# rational_funcs man page

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* [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 functions

## Category

Mathematics

## Copyright

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