math::rationalfunctions - Polynomial functions
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
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.
- ::math::rationalfunctions::subRatio ratio1
ratio2
- Return a new rational function which is the difference of the two
others.
- ::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
- ::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.
- ::math::rationalfunctions::coeffsDenominator ratio
- Return the coefficients of the denominator of the rational function.
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
[http://sourceforge.net/tracker/?group_id=12883]. Please also report any
ideas for enhancements you may have for either package and/or
documentation.
Copyright (c) 2005 Arjen Markus <arjenmarkus@users.sourceforge.net>