[//000000001]: # (math::rationalfunctions \- Math) [//000000002]: # (Generated from file 'rational\_funcs\.man' by tcllib/doctools with format 'markdown') [//000000003]: # (Copyright © 2005 Arjen Markus ) [//000000004]: # (math::rationalfunctions\(n\) 1\.0\.1 tcllib "Math")
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# NAME math::rationalfunctions \- Polynomial functions # Table Of Contents - [Table Of Contents](#toc) - [Synopsis](#synopsis) - [Description](#section1) - [PROCEDURES](#section2) - [REMARKS ON THE IMPLEMENTATION](#section3) - [Bugs, Ideas, Feedback](#section4) - [Keywords](#keywords) - [Category](#category) - [Copyright](#copyright) # SYNOPSIS package require Tcl ?8\.4? package require math::rationalfunctions ?1\.0\.1? [__::math::rationalfunctions::rationalFunction__ *num* *den*](#1) [__::math::rationalfunctions::ratioCmd__ *num* *den*](#2) [__::math::rationalfunctions::evalRatio__ *rational* *x*](#3) [__::math::rationalfunctions::addRatio__ *ratio1* *ratio2*](#4) [__::math::rationalfunctions::subRatio__ *ratio1* *ratio2*](#5) [__::math::rationalfunctions::multRatio__ *ratio1* *ratio2*](#6) [__::math::rationalfunctions::divRatio__ *ratio1* *ratio2*](#7) [__::math::rationalfunctions::derivPolyn__ *ratio*](#8) [__::math::rationalfunctions::coeffsNumerator__ *ratio*](#9) [__::math::rationalfunctions::coeffsDenominator__ *ratio*](#10) # 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 - __::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 - __::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 Trackers](http://core\.tcl\.tk/tcllib/reportlist)\. Please also report any ideas for enhancements you may have for either package and/or documentation\. When proposing code changes, please provide *unified diffs*, i\.e the output of __diff \-u__\. Note further that *attachments* are strongly preferred over inlined patches\. Attachments can be made by going to the __Edit__ form of the ticket immediately after its creation, and then using the left\-most button in the secondary navigation bar\. # KEYWORDS [math](\.\./\.\./\.\./\.\./index\.md\#math), [rational functions](\.\./\.\./\.\./\.\./index\.md\#rational\_functions) # CATEGORY Mathematics # COPYRIGHT Copyright © 2005 Arjen Markus