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:

       •      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>