math::rationalfunctions - Polynomial functions
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:
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]]
Coefficients of the numerator of the rational function (in ascending order)
Coefficients of the denominator of the rational function (in ascending order)
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.
Coefficients of the numerator of the rational function (in ascending order)
Coefficients of the denominator of the rational function (in ascending order)
Evaluate the rational function at x.
The rational function's definition (as returned by the rationalFunction command). order)
The coordinate at which to evaluate the function
Return a new rational function which is the sum of the two others.
The first rational function operand
The second rational function operand
Return a new rational function which is the difference of the two others.
The first rational function operand
The second rational function operand
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.
The first rational function operand or a scalar
The second rational function operand or a scalar
Divide the first rational function by the second rational function and return the result. The remainder is dropped
The first rational function operand
The second rational function operand
Differentiate the rational function and return the result.
The rational function to be differentiated
Return the coefficients of the numerator of the rational function.
The rational function to be examined
Return the coefficients of the denominator of the rational function.
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 Trackers. Please also report any ideas for enhancements you may have for either package and/or documentation.
Mathematics
Copyright © 2005 Arjen Markus <arjenmarkus@users.sourceforge.net>