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Series-Expansion of Multivariate Algebraic Functions at Singular Points: Nonmonic Case

In: Computer Mathematics

Author

Listed:
  • Tateaki Sasaki

    (University of Tsukuba, Institute of Mathematics)

  • Daiju Inaba

    (Mathematics Certification Institute of Japan)

Abstract

In a series of papers, we have developed a method of expanding multivariate algebraic functions at their singular points. The method applies the Hensel construction to the defining polynomial of the algebraic function, so we named the resulting series “Hensel series”. In [1], we derived a concise representation of Hensel series for the monic defining polynomial, and clarified several characteristic properties of Hensel series theoretically. In this paper, we study the case of nonmonic defining polynomial. We show that, by determining the so-called Newton polynomial suitably, we can construct Hensel series which show reasonable behaviors at zero-points of the leading coefficients and we can derive a representation of Hensel series in the nonmonic case just similarly as in the monic case. Furthermore, we investigate the convergence/divergence behavior and many-valuedness of Hensel series in the nonmonic case.

Suggested Citation

  • Tateaki Sasaki & Daiju Inaba, 2014. "Series-Expansion of Multivariate Algebraic Functions at Singular Points: Nonmonic Case," Springer Books, in: Ruyong Feng & Wen-shin Lee & Yosuke Sato (ed.), Computer Mathematics, edition 127, pages 125-140, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-43799-5_11
    DOI: 10.1007/978-3-662-43799-5_11
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