeros, assigns a truth value to whether or not it 
+is within 0.0001 of an integer (1=true, 0=false)
sub is_approximately_an_integer {
    my $eps = 0.0001;
    while( my $x = shift ) {
        
    # need to use "round", "int" does not work!
    
    return 0 if abs( $x-round($x) ) > $eps;
    }
    return 1
}

# this returns only the arrays but loses keys
#print "\nSelected arrays\n";
my @wants = grep { is_approximately_an_integer( @$_ ) } values %haysta
+ck;
#print Dumper( @wants );

# this returns the keys
#print "\nSelected keys...\n";
@wants = grep { is_approximately_an_integer( @{$haystack{$_}} ) } keys
+ %haystack;
print Dumper( @wants );

# and you can get the arrays as well
#print "\n...and the associated array.\n";
#print Dumper( @haystack{@wants} );

my $polys = $#wants + 1;
    
# prints out the corresponding values from %haystack
#if ( @wants ) {
#    print "\nWe found $polys polynomials!\n";
#} else {
#    print "No polynomials here. Try another interval.\n";
#};

my $size = size(\%haystack);
my $total_size = total_size(\%haystack);
print "\nThe size of haystack is $size bytes.\n";
print "The size of haystack including references is $total_size bytes.
+\n";

my $sizewants = size(\@wants);
my $totalsizewants = total_size(\@wants);
print "\nThe size of wants is $sizewants bytes.\n";
print "The size of wants including references is $totalsizewants bytes
+.\n";
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