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A Simple Algorithm for Deciding Primes in K[[x,y]]
Published online by Cambridge University Press: 20 November 2018
Abstract
The well-known Tschirnhausen transformation, , eliminates the second term of the polynomial xn + axn-l + …. By a mere repeated application of this transformation, one can decide whether a given element of k[[x,y]] is prime (irreducible) or not. Here K is an algebraically closed field of characteristic 0. A generalised version of Hensel's Lemma is developed for the proofs. The entire paper can be understood by undergraduate students.
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- Copyright © Canadian Mathematical Society 1995
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