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javascriptsymbolic-math

JS: Resolve a Formula for x

I have a formula with several components, let's say w = x * y / z^2 + c. Now I have an input-field for each variable. My goal is, to calculate the missing one as soon, as all the others were entered. Difficulty is, that you can choose which fields you fill and which you want to leave free.

The easy (naive) way would of course be to resolve it for each variable by hand, detect the missing var, and have seperate js functions for each case. But I even have linked formulas (like x in the above formula is x = a + b, too) as well and the options are almost infinitive. Is there any option in JS to solve a formula by a specified variable? I could then replace each variable string with the assigned value and then eval the string.

First I thought Nerdamer would be the thing, but it turned out that it can only evaluate expressions and can't handle equations.

Is this possible? Any better idea?

Thanks in advance!

P.S.: My actual set of formula is:

dR = c * I^2 / A
R = L * dR
P = I * U
DV = R * I
DW = DV * I

It's for calculating losses in a cable due to ohm's resistance. Each Variable has a corresponding input field.

Solution

  • The following solution can be built for finding "R" using nerdamer. The logic can be extended to solve for the remaining variables. Do keep in mind that the current limitation is that nerdamer can currently only solve up to cubic functions algebraically. Higher order functions will be solved numerically.

    //You can then take care of the non linear containing I. I is quadratic
var dR = nerdamer('R=L*dR').solveFor('dR');
var I = nerdamer('dR=c*I^2/A').sub('dR', dR).solveFor('I');
//You can first start by reducing the first few equations since they are linear and you can solve them as a linear system
var solutions = nerdamer.solveEquations(['P = I * U', 'DV = R * I', 'DW = DV * I'], ['I', 'DW', 'P']);
//the solutions come back as an array arrays in the form of [variable, value]
//you can see what they look like. In your case all your solutions will be in terns of DV & U since these are the only actual knowns
//You can see what the solutions look like
solutions.map(function(x) {
    console.log('-'+x[0]+' = '+x[1]);
});
console.log('------------------ R ----------------');
var R = nerdamer.setEquation(I[0], solutions[0][1]).solveFor('R');
//I will have 3 solutions since it's cubic. You can console.log them below
R.map(function(x) {
    console.log('R = '+x.toString());
});
    <script src="https://cdn.jsdelivr.net/npm/nerdamer@latest/nerdamer.core.js"></script>
<script src="https://cdn.jsdelivr.net/npm/nerdamer@latest/Algebra.js"></script>
<script src="https://cdn.jsdelivr.net/npm/nerdamer@latest/Calculus.js"></script>
<script src="https://cdn.jsdelivr.net/npm/nerdamer@latest/Extra.js"></script>
<script src="https://cdn.jsdelivr.net/npm/nerdamer@latest/Solve.js"></script>