minimizing simple linear equations

[beemshake]

Dear Monks,

Anybody know of a package that will allow me to minimize a string like

(foo * 2) + (foo * 3)

and get something like 'foo * 5' in return?

thanks!

[saintmike]

Math::Algebra::Symbols does a pretty good job if it doesn't get too complicated:

    use Math::Algebra::Symbols
    my ($foo) = symbols(qw(foo));

    my $result = ($foo * 2) + ($foo * 3);

    print "$result\n";

prints

    5 * $foo


Here's an article on it.

[beemshake]

Thanks for all the tips. I think Math::Algebra::Symbols was what I was looking for, but by the time I found it I had already written the script to just run the equations through mathomatic to simplify them.

[gjb]

First off, what you're trying to accomplish is called 'simplification', not minimization. I don't want to sound pedantic, but this could put your quest on the right track.

Secondly, you could have a look at Math::Symbolic. Unfortunately, the docs are sparse, so it's not clear to me what it does, but it seems to do at least some simplification.

Hope this helps, -gjb-

[Fletch]

That's not exactly a trivial task. If you have something like Mathematica or Maple you could open a pipe to that and let it do the heavy lifting.

[shotgunefx]

You might find this helpful.
Evaluate Expressions. This is one of my favorite things I've ever written. It parses expressions and evaluates them. It's the basis for a mini language that got put on hold for some time.

In the evaulate sub, right after  @$ops = grep { defined $_ } @$ops; You basically have a parse tree.

For your example, you'd have

(foo*2) + (foo*3)
$ops = [
          [
            'foo',
            '*',
            '2'
          ],
          '+',
          [
            'foo',
            '*',
            '3'
          ]
        ];

You could modify it there to optimize the tree the way you w ant.

[sgt]

symbolic stuff is tough; one good program that you can download from nikhef is __form__ by Jos Vermasern (at least some version if free...) I think you can easily generate a small form program, call form on it and parse it back... good luck http://www.nikhef.nl/~t68/ Math::Symbolic on CPAN can handle this too... -- sgt

[dynamo]

If you want comprehensive symbolic manipulation, I'm not sure where to point you to..

But for the case described above (and feel free to use this as a starting point to write your own comprehensive symbolic manipulation module), you can do:

$string =~ s/ //gs; # remove spaces
$string =~ s/\((\w+)\*(\d+)\)\+\(\1\*(\d+))/($1\*(?{$2+$3})\)/gsx;

Which should do only exactly the substitution you describe above. (Needs testing)