Swift Package Index


Discrete Mathematics algorithms.


  • The latest stable release is 2.0.0. Released over 1 year ago.
  • The last commit to master was over 1 year ago.

Swift Version Compatibility

  • 2.0.0 and master
    5.3
    5.2
    5.1
    5.0
    4.2
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Platform Compatibility

  • 2.0.0 and master
    iOS
    macOS(Intel)
    macOS(ARM)
    Linux
    tvOS
    watchOS
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Discrete Mathematics

Language Swift CI Status Release Version Platforms License SPM

DiscreteMathematics is a set of algorithm implementations from Discrete Mathematics.

Examples

Operators

Congruence Modulo n ==%:

The equivalence relation a ≡ b(mod m) ↔ m | (b - a).

-8 ==% (7, 5) // true
2 ==% (8, 5) // false

Divides |%:

Returns whether or not a|b ↔ ∃ q ∈ N, b = q · a.

3 |% 9 // true
2 |% 7 // false

Functions

Long Division

Performs division on two integers and returns the quotient and remainder.

a = q · b + r

longDivision(a: 8, b: 3) // (q: 2, r: 2)

Greatest Common Divisor

gcd() returns the greatest common divisor using the Euclidean Algorithm.

gcd(5005, 4410) // 35
gcd(175, 155) // 5

egcd() returns the GCD of two integers as an integer combination using the Extended Euclidean Algorithm.

a · x + b · y = d

egcd(5005, 4410) // (d: 35, x: -37, y: 42)
egcd(175, 155) // (d: 5, x: 8, y: -9)

Coprime

Two elements, a, b, are coprime if gcd(a, b) = 1.

coprime(17, -60) // true

Linear Diophantine Equation

lde() returns a solution to the given Linear Diophantine Equation or nil if it has no solutions.

lde(a: 175, b: 155, c: 50) // (x: 80, y: -90)
lde(a: 234, b: 182, c: 10) // nil

ldeSolutions() returns a function that will compute all possible solutions to an LDE.

let solutions = ldeSolutions(a: 175, b: 155, c: 50)
solutions!(3) // (173, -195)

Installation

Swift Package Manager

The recommended way to install DiscreteMathematics is by using the Swift Package Manager.

To install it, add the following to your Package.swift's dependencies array:

.package(url: "https://github.com/cszatma/DiscreteMathematics.git", from: "2.0.0")

CocoaPods

DiscreteMathematics is also available through CocoaPods.

To install it, add the following line to your Podfile:

pod 'DiscreteMathematics', '~> 2.0'

License

DiscreteMathematics is available under the MIT License.

Contributing

Open an issue or submit a pull request.