use strict;
use warnings;
use List::Util q(reduce);

sub xdi {
    my ($x, $d, $i) = @_;
    reduce{ $a*$b }map{ $_==$i || $d - $x->[$_] }keys @$x
}
sub lagc {
    my ($x, $f) = @_;
    [map{ $f->[$_] / xdi($x,$x->[$_],$_) }keys @$x]
}
sub lagx {
    my ($x, $L, $x0) = @_;
    reduce{ $a+$b }map{ $L->[$_] * xdi($x,$x0,$_) }keys @$x
}