Math::Calculus::Differentiate - Algebraic Differentiation Engine
use Math::Calculus::Differentiate; # Create an object. my $exp = Math::Calculus::Differentiate->new; # Set a variable and expression. $exp->addVariable('x'); $exp->setExpression('x^2 + 5*x') or die $exp->getError; # Differentiate and simplify. $exp->differentiate or die $exp->getError;; $exp->simplify or die $exp->getError;; # Print the result. print $exp->getExpression; # Prints 2*x + 5
This module can take an algebraic expression, parse it into a tree structure, modify the tree to give a representation of the differentiated function, simplify the tree and turn the tree back into an output of the same form as the input.
It supports differentiation of expressions including the +, -, *, / and ^ (raise to power) operators, bracketed expressions to enable correct precedence and the functions ln, exp, sin, cos, tan, sec, cosec, cot, sinh, cosh, tanh, sech, cosech, coth, asin, acos, atan, asinh, acosh and atanh.
None by default.
$exp = Math::Calculus::Differentiate->new;
Creates a new instance of the differentiation engine, which can hold an individual expression.
$exp->addVariable('x');
Sets a certain named value in the expression as being a variable. A named value must be an alphabetic chracter.
$exp->setExpression('x^2 + 5*x);
Takes an expression in human-readable form and stores it internally as a tree structure, checking it is a valid expression that the module can understand in the process. Note that the engine is strict about syntax. For example, note above that you must write 5*x and not just 5x. Whitespace is allowed in the expression, but does not have any effect on precedence. If you require control of precedence, use brackets; bracketed expressions will always be evaluated first, as you would normally expect. The module follows the BODMAS precedence convention. Returns undef on failure and a true value on success.
$expr = $exp->getExpression;
Returns a textaul, human readable representation of the expression that is being stored.
$exp->differentiate('x');
Differentiates the expression that was stored with setExpression with respect to the variable passed as a parameter. Returns undef on failure and a true value on success.
$exp->simplify;
Attempts to simplify the expression that is stored internally. It is a very good idea to call this after calling differentiate, as the tree will often not be in the most compact possible form, and this will affect the readability of output from getExpression and the performance of future calls to differentiate if you are intending to obtain higher derivatives. Returns undef on failure and a true value on success.
$exp->getTraceback;
When setExpression and differentiate are called, a traceback is generated to describe what these functions did. If an error occurs, this traceback can be extremely useful in helping track down the source of the error.
$exp->getError;
When any method other than getTraceback is called, the error message stored is cleared, and then any errors that occur during the execution of the method are stored. If failure occurs, call this method to get a textual representation of the error.
The author of this module has a website at http://www.jwcs.net/~jonathan/, which has the latest news about the module and a web-based frontend to allow you to test the module out for yourself.
Jonathan Worthington, <jonathan@jwcs.net>
Copyright (C) 2004 by Jonathan Worthington
This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.8.1 or, at your option, any later version of Perl 5 you may have available.