math::rationalfunctions(3tcl)					       Math					     math::rationalfunctions(3tcl)

__________________________________________________________________________________________________________________________________________________

NAME

       math::rationalfunctions - Polynomial functions

SYNOPSIS

       package require Tcl  ?8.4?

       package require math::rationalfunctions	?1.0.1?

       ::math::rationalfunctions::rationalFunction num den

       ::math::rationalfunctions::ratioCmd num den

       ::math::rationalfunctions::evalRatio rational x

       ::math::rationalfunctions::addRatio ratio1 ratio2

       ::math::rationalfunctions::subRatio ratio1 ratio2

       ::math::rationalfunctions::multRatio ratio1 ratio2

       ::math::rationalfunctions::divRatio ratio1 ratio2

       ::math::rationalfunctions::derivPolyn ratio

       ::math::rationalfunctions::coeffsNumerator ratio

       ::math::rationalfunctions::coeffsDenominator ratio

_________________________________________________________________

DESCRIPTION

       This package deals with rational functions of one variable:

       o      the basic arithmetic operations are extended to rational functions

       o      computing the derivatives of these functions

       o      evaluation through a general procedure or via specific procedures)

PROCEDURES

       The package defines the following public procedures:

       ::math::rationalfunctions::rationalFunction num den
	      Return an (encoded) list that defines the rational function. A rational function

			   1 + x^3
		 f(x) = ------------
			1 + 2x + x^2

	      can be defined via:

		 set f [::math::rationalfunctions::rationalFunction [list 1 0 0 1]  [list 1 2 1]]

	      list num
		     Coefficients of the numerator of the rational function (in ascending order)

	      list den
		     Coefficients of the denominator of the rational function (in ascending order)

       ::math::rationalfunctions::ratioCmd num den
	      Create a new procedure that evaluates the rational function. The name of the function is automatically generated. Useful if you need
	      to evaluate the function many times, as the procedure consists of a single [expr] command.

	      list num
		     Coefficients of the numerator of the rational function (in ascending order)

	      list den
		     Coefficients of the denominator of the rational function (in ascending order)

       ::math::rationalfunctions::evalRatio rational x
	      Evaluate the rational function at x.

	      list rational
		     The rational function's definition (as returned by the rationalFunction command).	order)

	      float x
		     The coordinate at which to evaluate the function

       ::math::rationalfunctions::addRatio ratio1 ratio2
	      Return a new rational function which is the sum of the two others.

	      list ratio1
		     The first rational function operand

	      list ratio2
		     The second rational function operand

       ::math::rationalfunctions::subRatio ratio1 ratio2
	      Return a new rational function which is the difference of the two others.

	      list ratio1
		     The first rational function operand

	      list ratio2
		     The second rational function operand

       ::math::rationalfunctions::multRatio ratio1 ratio2
	      Return a new rational function which is the product of the two others.  If one of the arguments is a scalar value, the other  ratio-
	      nal function is simply scaled.

	      list ratio1
		     The first rational function operand or a scalar

	      list ratio2
		     The second rational function operand or a scalar

       ::math::rationalfunctions::divRatio ratio1 ratio2
	      Divide the first rational function by the second rational function and return the result. The remainder is dropped

	      list ratio1
		     The first rational function operand

	      list ratio2
		     The second rational function operand

       ::math::rationalfunctions::derivPolyn ratio
	      Differentiate the rational function and return the result.

	      list ratio
		     The rational function to be differentiated

       ::math::rationalfunctions::coeffsNumerator ratio
	      Return the coefficients of the numerator of the rational function.

	      list ratio
		     The rational function to be examined

       ::math::rationalfunctions::coeffsDenominator ratio
	      Return the coefficients of the denominator of the rational function.

	      list ratio
		     The rational function to be examined

REMARKS ON THE IMPLEMENTATION

       The  implementation  of	the  rational functions relies on the math::polynomials package. For further remarks see the documentation on that
       package.

BUGS, IDEAS, FEEDBACK
       This document, and the package it describes, will undoubtedly contain bugs and other problems.  Please report such in the category math	::
       rationalfunctions  of  the  Tcllib SF Trackers [http://sourceforge.net/tracker/?group_id=12883].  Please also report any ideas for enhance-
       ments you may have for either package and/or documentation.

KEYWORDS

       math, rational functions

CATEGORY

       Mathematics

COPYRIGHT

       Copyright (c) 2005 Arjen Markus <arjenmarkus@users.sourceforge.net>

math								       1.0.1					     math::rationalfunctions(3tcl)