Decomposition of algebraic functions

  • Dexter Kozen
  • Susan Landau
  • Richard Zippel
Conference paper

DOI: 10.1007/3-540-58691-1_46

Part of the Lecture Notes in Computer Science book series (LNCS, volume 877)
Cite this paper as:
Kozen D., Landau S., Zippel R. (1994) Decomposition of algebraic functions. In: Adleman L.M., Huang MD. (eds) Algorithmic Number Theory. ANTS 1994. Lecture Notes in Computer Science, vol 877. Springer, Berlin, Heidelberg

Abstract

Functional decomposition—whether a function f(x) can be written as a composition of functions g(h(x)) in a nontrivial way—is an important primitive in symbolic computation systems. The problem of univariate polynomial decomposition was shown to have an efficient solution by Kozen and Landau [9]. Dickerson [5] and von zur Gathen [13] gave algorithms for certain multivariate cases. Zippel [15] showed how to decompose rational functions. In this paper, we address the issue of decomposition of algebraic functions. We show that the problem is related to univariate resultants in algebraic function fields, and in fact can be reformulated as a problem of resultant decomposition. We characterize all decompositions of a given algebraic function up to isomorphism, and give an exponential time algorithm for finding a nontrivial one if it exists. The algorithm involves genus calculations and constructing transcendental generators of fields of genus zero.

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Dexter Kozen
    • 1
  • Susan Landau
    • 2
  • Richard Zippel
    • 1
  1. 1.Computer Science DepartmentCornell UniversityIthaca
  2. 2.Computer Science DepartmentUniversity of MassachusettsAmherst

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