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
              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.

       ::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  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.

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  Trackers
       [http://core.tcl.tk/tcllib/reportlist].  Please also report any ideas for enhancements you
       may have for either package and/or documentation.

       When proposing code changes, please provide unified diffs, i.e the output of diff -u.

       Note further that attachments are strongly preferred over inlined patches. Attachments can
       be  made  by going to the Edit form of the ticket immediately after its creation, and then
       using the left-most button in the secondary navigation bar.

KEYWORDS

       math, polynomial functions

CATEGORY

       Mathematics

COPYRIGHT

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