Computing the resolution regularity of bi-homogeneous ideals. (March 2021)

• Record Type: Journal Article
• Authors: Aramideh, Nasibeh; Hashemi, Amir; Seiler, Werner M.
• Is Part Of: Journal of symbolic computation. Volume 103(2021)
• Page Start: 141
• Page End: 156
• Publication Date: 2021-03
• Subjects: Polynomial ideals -- Bi-homogeneous ideals -- Gröbner bases -- Involutive bases -- Castelnuovo-Mumford regularity -- Resolution regularity; 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.2019.12.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We present an effective method to compute the resolution regularity (vector) of bi-homogeneous ideals. For this purpose, we first introduce the new notion of an x-Pommaret basis and describe an algorithm to compute a linear change of coordinates for a given bi-homogeneous ideal such that the new ideal obtained after performing this change possesses a finite x -Pommaret basis. Then, we show that the x -component of the bi-graded regularity of a bi-homogeneous ideal is equal to the x -degree of its x -Pommaret basis (after performing the mentioned linear change of variables). Finally, we introduce the new notion of an ideal in x-quasi stable position and show that a bi-homogeneous ideal has a finite x -Pommaret basis iff it is in x -quasi stable position.