DiscreteMathematics is a set of algorithm implementations from Discrete Mathematics.
The equivalence relation a ≡ b(mod m) ↔ m | (b - a).
-8 ==% (7, 5) // true
2 ==% (8, 5) // falseReturns whether or not a|b ↔ ∃ q ∈ N, b = q · a.
3 |% 9 // true
2 |% 7 // falsePerforms division on two integers and returns the quotient and remainder.
a = q · b + r
longDivision(a: 8, b: 3) // (q: 2, r: 2)gcd() returns the greatest common divisor using the Euclidean Algorithm.
gcd(5005, 4410) // 35
gcd(175, 155) // 5egcd() 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)Two elements, a, b, are coprime if gcd(a, b) = 1.
coprime(17, -60) // truelde() 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) // nilldeSolutions() 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)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")DiscreteMathematics is also available through CocoaPods.
To install it, add the following line to your Podfile:
pod 'DiscreteMathematics', '~> 2.0'DiscreteMathematics is available under the MIT License.
Open an issue or submit a pull request.