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 character.

       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.