math.real-set

Class to work with subsets of real numbers.

Version

0.4.0

Install

npm install math.real-set

Usage

const RealSet = require('math.real-set')

const A = RealSet.parse('(0, 2] U {6, 7, 8}')
const B = RealSet.parse('(5, 5)')
const C = RealSet.parse('[1, 2)')
const D = RealSet.parse('(2, 7)')
const E = RealSet.parse('(8, 9]')

// emptyness
A.isEmpty() // false
B.isEmpty() // true

// Containing numbers
A.contains(4) // false
A.contains(6) // true
B.contains(3) // false

// Containing sets
A.contains(C) // true

// joining sets
A.union(D) // A U D is equivalent to RealSet.parse('(0, 7] U {8}')
A.union(E) // A U E is equivalent to RealSet.parse('(0, 2] U {6, 7} U [8, 9]')

// converting to string
A.toString() // '{6, 7, 8} U (0, 2]'
B.toString() // '{}'
const F = RealSet.parse('[3, 3]')
F.toString() // '{3}'

API

Real subsets creation

parse :: String -> RealSet

Static method that takes and string as a representation of RealSet and returns a RealSet instance. It throws an error if string is not parsable to RealSet.

Example:

const RealSet = require('math.real-set')

const set = RealSet.parse('(2, 5] U {6} U [8, 9)')

fromIntervals :: [Interval] -> RealSet

Static method that takes an array of Intervals and returns a RealSet instance.

Example:

const RealSet = require('math.real-set')

const set = RealSet.fromIntervals([
    [{value: 2, limit: 1}, {value: 5, limit: 0}], // (2, 5]
    [{value: 6, limit: 0}, {value: 6, limit: 0}], // {6}
    [{value: 8, limit: 0}, {value: 9, limit: -1}] // [8, 9)
])

Predicates

contains :: RealSet ~> RealSet -> Boolean

Returns true or false depending on real set param is contained inside the set or not, respectively.

Example:

const RealSet = require('math.real-set')

const A = RealSet.parse('[1, 3) U [4, 8]')
const B = RealSet.parse('(1, 2) U [4, 7)')
const C = RealSet.parse('{3, 6}')

A.contains(B) // true
A.contains(C) // false
C.contains(A) // false

has :: RealSet ~> Number -> Boolean

Returns true or false if the set has a number or not, respectively.

Example:

const RealSet = require('math.real-set')
const set = RealSet.parse('(1, 5] U {8}')

set.has(1) // false
set.has(3) // true
set.has(5) // true
set.has(7) // false
set.has(8) // true

isEmpty :: RealSet ~> Boolean

Returns true or false if set is empty or not.

Example:

const RealSet = require('math.real-set')

const A = RealSet.parse('[2, 4)')
const B = RealSet.parse('[4, 2)')

A.isEmpty() // false
B.isEmpty() // true

Real subset operations

union :: RealSet ~> RealSet -> RealSet

Instance method that returns the union of two sets.

const RealSet = require('math.real-set')

const A = RealSet.parse('[1, 3) U (3, 4]')
const B = RealSet.parse('(2, 4) U {5}', '{5} U (6, 7)')

A.union(B) // [1, 4] U {5} U (6, 7)

union :: [RealSet] -> RealSet

Static method that takes an array of RealSet instances and returns a RealSet instance that represents the union of the list of sets.

const RealSet = require('math.real-set')
const A = RealSet.parse('[1, 3) U (3, 4]')
const B = RealSet.parse('(2, 4) U {5}')
const C = RealSet.parse('{5} U (6, 7)')

RealSet.union([A, B, C]) // [1, 4] U {5} (6, 7)

RealSet converters

toString :: RealSet ~> String

Converts the real set into a string representation.

const RealSet = require('math.real-set')

const A = RealSet.parse('(5, 2] U (3, 3)') // empty
const B = RealSet.parse('[2, 2] U (5, 6)') // singleton interval

A.toString() // '{}'
B.toString() // '{2} U (5, 6)'

toIntervals :: RealSet ~> [Interval]

Converts the real set into an array of disjoint Intervals ordered from lowest to highest.

const RealSet = require('math.real-set')

const A = RealSet.parse('(5, 6) U [2, 2] U {4, 8}')

A.toIntervals() /* [
    [{value: 2, limit: 0}, {value: 2, limit: 0}], // {2}
    [{value: 4, limit: 0}, {value: 4, limit: 0}], // {4}
    [{value: 5, limit: 1}, {value: 6, limit: -1}], // (5, 6)
    [{value: 8, limit: 0}, {value: 8, limit: 0}]  // {8}
]

LICENSE

MIT