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
Σfor summation &πfor the ratio of a circle's circumference to its diameter, the letterseto denote the base of the natural logarithm &ito denote the imaginary unit,sin&cosfor trigonometric functions, andf(x)to denote the functionfwith argumentx.
Example Usage
import Foundation
import Euler
import PlaygroundSupport
? // 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?- Tau?- eε- 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)