2013/10/15 by Danko Adrovic, Adrovic, Danko, Jan Verschelde +1 · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Computer and information sciences #FOS: Mathematics #Formal Methods in Verification #Polynomial and algebraic computation #Symbolic Computation (cs.SC)
paper · pdf · doi:10.48550/arxiv.1310.4128
openalex publication_date 2013/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To compute solutions of sparse polynomial systems efficiently we have to\nexploit the structure of their Newton polytopes. While the application of\npolyhedral methods naturally excludes solutions with zero components, an\nirreducible decomposition of a variety is typically understood in affine space,\nincluding also those components with zero coordinates. We present a polyhedral\nmethod to compute all affine solution sets of a polynomial system. The method\nenumerates all factors contributing to a generalized permanent. Toric solution\nsets are recovered as a special case of this enumeration. For sparse systems as\nadjacent 2-by-2 minors our methods scale much better than the techniques from\nnumerical algebraic geometry.\n