Bases of canonical number systems in quartic algebraic number fields

Brunotte, Horst; Huszti, Andrea; Pethő, Attila

Journal de théorie des nombres de Bordeaux, Tome 18 (2006) no. 3, pp. 537-557.

Les systèmes canoniques de numération peuvent être considérés comme des généralisations naturelles de la numération classique des entiers. Dans la présente note, une modification d’un algorithme de B. Kovács et A. Pethő est établie et appliquée au calcul des systèmes canoniques de numération dans certains anneaux d’entiers de corps de nombres algébriques. L’algorithme permet de déterminer tous les systèmes canoniques de numération de quelques corps de nombres de degré quatre.

Canonical number systems can be viewed as natural generalizations of radix representations of ordinary integers to algebraic integers. A slightly modified version of an algorithm of B. Kovács and A. Pethő is presented here for the determination of canonical number systems in orders of algebraic number fields. Using this algorithm canonical number systems of some quartic fields are computed.

Mots clés : canonical number system, radix representation, power integral basis

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