math::rationalfunctions(3tcl)

NAME
math::rationalfunctions - Polynomial functions

SYNOPSIS
package require Tcl ?8.5 9?

package require math::rationalfunctions ?1.0.2?

::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)

::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, rational functions

CATEGORY
Mathematics

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