2014/12/16 by Yong Yao, Jia Xu, Yao, Yong +4 · 1 citation
Computer Science · Engineering · Mathematics · #12Y05 #13P15 #14P10 #68W30 #Advanced Numerical Analysis Techniques #Algebraic number #Algorithm #Combinatorics #Decomposition #Equivalence (formal languages) #FOS: Computer and information sciences #G.1.5 #Mathematical analysis #Mathematics #Numerical methods for differential equations #Polynomial #Polynomial and algebraic computation #Projection (relational algebra) #Pure mathematics #Symbolic Computation (cs.SC) #Univariate #acm:12Y05 #acm:13P15 #acm:14P10 #acm:68W30 #cs.SC #msc:12Y05 #msc:13P15 #msc:14P10 #msc:68W30
paper · pdf · doi:10.48550/arxiv.1412.4861
published in arXiv (Cornell University) (Cornell University) · 6 pages
arxiv created 2014/12/16 · openalex publication_date 2014/12/16 · arxiv updated 2014/12/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
This note shows the equivalence of two projection operators which both can be used in cylindrical algebraic decomposition (CAD) . One is known as Brown's Projection (C. W. Brown (2001)); the other was proposed by Lu Yang in his earlier work (L.Yang and S.~H. Xia (2000)) that is sketched as follows: given a polynomial f in x1, x2, ⋯, by f1 denote the resultant of f and its partial derivative with respect to x1 (removing the multiple factors), by f2 denote the resultant of f1 and its partial derivative with respect to x2, (removing the multiple factors), ⋯, repeat this procedure successively until the last resultant becomes a univariate polynomial. Making use of an identity, the equivalence of these two projection operators is evident.