Polynomial ring automorphisms, rational (w, o)-canonical forms, and the asignment problem

• Autores: S. A. Abramov, M. Petkovsek
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 45, Nº 6, 2010, págs. 684-708
• Idioma: inglés
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• Resumen

  • We investigate the representations of a rational function Rk(x) where k is a field of characteristic zero, in the form R=KsS/S. Here K,Sk(x), and s is an automorphism of k(x) which maps k[x] onto k[x]. We show that the degrees of the numerator and denominator of K are simultaneously minimized iff K=r/s where r,sk[x] and r is coprime with sns for all . Assuming existence of algorithms for computing orbital decompositions of Rk(x) and semi-periods of irreducible pk[x]k, we present an algorithm for minimizing among representations with minimal K, where w is any appropriate weight function. This algorithm is based on a reduction to the well-known assignment problem of combinatorial optimization. We show how to use these representations of rational functions to obtain succinct representations of s-hypergeometric terms.