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math::polynomials - Polynomial functions

- package require
**Tcl ?8.3?** - package require
**math::polynomials ?1.0.1?**

**::math::polynomials::polynomial***coeffs***::math::polynomials::polynCmd***coeffs***::math::polynomials::evalPolyn***polynomial**x***::math::polynomials::addPolyn***polyn1**polyn2***::math::polynomials::subPolyn***polyn1**polyn2***::math::polynomials::multPolyn***polyn1**polyn2***::math::polynomials::divPolyn***polyn1**polyn2***::math::polynomials::remainderPolyn***polyn1**polyn2***::math::polynomials::derivPolyn***polyn***::math::polynomials::primitivePolyn***polyn***::math::polynomials::degreePolyn***polyn***::math::polynomials::coeffPolyn***polyn**index***::math::polynomials::allCoeffsPolyn***polyn*

This package deals with polynomial functions of one variable:

the basic arithmetic operations are extended to polynomials

computing the derivatives and primitives of these functions

evaluation through a general procedure or via specific procedures)

The package defines the following public procedures:

**::math::polynomials::polynomial***coeffs*Return an (encoded) list that defines the polynomial. A polynomial

f(x) = a + b.x + c.x**2 + d.x**3

can be defined via:

set f [::math::polynomials::polynomial [list $a $b $c $d]

- list
*coeffs* Coefficients of the polynomial (in ascending order)

- list
**::math::polynomials::polynCmd***coeffs*Create a new procedure that evaluates the polynomial. The name of the polynomial is automatically generated. Useful if you need to evualuate the polynomial many times, as the procedure consists of a single [expr] command.

- list
*coeffs* Coefficients of the polynomial (in ascending order) or the polynomial definition returned by the

*polynomial*command.

- list
**::math::polynomials::evalPolyn***polynomial**x*Evaluate the polynomial at x.

- list
*polynomial* The polynomial's definition (as returned by the polynomial command). order)

- float
*x* The coordinate at which to evaluate the polynomial

- list
**::math::polynomials::addPolyn***polyn1**polyn2*Return a new polynomial which is the sum of the two others.

- list
*polyn1* The first polynomial operand

- list
*polyn2* The second polynomial operand

- list
**::math::polynomials::subPolyn***polyn1**polyn2*Return a new polynomial which is the difference of the two others.

- list
*polyn1* The first polynomial operand

- list
*polyn2* The second polynomial operand

- list
**::math::polynomials::multPolyn***polyn1**polyn2*Return a new polynomial which is the product of the two others. If one of the arguments is a scalar value, the other polynomial is simply scaled.

- list
*polyn1* The first polynomial operand or a scalar

- list
*polyn2* The second polynomial operand or a scalar

- list
**::math::polynomials::divPolyn***polyn1**polyn2*Divide the first polynomial by the second polynomial and return the result. The remainder is dropped

- list
*polyn1* The first polynomial operand

- list
*polyn2* The second polynomial operand

- list
**::math::polynomials::remainderPolyn***polyn1**polyn2*Divide the first polynomial by the second polynomial and return the remainder.

- list
*polyn1* The first polynomial operand

- list
*polyn2* The second polynomial operand

- list
**::math::polynomials::derivPolyn***polyn*Differentiate the polynomial and return the result.

- list
*polyn* The polynomial to be differentiated

- list
**::math::polynomials::primitivePolyn***polyn*Integrate the polynomial and return the result. The integration constant is set to zero.

- list
*polyn* The polynomial to be integrated

- list
**::math::polynomials::degreePolyn***polyn*Return the degree of the polynomial.

- list
*polyn* The polynomial to be examined

- list
**::math::polynomials::coeffPolyn***polyn**index*Return the coefficient of the term of the index'th degree of the polynomial.

- list
*polyn* The polynomial to be examined

- int
*index* The degree of the term

- list
**::math::polynomials::allCoeffsPolyn***polyn*Return the coefficients of the polynomial (in ascending order).

- list
*polyn* The polynomial in question

- list

The implementation for evaluating the polynomials at some point uses Horn's rule, which guarantees numerical stability and a minimum of arithmetic operations. To recognise that a polynomial definition is indeed a correct definition, it consists of a list of two elements: the keyword "POLYNOMIAL" and the list of coefficients in descending order. The latter makes it easier to implement Horner's rule.

This document, and the package it describes, will undoubtedly contain
bugs and other problems.
Please report such in the category *math :: polynomials* of the
Tcllib Trackers.
Please also report any ideas for enhancements you may have for either
package and/or documentation.

Mathematics

Copyright © 2004 Arjen Markus <[email protected]>