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math::rationalfunctions(n) 1.0.1 "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:
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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>