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## man page of math::rationalfunctions

### math::rationalfunctions: Polynomial functions

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NAME

math::rationalfunctions - Polynomial functions## SYNOPSIS

package requireTcl ?8.4?package requiremath::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: o the basic arithmetic operations are extended to rational functions o computing the derivatives of these functions o evaluation through a general procedure or via specific procedures)## PROCEDURES

The package defines the following public procedures:::math::rationalfunctions::rationalFunction num denReturn 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::ratioCmd num denCreate 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::evalRatio rational xEvaluate 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::addRatio ratio1 ratio2Return a new rational function which is the sum of the two others. listratio1The first rational function operand listratio2The second rational function operand::math::rationalfunctions::subRatio ratio1 ratio2Return a new rational function which is the difference of the two others. listratio1The first rational function operand listratio2The second rational function operand::math::rationalfunctions::multRatio ratio1 ratio2Return 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::divRatio ratio1 ratio2Divide 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::derivPolyn ratioDifferentiate the rational function and return the result. listratioThe rational function to be differentiated::math::rationalfunctions::coeffsNumerator ratioReturn the coefficients of the numerator of the rational function. listratioThe rational function to be examined::math::rationalfunctions::coeffsDenominator ratioReturn 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 theTcllib SF Trackers[//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> MATH::RATIONALFUNCTIONS(3)

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