Validating linear equations with regular expressions?

How can I validate linear equations with regular expressions or is there another way besides using regular expressions. I will use ^ to denote an exponent.

2x + 3 = 8 //This should validate fine

3x + 2y + 4z = 12 //This should validate fine

4x^2 + 2y = 22 //This should not validate because of the power.

4xy + 3y = 45 //This should not validate because of the product of two unknowns.

2/x + 4y = 22 //This should not validate becaus开发者_开发问答e of the unknown in the denominator

(3/4)x + 3y + 2z = 40 //This should validate fine.

I'd start by writing a definition of a valid linear equation using Backus-Naur notation, with things like:

<integer> := <digit> | <integer> <digit>
<constant> := <integer> | ...
<variable> := <letter>
<term> := <constant> | <variable> | <constant> <variable>

and so on.

There are many ways to turn that into a validator. Having some experience with it, I'd use yacc or bison to write a parser that would only generate a parse tree if the input was a valid linear equation.

You might find regular expressions are too limited to do what you need - I just don't use them enough to know.

The cases you've mentioned are easy:

fail if /[xyz]\s*\^/;
fail if /\/\s*[xyz]/;
fail if /([xyz]\s*){2,}/;

(this is Perl syntax, assuming $_ contains the expression, and fail is whatever it is you do when you want to give up.)

Here you can replace xyz with whatever is a valid expression for one variable.

But in general this will require actual parsing of the expression, which is a job for lex/yacc or something like that, not a regular expression.

For example if "xy" is a legitimate variable name, then of course this all crumbles.