Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Irreducibility testing over local fields

Author: P. G. Walsh
Journal: Math. Comp. 69 (2000), 1183-1191
MSC (1991): Primary 12Y05, 12E05
Published electronically: March 2, 2000
MathSciNet review: 1710699
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information


The purpose of this paper is to describe a method to determine whether a bivariate polynomial with rational coefficients is irreducible when regarded as an element in $\mathbf{Q}((x))[y]$, the ring of polynomials with coefficients from the field of Laurent series in $x$ with rational coefficients. This is achieved by computing certain associated Puiseux expansions, and as a result, a polynomial-time complexity bound for the number of bit operations required to perform this irreducibility test is computed.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation of the American Mathematical Society with MSC (1991): 12Y05, 12E05

Retrieve articles in all journals with MSC (1991): 12Y05, 12E05

Additional Information

P. G. Walsh
Affiliation: Department of Mathematics, University of Ottawa, Ontario, Canada

Keywords: Algebraic function, Puiseux expansion, irreducibility testing, computational complexity, local field
Received by editor(s): September 5, 1994
Received by editor(s) in revised form: June 12, 1995
Published electronically: March 2, 2000
Additional Notes: This work constitutes part of the author’s doctoral dissertation at the University of Waterloo
Article copyright: © Copyright 2000 American Mathematical Society