A toy Haskell library for symbolic algebra, especially derivatives. I wrote it to learn to do a bunch of things, mainly.

I got a lot of the ideas and some of the code (I almost copied the simplify function from him) from 5outh's tutorial, although I rewrote the code for derivatives on my own without looking at his.

I've implemented:

• Polynomials
• Trigonometric functions
• exp and log
• Four fundamental operations and exponentiation
• Symbolic derivatives
• Simplification of expressions, using:
  • A few trigonometric identities (stuff like sin x sec x = tan x)
  • Basic algebraic identities (a^0 = 1 etc.)

To use it, clone the repo into a folder and run Main.hs in ghci:

$ git clone https://github.com/mrkgnao/pebble.git
$ cd pebble
$ ghci Main.hs

• :+, :-, :*, :/ and :^ are what you think they are
• The same goes for X
• Unary functions are given their Prelude names with an uf prefix, and you apply them to an expression with (Apply uffunc expr), where uffunc is something like ufsin.
• Operators have precedence, so you don't have to wrap everything in parens

• X :^ X is x^x
• Apply ufsin (Apply uflog X) is sin (log x)
• (Apply ufsin (2 :+ X)) :* (Apply ufcot X) is sin (2+x) cot x

The derivative function computes the derivative of an expression, simplifies it as best as it can and pretty-prints it.

The bane of every eleventh-grader:

λ> derivative (X :^ X)
((x ^ x) * (1.0 + (log x)))

A composition of two functions:

λ> derivative ((Apply ufsin (Apply ufcos X)))
((cos (cos x)) * (-(sin x)))

This pushes the, uh, Synergized Algebraic Simplification Engine™ to its limit:

λ> derivative (Apply uflog (Apply ufsin X))
(cot x)

What do you think 'calculus' originally meant?