Beyond the First Class of Analytic Complexity
We investigate the notion of analytic complexity of a bivariate 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.
KeywordsAnalytic complexity Differential polynomial Differentially algebraic function
This research has been performed in the framework of the basic part of the scientific research state task in the field of scientific activity of the Ministry of Education and Science of the Russian Federation, project No. 2.9577.2017/8.9.
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