Diophantine Equation Solver

[japhy]

   1: # working on making it allow negative numbers via some
   2: # crazy form of look-behind and look-ahead
   3: 
   4: # NOTE: just because you CAN use a regex to do this
   5: # doesn't mean you should!
   6: 
   7: use Carp;
   8: 
   9: if (%results = solve_dio('5x + 7y + 4z = 50')) {
  10:   print map "$_ => $results{$_}\n", keys %results;
  11: }
  12: 
  13: if (solve_dio(x => 3, y => 2, z => 5, 102)) {
  14:   print "solution found!\n";
  15: }
  16: 
  17: 
  18: # solve_dio('3x + 2y + 5z = 102');
  19: # solve_dio(x => 3, y => 2, z => 5, 102);
  20: 
  21: sub solve_dio {
  22:   my ($sum,%args,$regex,@values);
  23: 
  24:   if (@_ > 1) {
  25:     $sum = pop;
  26:     %args = @_;
  27:   }
  28:   elsif (@_ == 1) {
  29:     ($sum,%args) = parseEQN(shift);
  30:   }
  31:   else {
  32:     croak << "USAGE";
  33: not enough args to solve_dio()
  34:   solve_dio(EQN)
  35:   solve_dio(VAR => COEFF, [VAR => COEFF, ] SUM)
  36: USAGE
  37:   }
  38: 
  39:   $regex = join " ", map "((?:@{[ 0 x $args{$_} ]})+)", keys %args;
  40: 
  41:   if (@values = (0 x $sum) =~ /^ $regex $/x) {
  42:     return 1 if !wantarray;
  43:     for (@values) {
  44:       my ($var) = each %args;
  45:       $args{$var} = length() / $args{$var};
  46:     }
  47:     return %args;
  48:   }
  49: }
  50: 
  51: sub parseEQN {
  52:   (my $EQN = shift) =~ tr/A-Za-z0-9 //cd;
  53:   my (@parts,$sum,%args);
  54: 
  55:   @parts = split ' ', $EQN;
  56:   $sum = pop @parts;
  57:   %args = map reverse(/(\d+)([a-z])/), @parts;
  58: 
  59:   return ($sum, %args);
  60: }

[kryten]

For all, like me, wondering what a Diophantine equation actually is:

Diophantine equation
(from: britannica.com who seem to hand out far too many cookies.)

[An] equation involving only addition, multiplication, or taking power
+s in which all the constants are
natural numbers or their negatives and the only solutions of interest 
+are natural numbers or their
negatives. Named in honour of the 3rd-century Greek mathematician Diop
+hantus of Alexandria,
these equations were not systematically solved until the 7th century b
+y the Hindus.

Maybe a maths type person can elaborate.