Compositional representation of rational functions

Abstract

The rational functions are shown to coincide with the compositions of endmarkings, morphisms and inverses of injective morphisms. To represent a rational function τ we need one endmarking µ m , two morphisms α 1 , α 3 and one inverse of an injective morphism α 2 and then τ = µ m α 1 α −1 2 α 3 .