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Polynomial Ring Automorphisms, Rational (w, )-Canonical Forms,

Summary: Polynomial Ring Automorphisms,
Rational (w, )-Canonical Forms,
and the Assignment Problem
Dedicated to the memory of Manuel Bronstein
(1963 2005)
S. A. Abramov
Russian Academy of Sciences
Dorodnicyn Computing Centre
Vavilova 40, 119991, Moscow GSP-1, Russia
M. Petkovsek
Faculty of Mathematics and Physics
University of Ljubljana
Jadranska 19, SI-1000 Ljubljana, Slovenia
We investigate representations of a rational function R k(x) where k is a field of characteristic
zero, in the form R = K S/S. Here K, S k(x), and 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 simultane-
ously minimized iff K = r/s where r, s k[x] and r is coprime with n
s for all n Z. Assuming
existence of algorithms for computing orbital decompositions of R k(x) and semi-periods of ir-


Source: Abramov, Sergei A. - Dorodnicyn Computing Centre of the Russian Academy of Sciences


Collections: Mathematics; Computer Technologies and Information Sciences