Symbolic sqrt?

Is it possible to treat a square root as it is, e.g. √5, without converting it to a number?

Specifically, I’d like to do the following:

sqrt(5) //=> √5 object
sqrt(2) + sqrt(3) //=> √2 + √3
sqrt(2) + sqrt(2) //=> 2 * √2
sqrt(3 * 3) //=> 3

I have read some examples and, like in the custom_datatatype.js example, I thought I could add a custom data type for √. But I couldn’t figure out how to return the value as it is of add, sub, etc.

If anyone knows how to do it right, please let me know! Finally, thank you for such a wonderful library.

[josdejong]

That’s good to hear 👍

About simplifying expressions with matrices: that is an open feature request, see #1913. Help is welcome 😃

[josdejong]

@yasuhito you could try another lib like https://nerdamer.com/demo or my lib while it is not supported here.

Thanks for the link Viktor, I hadn’t heard about Nerdamer before, it looks great! I’ve linked to it from the downloads page.

@yasuhito The reason is that there is a built-in rule which evaluates functions containing constants, also for sqrt. This is the simplifyConstant rule: simplify.js#L300. So, what you need is create your own version of this function, which first checks the special sqrt rule, and otherwise fallback to the old behavior. Here a full example:

const { simplify, isFunctionNode, isInteger, ConstantNode } = require('mathjs')

const rules = simplify.rules.map(rule => {
  if (typeof rule === 'function' && rule.name === 'simplifyConstant') {
    // replace the built-in simplifyConstant with our own extended version
    const simplifyConstant = rule

    return function customSimplifyConstant(node) {
      if (isFunctionNode(node) && node.name === 'sqrt') {
        const result = node.compile().evaluate({})
        if (isInteger(result)) {
          // return the integer result (for example `sqrt(25)`
          return new ConstantNode(result)
        } else {
          // do not replace sqrt functions not resulting in an integer result, like `sqrt(5)`
          return node
        }
      }
      else {
        // fall back on the original behavior
        return simplifyConstant(node, {})
      }
    }
  }
  else {
    // leave all other built-in rules untouched
    return rule
  }
})

function simplifyAndPrint(expression) {
  console.log(`${expression}=${simplify(expression, rules)}`)
}

simplifyAndPrint('2 + 5')     // 7
simplifyAndPrint('sqrt(25)')  // 5
simplifyAndPrint('sqrt(5)')   // sqrt(5)

You’re fully flexible in which rules you do or do not want to apply with the function simplify 😄