Symbolic Derivative

Program written as a final project for Functional Programming course.

Description

A program written in Haskell computing symbolic derivative of a given function and simplifying it.

Available Functions

parse <String s>
Converts string s into object of type Maybe ExprThree. Returns Nothing if s doesn't represent a valid expression. Expression can contain:

• brackets
• spaces
• operations: +, -, *, /
• functions: sin, cos, tg, exp, ln
• variables: x, y, z
• constants as lowercase letters
• integer numeric constants

derivative <ExprThree expr> <Var v>
Returns the partial derivative of a given expression expr with respect to the variable v. Possible values of v are X, Y or Z.

allDerivatives <ExprThree expr>
Returns a tuple of partial derivatives with respect to variables x, y and z.

simplify <ExprThree expr>
Simplifies the expression expr.

simplifyM <Maybe ExprThree expr>
derivativeM <Maybe ExprThree expr>
allDerivativesM <Maybe ExprThree expr>
versions of the above functions taking Maybe ExprtThree as argument instead of ExprThree. It's more comfortable to use them after using parse.

Usage

To use it in GHC interactive mode:

ghci
:load SymbolicDerivative

Example:

*SymbolicDerivative> x = parse "(x+y)*(y+z)"
*SymbolicDerivative> x
Just (x + y) * (y + z)
*SymbolicDerivative> derivativeM x X
Just y + z
*SymbolicDerivative> allDerivativesM x
Just (y + z,2.0 * y + z + x,x + y)
*SymbolicDerivative> y = parse "(x+1)*sin(x)*a + a*exp(2*x)*(1+x)"
*SymbolicDerivative> y
Just (x + 1.0) * sin(x) * a + a * exp(2.0 * x) * (1.0 + x)
*SymbolicDerivative> simplifyM y
Just (x + 1.0) * a * (sin(x) + exp(2.0 * x))