Abstract
When we compute arithmetical algorithms in a sofic number system, we perform arithmetical operations with the entries of its transformations, intervals and vectors. These operations are algorithmic provided the entries are rational numbers. Since we work with projective matrices and vectors, we can assume that their entries are integers whose greatest common divisor is 1. Then each projective tensor, matrix or vector with rational entries has exactly two representations with coprime integers.
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Kůrka, P. (2016). Integer Vectors and Matrices. In: Dynamics of Number Systems. Studies in Systems, Decision and Control, vol 59. Springer, Cham. https://doi.org/10.1007/978-3-319-33367-0_6
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DOI: https://doi.org/10.1007/978-3-319-33367-0_6
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