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On the Complexity of Computing Multi-Homogeneous Bézout Numbers

Authors Klaus Meer, Gregorio Malajovich

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Klaus Meer
Gregorio Malajovich

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


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.
  • multi-homogeneous Bézout numbers
  • number of roots of polynomials
  • approximation algorithms


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