math::rationalfunctions(3tcl) 1.0.1 math "Math"
math::rationalfunctions - Polynomial functions
TABLE OF CONTENTS
SYNOPSIS
DESCRIPTION
PROCEDURES
REMARKS ON THE IMPLEMENTATION
BUGS, IDEAS, FEEDBACK
KEYWORDS
COPYRIGHT
package require Tcl ?8.4?
package require math::rationalfunctions ?1.0.1?
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)
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.
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.
Please also report any ideas for enhancements you may have for either
package and/or documentation.
math, rational functions
Copyright © 2005 Arjen Markus <arjenmarkus@users.sourceforge.net>