Bases of subalgebras of K〚x〛 and K[x]. (March 2017)

• Record Type: Journal Article
• Authors: Assi, A.; García-Sánchez, P.A.; Micale, V.
• Is Part Of: Journal of symbolic computation. Volume 79(2017)Part 1
• Page Start: 4
• Page End: 22
• Publication Date: 2017-03
• Subjects: Bases of subalgebras -- Value semigroup -- Numerical semigroup; 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.2016.08.002
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Let f 1, …, f s be formal power series (respectively polynomials) in the variable x . We study the semigroup of orders of the formal series in the algebra K 〚 f 1, …, f s 〛 ⊆ K 〚 x 〛 (respectively the semigroup of degrees of polynomials in K [ f 1, …, f s ] ⊆ K [ x ] ). We give procedures to compute these semigroups and several applications. We prove in particular that the space curve parametrized by f 1, …, f s has a flat deformation into a monomial curve.