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.
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.