a1951c3aeb
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30 lines
704 B
JavaScript
30 lines
704 B
JavaScript
/*
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Fraction.js v5.0.0 10/1/2024
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https://raw.org/article/rational-numbers-in-javascript/
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Copyright (c) 2024, Robert Eisele (https://raw.org/)
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Licensed under the MIT license.
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*/
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const Fraction = require('fraction.js');
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// Calculates (a/b)^(c/d) if result is rational
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// Derivation: https://raw.org/book/analysis/rational-numbers/
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function root(a, b, c, d) {
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// Initial estimate
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let x = Fraction(100 * (Math.floor(Math.pow(a / b, c / d)) || 1), 100);
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const abc = Fraction(a, b).pow(c);
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for (let i = 0; i < 30; i++) {
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const n = abc.mul(x.pow(1 - d)).sub(x).div(d).add(x)
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if (x.n === n.n && x.d === n.d) {
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return n;
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}
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x = n;
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}
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return null;
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}
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root(18, 2, 1, 2); // 3/1
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