math::rationalfunctions(n) 1.0.1 math "Math"
math::rationalfunctions - Polynomial functions
TABLE OF CONTENTS
SYNOPSIS
DESCRIPTION
PROCEDURES
REMARKS ON THE IMPLEMENTATION
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.
math, rational functions
Copyright © 2005 Arjen Markus <arjenmarkus@users.sourceforge.net>