1998/09/14 by J. Maurice Rojas, Rojas, J. Maurice
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Coding theory and cryptography #Commutative Algebra and Its Applications #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA) #Polynomial and algebraic computation #cs.CC #cs.NA #math.AG #math.NA
paper · pdf · doi:10.48550/arxiv.math/9809071
This is the final journal version of math.AG/9702222 (``Toric Generalized Characteristic Polynomials''). This final version is a major revision with several new theorems, examples, and references. The prior results are also significantly improved
openalex publication_date 1998/09/14 · arxiv created 1998/09/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a system F of n polynomial equations in n unknowns, over an algebraically closed field of arbitrary characteristic. We present a fast method to find a point in every irreducible component of the zero set Z of F. Our techniques allow us to sharpen and lower prior complexity bounds for this problem by fully taking into account the monomial term structure. As a corollary of our development we also obtain new explicit formulae for the exact number of isolated roots of F and the intersection multiplicity of the positive-dimensional part of Z. Finally, we present a combinatorial construction of non-degenerate polynomial systems, with specified monomial term structure and maximally many isolated roots, which may be of independent interest.