math::polynomials - Polynomial functions

       This document, and the package it describes, will undoubtedly contain bugs and  other  problems.   Please
       report     such     in    the    category    math::polynomials    of    the    TcllibTrackers
       [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 unifieddiffs, 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.

       Mathematics

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

tcllib                                                1.0.2                              math::polynomials(3tcl)

       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)

       math, polynomial functions

       math::polynomials - Polynomial functions

       The package defines the following public procedures:

       ::math::polynomials::polynomialcoeffs
              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::polynCmdcoeffs
              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::evalPolynpolynomialx
              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::addPolynpolyn1polyn2
              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::subPolynpolyn1polyn2
              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::multPolynpolyn1polyn2
              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::divPolynpolyn1polyn2
              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::remainderPolynpolyn1polyn2
              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::derivPolynpolyn
              Differentiate the polynomial and return the result.

              list polyn
                     The polynomial to be differentiated

       ::math::polynomials::primitivePolynpolyn
              Integrate the polynomial and return the result. The integration constant is set to zero.

              list polyn
                     The polynomial to be integrated

       ::math::polynomials::degreePolynpolyn
              Return the degree of the polynomial.

              list polyn
                     The polynomial to be examined

       ::math::polynomials::coeffPolynpolynindex
              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::allCoeffsPolynpolyn
              Return the coefficients of the polynomial (in ascending order).

              list polyn
                     The polynomial in question

       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.

       package require Tcl?8.5?

       package require math::polynomials?1.0.2?::math::polynomials::polynomialcoeffs::math::polynomials::polynCmdcoeffs::math::polynomials::evalPolynpolynomialx::math::polynomials::addPolynpolyn1polyn2::math::polynomials::subPolynpolyn1polyn2::math::polynomials::multPolynpolyn1polyn2::math::polynomials::divPolynpolyn1polyn2::math::polynomials::remainderPolynpolyn1polyn2::math::polynomials::derivPolynpolyn::math::polynomials::primitivePolynpolyn::math::polynomials::degreePolynpolyn::math::polynomials::coeffPolynpolynindex::math::polynomials::allCoeffsPolynpolyn

________________________________________________________________________________________________________________