math::polynomials - Polynomial functions
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
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.
- ::math::polynomials::subPolyn polyn1 polyn2
- Return a new polynomial which is the difference of the two others.
- ::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.
- ::math::polynomials::divPolyn polyn1 polyn2
- Divide the first polynomial by the second polynomial and return the
result. The remainder is dropped
- ::math::polynomials::remainderPolyn polyn1
polyn2
- Divide the first polynomial by the second polynomial and return the
remainder.
- ::math::polynomials::derivPolyn polyn
- Differentiate the polynomial and return the result.
- ::math::polynomials::primitivePolyn polyn
- Integrate the polynomial and return the result. The integration constant
is set to zero.
- ::math::polynomials::degreePolyn polyn
- Return the degree of the polynomial.
- ::math::polynomials::coeffPolyn polyn index
- Return the coefficient of the term of the index'th degree of the
polynomial.
- ::math::polynomials::allCoeffsPolyn polyn
- Return the coefficients of the polynomial (in ascending order).
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
[http://sourceforge.net/tracker/?group_id=12883]. Please also report any
ideas for enhancements you may have for either package and/or
documentation.
math, polynomial functions
Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>