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Re: Polynomial specifications
I think it is important to make a clear distinctions between
"Polynomials" that are no more than a sequence of coefficients and
"Polynomial Functions" that are interpretations of a polynomial in a
field or a ring over this field. Let me illustrated that by two
examples.
Consider the field Z2 which is either the Boolean with "disjunctive
or" and "and" as operators or the integers modulo 2. It is known that
x^2 = x. Therefore to represent polynomial functions, polynomial of
degree at most 1 will be enough, but in computations one may wish to
consider polynomials of any degree.
Polynomial functions on matrices over a field are interpretations of
polynomials over this field.
N.B. (for people interested in inter-cultural confrontation) In French
the confusion is better avoided because we used a different word for
the noun and the adjective. Indeed, what is called "Polynomial" in
English is called "Polynome" and what is called "Polynomial Function"
in English is called "Fonction polynomiale".
--
Pierre LESCANNE | Tel: (work) (33) 83 59 30 07
CRIN (CNRS) & INRIA-Lorraine & GDR Progra | (home) (33) 83 22 76 92
Centre Charles Hermite | Fax: (33) 83 27 83 19
F54506 VANDOEUVRE-les-NANCY Cedex FRANCE | E-mail: lescanne@loria.fr
more information on www at http://www.loria.fr/~lescanne/
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