The expansion base algorithm, which was devised by Ab-hyankar, Kuo and McCallum is very efficient for analytic factorization of bivariate polynomials. The author had extended it to more than two variables but it was only for polynomials with non-vanishing leading coefficient at the expansion point. In this paper, we improve it to be able to apply to polynomials including the case of vanishing leading coefficient, that is, singular leading coefficient, which comes to a specific problem only for more than two variables.
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