Operations for D-Algebraic Functions

04/19/2023

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by   Bertrand Teguia Tabuguia, et al.

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A function is differentially algebraic (or simply D-algebraic) if there is a polynomial relationship between some of its derivatives and the indeterminate variable. Many functions in the sciences, such as Mathieu functions, the Weierstrass elliptic functions, and holonomic or D-finite functions are D-algebraic. These functions form a field, and are closed under composition, taking functional inverse, and derivation. We present implementation for each underlying operation. We also give a systematic way for computing an algebraic differential equation from a linear differential equation with D-finite function coefficients. Each command is a feature of our Maple package NLDE available at https://mathrepo.mis.mpg.de/OperationsForDAlgebraicFunctions.