SYNOPSIS

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

::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.

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

REMARKS ON THE IMPLEMENTATION

KEYWORDS

CATEGORY

COPYRIGHT

Copyright (c) 2005 Arjen Markus <[email protected]>