NAME

       Math::Symbolic::Derivative - Derive Math::Symbolic trees

SYNOPSIS

         use Math::Symbolic::Derivative qw/:all/;
         $derived = partial_derivative($term, $variable);
         # or:
         $derived = total_derivative($term, $variable);

DESCRIPTION

       This module implements derivatives for Math::Symbolic trees.  Derivatives are
       Math::Symbolic::Operators, but their implementation is drawn from this module because it
       is significantly more complex than the implementation of most operators.

       Derivatives come in two flavours. There are partial- and total derivatives.

       Explaining the precise difference between partial- and total derivatives is beyond the
       scope of this document, but in the context of Math::Symbolic, the difference is simply
       that partial derivatives just derive in terms of explicit dependency on the differential
       variable while total derivatives recongnize implicit dependencies from variable
       signatures.

       Partial derivatives are faster, have been tested more thoroughly, and are probably what
       you want for simpler applications anyway.

   EXPORT
       None by default. But you may choose to import the total_derivative() and
       partial_derivative() functions.

CLASS DATA

       The package variable %Partial_Rules contains partial derivative rules as key-value pairs
       of names and subroutines.

SUBROUTINES

   partial_derivative
       Takes a Math::Symbolic tree and a Math::Symbolic::Variable as argument.  third argument is
       an optional boolean indicating whether or not the tree has to be cloned before being
       derived. If it is true, the subroutine happily stomps on any code that might rely on any
       components of the Math::Symbolic tree that was passed to the sub as first argument.

   total_derivative
       Takes a Math::Symbolic tree and a Math::Symbolic::Variable as argument.  third argument is
       an optional boolean indicating whether or not the tree has to be cloned before being
       derived. If it is true, the subroutine happily stomps on any code that might rely on any
       components of the Math::Symbolic tree that was passed to the sub as first argument.

AUTHOR

       Please send feedback, bug reports, and support requests to the Math::Symbolic support
       mailing list: math-symbolic-support at lists dot sourceforge dot net. Please consider
       letting us know how you use Math::Symbolic. Thank you.

       If you're interested in helping with the development or extending the module's
       functionality, please contact the developers' mailing list: math-symbolic-develop at lists
       dot sourceforge dot net.

       List of contributors:

         Steffen MXller, symbolic-module at steffen-mueller dot net
         Stray Toaster, mwk at users dot sourceforge dot net
         Oliver EbenhXh

SEE ALSO

       New versions of this module can be found on http://steffen-mueller.net or CPAN. The module
       development takes place on Sourceforge at http://sourceforge.net/projects/math-symbolic/

       Math::Symbolic