Algorithm for studying polynomial maps and reductions modulo prime number

Abstract

In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. Also the class of Pascal finite polynomial automorphisms was introduced. Pascal finite polynomial maps constitute a generalization of exponential automorphisms to positive characteristic. In this note we explore properties of the algorithm while using Segre homotopy and reductions modulo prime number. We give a method of retrieving an inverse of a given polynomial automorphism $F$ with integer coefficients form a finite set of the inverses of its reductions modulo prime numbers. Some examples illustrate effective aspects of our approach.