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Original Articles

A New Multidimensional Slow Continued Fraction Algorithm and Stepped Surface

, , , &
Pages 390-410 | Published online: 14 Nov 2014
 

Abstract

We give a new algorithm of slow continued fraction expansion related to an arbitrary real cubic number field as a 2-dimensional version of the Farey map. Using our algorithm, we can find the generators of dual substitutions (so-called tiling substitutions) for any stepped surface for any cubic direction.

2010 AMS Subject Classification::

Notes

1GiNaC is available at http://www.ginac.de/. The routine that was written for this purpose can be downloaded from the website http://www.lab2.toho-u.ac.jp/sci/c/math/yasutomi/mfarey.html.

2The routine that was written for this purpose can be downloaded from the website http://www.lab2.toho-u.ac.jp/sci/c/math/yasutomi/mfarey.html.

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