Semialgebraic sets and real binary forms decompositions. (November 2021)

• Record Type: Journal Article
• Authors: Ansola, M.; Díaz-Cano, A.; Zurro, M.A.
• Is Part Of: Journal of symbolic computation. Volume 107(2021)
• Page Start: 209
• Page End: 220
• Publication Date: 2021-11
• Subjects: 14P10 -- 12D10; Real binary forms -- Waring decompositions -- Semialgebraic sets; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2021.03.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: The Waring Problem over polynomial rings asks how to decompose a homogeneous polynomial p of degree d as a linear combination of d -th powers of linear forms. In this work we give an algorithm to obtain a real Waring decomposition of any given real binary form p of length at most its degree. In fact, we construct a semialgebraic family of Waring decompositions for p . We illustrate our results with some examples.