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Rational and irrational positive numbers can be represented by Christoffel words. The aim of this Note is to propose methods which realize some classical operations on real numbers, using their representation by Christoffel words: linear fractional image, especially multiplication by a given positive rational number. These transforms can be realized by using transducers and, in the special case of multiplication, by using a periodic mecanism of cancellation of letters 0 and 1 on a power of the initial Christoffel word. Proofs are based on geometrical arguments on two dimensional lattice. |
