Math::Expr does exactly what you want. Release date is 2001-10-01, so it's fairly up to date.

     NAME
         Math::Expr - Parses mathematical expressions


     SYNOPSIS
         use Math::Expr;

         SetOppDB(new Math::Expr::OpperationDB('<DBFileName>'));
         $e=Parse("a+4*b-d/log(s)+f(d,e)");

     DESCRIPTION
         Parses mathematical expressions into a tree structure. The expressions
         may contain integers, real numbers, alphanumeric variable names,
         alphanumeric function names and most other characters might be used
         as operators...

From the pod. That's no reason not to write your own as an exercise :)

After Compline,
Zaxo

Something like this needs a recursive parser. Aside from suggesting Parse::RecDescent or the example in Japhy's book, I'll give a few suggestions on how I would approach this.

First off, you are correct in storing it a tree-type data structure. However, don't use a normal hash; I recommend Tie::IxHash to keep an ordered hash since you will need to reorder later.

Next, you will need to figure out a way of determining whether a term is top level, and separate those terms from each other. Simply splitting on /[+-]/ wont be enough; you'll need to inchworm through in order and determine context. Next, you'll have to separate those terms which are /[*\/]/, and mark those as separate parts of one term. Finally, you'll need to deal with leftovers, such as exponentiation, function calls, etc.

Once you have the top level terms in the tree, you'll have descend into each node and repeat the process (here is where the recursion comes in.) You'll need to do it again, and again, and again, until everything is parsed to its lowest level. Finally, you'll have to work backwards from the bottom to perform the calculations.

Not as easy as you thought, was it? That's why there is CPAN :)

      +
     / \
    /   \
   /     \
 tan     *
  |     / \
  ^    2 sin
 / \      |
x   4     x
[download]

=cut
--Brent Dax
There is no sig.

Computer languages get around this by requiring explicit multiplication symbols: The expression above becomes b*(x+1) if multiplication is intended. Your example above indicates that you want implicit multiplication, and that can be very tricky. If you see something like y = mx, how will you know how to parse it? Is mx one variable, or is it the product of m and x? These are the sorts of side problems that you'll have to solve to build a parser that works the way you want it to.

You might want to consider first writing a parser for a simpler and less ambiguous language---say, arithmetic expressions involving only numerals, with explicit multiplication. Once you have some experience solving the simple problem, you can go back and embellish it to handle more complex expressions.

--
Mark Dominus
Perl Paraphernalia

1. Parantheses (I would imagine trig functions go here)
2. Exponents (I would imagine logarythms go here)
3. Multiplication, Division
4. Addition, Subtraction

For the second part you can be smart. Declare your parser as not lazy, then if mx has not yet been seen but m and x have there is implicit multiplication. On the gripping hand say m, x, and mx are defined. I'd opt for mx and force explicit multiplcation for m and x.

--
perl -pe "s/\b;([st])/'\1/mg"

Also I think I might have a different preference for the way you order things in your tree. That said, perhaps the problem could be redefined by designing a converter from the above infix notation to Reverse-Polish (postfix) Notation? Some linx: <a href=http://www.onthenet.com.au/~grahamis/int2008/week02/lect02.html#stackapp">1 2 3

Move SIG!

Math::Expr at search.cpan.org. Maybe the site was down, or you typed it wrong.
Also I did

perl -MCPAN -e 'install Math::Expr'
[download]

and it found it and installed it...
--
Snazzy tagline here

This is wierd. I have been totally unable to reach any links to modules inside search.cpan.org, using different computers, for the past week. People are posting links I can't see, and I can't search through their search form.

I wonder if it is something to do with a configuration they did and me not being in the right hemisphere?

I get:

Forbidden
You don't have permission to access /search on this server.


----------------------------------------------------------------------
+----------

Apache/1.3.22 Server at search.cpan.org Port 80
[download]

Math::ParseEquation was the name I originally planned to use, since no one has suggested I change it, I guess I'm sticking with it.



---


"Weird things happen, get used to it."

Flame ~ Lead Programmer: GMS