Algorithm for studying polynomial maps and reductions modulo prime number. (September 2022)

• Record Type: Journal Article
• Authors: Adamus, Elżbieta; Bogdan, Paweł
• Is Part Of: Journal of symbolic computation. Volume 112(2022)
• Page Start: 1
• Page End: 24
• Publication Date: 2022-09
• Subjects: Polynomial automorphism -- Jacobian problem; 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.2021.12.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We explore further properties of the algorithm and the class of Pascal finite maps described in Adamus et al. (2017), when using Segre homotopy and reductions modulo prime number. We consider polynomial maps over Q . Those can be transformed into maps with coefficients in Z by denominators clearing procedure. We give a method of retrieving an inverse of a given polynomial automorphism F with integer coefficients from a finite set of inverses of its reductions modulo prime numbers. We estimate the computational complexity of the proposed algorithm. Some examples illustrate effective aspects of our approach.