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| 1 | /*
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| 2 | Fraction.js v5.0.0 10/1/2024
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| 3 | https://raw.org/article/rational-numbers-in-javascript/
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| 4 |
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| 5 | Copyright (c) 2024, Robert Eisele (https://raw.org/)
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| 6 | Licensed under the MIT license.
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| 7 | */
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| 8 | const Fraction = require('fraction.js');
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| 9 |
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| 10 | // Calculates (a/b)^(c/d) if result is rational
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| 11 | // Derivation: https://raw.org/book/analysis/rational-numbers/
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| 12 | function root(a, b, c, d) {
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| 13 |
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| 14 | // Initial estimate
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| 15 | let x = Fraction(100 * (Math.floor(Math.pow(a / b, c / d)) || 1), 100);
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| 16 | const abc = Fraction(a, b).pow(c);
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| 17 |
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| 18 | for (let i = 0; i < 30; i++) {
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| 19 | const n = abc.mul(x.pow(1 - d)).sub(x).div(d).add(x)
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| 20 |
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| 21 | if (x.n === n.n && x.d === n.d) {
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| 22 | return n;
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| 23 | }
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| 24 | x = n;
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| 25 | }
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| 26 | return null;
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| 27 | }
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| 28 |
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| 29 | root(18, 2, 1, 2); // 3/1
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