math::rationalfunctions(n)           Math           math::rationalfunctions(n)



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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::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

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




math                                 1.0.1          math::rationalfunctions(n)
