Exhaustive search methods for CNS polynomials

In this paper, we present a method for finding all expansive polynomials with a prescribed degree n and constant term c0. Our research is motivated by the fact that expansivity is a necessary condition for number system constructions. We use the algorithm for an exhaustive search of CNS polynomials for small values of n and c0. We also define semi-CNS polynomials and show that producing them the same search method can be used.

[1]  Attila Pethö.  On a polynomial transformation and its application to the construction of a public key cryptosystem , 1991 .

[4]  Béla Kovács.  Canonical number systems in algebraic number fields , 1981 .

[5]  I. Kátai,et al.  Canonical number systems in imaginary quadratic fields , 1981 .

[6]  J. Dufresnoy,et al.  Étude de certaines fonctions méromorphes bornées sur le cercle unité. Application à un ensemble fermé d'entiers algébriques , 1955 .

[7]  D. H. Lehmer.  A Machine Method for Solving Polynomial Equations , 1961, JACM.

[8]  David W. Boyd.  Pisot and Salem numbers in intervals of the real line , 1978 .

[9]  A. Ralston.  A first course in numerical analysis , 1965 .

[10]  Attila Pethö,et al.  Computational number theory : proceedings of the Colloquium on Computational Number Theory held at Kossuth Lajos University, Debrecen (Hungary), September 4-9, 1989 , 1991 .

[11]  J. Schur,et al.  Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind. , 1917 .

[12]  C. Chamfy.  Fonctions méromorphes dans le cercle-unité et leurs séries de Taylor , 1958 .

[13]  William J. Gilbert.  Radix representations of quadratic fields , 1981 .

[14]  Shigeki Akiyama,et al.  Generalized radix representations and dynamical systems. I , 2005 .

[15]  Péter Burcsi.  AN ALGORITHM CHECKING A NECESSARY CONDITION OF NUMBER SYSTEM CONSTRUCTIONS , 2005 .

[16]  S. Akiyama.  On a generalization of the radix representation-a survey , 2004 .

[17]  Cubic CNS polynomials, notes on a conjecture of W.J. Gilbert , 2003 .

[18]  J. Thuswaldner,et al.  On the characterization of canonical number systems , 2004 .

[19]  Shigeki Akiyama,et al.  On canonical number systems , 2002, Theor. Comput. Sci..