I see two problems, and I have a feeling there are others.

1. You're calling P_j with an argument of 4. This number is used as an index into @pair_points, which might not have any data at that index. With your sample data, for example, it doesn't.

2. In the for loop, you give $generic_pol a value only conditionally (i.e. when $k != $j) but you always multiply $pol by it, regardless. Perhaps the for loop should be something like this:

    for( my $k = 0 ; $k < $n ; $k++ ) {
        next if $k == $j;
        my $generic_pol = Math::Polynomial->new( 1, -$pair_points[$k]-
+>[0] )
                        / ( $pair_points[$j]->[0] - $pair_points[$k]->
+[0]);
        $pol *= $generic_pol;
    }
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