2006/08/29 by Gabriela Jeronimo, Jeronimo, Gabriela, Guillermo Matera +6 · 1 citation
Computer Science · Engineering · Mathematics · #13F25 #14Q05 #14Q20 #52B20 #68W30 (Primary) 12Y05 #68W40 (Secondary) #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #math.CA #msc:12Y05 #msc:13F25 #msc:14Q05 #msc:14Q20 #msc:52B20 #msc:68W30 #msc:68W40
paper · pdf · doi:10.48550/arxiv.math/0608714
arxiv created 2006/08/29 · openalex publication_date 2006/08/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We exhibit a probabilistic symbolic algorithm for solving zero-dimensional sparse systems. Our algorithm combines a symbolic homotopy procedure, based on a flat deformation of a certain morphism of affine varieties, with the polyhedral deformation of Huber and Sturmfels. The complexity of our algorithm is quadratic in the size of the combinatorial structure of the input system. This size is mainly represented by the mixed volume of Newton polytopes of the input polynomials and an arithmetic analogue of the mixed volume associated to the deformations under consideration.