This is the part of the program it comes from. I thought all the math stuff would be Math::Something so I didn't know about that combinatorics module! That sounds very interesting. I wonder if/how it could be applied here? It runs through all the possible polynomials of a certain form and spits out the ones whose derivatives have (approximately) integer roots.

`# $lep means smallest nonzero root in the interval [0, $rep]
# $rep means right endpoint of the interval [0, $rep]
my $lep = int 1;
my $rep = int 100;
foreach my $x ($lep+2 .. $rep ) {
foreach my $y ($lep+1 .. $x-1 ) {
foreach my $z ($lep .. $y-1 ) {
foreach my $s (1..$rep/4) {
unless ($y == $x + $s && $z == $y + $s ) {
# assigns a truth value to whether or not it is wi
+thin 0.0001 of an integer (1=true, 0=false)
sub is_approximately_an_integer {
my $eps = 0.0001;
while( my $w = shift ) {
# need to use "round", "int" does not work!
return 0 if abs( $w-round($w) ) > $eps;
}
return 1
}
}
}
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
)
)
];
}
}
}
`

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