From positional representation of numbers to positional representation of vectors

03/17/2023

∙

by   Izabella Ingrid Farkas, et al.

∙

0

∙

share

To represent real m-dimensional vectors, a positional vector system given by a non-singular matrix M ∈ℤ^m × m and a digit set 𝒟⊂ℤ^m is used. If m = 1, the system coincides with the well known numeration system used to represent real numbers. We study some properties of the vector systems which are transformable from the case m = 1 to higher dimensions. We focus on algorithm for parallel addition and on systems allowing an eventually periodic representation of vectors with rational coordinates.