79 lines
2.3 KiB
JavaScript
79 lines
2.3 KiB
JavaScript
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class BigRational {
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constructor(numerator, denominator) {
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this.numerator = BigInt(numerator);
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this.denominator = BigInt(denominator);
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const gcd = this.gcd(this.numerator, this.denominator);
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this.numerator = this.numerator / gcd;
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this.denominator = this.denominator / gcd;
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}
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gcd(a, b) {
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a = a < 0n ? -a : a;
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b = b < 0n ? -b : b;
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while (b !== 0n) {
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const temp = b;
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b = a % b;
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a = temp;
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}
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return a;
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}
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add(other) {
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const numer = this.numerator * other.denominator + this.denominator * other.numerator;
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const denom = this.denominator * other.denominator;
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return new BigRational(numer, denom);
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}
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toDecimal(decimalPlaces) {
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// Scale up the numerator to get the desired precision
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const scale = BigInt(10) ** BigInt(decimalPlaces + 10);
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const scaledNumerator = this.numerator * scale;
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const quotient = scaledNumerator / this.denominator;
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// Convert to string and insert decimal point
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let str = quotient.toString();
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const totalDigits = str.length;
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const integerDigits = totalDigits - decimalPlaces - 10;
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if (integerDigits <= 0) {
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str = '0.' + '0'.repeat(-integerDigits) + str;
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} else {
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str = str.slice(0, integerDigits) + '.' + str.slice(integerDigits);
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}
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// Round and truncate to the desired decimal places
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const dotIndex = str.indexOf('.');
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return str.slice(0, dotIndex + decimalPlaces + 1);
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}
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toString() {
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return `${this.numerator} / ${this.denominator}`;
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}
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static get ZERO() {
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return new BigRational(0n, 1n);
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}
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}
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function main() {
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console.log("The first 10 terms in Sylvester's sequence are:");
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let term = 2n;
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let sum = BigRational.ZERO;
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for (let i = 1; i <= 10; i++) {
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console.log(term.toString());
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sum = sum.add(new BigRational(1n, term));
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term = term * term - term + 1n;
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}
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console.log();
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console.log("The sum of their reciprocals as a rational number is:");
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console.log(sum.toString() + '\n');
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console.log("The sum of their reciprocals as a decimal number, to 235 decimal places, is:");
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console.log(sum.toDecimal(235));
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}
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main();
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