Published at Aug 06 2019
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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 * b1`

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 `q`

th 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.

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

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

Install assignment dependencies:

```
$ yarn install
```

Execute the tests with:

```
$ yarn 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 `xit`

to
`it`

.

Wikipedia https://en.wikipedia.org/wiki/Rational_number

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

```
import Rational from './rational-numbers'
describe('Addition', () => {
it('Add two positive rational numbers', () => {
const expected = new Rational(7, 6)
expect(new Rational(1, 2).add(new Rational(2, 3))).toEqual(expected)
})
xit('Add a positive rational number and a negative rational number', () => {
const expected = new Rational(-1, 6)
expect(new Rational(1, 2).add(new Rational(-2, 3))).toEqual(expected)
})
xit('Add two negative rational numbers', () => {
const expected = new Rational(-7, 6)
expect(new Rational(-1, 2).add(new Rational(-2, 3))).toEqual(expected)
})
xit('Add a rational number to its additive inverse', () => {
const expected = new Rational(0, 1)
expect(new Rational(1, 2).add(new Rational(-1, 2))).toEqual(expected)
})
})
describe('Subtraction', () => {
xit('Subtract two positive rational numbers', () => {
const expected = new Rational(-1, 6)
expect(new Rational(1, 2).sub(new Rational(2, 3))).toEqual(expected)
})
xit('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)
})
xit('Subtract two negative rational numbers', () => {
const expected = new Rational(1, 6)
expect(new Rational(-1, 2).sub(new Rational(-2, 3))).toEqual(expected)
})
xit('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', () => {
xit('Multiply two positive rational numbers', () => {
const expected = new Rational(1, 3)
expect(new Rational(1, 2).mul(new Rational(2, 3))).toEqual(expected)
})
xit('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)
})
xit('Multiply two negative rational numbers', () => {
const expected = new Rational(1, 3)
expect(new Rational(-1, 2).mul(new Rational(-2, 3))).toEqual(expected)
})
xit('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)
})
xit('Multiply a rational number by 1', () => {
const expected = new Rational(1, 2)
expect(new Rational(1, 2).mul(new Rational(1, 1))).toEqual(expected)
})
xit('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', () => {
xit('Divide two positive rational numbers', () => {
const expected = new Rational(3, 4)
expect(new Rational(1, 2).div(new Rational(2, 3))).toEqual(expected)
})
xit('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)
})
xit('Divide two negative rational numbers', () => {
const expected = new Rational(3, 4)
expect(new Rational(-1, 2).div(new Rational(-2, 3))).toEqual(expected)
})
xit('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', () => {
xit('Absolute value of a positive rational number', () => {
const expected = new Rational(1, 2)
expect(new Rational(1, 2).abs()).toEqual(expected)
})
xit('Absolute value of a negative rational number', () => {
const expected = new Rational(1, 2)
expect(new Rational(-1, 2).abs()).toEqual(expected)
})
xit('Absolute value of zero', () => {
const expected = new Rational(0, 1)
expect(new Rational(0, 1).abs()).toEqual(expected)
})
})
describe('Exponentiation of a rational number', () => {
xit('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)
})
xit('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)
})
xit('Raise zero to an integer power', () => {
const expected = new Rational(0, 1)
expect(new Rational(0, 1).exprational(5)).toEqual(expected)
})
xit('Raise one to an integer power', () => {
const expected = new Rational(1, 1)
expect(new Rational(1, 1).exprational(4)).toEqual(expected)
})
xit('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)
})
xit('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', () => {
xit('Raise a real number to a positive rational number', () => {
const expected = 16.0
expect(new Rational(4, 3).expreal(8)).toEqual(expected)
})
xit('Raise a real number to a negative rational number', () => {
const expected = 1.0/3.0
expect(new Rational(-1, 2).expreal(9)).toBeCloseTo(expected, 15)
})
xit('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', () => {
xit('Reduce a positive rational number to lowest terms', () => {
const expected = new Rational(1, 2)
expect(new Rational(2, 4).reduce()).toEqual(expected)
})
xit('Reduce a negative rational number to lowest terms', () => {
const expected = new Rational(-2, 3)
expect(new Rational(-4, 6).reduce()).toEqual(expected)
})
xit('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)
})
xit('Reduce zero to lowest terms', () => {
const expected = new Rational(0, 1)
expect(new Rational(0, 6).reduce()).toEqual(expected)
})
xit('Reduce an integer to lowest terms', () => {
const expected = new Rational(-2, 1)
expect(new Rational(-14, 7).reduce()).toEqual(expected)
})
xit('Reduce one to lowest terms', () => {
const expected = new Rational(1, 1)
expect(new Rational(13, 13).reduce()).toEqual(expected)
})
})
```

```
class Rational {
public a:number;
public b:number;
constructor(numerator:number, denominator:number) {
this.a = numerator;
this.b = denominator;
if (this.b === 0) {
throw new Error('denominator must not be zero!');
}
}
public add(rational:Rational):Rational {
return new Rational(this.a*rational.b + this.b*rational.a, this.b*rational.b).reduce();
}
public sub(rational:Rational):Rational {
return new Rational(this.a*rational.b - this.b*rational.a, this.b*rational.b).reduce();
}
public mul(rational:Rational):Rational {
return new Rational(this.a*rational.a, this.b*rational.b).reduce();
}
private invert(rational:Rational):Rational {
return new Rational(rational.b, rational.a);
}
public div(rational:Rational):Rational {
return this.mul(this.invert(rational));
}
public abs():Rational {
return new Rational(Math.abs(this.a), Math.abs(this.b));
}
public exprational(exp:number):Rational {
return new Rational(Math.pow(this.a, exp), Math.pow(this.b, exp)).reduce();
}
public expreal(exp:number):number {
return parseFloat(Math.pow(Math.pow(exp, this.a), 1/this.b).toPrecision(15));
}
public reduce():Rational {
let a:number = this.a;
let b:number = this.b;
if (a % b === 0) {
a = a/b;
b = 1;
}
else {
const gcd = this.gcd(a, b);
a = a/gcd;
b = b/gcd;
}
if (b < 0) {
a = -a;
b = -b;
}
return new Rational(a, b);
}
private gcd(a:number, b:number):number {
if( a===b || b===0 ) {
return a;
}
return this.gcd(b, a%b);
}
}
export default Rational
```

A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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