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
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>