


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


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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

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DESCRIPTION
       This package deals with polynomial functions of one variable:

       o      the basic arithmetic operations are extended to polynomials

       o      computing the derivatives and primitives of these functions

       o      evaluation  through  a  general procedure or via specific proce-
              dures)


PROCEDURES
       The package defines the following public procedures:

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



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


              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 con-
              sists of a single [expr] command.

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


       ::math::polynomials::evalPolyn polynomial x
              Evaluate the polynomial at x.

              list polynomial
                     The polynomial's definition (as returned by  the  polyno-
                     mial 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 oth-
              ers.

              list polyn1
                     The first polynomial operand





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


              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






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


       ::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    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>









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