Computing rational powers of monomial ideals. (May 2023)

• Record Type: Journal Article
• Authors: Dongre, Pratik; Drabkin, Benjamin; Lim, Josiah; Partida, Ethan; Roy, Ethan; Ruff, Dylan; Seceleanu, Alexandra; Tang, Tingting
• Is Part Of: Journal of symbolic computation. Volume 116(2023)
• Page Start: 39
• Page End: 57
• Publication Date: 2023-05
• Subjects: primary 13F55 13F20; Monomial ideals -- Rational powers -- Newton polyhedron -- Computational algebra -- Jumping numbers; 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.2022.08.018
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: This paper concerns fractional powers of monomial ideals. Rational powers of a monomial ideal generalize the integral closure operation as well as recover the family of symbolic powers. They also highlight many interesting connections to the theory of convex polytopes. We provide multiple algorithms for computing the rational powers of a monomial ideal. We also introduce a mild generalization allowing real powers of monomial ideals. An important result is that given any monomial ideal I, the function taking a real number to the corresponding real power of I is a step function which is left continuous and has rational discontinuity points.