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# math::rationalfunctions

## man page of math::rationalfunctions

### math::rationalfunctions: Polynomial functions

```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::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
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

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
any  ideas  for  enhancements  you  may  have for either package and/or
documentation.

KEYWORDS
math, rational functions

CATEGORY
Mathematics

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

MATH::RATIONALFUNCTIONS(3)
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