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math::rationalfunctions(n)		       Math		       math::rationalfunctions(n)

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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  func-
	      tion  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 com-
		     mand).  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 rational 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 prob-
       lems.  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 enhancements you may have for either package and/or documentation.

KEYWORDS
       math, rational functions

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

math					      1.0.1		       math::rationalfunctions(n)
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