NAME

math::rationalfunctions -
Polynomial functions

SYNOPSIS

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

DESCRIPTION

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)

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

REMARKS ON THE IMPLEMENTATION

The implementation of the rational functions relies on the math::polynomials package. For further remarks see the documentation on that package.

KEYWORDS

math, rational functions