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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]








  

  
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.







  

  
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.







  

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

  

  
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.







  

  
The first polynomial operand

  

  
The second polynomial operand









  
::math::polynomials::subPolyn polyn1 polyn2

  
Return a new polynomial which is the difference of the two others.







  

  
The first polynomial operand

  

  
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.







  

  
The first polynomial operand or a scalar

  

  
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







  

  
The first polynomial operand

  

  
The second polynomial operand









  
::math::polynomials::remainderPolyn polyn1
    polyn2

  
Divide the first polynomial by the second polynomial and return the
      remainder.







  

  
The first polynomial operand

  

  
The second polynomial operand









  
::math::polynomials::derivPolyn polyn

  
Differentiate the polynomial and return the result.







  

  
The polynomial to be differentiated









  
::math::polynomials::primitivePolyn polyn

  
Integrate the polynomial and return the result. The integration constant
      is set to zero.







  

  
The polynomial to be integrated









  
::math::polynomials::degreePolyn polyn

  
Return the degree of the polynomial.







  

  
The polynomial to be examined









  
::math::polynomials::coeffPolyn polyn index

  
Return the coefficient of the term of the index'th degree of the
      polynomial.







  

  
The polynomial to be examined

  

  
The degree of the term









  
::math::polynomials::allCoeffsPolyn polyn

  
Return the coefficients of the polynomial (in ascending order).







  

  
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>








  

    1.0.1
    tcllib