Variable as parameter of custom function

[NullDev]

So, I'm building a simple sigmaSum function that I'm importing via mathjs.import

and the function works perfectly fine. e.g.:

sigmaSum("n=1", "k=5", "n^2 + k")
-> 80

Now the problem is, because it's a custom function and I have to use quotes for the arguments, I can't actually pass variables. e.g.: this does not work:

f(n) = sigmaSum("i=1","k=n-1", "floor(1 / gcd(i, k))"); f(15)

because n defined in f(n), which thus should be 15, is unknown to sigmaSum.
Is there a way to actually get the context and all variables defined "outside" of sigmaSum?
it would be ideal if I wouldn't need the quotes all together and can just parse the math as-is but I think that's not possible.

I could live with f(n) = sigmaSum("i=1", "k=${n}-1", "i + k"); f(10) as well, but this doesn't seem to work. I'm not sure when and how to use toTex() with my code since its literally just

const sigmaSum = function(n, k, expr){
    const [n_Symbol, n_Value] = parseVar(n);
    const [k_Symbol, k_Value] = parseVar(k);   

    let result = 0;
    for (let i = n_Value; i <= k_Value; i++){
        result += mathjs.evaluate(expr.replaceAll(n_Symbol, i).replaceAll(k_Symbol, k_Value))
     }
     return result;
};

mathjs.import({
    sigmaSum,
});

any help would be appreciated :)

[dvd101x]

Hi, here are a few pointers

To access variables outside sigmaSum you need to use either a parser or a scope. I guess your mathjs isn't a parser. https://mathjs.org/docs/expressions/parsing.html

To be able to use "k=${n}-1" it seems you intend to use template literals so you need to use back ` instead of " like so: `k=${n}-1`

Your function definition might be more usable if you don't assign it to a constant:

Instead of

const sigmaSum = function(n, k, expr){
}

Try

function sigmaSum(n, k, expr){
  // this way you could call the function in lines before its definition
}

You could remove the for loop by using math.sum directly over an array.

Maybe use a helper function that always receives the arguments in the exact format.

function summation(i0, n, f) {
  const I = math.range(i0, n, true)
  return math.sum(I.map(i => f(i, n)))
}
console.log(summation(1, 5, (n, k) => n ** 2 + k))                // 80
console.log(summation(1, 5, math.evaluate("f(n, k) = n^2 + k")))  // 80

[NullDev]

Hey! Thank you for your reply :)

---

I guess your mathjs isn't a parser.

That's correct. I'm using the evaluator for that (or rather, a wrapper for mathjs.evaluate())

---

To be able to use "k=${n}-1" it seems you intend to use template literals so you need to use back instead of " like so:k=${n}-1`

Template literals don't really work in that case. e.g. f(n) = sigmaSum("i=1",`k=${n}-1`, "floor(1 / gcd(i,k))"); f(15) doesn't actually interpolate the n from f() into my function. I was referring to .toTex() here: https://mathjs.org/docs/expressions/customization.html#custom-latex-handlers - which I thought could be an option.

---

this way you could call the function in lines before its definition

That's an intentional design choice. Hoisting can be rather counterproductive at times which is why I explicitly use const lambda functions

---

You could remove the for loop by using math.sum directly over an array.

That was intentional as well because I limit the computation time of my iterative calculator function. I omitted that part in the code because it wasn't really relevant to my question.

const sigmaSum = function(n, k, expr){
    const [n_Symbol, n_Value] = parseVar(n);
    const [k_Symbol, k_Value] = parseVar(k);   

    let result = 0;
    const startTime = Date.now();

    for (let i = n_Value; i <= k_Value; i++){
        if (Date.now() - startTime > computationLimitSecs * 1000){
            throw new Error("Function execution exceeded " + computationLimitSecs + " seconds");
        }

        result += mathjs.evaluate(expr.replaceAll(n_Symbol, i).replaceAll(k_Symbol, k_Value))
     }
     return result;
};

a rather naive approach, but it's good enough I guess.
The whole thing is here

---

I really appreciate all the feedback though, thanks!
Im just still not sure how I'd go about passing "outside" variables to my custom function.

[dvd101x]

Oh thanks for reviewing the reply and for sharing your project it's very cool.

I misunderstood the purpose of your code. Thanks for your clarifications.

[josdejong]

@NullDev you can use the rawArgs feature, then you can use sigmaSum(n=1, k=5, n^2 + k) and
f(n) = sigmaSum(i=1, k=n-1, floor(1 / gcd(i, k))); f(15) just like you want.

Docs: https://mathjs.org/docs/expressions/customization.html#custom-argument-parsing

Here a full example:

import { create, all } from 'mathjs'

const mathjs = create(all)

function sigmaSum (args, math, scope){
  const [nNode, kNode, exprNode] = args

  if (!nNode.isAssignmentNode || !nNode.object.isSymbolNode) {
    throw Error('First argument must define a variable, like "i=1"')
  }
  const nName = nNode.object.name

  if (!kNode.isAssignmentNode || !kNode.object.isSymbolNode) {
    throw Error('Second argument must define a variable, like "k=5"')
  }
  const kName = kNode.object.name

  const n = nNode.compile().evaluate(scope);
  const k = kNode.compile().evaluate(scope);
  const expr = exprNode.compile()

  let result = 0;
  for (let i = n; i <= k; i++) {
    const newScope = new Map()
    scope.forEach((value, key) => newScope.set(key, value))
    newScope.set(nName, i)
    newScope.set(kName, k)
    result += expr.evaluate(newScope)
  }
  return result;
}
sigmaSum.rawArgs = true

mathjs.import({
  sigmaSum,
});

// Usage
const result1 = mathjs.evaluate('sigmaSum(n=1, k=5, n^2 + k)')
console.log('result1:', result1) // 80

const scope2 = new Map()
mathjs.evaluate('f(n) = sigmaSum(i=1, k=n-1, floor(1 / gcd(i, k)))', scope2)
const result2 = mathjs.evaluate('f(15)', scope2)
console.log('result2:', result2) // 6

const scope3 = new Map()
mathjs.evaluate('f(x) = sigmaSum(n=1, k=5, sigmaSum(a=1, b=5, x + a))', scope3)
const result3 = mathjs.evaluate('f(10)', scope3)
console.log('result3:', result3)

EDIT: added copying the all existing scope variables before passing them to result += expr.evaluate(...)

[NullDev]

Works like a charm. Thank you so much for your help (again 😅) and your amazing work on the library!

[josdejong]

Thanks, you're welcome 😊

[josdejong]

The issue with new Map(scope) is fixed via a7f84ab (not yet published)

[josdejong]

The fix for new Map(scope) is now published in v12.4.0

[NullDev]

Awesome, thanks!