On the power series solution of a system of algebraic equations

Authors:
S. Moritsugu
Affiliations:
Univ. of Tokyo, Tokyo, Japan
Venue:
ACM SIGSAM Bulletin
Year:
1987

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Abstract

This paper discusses the power series solution of a system of algebraic equations which is computed by the multivariate symbolic Newton's method. Applying Newton's method naively, we obtain a power series solution the coefficients of which are large rational function of the initial approximation. An algorithm is given to reduce the solution to the normal form by using Gröbner basis method.