Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
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
Multi-variate polynomials and Newton-Puiseux expansions
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
A study of Hensel series in general case
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
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Hensel series is an expansion of multivariate algebraic function at a singular point, computed from the defining polynomial by the Hensel construction. The Hensel series is well-structured and tractable, hence it seems to be useful in various applications. In SNC'07, the present authors reported the following interesting properties of Hensel series, which were found numerically. 1) The convergence and the divergence domains co-exist in any small neighborhood of the expansion point. 2) If we trace a Hensel series by passing a divergence domain, the series may jump from a branch to another branch of the original algebraic function. In this paper, we clarify these properties theoretically and derive stronger properties.