Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We present algorithms to compute algebraic differential equations for compositions and arithmetic manipulations of univariate D-algebraic functions and derive bounds for the order of the resulting differential equations. We apply our methods to examples in the sciences.

翻译：微分代数（D-代数）函数是满足关于函数、其导数及自变量多项式方程的解。我们通过提供构造性证明重新审视了这些函数的闭包性质。我们提出了算法，用于计算单变量D-代数函数复合运算和算术操作所对应的代数微分方程，并推导了所得微分方程阶数的上界。我们将这些方法应用于科学领域的实例中。