A note on the computation of the fraction of smallest denominator in between two irreducible fractions

Isabelle Sivignon (1)

1 GIPSA-AGPIG - GIPSA - Architecture, Géométrie, Perception, Images, Gestes

Given two irreducible fractions f and g, with f < g, we characterize the fraction h such that f < h < g and the denominator of h is as small as possible. An output-sensitive algorithm of time complexity O(d), where d is the depth of h is derived from this characterization.

Mots clés: simplest fraction; continued fractions; algorithm

Domaines: Théorie des nombres [math.NT]; Mathématique discrète [cs.DM]

Isabelle Sivignon. A note on the computation of the fraction of smallest denominator in between two irreducible fractions. Discrete Applied Mathematics, 2016, ⟨10.1016/j.dam.2015.08.029⟩. ⟨hal-01228572⟩