Characterizations of the Macaulay Matrix and Their Algorithmic Impact
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.
KeywordsVector Space Homogeneous Polynomial Central Tool Extraneous Factor Zero Entry
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