bionic (3) rational_funcs.3tcl.gz

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>