License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.04401.9
URN: urn:nbn:de:0030-drops-1460
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Meer, Klaus ; Malajovich, Gregorio

On the Complexity of Computing Multi-Homogeneous Bézout Numbers

04401.MeerKlaus.Paper.146.pdf (0.3 MB)


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.

BibTeX - Entry

  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 =		{},
  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}

Keywords: multi-homogeneous Bézout numbers , number of roots of polynomials , approximation algorithms
Collection: 04401 - Algorithms and Complexity for Continuous Problems
Issue Date: 2005
Date of publication: 19.04.2005

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