mattt / euler

Swift Custom Operators for Mathematical Notation

Euler

Euler uses custom operators in the "Math Symbols" character set to implement functions using traditional mathematical notation.

Please keep in mind that this is not intended or recommended for production. Custom operators of any breed are ripe for misuse and abuse, and should be used with as much care and caution as you would something like method swizzling or complex macros.

Euler is much better-suited to a Playground, where it could be used for teaching and learning logic and mathematics using a more vernacular notation.

Euler is named after Leonhard Euler, the Swiss mathematician credited for the popularization of modern mathematical notation such as the Greek letters Σ for summation & π for the ratio of a circle's circumference to its diameter, the letters e to denote the base of the natural logarithm & i to denote the imaginary unit, sin & cos for trigonometric functions, and f(x) to denote the function f with argument x.

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Example Usage

import Foundation
import Euler
import PlaygroundSupport

𝑒 // 2.718281828459045

¬true // false

3 × 4 // 12

let prime = [2, 3, 5, 7, 11]
let fibonacci = [1, 1, 2, 3, 5, 8, 13]
prime ∩ fibonacci // {2, 3, 5}

∑[1, 2, 3, 4, 5] // 15

[1, 2] ⋅ [3, 4] // 11

7 ≠ 9 // true

var f: (Double) -> Double = sin
let g: (Double) -> Double = cos

for x in stride(from: 0, to: 4 * π, by: π / 8) {
    (f ∘ g)(x) // ∿∿∿
}

(f′)(π) // -1

Inventory

Mathematical Constants

• π - Pi
• 𝝉 - Tau
• 𝑒 - e
• ε - Machine Epsilon

Logic

• ¬, ~ - Logical Negation
• ∧ - Logical Conjunction
• ∨ - Logical Disjunction
• ⊻, ⊕, ↮, ≢ - Logical XOR
• ⊼, ↑ - Logical NAND
• ⊽, ↓ - Logical NOR
• ⊦ - Logical Assertion

Arithmetic

• × - Multiplication
• ÷, ∕ - Division
• √ - Square Root
• ∛ - Cube Root
• ∜ - Tesseract Root
• ± - Plus/Minus
• ∓ - Minus/Plus
• ∣ - Divides
• ∤ - Does Not Divide

Sets

• ∈ - Set Membership
• ∉ - Set Non-Membership
• ∋ - Converse Set Membership
• ∌ - Converse Set Membership
• ∩ - Set Intersection
• ∪ - Set Union
• ⊆ - Subset
• ⊂ - Proper Subset
• ⊄ - Not A Subset Of
• ⊇ - Superset
• ⊃ - Proper Superset
• ⊅ - Not A Superset Of

Sequences

• ∑ - Summation
• ∏ - Cartesian Product

Vectors

• ⋅ - Dot Product
• × - Cross Product
• ‖ - Vector Norm
• ⦡ - Angle Between Vectors

Comparison

• ⩵ - Equality
• ≠ - Inequality
• ≤ - Less Than Or Equal To
• ≨ - Less Than And Not Equal To
• ≥ - Greater Than Or Equal To
• ≩ - Greater Than And Not Equal To
• ≬ - Between
• ≈ - Approximate Equality
• ≉ - Approximate Inequality

Calculus

• ′ - Derivative
• ∫ - Integral

Functions

• ∘ - Composition

---

License

MIT

Contact

Mattt (@mattt)

euler's Issues

`SignedInteger & UnsignedInteger` is probably the wrong bounds

What I assume was meant was one of (the non-existent) P | Q, duplicating the functions for SignedInteger and UnsignedInteger separately, or use BinaryInteger.

This is because no type does, should, or is semantically permitted to conform to both SignedInteger & UnsignedInteger.

Error in doc

Support for math symbols is documented for Swift.

Swift 3 compatibility

Hey, I'd love to see this lib available in Swift 3 so I can implement it in my project.

Thanks 😄