About the Newton algorithm for non-linear ordinary differential equations
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
On testing a bivariate polynomial for analytic reducibility
Journal of Symbolic Computation
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Factorization of multivariate polynomials by extended Hensel construction
ACM SIGSAM Bulletin
Computing monodromy groups defined by plane algebraic curves
Proceedings of the 2007 international workshop on Symbolic-numeric computation
A numerical study of extended Hensel series
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Continuations and monodromy on random riemann surfaces
Proceedings of the 2009 conference on Symbolic numeric computation
Convergence and many-valuedness of hensel seriesnear the expansion point
Proceedings of the 2009 conference on Symbolic numeric computation
Multi-variate polynomials and Newton-Puiseux expansions
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
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The Hensel series is a series expansion of multivariate algebraic function at its singular point. The Hensel series is computed by the (extended) Hensel construction, and it is expressed in a well-structured form. In previous papers, we clarified theoretically various interesting properties of Hensel series in restricted cases. In this paper, we present a theory of Hensel series in general case. In particular, we investigate the Hensel series arising from non-squarefree initial factor, and derive a formula which shows "fine structure" of the Hensel series. If we trace a Hensel series along a path passing a divergence domain, the Hensel series often jumps from one branch of the algebraic function to another. We investigate the jumping phenomenon near the ramification point, which has not been clarified in our previous papers.