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Journal of the ACM
Multivariate resultants generalize the Sylvester resultant o f t wo polynomials and characterize the solvability of a polynomial system. They also reduce the computation of all common roots to a problem in linear algebra. We propose a determinantal formula for the sparse resultant of an arbitrary system of n + 1 polynomials in n variables. This resultant generalizes the classical one and has signi cantly lower degree for polynomials that are sparse in the sense that their mixed volume is lowerdoi:10.1145/337244.337247 fatcat:z7z4myffu5a65m7jiug7jaeftu