CODEWITHSUNDEEP
javascriptregexmathstring-parsing
Patrick Roberts
Patrick Roberts

Reputation: 51846

RegExp for parsing a Math Expression?

Hey I've written a fractal-generating program in JavaScript and HTML5 (here's the link), which was about a 2 year process including all the research I did on Complex math and fractal equations, and I was looking to update the interface, since it is quite intimidating for people to look at. While looking through the code I noticed that some of my old techniques for going about doing things were very inefficient, such as my Complex.parseFunction.

I'm looking for a way to use RegExp to parse components of the expression such as functions, operators, and variables, as well as implementing the proper order of operations for the expression. An example below might demonstrate what I mean:

//the first example parses an expression with two variables and outputs to string
console.log(Complex.parseFunction("i*-sinh(C-Z^2)", ["Z","C"], false))

"Complex.I.mult(Complex.neg(Complex.sinh(C.sub(Z.cPow(new Complex(2,0,2,0))))))"

//the second example parses the same expression but outputs to function
console.log(Complex.parseFunction("i*-sinh(C-Z^2)", ["Z","C"], true))

function(Z,C){
  return Complex.I.mult(Complex.neg(Complex.sinh(C.sub(Z.cPow(new Complex(2,0,2,0))))));
}

I know how to handle RegExp using String.prototype.replace and all that, all I need is the RegExp itself. Please note that it should be able to tell the difference between the subtraction operator (e.g. "C-Z^2") and the negative function (e.g. "i*-(Z^2+C)") by noting whether it is directly after a variable or an operator respectively.

Upvotes: 1

Views: 1156

Answers (1)

DrC
DrC

Reputation: 7698

While you can use regular expressions as part of an expression parser, for example to break out tokens, regular expressions do not have the computational power to parse properly nested mathematical expressions. That is essentially one of the core results of computing theory (finite state automata vs. push down automata). You probably want to look at something like recursive-descent or LR parsing.

I also wouldn't worry too much about the efficiency of parsing an expression provided you only do it once. Given all of the other math you are doing, I doubt it is material.

Upvotes: 2

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