In this paper we discuss several notions of decomposition for multivariate rational functions, and we present algorithms for decomposing multivariate rational functions over an arbitrary field. We also provide a very efficient method to decide if a unirational field has transcendence degree one, and in the affirmative case to compute the generator.
In this paper we present an algorithm to compute all unirational fields of transcendence degree one containing a given finite set of multivariate rational functions. In particular, we provide an algorithm to decompose a multivariate rational function f of the form f = g(h), where g is a univariate rational function and h a multivariate one.
Abstract. In this paper we introduce the D-resultant of two rational functions f (t), g(t) ∈ K(t) and show how it can be used to decide if g(t)] and to find the singularities of the parametric algebraic curve define by X = f (t), Y = g(t). In the course of our work we extend a result about implicitization of polynomial parametric curves to the rational case, which has its own interest.
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