Algorithms, Dynamics and Geometry of Numeration systems
Czech Science Foundation 13-03538S board no. P202
Technical parameters of contemporary computers increasingly challenge the usage of non-standard numeration systems which may have essential impact on the complexity of arithmetic algorithms and on the precision of computation. The project concentrates on analysis of algorithmic, dynamic and geometric aspects of positional systems with real and complex algebraic bases, and as a generalization, on number representations generated by Möbius transformations. We will concentrate on the construction of Möbius number systems with better coding and distribution properties and more efficient arithmetic algorithms than the classical algorithms for positional systems. We will focus on the identification of Pisot or complex Pisot bases suitable for arithmetic in general algebraic number fields. We will describe the influence of redundancy of the digit set on the possibility and efficiency of parallel algorithms with beta-expansions. Essential will be the description of geometric properties of betaintegers using cut-and-project sets and methods of combinatorics on words. Principal investigator: doc. Ing. Zuzana Masáková, Ph.D. (Czech Technical University in Prague) Associate investigator: prof. RNDr. Petr Kůrka, CSc.