30 lines
704 B
JavaScript
30 lines
704 B
JavaScript
/*
|
|
Fraction.js v5.0.0 10/1/2024
|
|
https://raw.org/article/rational-numbers-in-javascript/
|
|
|
|
Copyright (c) 2024, Robert Eisele (https://raw.org/)
|
|
Licensed under the MIT license.
|
|
*/
|
|
const Fraction = require('fraction.js');
|
|
|
|
// Calculates (a/b)^(c/d) if result is rational
|
|
// Derivation: https://raw.org/book/analysis/rational-numbers/
|
|
function root(a, b, c, d) {
|
|
|
|
// Initial estimate
|
|
let x = Fraction(100 * (Math.floor(Math.pow(a / b, c / d)) || 1), 100);
|
|
const abc = Fraction(a, b).pow(c);
|
|
|
|
for (let i = 0; i < 30; i++) {
|
|
const n = abc.mul(x.pow(1 - d)).sub(x).div(d).add(x)
|
|
|
|
if (x.n === n.n && x.d === n.d) {
|
|
return n;
|
|
}
|
|
x = n;
|
|
}
|
|
return null;
|
|
}
|
|
|
|
root(18, 2, 1, 2); // 3/1
|