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On testing a bivariate polynomial for analytic reducibility. (English) Zbl 0895.68073

Summary: Let \(K\) be an algebraically closed field of characteristic zero. We present an efficient algorithm for determining whether or not a given polynomial \(f(x,y)\) in \(K[x,y]\) is analytically reducible over \(K\) at the origin. The algorithm presented is based upon an informal method sketched by T. Kuo [Can J. Math. 41, No. 6, 1101-1116 (1989; Zbl 0716.13015)] which is in turn derived from ideas of S. Abhyankar [Math. Intell. 10, No. 4, 36-43 (1988; Zbl 0698.14061)]. The presentation contained herein emphasises the proofs of the algorithm’s correctness and termination, and is suitable for computer implementation. A polynomial worst case time complexity bound is proved for a partial version of the algorithm.

MSC:

68W30 Symbolic computation and algebraic computation
13F25 Formal power series rings
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