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# morganbarrett's solution

## to Rational Numbers in the JavaScript Track

Published at Jan 13 2021 · 0 comments
Instructions
Test suite
Solution

A rational number is defined as the quotient of two integers a and b, called the numerator and denominator, respectively, where b != 0.

The absolute value |r| of the rational number r = a/b is equal to |a|/|b|.

The sum of two rational numbers r₁ = a₁/b₁ and r₂ = a₂/b₂ is r₁ + r₂ = a₁/b₁ + a₂/b₂ = (a₁ * b₂ + a₂ * b₁) / (b₁ * b₂).

The difference of two rational numbers r₁ = a₁/b₁ and r₂ = a₂/b₂ is r₁ - r₂ = a₁/b₁ - a₂/b₂ = (a₁ * b₂ - a₂ * b₁) / (b₁ * b₂).

The product (multiplication) of two rational numbers r₁ = a₁/b₁ and r₂ = a₂/b₂ is r₁ * r₂ = (a₁ * a₂) / (b₁ * b₂).

Dividing a rational number r₁ = a₁/b₁ by another r₂ = a₂/b₂ is r₁ / r₂ = (a₁ * b₂) / (a₂ * b₁) if a₂ is not zero.

Exponentiation of a rational number r = a/b to a non-negative integer power n is r^n = (a^n)/(b^n).

Exponentiation of a rational number r = a/b to a negative integer power n is r^n = (b^m)/(a^m), where m = |n|.

Exponentiation of a rational number r = a/b to a real (floating-point) number x is the quotient (a^x)/(b^x), which is a real number.

Exponentiation of a real number x to a rational number r = a/b is x^(a/b) = root(x^a, b), where root(p, q) is the qth root of p.

Implement the following operations:

• addition, subtraction, multiplication and division of two rational numbers,
• absolute value, exponentiation of a given rational number to an integer power, exponentiation of a given rational number to a real (floating-point) power, exponentiation of a real number to a rational number.

Your implementation of rational numbers should always be reduced to lowest terms. For example, 4/4 should reduce to 1/1, 30/60 should reduce to 1/2, 12/8 should reduce to 3/2, etc. To reduce a rational number r = a/b, divide a and b by the greatest common divisor (gcd) of a and b. So, for example, gcd(12, 8) = 4, so r = 12/8 can be reduced to (12/4)/(8/4) = 3/2.

Assume that the programming language you are using does not have an implementation of rational numbers.

## Setup

Go through the setup instructions for Javascript to install the necessary dependencies:

https://exercism.io/tracks/javascript/installation

## Requirements

Please cd into exercise directory before running all below commands.

Install assignment dependencies:

\$ npm install

## Making the test suite pass

Execute the tests with:

\$ npm test

In the test suites all tests but the first have been skipped.

Once you get a test passing, you can enable the next one by changing xtest to test.

## Submitting Solutions

Once you have a solution ready, you can submit it using:

exercism submit rational-numbers.js

## Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

## Exercise Source Credits

### rational-numbers.spec.js

import { Rational } from './rational-numbers';

test('Add two positive rational numbers', () => {
const expected = new Rational(7, 6);
});

xtest('Add a positive rational number and a negative rational number', () => {
const expected = new Rational(-1, 6);
});

xtest('Add two negative rational numbers', () => {
const expected = new Rational(-7, 6);
});

const expected = new Rational(0, 1);
});
});

describe('Subtraction', () => {
xtest('Subtract two positive rational numbers', () => {
const expected = new Rational(-1, 6);
expect(new Rational(1, 2).sub(new Rational(2, 3))).toEqual(expected);
});

xtest('Subtract a positive rational number and a negative rational number', () => {
const expected = new Rational(7, 6);
expect(new Rational(1, 2).sub(new Rational(-2, 3))).toEqual(expected);
});

xtest('Subtract two negative rational numbers', () => {
const expected = new Rational(1, 6);
expect(new Rational(-1, 2).sub(new Rational(-2, 3))).toEqual(expected);
});

xtest('Subtract a rational number from itself', () => {
const expected = new Rational(0, 1);
expect(new Rational(1, 2).sub(new Rational(1, 2))).toEqual(expected);
});
});

describe('Multiplication', () => {
xtest('Multiply two positive rational numbers', () => {
const expected = new Rational(1, 3);
expect(new Rational(1, 2).mul(new Rational(2, 3))).toEqual(expected);
});

xtest('Multiply a negative rational number by a positive rational number', () => {
const expected = new Rational(-1, 3);
expect(new Rational(-1, 2).mul(new Rational(2, 3))).toEqual(expected);
});

xtest('Multiply two negative rational numbers', () => {
const expected = new Rational(1, 3);
expect(new Rational(-1, 2).mul(new Rational(-2, 3))).toEqual(expected);
});

xtest('Multiply a rational number by its reciprocal', () => {
const expected = new Rational(1, 1);
expect(new Rational(1, 2).mul(new Rational(2, 1))).toEqual(expected);
});

xtest('Multiply a rational number by 1', () => {
const expected = new Rational(1, 2);
expect(new Rational(1, 2).mul(new Rational(1, 1))).toEqual(expected);
});

