To represent real $m$-dimensional vectors, a positional vector system given by a non-singular matrix $M \in \mathbb{ Z}^{ m \times m}$ and a digit set $\mathcal{ D} \subset \mathbb{ Z}^m$ 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.
Categories: cs.DC