Bounding the degrees of a minimal μ-basis for a rational surface parametrization. (November 2019)

• Record Type: Journal Article
• Authors: Cid-Ruiz, Yairon
• Is Part Of: Journal of symbolic computation. Volume 95(2019)
• Page Start: 134
• Page End: 150
• Publication Date: 2019-11
• Subjects: 13D02 -- 14Q10; Syzygies -- μ-basis -- Koszul complex -- Quillen-Suslin Theorem -- Unimodular matrix -- Liaison; 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.2019.02.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this paper, we study how the degrees of the elements in a minimal μ -basis of a parametrized surface behave. For an arbitrary rational surface parametrization P ( s, t ) = ( a 1 ( s, t ), a 2 ( s, t ), a 3 ( s, t ), a 4 ( s, t ) ) ∈ F [ s, t ] 4 over an infinite field F, we show the existence of a μ -basis with polynomials bounded in degree by O ( d 33 ), where d = max ⁡ ( deg ⁡ ( a 1 ), deg ⁡ ( a 2 ), deg ⁡ ( a 3 ), deg ⁡ ( a 4 ) ) . Under additional assumptions we can obtain tighter bounds.