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math::polynomials(n)                          Tcl Math Library                          math::polynomials(n)



____________________________________________________________________________________________________________

NAME
       math::polynomials - Polynomial functions

SYNOPSIS
       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

____________________________________________________________________________________________________________

DESCRIPTION
       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)


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)


       ::math::polynomials::polynCmd coeffs
              Create  a new procedure that evaluates the polynomial. The name of the polynomial is automati-cally automatically
              cally 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.


       ::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


       ::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


       ::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


       ::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


       ::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


       ::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


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

              list polyn
                     The polynomial to be differentiated


       ::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


       ::math::polynomials::degreePolyn polyn
              Return the degree of the polynomial.

              list polyn
                     The polynomial to be examined


       ::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


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

              list polyn
                     The polynomial in question


REMARKS ON THE IMPLEMENTATION
       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 defini-tion definition
       tion 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.

BUGS, IDEAS, FEEDBACK
       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 SF Trackers [http://source -
       forge.net/tracker/? group_id=12883].  Please also report any ideas for enhancements you may  have  for
       either package and/or documentation.

KEYWORDS
       math, polynomial functions

CATEGORY
       Mathematics

COPYRIGHT
       Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>




math                                                1.0.1                               math::polynomials(n)