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Irreducibility testing over local fields


Author: P. G. Walsh
Journal: Math. Comp. 69 (2000), 1183-1191
MSC (1991): Primary 12Y05, 12E05
DOI: https://doi.org/10.1090/S0025-5718-00-01247-3
Published electronically: March 2, 2000
MathSciNet review: 1710699
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Abstract:

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.


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Additional Information

P. G. Walsh
Affiliation: Department of Mathematics, University of Ottawa, Ontario, Canada
Email: gwalsh@mathstat.uottawa.ca

DOI: https://doi.org/10.1090/S0025-5718-00-01247-3
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

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