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arXiv · 2303.10027

From positional representation of numbers to positional representation of vectors

Izabella Ingrid Farkas·Edita Pelantová·Milena Svobodová
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Abstract

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.

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Izabella Ingrid Farkas, Edita Pelantová, Milena Svobodová. 2023-03-17. From positional representation of numbers to positional representation of vectors. https://arxiv.org/abs/2303.10027

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