NAME

       Math::Calculus::Differentiate - Algebraic Differentiation Engine

SYNOPSIS

         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

DESCRIPTION

       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.

EXPORT

       None by default.

METHODS

       new
             $exp = Math::Calculus::Differentiate->new;

           Creates a new instance of the differentiation engine, which can hold an individual expression.

       addVariable
             $exp->addVariable('x');

           Sets a certain named value in the expression as being a variable. A named value must be an alphabetic
           chracter.

       setExpression
             $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.

       getExpression
             $expr = $exp->getExpression;

           Returns a textaul, human readable representation of the expression that is being stored.

       differentiate
             $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.

       simplify
             $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.

       getTraceback
             $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.

       getError
             $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.

SEE ALSO

       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.

AUTHOR

       Jonathan Worthington, <jonathan@jwcs.net>

COPYRIGHT AND LICENSE

       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.

POD ERRORS

       Hey! The above document had some coding errors, which are explained below:

       Around line 55:
           '=item' outside of any '=over'

       Around line 150:
           You forgot a '=back' before '=head1'