Set Theory

This library attempts to create a set of utils to apply set theory on JS/TS. (pun intended).

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Motivation.

Currently, Vanilla JS includes the Set Object with some methods to do set operations. But this methods stop working properly when the rank of a set is greater than 1.

e.g. With sets such that:

S = { 1 , {2} }

S = { 1 , {2, { 3, {4} } } }

In other words. Vanilla JS fails when applying the operations to sets that have sets within.

The objective of this library is to provide functions that work with the basic sets but also with those sets described above.

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Instalation

Package

npm

npx jsr add @discrete-math/set-theory

import * as set_theory from "@discrete-math/set-theory";

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deno

deno add jsr:@discrete-math/set-theory

import * as set_theory from "@discrete-math/set-theory";

Import directly with a jsr specifier

import * as set_theory from "jsr:@discrete-math/set-theory";

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Usage.

The library provide the SetOf class. A class that can be used to create discrete math set objects and manipulate them through set operations.

Set Equality

const p = new SetOf([1, 2]).isEqualTo(new SetOf([2, 1]));
//p is true. Returns a boolean.

Cartesian Product

const a = [ 1, [2, 5] ]
const b = [ 3, 4 ]

const cartesianProduct = new SetOf(a).cartesianProduct(new SetOf(b)) 
// returns a SetOf object.

Set Difference

const difference = new SetOf([1, [2]]).difference(new SetOf([2]))
// returns a SetOf object.

Intersection

const a = [1, [2]];
const b = [1, 2];

const intersection = new SetOf(a).intersection(new SetOf(b))
// returns a SetOf object.

Union

const a = [1, 2, [3, 4]]
const b = [[3, 4]]

const aUnionb = new SetOf(a).union(new SetOf(b))
// returns a SetOf object.

Powerset

const setB = new SetOf(['A', 'B', 'C', 'D']);

const p_of_b = setB.powerSet()
// returns a SetOf object.

Cardinality

const cardinality = new SetOf([1, 2, 3, 4]).cardinality
// returns a number

Get Value

Gets the values of the set in Array_Set Notation

new SetOf([1, 2, 3, 4]).getValue()
// [1, 2, 3, 4]

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Also, this library provides the SetOperations abstract class. The abstract class is a set of utils that can directly be used with sets in array_set notation. Array_Set Notation But I highly recommend ratter using the SetOf class.

Set Equality

const a = [1, [2, 3]]
const b = [[3,2] , 1]
SetOperations.areSetsEqual<number | number[]>(a, b) // true

Cartesian product

const a = [1, 2]
const b = [3, 4]

const product = SetOperations.cartesianProduct(a, b);

// [ (1, 3), (1, 4), (2, 3), (2, 4) ]

Set Difference

const a = [1, 2]
const b = [2]

const difference = SetOperations.setDifference(a, b);

// [1]

Set Intersection

const a = [1, [2]];
const b = [1, 2];

const intersection = SetOperations.setIntersection(a, b)
// [1]

Set Union

const a = [1, 2, [3, 4]]
const b = [[3, 4], 5]

const aUnionb = SetOperations.setUnion(a, b)

// [1, 2, [3, 4], 5]

Is Part Of

SetOperations.isSetPartOf([1], [1, 2, [1]]) // true

PowerSet

const setB = ['1', '2', '3'];
const p_of_b = powerSet(setB);

Output

[
  [],
  [ "1" ],
  [ "2" ],
  [ "1", "2" ],
  [ "3" ],
  [ "1", "3" ],
  [ "2", "3" ],
  [ "1", "2", "3" ]
]

Contributing

Please read the CONTRIBUTING.md file. (under construction)