NAME

       Math::Calculus::Expression - Algebraic Calculus Tools Expression Class

SYNOPSIS

         use Math::Calculus::Expression;

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

         # Set a variable and expression.
         $exp->addVariable('x');
         $exp->setExpression('x^(2+1) + 6*5*x') or die $exp->getError;

         # Simplify
         $exp->simplify or die $exp->getError;;

         # Print the result.
         print $exp->getExpression; # Prints x^3 + 30*x

DESCRIPTION

       This module can take an algebraic expression, parse it into a tree structure, simplify the tree,
       substitute variables and named constants for other variables or constants (which may be numeric),
       numerically evaluate the tree and turn the tree back into an output of the same form as the input.

       It supports a wide range 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::Expression->new;

           Creates a new instance of the expression object, which can hold an individual expression and perform
           basic operations on it.

       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 module 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.

       simplify
             $exp->simplify;

           Attempts to simplify the expression that is stored internally.

       evaluate
             $exp->evaluate(x => 0.5, a => 4);

           This method takes a hash mapping any variables and named constants (represented by letters) in the
           expression to numerical values, and attempts to evaluate the expression and return a numerical value.
           It fails and returns undef if it finds letters that have no mapping or an error such as division by
           zero occurs during the evaluation.

       sameRepresentation
             $same = $exp->sameRepresentation($exp2);

           The sameRepresentation method takes another expression object as its parameter and returns true if
           that expression has the same internal representation as the expression the method is invoked on. Be
           careful - while it can be said that if two expressions have the same representation they are equal,
           it would be wrong to say that if they have different representations they are not equal. It is clear
           to see that "x + 2" and "2 + x" are equal, but their internal representation may well differ.

       clone
             $expCopy = $exp->clone;

           The clone method returns a deep copy of the expression object (deep copy meaning that if the original
           is modified the copy will not be affected and vice versa).

       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.

       Other Methods
           Any other method call is taken to refer to a subclass of Expression. The first letter of the name of
           the method invoked is capitalized, then a module by that name is loaded (if it exists) and the method
           is called on it. This works for, for example, the Differentiate module; calling the differentiate
           method on an Expression will load the Differentiate module and call the differentiate method. If a
           module cannot be loaded or the method cannot be called, then this module will die.

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 try out this module and, more specifically, its
       subclasses.

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.