@rgsoft/math

math-js

Yet another JS math library

Installation

npm install @rgsoft/math

Tests

npm run test

Complex Numbers

The complex number library has some methods for performing calculations on complex numbers. To create a complex number of the form a + bi:

const cpx = new Complex(a, b);

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📝 Every complex number is inmutable; both, the real and the imaginary parts are readonly.

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Magnitude

const c = new Complex(5, 12);
console.log(c.mag); // 13

Conjugate

const c = new Complex(2, 7);
console.log(`${c.conjugate()}`); // 2 - 7i

Addition

Scalar Addition

// r + (a + bi) = (a + r) + bi
const c1 = new Complex(5, 12);
const c2 = c1.add(4);
console.log(`${c2}`); // 9 + 12i

Complex Addition

// (a + bi) + (c + di) = (a + c) + (b + d)i
const c1 = new Complex(4, -8);
const c2 = new Complex(-3, 6);
const c3 = c1.add(c2);
console.log(`${c3}`); // 1 + 2i

Substraction

Scalar Substraction

// (a + bi) - r = (a - r) + bi
const c1 = new Complex(9, 1);
const c2 = c1.sub(10);
console.log(`${c2}`); // -1 + 1i

Complex Substraction

// (a + bi) - (c + di) = (a - c) + (b - d)i
const c1 = new Complex(4, -8);
const c2 = new Complex(-3, 6);
const c3 = c1.add(c2);
console.log(`${c3}`); // 1 + 2i

Multiplication

Scalar Multiplication

// r (a + bi) = ra + bi
const c1 = new Complex(4, -1);
const c2 = c1.mult(-5);
console.log(`${c2}`); // -20 + 5i

Complex Multiplication

// (a + bi) (c + di) = (ac - bd) + (ad + bc)i
const c1 = new Complex(3, -1);
const c2 = new Complex(-2, 1);
const c3 = c2.mult(c2);
console.log(`${c3}`); // -5 + 5i

Division

Scalar Division

// (a + bi) / r = a / r + (b / r)i
const c1 = new Complex(4, -1);
const c2 = c1.div(-2);
console.log(`${c2}`); // -2 + 0.5i

Complex Division

let c1 = new Complex(2, 1);
let c2 = new Complex(-1, -1);
let c3 = c1.div(c2);
console.log(`${c3}`); // -1.5 + 0.5i

Square Root

let c = new Complex(4, 0);
c = c.sqrt();
console.log(`${c}`); // 2 + 0i

Vectors

Instantiation:

const vector = new Vector(x, y);

Angle

const v = new Vector(1, 1);
console.log(v.angle); // (Math.PI * 0.5);

Magnitude

const v = new Vector(1, 1);
console.log(v.mag); // (Math.SQRT2);

Normalization

const v = new Vector(4, 4);
v.nomalize();
console.log(v.mag); // 1;

Scalar Multiplication

const v = new Vector(0, 3);
v.mult(4);
console.log(v.mag); // 12;
console.log(v.y); // 12;

Addition

const v = new Vector(-2, 3);
v.add(new Vector(3, -5));
console.log(v.x); // 1
console.log(v.y); // -2

Substraction

const v = new Vector(-2, 3);
v.sub(new Vector(3, -5));
console.log(v.x); // -5
console.log(v.y); // 8

Distance to Another Vector

const v = new Vector(7, 2);
console.log(v.dist(new Vector(3, -1))); // 5

Angle to Another Vector

const v1 = new Vector(0, 1);
const v2 = new Vector(1, 0);
console.log(v1.angleTo(v2)); // Math.PI * 0.5

Create Vector from Angle

let v = Vector.fromAngle(Math.PI * 0.5);
console.log(v.x); //  0
console.log(v.y); //  1

Equality with Other Vector

const v1 = new Vector(7, 2);
const v2 = new Vector(7, 2);
console.log(v1.equals(v2)); // true

Copy Vector

const v = new Vector(7, 2);
const cv = v.copy();

Modulo

The mod function calculates the modular remainder of a number n modulo m. The main diference between this function and the remainder operator % is that the mod function applies the modular arithmetic strictly. For example

console.log(-1 % 4);

will output -1. Whereas using the mod:

console.log(mod(-1, 4));

we should get 3.

The mod function will fail if it receives a negative modulo or any non-integer number.

Greatest Common Divisor

The gcd function calculates greatest common divisor between to positive integers

console.log(gcd(18, 4));

will ouput 2.

Least Common Multiple

The lcm function calculates least common multple between to positive integers

console.log(lcm(18, 4));

will ouput 36.

Is a Number Prime

The prime checks if a positive integer is prime or not

console.log(prime(17));

will ouput true.

Prime Factorization

The factors function gets the prime factors with their respective exponents

console.log(factors(48));

will ouput [ [2, 4], [3, 1] ], where each element of the array is another array with two numbers:

1. The prime factor
2. The exponent of the factor

In the example, this means that 48 is 2^4 + 3^1.

Number Totient

The totient function gets the totient from a positive integer, that is, the number of prime numbers from 1 to n-1 for a given integer n.

console.log(totient(100));

will ouput 40.

Collatz Sequence

The collatz function gets the collatz sequence from a positive integer.

console.log(collatz(5));

will ouput [ 5, 16, 8, 4, 2, 1 ].

Optionally, it accepts a second parameter that limits the maximum length of the resulting sequence.

console.log(collatz(5, 5));

will ouput [ 5, 16, 8, 4, 2 ].

Digital Roots

The digitalRoots function gets the digital roots from a positive integer, that is, the sum of all its digits.

console.log(digitalRoots(19));

will ouput 1.

Converting to Other Bases

The toBase function gets the string representation of a given positive integer in a certain base.

console.log(toBase(255, 16), toBase(255, 2));

will ouput FF 11111111.

The inverse process is achieved with the fromBase function.

 console.log(fromBase('FF', 16), fromBase('11111111', 2));

outputs 255 255.