math::polynomials(3tcl) 1.0.1 math "Tcl Math Library"
math::polynomials - Polynomial functions
TABLE OF CONTENTS
SYNOPSIS
DESCRIPTION
PROCEDURES
REMARKS ON THE IMPLEMENTATION
BUGS, IDEAS, FEEDBACK
KEYWORDS
COPYRIGHT
package require Tcl ?8.3?
package require math::polynomials ?1.0.1?
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)
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
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.
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.
Please also report any ideas for enhancements you may have for either
package and/or documentation.
math, polynomial functions
Copyright © 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>