math::symbolic::auxfunctions(3pm) [debian man page]

Math::Symbolic::AuxFunctions(3pm)			User Contributed Perl Documentation			 Math::Symbolic::AuxFunctions(3pm)

NAME

       Math::Symbolic::AuxFunctions - Auxiliary functions for Math::Symbolic hierarchy

SYNOPSIS

	 use Math::Symbolic::AuxFunctions;

	 Math::Symbolic::AuxFunctions::acos($x);
	 # etc

DESCRIPTION

       This module contains implementations of some auxiliary functions that are used within the Math::Symbolic hierarchy of modules. In
       particular, this module holds all trigonometric functions used for numeric evaluation of trees by Math::Symbolic::Operator.

   EXPORT
       None. On purpose. If I wished this module would pollute others' namespaces, I'd have put the functions right where they're used.

TRIGONOMETRIC FUNCTIONS

   tan
       Computes the tangent sin(x) / cos(x).

   cot
       Computes the cotangent cos(x) / sin(x).

   asin
       Computes the arc sine asin(z) = -i log(iz + sqrt(1-z*z)).  Above formula is for complex numbers.

   acos
       Computes the arc cosine acos(z) = -i log(z + sqrt(z*z-1)).  Above formula is for complex numbers.

   atan
       Computes the arc tangent atan(z) = i/2 log((i+z) / (i-z)).  Above formula is for complex numbers.

   acot
       Computes the arc cotangent ( atan( 1 / x ) ).

   asinh
       Computes the arc hyperbolic sine asinh(z) = log(z + sqrt(z*z+1))

   acosh
       Computes the arc hyperbolic cosine acosh(z) = log(z + sqrt(z*z-1)).

OTHER FUNCTIONS

   binomial_coeff
       Calculates the binomial coefficient n over k of its first two arguments (n, k).

       Code taken from Orwant et al, "Mastering Algorithms with Perl"

   bell_number
       The Bell numbers are defined as follows:

	 B_0   = 1
	 B_n+1 = sum_k=0_to_n( B_k * binomial_coeff(n, k) )

       This function uses memoization.

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 Mueller, symbolic-module at steffen-mueller dot net
	 Stray Toaster, mwk at users dot sourceforge dot net
	 Oliver Ebenhoeh

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

perl v5.10.1							    2011-01-01					 Math::Symbolic::AuxFunctions(3pm)

Math::Symbolic::Custom(3pm)				User Contributed Perl Documentation			       Math::Symbolic::Custom(3pm)

NAME

       Math::Symbolic::Custom - Aggregate class for tree tests and transformations

SYNOPSIS

	 # Extending the class:
	 package Math::Symbolic::Custom::MyTransformations;
	 use Math::Symbolic::Custom::Base;
	 BEGIN {*import = &Math::Symbolic::Custom::Base::aggregate_import}

	 our $Aggregate_Export = [qw/apply_transformation1 .../];
	 sub apply_transformation1 {
	    # ...
	 }
	 # ...

	 # Using the custom class:
	 use Math::Symbolic;
	 use Math::Symbolic::Custom::MyTransformations;

	 # later...
	 $tree->apply_transformation1();
	 $tree->mod_transformation2();
	 die unless $tree->is_type1();
	 die unless $tree->test_condition1();
	 die if $tree->contains_something1();
	 print $tree->to_latex();

DESCRIPTION

       This is an aggregate class for all custom modification, transformation, testing and output extensions for Math::Symbolic trees.	Some
       default transformations and tests are implemented in the Math::Symbolic::Custom::DefaultMods and Math::Symbolic::Custom::DefaultTests
       packages, default output routines in Math::Symbolic::Custom::DefaultDumpers which are automatically loaded by the Math::Symbolic::Custom
       class.

       Math::Symbolic::Custom imports all constants from Math::Symbolic::ExportConstants

   EXPORT
       None by default.

EXTENDING THE MODULE

       In order to extend the functionality of Math::Symbolic, you have to go through the following steps: (also see the synopsis in this
       document.)

       o   Choose an appropriate namespace in the Math::Symbolic::Custom::* hierarchy or if you desparately wish, somewhere else.

       o   Create a new module (probably using "h2xs -AX MODULENAME") and put the following lines of code in it:

	     # To make sure we're cooperating with Math::Symbolic's idea of
	     # method delegation.
	     use Math::Symbolic::Custom::Base;
	     BEGIN {*import = &Math::Symbolic::Custom::Base::aggregate_import}

	     our $Aggregate_Export = [
	       # Put the list of method names to be exported.
	     /];

       o   Think well about the naming of your exported methods. Answer the following questions:

	   Does the name start with 'is_', 'test_', 'mod_', 'apply_', 'contains_', or 'to_'?  If not, find a suitable name that does.

	   Does the name clash with any of the methods exported by Math::Symbolic::Custom::DefaultTests, Math::Symbolic::Custom::DefaultMods, or
	   Math::Symbolic::Custom::DefaultDumpers?  If so, please consider choosing a different name.

	   Does the name map to the idea behind the method prefix ('is_', ...)?  Only methods starting with one of the prefixes listed above can
	   be delegated. Any others will never be called. The idea behind delegating methods with several prefixes is to provide for a reasonable
	   choice for naming methods. 'is_' and 'contains_' are meant to be used for accurate tests like "is_constant". 'test_' is meant for all
	   tests that either make use of heuristics or can't be fitted into either 'is_' or 'contains_'. The prefixes 'mod_' and 'apply_' are
	   meant for use with methods that modify the Math::Symbolic tree.  Finally, the prefix 'to_' is meant to be used with conversion and
	   output methods like 'to_latex' or 'to_string'. (Though as of version 0.122, to_string is implemented in the core Math::Symbolic
	   modules.)

       o   Make sure you document exactly what your methods do. Do they modify the Math::Symbolic tree in-place or do they clone using the new()
	   constructor and return a copy? Make sure you mention the behaviour in the docs.

       o   Consider packaging your extensions as a CPAN distribution to help others in their development with Math::Symbolic. If you think the
	   extensions are generic enough to be a worthwhile addition to the core distribution, try sending your extensions to the Math::Symbolic
	   developers mailing list instead.

       o   Load your extension module after loading the Math::Symbolic module.

       o   Start using your custom enhancements as methods to the Math::Symbolic trees (any term types).

       o   Send bug reports and feedback to the Math::Symbolic support mailing list.

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 Mueller, symbolic-module at steffen-mueller dot net
	 Stray Toaster, mwk at users dot sourceforge dot net
	 Oliver Ebenhoeh

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::Custom::Base Math::Symbolic::Custom::DefaultTests Math::Symbolic::Custom::DefaultMods
       Math::Symbolic::Custom::DefaultDumpers

       Math::Symbolic

perl v5.10.1							    2011-01-01					       Math::Symbolic::Custom(3pm)