Algorithms for curves with one place at infinity. (May 2016)

• Record Type: Journal Article
• Authors: Assi, Abdallah; García-Sánchez, Pedro A.
• Is Part Of: Journal of symbolic computation. Volume 74(2016)
• Page Start: 475
• Page End: 492
• Publication Date: 2016-05
• Subjects: 14R05 -- 14Q05 -- 68W01 -- 20M14; One place curve -- Semigroup of values -- Approximate roots; 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.2015.08.008
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Let f be a plane curve. We give a procedure based on Abhyankar's approximate roots to detect if it has a single place at infinity, and if so construct its associated δ -sequence, and consequently its value semigroup. For a δ -sequence we present a procedure to construct all curves having this associated sequence. Also for a fixed genus (equivalently Frobenius number) we construct all δ -sequences generating numerical semigroups with this given genus. We also study the embeddings of such curves in the plane. In particular, we prove that polynomial curves might not have a unique embedding.