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Multivariate Polynomial Decomposition

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

 In this paper, we discuss several notions of decomposition for multivariate polynomials, focussing on the relation with Lüroth's theorem in field theory, and the finiteness and uniqueness of decompositions. We also present two polynomial time algorithms for decomposing (sparse) multivariate polynomials over an arbitrary field.

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Authors and Affiliations

  1. FB 17 Mathematik-Informatik, Universität-GH Paderborn, 33095 Paderborn, Germany (e-mail:gathen@uni-paderbrn.de), , , , , , DE

    Joachim von zur Gathen

  2. Departamento de Matematicas y Computacion, Universidad de Cantabria, 39071 Santander, Spain (e-mail:jaime@matesco.unian.es), , , , , , ES

    Jaime Gutierrez

  3. Dep. Industriales, Universidad Antonio de Nebrija, 38040 Madrid, Spain (e-mail:mrubio@nebrja.es), , , , , , ES

    Rosario Rubio

Authors
  1. Joachim von zur Gathen
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  2. Jaime Gutierrez
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  3. Rosario Rubio
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Additional information

Received: March 2, 2001; revised version: February 2, 2003

Keywords: Polynomial decomposition algorithms, Lüroth's theorem.

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Gathen, J., Gutierrez, J. & Rubio, R. Multivariate Polynomial Decomposition. AAECC 14, 11–31 (2003). https://doi.org/10.1007/s00200-003-0122-8

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  • DOI: https://doi.org/10.1007/s00200-003-0122-8

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