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Description
| - We consider positional numeration system with negative base -betafi, as introduced by Ito and Sadahiro. In particular, we focus on arithmetical properties of such systems when fi is a quadratic Pisot number. We study a class of roots fi beta > 1 of polynomials x^2 - mx - n, m >=n >= 1, and show that in this case the set Fin(-fibeta) of finite (-betafi)-expansions is closed under addition, although it is not closed under subtraction. A particular example is fi beta =tau Fi = (1 + sqrt5)/2, the golden ratio. For such fi, we determine the exact bound on the number of fractional digits appearing in arithmetical operations. We also show that the set of (-Fibeta )-integers coincides on the positive half-line with the set of (Fi tau^2)-integers.
- We consider positional numeration system with negative base -betafi, as introduced by Ito and Sadahiro. In particular, we focus on arithmetical properties of such systems when fi is a quadratic Pisot number. We study a class of roots fi beta > 1 of polynomials x^2 - mx - n, m >=n >= 1, and show that in this case the set Fin(-fibeta) of finite (-betafi)-expansions is closed under addition, although it is not closed under subtraction. A particular example is fi beta =tau Fi = (1 + sqrt5)/2, the golden ratio. For such fi, we determine the exact bound on the number of fractional digits appearing in arithmetical operations. We also show that the set of (-Fibeta )-integers coincides on the positive half-line with the set of (Fi tau^2)-integers. (en)
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Title
| - Arithmetics in Numeration Systems with Negative Quadratic Base
- Arithmetics in Numeration Systems with Negative Quadratic Base (en)
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skos:prefLabel
| - Arithmetics in Numeration Systems with Negative Quadratic Base
- Arithmetics in Numeration Systems with Negative Quadratic Base (en)
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skos:notation
| - RIV/68407700:21340/11:00174144!RIV12-MSM-21340___
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http://linked.open...avai/predkladatel
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
| - P(GA201/09/0584), P(LC06002), S, Z(MSM6840770039)
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/68407700:21340/11:00174144
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - numeration systems, negative base, Pisot number (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
| - Masáková, Zuzana
- Vávra, Tomáš
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http://linked.open...ain/vavai/riv/wos
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http://linked.open...n/vavai/riv/zamer
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issn
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number of pages
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http://localhost/t...ganizacniJednotka
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