This project is a simple computer algebra system (CAS), written entirely in pure F#, for pure fun. It uses an extremely simple expression language modelled by the union:
type Expr =
| Const of float
| Id of string
| Func of string * Expr list
Constructs in this expression language are either constants that are floats, symbolic identifiers of string or functions that have a name (the string part) and arguments (the Expr list part)
Active patterns are used extensively in this project to faciliate writing functions that operate on these kinds of expressions, example:
let (|Sin|_|) = function
| Func("sin", [expr]) -> Some expr
| _ -> None
let (|Cos|_|) = function
| Func("cos", [expr]) -> Some expr
| _ -> None
let (|Tan|_|) = function
| Func("tan", [expr]) -> Some expr
| _ -> None
Having these patterns defined, you could write the following:
// val isTrigonometric : Expr -> bool
let isTrigonometric = function
| Sin x -> true
| Cos x -> true
| Tan x -> true
| _ -> falseSo the library is built around these patterns, evaluating an expression and differentiating a single variable (real) functions is built-in, example:
"sin(5x^2)"
|> Parser.tryParse
|> function
| ParseError msg -> printf "Parse error: %s" msg
| Parsed expr ->
Calculus.derivative expr (Id "x")
|> Algebra.fullSimplify
|> Printer.pretty
|> printfn "%s" // returns "cos(5*x^2) * 10x"
React
Typescript
Django
Laravel
Facebook
Microsoft
Google
Alibaba
D3
Tencent