Decoupling Multivariate Fractions

François Lemaire, Adrien Poteaux

Abstract: We present a new algorithm for computing compact forms of multivariate fractions. Given a fraction presented as a quotient of two polynomials, our algorithm builds a tree where internal nodes are operators, and leaves are fractions depending on pairwise disjoint sets of variables. The motivation of this work is to obtain compact forms of fractions, which are more readable and meaningful for the user or the modeler, and better suited for interval arithmetic.