xtest('Multiply a rational number by 0', () => {
const expected = new Rational(0, 1);
expect(new Rational(1, 2).mul(new Rational(0, 1))).toEqual(expected);
});
});

describe('Division', () => {
xtest('Divide two positive rational numbers', () => {
const expected = new Rational(3, 4);
expect(new Rational(1, 2).div(new Rational(2, 3))).toEqual(expected);
});

xtest('Divide a positive rational number by a negative rational number', () => {
const expected = new Rational(-3, 4);
expect(new Rational(1, 2).div(new Rational(-2, 3))).toEqual(expected);
});

xtest('Divide two negative rational numbers', () => {
const expected = new Rational(3, 4);
expect(new Rational(-1, 2).div(new Rational(-2, 3))).toEqual(expected);
});

xtest('Divide a rational number by 1', () => {
const expected = new Rational(1, 2);
expect(new Rational(1, 2).div(new Rational(1, 1))).toEqual(expected);
});
});

describe('Absolute value', () => {
xtest('Absolute value of a positive rational number', () => {
const expected = new Rational(1, 2);
expect(new Rational(1, 2).abs()).toEqual(expected);
});

xtest('Absolute value of a negative rational number', () => {
const expected = new Rational(1, 2);
expect(new Rational(-1, 2).abs()).toEqual(expected);
});

xtest('Absolute value of zero', () => {
const expected = new Rational(0, 1);
expect(new Rational(0, 1).abs()).toEqual(expected);
});
});

describe('Exponentiation of a rational number', () => {
xtest('Raise a positive rational number to a positive integer power', () => {
const expected = new Rational(1, 8);
expect(new Rational(1, 2).exprational(3)).toEqual(expected);
});

xtest('Raise a negative rational number to a positive integer power', () => {
const expected = new Rational(-1, 8);
expect(new Rational(-1, 2).exprational(3)).toEqual(expected);
});

xtest('Raise zero to an integer power', () => {
const expected = new Rational(0, 1);
expect(new Rational(0, 1).exprational(5)).toEqual(expected);
});

xtest('Raise one to an integer power', () => {
const expected = new Rational(1, 1);
expect(new Rational(1, 1).exprational(4)).toEqual(expected);
});

xtest('Raise a positive rational number to the power of zero', () => {
const expected = new Rational(1, 1);
expect(new Rational(1, 2).exprational(0)).toEqual(expected);
});

xtest('Raise a negative rational number to the power of zero', () => {
const expected = new Rational(1, 1);
expect(new Rational(-1, 2).exprational(0)).toEqual(expected);
});
});

describe('Exponentiation of a real number to a rational number', () => {
xtest('Raise a real number to a positive rational number', () => {
const expected = 16.0;
expect(new Rational(4, 3).expreal(8)).toEqual(expected);
});

xtest('Raise a real number to a negative rational number', () => {
expect(new Rational(-1, 2).expreal(9)).toBeCloseTo(0.33, 2);
});

xtest('Raise a real number to a zero rational number', () => {
const expected = 1.0;
expect(new Rational(0, 1).expreal(2)).toEqual(expected);
});
});

describe('Reduction to lowest terms', () => {
xtest('Reduce a positive rational number to lowest terms', () => {
const expected = new Rational(1, 2);
expect(new Rational(2, 4).reduce()).toEqual(expected);
});

xtest('Reduce a negative rational number to lowest terms', () => {
const expected = new Rational(-2, 3);
expect(new Rational(-4, 6).reduce()).toEqual(expected);
});

xtest('Reduce a rational number with a negative denominator to lowest terms', () => {
const expected = new Rational(-1, 3);
expect(new Rational(3, -9).reduce()).toEqual(expected);
});

xtest('Reduce zero to lowest terms', () => {
const expected = new Rational(0, 1);
expect(new Rational(0, 6).reduce()).toEqual(expected);
});

xtest('Reduce an integer to lowest terms', () => {
const expected = new Rational(-2, 1);
expect(new Rational(-14, 7).reduce()).toEqual(expected);
});

xtest('Reduce one to lowest terms', () => {
const expected = new Rational(1, 1);
expect(new Rational(13, 13).reduce()).toEqual(expected);
});
});
const gcd = (a, b) => b ? gcd(b, a % b) : a;

export class Rational {
constructor(a, b){
let d = gcd(a, b);
this.a = (a / d) || 0;
this.b = (b / d) || 0;
}

return new Rational(this.a * r.b + r.a * this.b, r.b * this.b);
}

sub(r){
return new Rational(this.a * r.b - r.a * this.b, r.b * this.b);
}

mul(r){
return new Rational(this.a * r.a, r.b * this.b);
}

div(r){
return new Rational(this.a * r.b, r.a * this.b)
}

abs(){
return new Rational(Math.abs(this.a), Math.abs(this.b));
}

exprational(n){
return n >= 0 ?
new Rational(this.a ** n, this.b ** n) :
new Rational(this.b ** -n, this.a ** -n);
}

expreal(x){
return Math.round((x ** this.a) ** (1 / this.b) * 100) / 100;
}

reduce(){
return this;
}
}