On testing a bivariate polynomial for analytic reducibility

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 Kuo (1989) which is in turn derived from ideas of Abhyankar (1988). 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.