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# math::rationalfunctions(n) 1.0.1 tcllib "Math"

## 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:

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)

- list
**::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)

- list
**::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

- list
**::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

- list
**::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

- list
**::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

- list
**::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

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

- list
*ratio* The rational function to be differentiated

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

- list
*ratio* The rational function to be examined

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

- list
*ratio* The rational function to be examined

- list

## 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.
Please also report any ideas for enhancements you may have for either
package and/or documentation.

## Category

Mathematics

## Copyright

Copyright © 2005 Arjen Markus <arjenmarkus@users.sourceforge.net>