 
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 GSP1, Russia
M. Petkovsek
Faculty of Mathematics and Physics
University of Ljubljana
Jadranska 19, SI1000 Ljubljana, Slovenia
Abstract
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 semiperiods of ir
