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]]
| Type | Name | Mode |
| 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.
| Type | Name | Mode |
| 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.
| Type | Name | Mode |
| 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.
| Type | Name | Mode |
| 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.
| Type | Name | Mode |
| 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.
| Type | Name | Mode |
| 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
| Type | Name | Mode |
| 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.
| Type | Name | Mode |
| list | ratio | |
| | The rational function to be differentiated
|
-
::math::rationalfunctions::coeffsNumerator ratio
-
Return the coefficients of the numerator of the rational function.
| Type | Name | Mode |
| list | ratio | |
| | The rational function to be examined
|
-
::math::rationalfunctions::coeffsDenominator ratio
-
Return the coefficients of the denominator of the rational
function.
| Type | Name | Mode |
| 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
http://sourceforge.net/tracker/?group_id=12883.
Please also report any ideas for enhancements you may have for either
package and/or documentation.
math, rational functions