jbeeko / AlgebraFs

A simple computer algebra system (CAS), written in F# for fun and learning.

AlgebraFs

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)

Partial Active patterns

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
    | _ -> false

So 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"