math-ts

TypeScript implementation for mathematical concepts

Features

Implemented

• Equation
• Complex number
• Integer
• Probability (permutation, combination)
• Sequence / sigma
• Set
• Vector
• Identity
• Function
• Inequality
• Calculus

Todo

• Matrix
• Logarithm
• Trigonometry
• Line, circle equations
• Position vector

REPL

MathTS contains enhanced Node.js REPL that is able to render LaTeX expressions by using ANSI escape sequence

Prove theorems

yarn run test

API

Equation

// x^2 + x - 6 = 0
const p = new Equation([
  new Expression([
    new Variable('x', 1, 2),
    new Variable('x', 1),
    new Constant(-6)
  ]),
  new Expression([
    new Constant(0),
  ]),
]);

p.test(new Map([['x', 2]]) === true;
p.test(new Map([['x', -3]]) === true;

Inequality

const inequality = new Inequality(
  InequalityType.GT,
  new Expression([new Variable('x', 2, 1)]),
  new Expression([new Variable('x', 1, 1)]),
);

inequality.test(new Map([['x', 1]]));  // true
inequality.test(new Map([['x', -1]])); // false

Identity

const v1 = new Variable('x', 1, 2);
const v2 = new Variable('x', 1);
const c1 = new Constant(-6);

const id = Identity
  .create()
  .push(new Expression([ v1, v2, c1 ]))
  .moveToRight(c1)
  .moveToLeft(v2);

Function

const f = new Function(new Expression([
  new Variable('x', 1, 1),
]));

f.call(new Map([['x', 5]])).toNumber() === 5;

Integer

factorial(3) === 6;
gcd(36, 8) === 4;

Complex

const a = new Complex(2, 1);
const b = a.getConjugate();
const c = new Complex(2, 1);

a.toString() === '2 + 1i';
a.equals(c) === true;
a.add(b).toInteger() === 4;
a.multiply(b).toInteger() === 5;

Permutation

permute([1, 2, 3], 2) // [1,2] [1,3] [2,1] [2,3]..
nPr(3,2) === 6

Combination

combine(new Set([ 1,2,3 ]), 2) // {1,2} {1,3} {2,3}
nCr(3,2) === 3

Probability

let a = new Event(1 / 10), // P(A) = 1/10
    b = new Event(1 / 5),  // P(B) = 1/5
    c = new Event(1 / 3);  // P(C) = 1/3

let s = new SampleSpace([a, b, c])
  .relate(a, bind => bind.exclusiveTo(b));
  .relate(a, bind => bind.independentFrom(c))
  .relate(b, bind => bind.conditionalOn(c, new Event(1/2)));

// A and B are mutually exclusive <=> P(A∪B) = P(A) + P(B)
s.getUnion(a, b).probability === 1/10 + 1/5

// P_B(C) = 1/2 <=> P(B∩C)/P(B) = 1/2
s.getIntersection(b, c).probability / b.probability === 1/2

// You can invoke independent experiment w/ Math.random
a.experiment();

Sequence

// a = 1, d = 2, n = 10
const s1 = new ArithmeticSequence(1, 2, 10);
s1.getNth(5) === 11;
s1.getSum()  === 100;

// a = 1, r = 2, n = 10
const s2 = new GeometricSequence(1, 2, 10);
s2.getNth(4) === 16;
s2.getSum()  === 1024;

Set

const s = new Set([1,2,3])
const t = new Set([1,2])

isSuperset(s, t) === true;
isSubset(t, s)   === true;
getUnion(s, t).equals(s);
getIntersection(s, t).equals(t);
getComplement(s, t) // {3}

R.has(1);   // true
Z.has(0.1); // false
N.has(-1)   // false
C.has(new Complex(2, 1)); // true

Vector

const a = new Vector(1, 0, 0);
const b = new Vector(1, 1, 0);
const p = new Vector(4, 2, 0);

a.multiply(2).add(b.multiply(2)).equals(p);
a.getAngle(b) === Math.PI / 2;
a.dotProd(a) === a.norm ** 2;

Calculus

// f_1(x) = 1/3x^3 + C
const f1 = new Function(new Expression([
  new Variable('x', 1/3, 3), C,
]));

// f_2(x) = x^2
const f2 = new Function(new Expression([
  new Variable('x', 1, 2),
]));

differentiate(f1).d('x').equals(f2);
integrate(f2).d('x').equals(f1);

License

MIT