# rational_funcs (n) - Linux Man Pages

## 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::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

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 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

## CATEGORY

Mathematics

```Copyright (c) 2005 Arjen Markus <arjenmarkus [at] users.sourceforge.net>