Characterizations of the Macaulay Matrix and Their Algorithmic Impact

  • Georg Hagel
Conference paper
Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)


Since the late eighties, the Macaulay matrix has recently received renewed attention in the field of quantifier elimination. Grigor’ev (1988) and Renegar (1992a, 1992b, 1992c) made it a central tool in their study of the complexity of quantifier elimination. They developed algorithms which have better complexities than Collins’ quantifier elimination algorithm based on the CAD (Collins 1975), but until now Collins’ CAD is much faster in practice.


Vector Space Homogeneous Polynomial Central Tool Extraneous Factor Zero Entry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag/Wien 1998

Authors and Affiliations

  • Georg Hagel

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