Beyond the First Class of Analytic Complexity

摘要

We investigate the notion of analytic complexity of a bivari-ate holomorphic function by means of computer algebra tools. An estimate from below on the number of terms in the differential polynomials defining classes of analytic complexity is established. We provide an algorithm which allows one to explicitly compute the differential membership criteria for certain families of bivariate analytic functions in the second complexity class. The presented algorithm is implemented in the computer algebra system Singular 4-1-1.