OK, time to eat some crow.

While Perl no longer display integers without using exponential notation at 18!, when I tried to get a mistake in the display, I couldn't. Except for the fact that Perl did not like displaying large numbers, the results are right.

In retrospect I shouldn't be surprised at this. After all the internal calculation is carried out at a higher accuracy than what is displayed. Since the calculation is pretty short, roundoff errors are not readily visible. And testing this is pretty simple: 

#! /usr/bin/perl
my ($n, $m) = @ARGV;
my $ans = fact($n)/fact($m)/fact($n-$m);
my $err = $ans - sprintf("%.0f", $ans);
print "$n choose $m: $ans (error $err)\n";

sub fact {
  my $fact = 1;
  $fact *= $_ for 1..$_[0];
  $fact;
}

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To find a disagreement between theory and practice I had to go to 28 choose 14. Which was off from being an integer by about 1 part in a hundred million.

Sorry tye, but I find that error tolerable. For a simple example the formula works in this case, even though theoretically in practice it should show some difference between theory and practice.

OTOH I can guarantee you that trying to invert a 10x10 matrix using Cramer's formula is going to be a better example. For an nxn matrix you get n! terms being added and subtracted from each other. It doesn't take a large n to make that rather slow, and to get insane roundoff errors...

In reply to Re (tilly) 1: In theory, theory and practice are the same... by tilly
in thread Binomial Expansion by crazyinsomniac

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