cubic.p6

#!/usr/bin/env perl6

sub cubic(\a,\b,\c,\d) {
    my \Δ0 = b²	- 3 × a × c;
    my \Δ1 = 2 * b³ - 9 × a × b × c + 27 × a² × d;
    my \C = ( ( Δ1 + sqrt( Δ1² - 4 × Δ0³ + 0i) ) / 2 ).roots(3)[0];
    my \ς = 1.roots(3);  # cubic roots of unity
    return [0,1,2].map: -> \k {
        ( -1 / ( 3 × a ) ) × ( b + ς[k] × C + Δ0 / ( C × ς[k] ) )
    }
}

# note: special case when Δ0 == 0

my @vals = cubic(1,10,10,-10);

# test
use Test;
plan 3;

my $f = -> \x { x³ + 10 * x² + 10 * x - 10 };

is-approx $f( @vals[0] ), 0, 'first value';
is-approx $f( @vals[1] ), 0, 'second value';
is-approx $f( @vals[2] ), 0, 'third value';