Arithmetics in number systems with a negative base

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F11%3A00174152" target="_blank" >RIV/68407700:21340/11:00174152 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.tcs.2010.11.033" target="_blank" >http://dx.doi.org/10.1016/j.tcs.2010.11.033</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.tcs.2010.11.033" target="_blank" >10.1016/j.tcs.2010.11.033</a>

Result language
angličtina
Original language name
Arithmetics in number systems with a negative base
Original language description
We study the numeration system with a negative base, introduced by Ito and Sadahiro. We focus on arithmetic operations in the sets Fin(-?) and Z_(-?) of numbers having finite resp. integer (-?)-expansions. We show that Fin(-?) is trivial if ? is smallerthan the golden ratio (1+sqrt5)/2. For ?>= (1+sqrt5)/2 we show that Fin(-?) is a ring only if ? is a Pisot or Salem number with no negative conjugates. We prove the conjecture of Ito and Sadahiro that Fin(-?) is a ring if ? is a quadratic Pisot number with positive conjugate. For quadratic Pisot units, we determine the number of fractional digits that may appear when adding or multiplying two (-?)-integers.
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
—

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)