Result: ARITHMETICS IN NUMERATION SYSTEMS WITH NEGATIVE QUADRATIC BASE
Title:
ARITHMETICS IN NUMERATION SYSTEMS WITH NEGATIVE QUADRATIC BASE
Authors:
Source:
Kybernetika. 47(1):74-92
Publisher Information:
Praha: Institute of Information Theory and Automation of the Academy of Sciences of the Czech Republic, 2011.
Publication Year:
2011
Physical Description:
print, 20 ref
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Combinatoire, Combinatorics, Problèmes combinatoires classiques, Classical combinatorial problems, Algèbre, Algebra, Théorie des nombres, Number theory, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Algorithmique. Calculabilité. Arithmétique ordinateur, Algorithmics. Computability. Computer arithmetics, Arithmétique, Arithmetics, Aritmética, En ligne, On line, En línea, Equation Itô, Itô equation, Ecuación Itô, Intégrale stochastique, Stochastic integral, Integral estocástica, Polynôme, Polynomial, Polinomio, Soustraction, Subtraction, Sustracción, Système numération, Numeration system, Sistema numeración, Système quadratique, Quadratic system, Sistema cuadrático, 11K16, 68R15, Pisot number, negative base, numeration systems
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00 Praha, Czech Republic
ISSN:
0023-5954
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems
Mathematics
Mathematics
Accession Number:
edscal.24103680
Database:
PASCAL Archive
Further Information
We consider positional numeration system with negative base ―β, as introduced by Ito and Sadahiro. In particular, we focus on arithmetical properties of such systems when β is a quadratic Pisot number. We study a class of roots β > 1 of polynomials x2 ― mx ― n, m > n ≥ 1, and show that in this case the set Fin(―β) of finite (―β)-expansions is closed under addition, although it is not closed under subtraction. A particular example is β = T = 1/2(1 + √5), the golden ratio. For such β, we determine the exact bound on the number of fractional digits appearing in arithmetical operations. We also show that the set of (-T)-integers coincides on the positive half-line with the set of (τ2)-integers.