


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


______________________________________________________________________________

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

_________________________________________________________________

DESCRIPTION
       This package deals with rational functions of one variable:

       o      the  basic  arithmetic operations are extended to rational func-
              tions

       o      computing the derivatives of these functions

       o      evaluation through a general procedure or  via  specific  proce-
              dures)


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



math                          1.0.1                             1





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


              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  con-
              sists 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  oth-
              ers.

              list ratio1
                     The first rational function operand

              list ratio2
                     The second rational function operand






math                          1.0.1                             2





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


       ::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  func-
              tion 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 func-
              tion.

              list ratio
                     The rational function to be examined


       ::math::rationalfunctions::coeffsDenominator ratio
              Return the coefficients of the denominator of the rational func-
              tion.





math                          1.0.1                             3





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


              list ratio
                     The rational function to be examined



REMARKS ON THE IMPLEMENTATION
       The  implementation of the rational functions relies on the math::poly-
       nomials 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://source-
       forge.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                             4


