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.