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Latest 1.3.0 https://github.com/cszatma/DiscreteMathematics MIT ios 8.0, osx 10.9, watchos 2.0, tvos 9.0 Foundation Christopher Szatmary

Discrete Mathematics

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

• iOS 8.0+
• macOS 10.9+
• tvOS 9.0+
• watchOS 2.0+
• Linux
• Swift 4

CocoaPods

DiscreteMathematics is available through CocoaPods. To install

pod 'DiscreteMathematics', '~> 1.3'

Swift Package Manager

DiscreteMathematics is available through the Swift Package Manager

import PackageDescription

let package = Package(
name: "MyProject",
dependencies: [
.package(url: "https://github.com/cszatma/DiscreteMathematics.git", from: "1.3.0")
]
)

Contributing

Open an issue or submit a pull request.

Latest podspec

{
"name": "DiscreteMathematics",
"version": "1.3.0",
"summary": "Discrete Mathematics algorithms.",
"description": "A collection of implementations of various concepts from Discrete Mathematics.",
"homepage": "https://github.com/cszatma/DiscreteMathematics",
"type": "MIT",
},
"authors": {
"Christopher Szatmary": "[email protected]"
},
"source": {
"git": "https://github.com/cszatma/DiscreteMathematics.git",
"tag": "1.3.0"
},
"platforms": {
"ios": "8.0",
"osx": "10.9",
"watchos": "2.0",
"tvos": "9.0"
},
"source_files": "Sources/**/*",
"frameworks": "Foundation",
"pushed_with_swift_version": "4.0"
}