Provided by: tcllib_1.14-dfsg-1_all

**NAME**

math::rationalfunctions - Polynomial functions

**SYNOPSIS**

package requireTcl?8.4?package requiremath::rationalfunctions?1.0.1?::math::rationalfunctions::rationalFunctionnumden::math::rationalfunctions::ratioCmdnumden::math::rationalfunctions::evalRatiorationalx::math::rationalfunctions::addRatioratio1ratio2::math::rationalfunctions::subRatioratio1ratio2::math::rationalfunctions::multRatioratio1ratio2::math::rationalfunctions::divRatioratio1ratio2::math::rationalfunctions::derivPolynratio::math::rationalfunctions::coeffsNumeratorratio::math::rationalfunctions::coeffsDenominatorratio_________________________________________________________________

**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::rationalFunctionnumdenReturn 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]] listnumCoefficients of the numerator of the rational function (in ascending order) listdenCoefficients of the denominator of the rational function (in ascending order)::math::rationalfunctions::ratioCmdnumdenCreate 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. listnumCoefficients of the numerator of the rational function (in ascending order) listdenCoefficients of the denominator of the rational function (in ascending order)::math::rationalfunctions::evalRatiorationalxEvaluate the rational function at x. listrationalThe rational function's definition (as returned by the rationalFunction command). order) floatxThe coordinate at which to evaluate the function::math::rationalfunctions::addRatioratio1ratio2Return a new rational function which is the sum of the two others. listratio1The first rational function operand listratio2The second rational function operand::math::rationalfunctions::subRatioratio1ratio2Return a new rational function which is the difference of the two others. listratio1The first rational function operand listratio2The second rational function operand::math::rationalfunctions::multRatioratio1ratio2Return 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. listratio1The first rational function operand or a scalar listratio2The second rational function operand or a scalar::math::rationalfunctions::divRatioratio1ratio2Divide the first rational function by the second rational function and return the result. The remainder is dropped listratio1The first rational function operand listratio2The second rational function operand::math::rationalfunctions::derivPolynratioDifferentiate the rational function and return the result. listratioThe rational function to be differentiated::math::rationalfunctions::coeffsNumeratorratioReturn the coefficients of the numerator of the rational function. listratioThe rational function to be examined::math::rationalfunctions::coeffsDenominatorratioReturn the coefficients of the denominator of the rational function. listratioThe 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 categorymath::rationalfunctionsof theTcllibSFTrackers[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**

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