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On the Complexity of Computing Multi-Homogeneous BÃƒÂ©zout Numbers

Authors: Klaus Meer and Gregorio Malajovich

Published in: Dagstuhl Seminar Proceedings, Volume 4401, Algorithms and Complexity for Continuous Problems (2005)

Abstract

We study the question how difficult it is to compute the multi-homogeneous B\'ezout number for a polynomial system of given number $n$ of variables and given support $A$ of monomials with non-zero coefficients. We show that this number is NP-hard to compute. It cannot even be efficiently approximated within an arbitrary, fixed factor unless P = NP. This is joint work with Gregorio Malajovich.

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Klaus Meer and Gregorio Malajovich. On the Complexity of Computing Multi-Homogeneous BÃƒÂ©zout Numbers. In Algorithms and Complexity for Continuous Problems. Dagstuhl Seminar Proceedings, Volume 4401, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{meer_et_al:DagSemProc.04401.9,
  author =	{Meer, Klaus and Malajovich, Gregorio},
  title =	{{On the Complexity of Computing Multi-Homogeneous B\~{A}ƒ\^{A}©zout Numbers}},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4401},
  editor =	{Thomas M\"{u}ller-Gronbach and Erich Novak and Knut Petras and Joseph F. Traub},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.04401.9},
  URN =		{urn:nbn:de:0030-drops-1460},
  doi =		{10.4230/DagSemProc.04401.9},
  annote =	{Keywords: multi-homogeneous B\~{A}ƒ\^{A}©zout numbers , number of roots of polynomials , approximation algorithms}
}

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On the Complexity of Computing Multi-Homogeneous BÃƒÂ©zout Numbers

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