NAME

math::polynomials - Polynomial functions

Table Of Contents
Synopsis
Description
PROCEDURES
REMARKS ON THE IMPLEMENTATION
Bugs, Ideas, Feedback
Keywords
Category
Copyright

SYNOPSIS

package require Tcl ?8.3?
package require math::polynomials ?1.0.1?

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. 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

Tcl Library Source Code