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:
 the basic arithmetic operations are extended to rational functions
 computing the derivatives of these functions
 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 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 problems. Please report such in the category math :: rationalfunctions of the Tcllib Trackers [http://core.tcl.tk/tcllib/reportlist]. Please also report any ideas for enhancements you may have for either package and/or documentation.KEYWORDS
math, rational functionsCATEGORY
MathematicsCOPYRIGHT
Copyright (c) 2005 Arjen Markus <[email protected]>