A NEW SYMMETRIC TWO-DIMENSIONAL ALGORITHM
Pedro Fortuny Ayuso, Fritz Schweiger · International Journal of Number Theory · 2006
Continued fractions are deeply related to Singularity Theory, as the computation of the Puiseux exponents of a plane curve from its dual graph clearly shows. Another closely related topic is Euclid's Algorithm for computing the gcd of two integers (see [2] for a detailed overview). In the first section, we describe a subtractive algorithm for computing the gcd of n integers, related to singularities of curves in affine n-space. This gives rise to a multidimensional continued fraction algorithm whose version in dimension 2 is the main topic of the paper.