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.

翻译：如果一个函数与其若干阶导数及自变量之间存在多项式关系，则称该函数为微分代数函数（即D-algebraic函数）。科学领域中的许多函数，如Mathieu函数、Weierstrass椭圆函数以及全纯函数（即D-finite函数）均属于D-algebraic函数。此类函数构成一个域，并在复合运算、反函数运算及求导运算下保持封闭性。我们针对每种基本运算给出了实现方法，同时提出了一种系统化方法，用于从具有D-finite函数系数的线性微分方程中计算代数微分方程。上述每条命令均集成于我们的Maple软件包$NLDE$中，该软件包可通过https://mathrepo.mis.mpg.de/OperationsForDAlgebraicFunctions获取。