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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:

       •      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 -----------1
                        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 auto-matically automatically
              matically 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  argu-ments arguments
              ments 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)