Beyond the First Class of Analytic Complexity

  • T. M. SadykovEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11077)


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.


Analytic 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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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Plekhanov Russian UniversityMoscowRussia

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