compare math equations prior to evaluation javascript

Question

I'm running through algebra and attempting to create a JavaScript tester function which compares two equations and determines if they are considered associative properties. In other words, if I group (a + b) + c vs. a + (b + c) the result will be the same. Multiplication and addition only.

Up to this point, I've attempted to build a simple function that resolves whether the final value is equal to the compared equation value. What I would like is if I was able to compare both equations without their parenthesis. Thinking I need to look up regular expressions... but looking for a little help on direction.

 let a = 1, b = 2, c = 3, number1 = (a * b) * c, number2 = a * (b * c); function isAssociative(num1, num2) { let answer = num1 === num2; return `Are ${num1} and ${num2} associative... ${answer}`; } console.log(isAssociative(number1, number2)); 

Currently, this results in, 'Are 6 and 6 associative... true'. This is what I want, but if I changed the second argument to a static 6 when calling the function... then this is not an associative combo and I would like it to return false.

Answer 1

You can use Mathjs and the simplify method:

 console.clear(); term_a = 'a + ( b + c )' term_b = '( a + b ) + c'; tree_a = math.simplify(term_a); tree_b = math.simplify(term_b); console.log(term_a, tree_a.equals(tree_b) ? 'equals' : 'differs from', term_b); term_a = 'a + ( b + c + d )' term_b = '( a + b ) + c'; tree_a = math.simplify(term_a); tree_b = math.simplify(term_b); console.log(term_a, tree_a.equals(tree_b) ? 'equals' : 'differs from', term_b); 

 <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjs/5.4.2/math.min.js"></script> 

Answer 2

I found an answer I'm satisfied with.

let number1 = prompt('Enter an equation').toString().replace(/[^0-9,+,*]+/g,''),
  number2 = prompt('Enter equation 2').toString().replace(/[^0-9,+,*]+/g,'');

function isAssociative (num1, num2) {
  if (num1 === num2) {
    return eval(num1) === eval(num2);
  } else {
    return false;
  }
}

alert(isAssociative(number1, number2));

I could wait for the numbers to enter the function as a string, check for parenthesis first to verify it even qualifies... if parenthesis exist, then I could execute the regEx code and if they don't exist return 'not associative' at that point. For now, this works as well as I want it to.