Toric laminations, sparse generalized characteristic polynomials, and a renement of Hilbert's tenth problem (1997) [6 citations — 0 self]
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by J. Maurice Rojas
Proc. Workshop on Foundations of Computational Mathematics
http://www.math.tamu.edu/~rojas/newrio.ps.gz
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Abstract:
Abstract. This paper reexamines univariate reduction from a toric geometric point of view. We begin by constructing a binomial variant of the u-resultant and then retailor the generalized characteristic polynomial to fully exploit sparsity in the monomial structure of any given polynomial system. We thus obtain a fast new algorithm for univariate reduction and a better understanding of the underlying projections. As a corollary, we show that a renement of Hilbert's Tenth Problem is decidable within single-exponential time. We also show how certain multisymmetric functions of the roots of polynomial systems can be calculated with sparse resultants. 1.
