NAME

       Math::Calculus::NewtonRaphson - Algebraic Newton Raphson Implementation

SYNOPSIS

         use Math::Calculus::NewtonRaphson;

         # Create an object.
         my $exp = Math::Calculus::NewtonRaphson->new;

         # Set a variable and expression.
         $exp->addVariable('x');
         $exp->setExpression('x^2 - 5') or die $exp->getError;

         # Apply Newton Raphson.
         my $result = $exp->newtonRaphson(2) or die $exp->getError;
         print $result; # Prints 1.4142...

DESCRIPTION

       This module can take an algebraic expression, parses it and then uses the Newton Raphson
       method to solve the it. The Newton Raphson method relies on the fact that the expression
       you pass in evaluates to zero where there is a solution. That is, to solve:-

       x^2 = 5

       You would need to pass in:-

       x^2 - 5

       It understands expressions containing any of the operators +, -, *, / and ^ (raise to
       power), 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::NewtonRaphson->new;

           Creates a new instance of the Newton Raphson object, 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.

       newtonRaphson
             $result = $exp->newtonRaphson($variable, $guess, %mappings);

           Attempts to solve the expression for the given variable using the Newton Raphson
           method, using the passed value as the first guess. The mappings hash allows any other
           non-numeric constants to be mapped to numeric values - a pre-requisite for solving
           such equations.

       getTraceback
             $exp->getTraceback;

           When setExpression and newtonRaphson 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 65:
           '=item' outside of any '=over'

       Around line 186:
           You forgot a '=back' before '=head1'