反导数、积分指数和重对数的延拓
Extensions by Antiderivatives, Exponentials of Integrals and by Iterated Logarithms
摘要：
设F是一个具有常数代数闭域的特征零微分域，E是F的反导数的非新常数扩张，设y 1，.，yn是E.反导数y1，...，如果yi在E中的导数满足一定的条件，则称E的yn为J-I-E反导数.我们将讨论Kolchin-Ostrowski定理的一个新的证明，并通过J-I-E反导数将这个定理推广到一个扩张塔，并使用这个定理的推广版本来分类这个塔的非微分生成的子域。在这个过程中，我们将证明J-I-E反导数在基微分场上是代数独立的。J-I-E塔的一个例子是迭代算法的扩展。我们将讨论扩张的正规性迭代算法，并产生一个算法来计算它的非正规差分生成的子域。
英文摘要：
Let F be a characteristic zero differential field with an algebraically closed field of constants, E be a no-new-constant extension of F by antiderivatives of F and let y1, ..., yn be antiderivatives of E. The antiderivatives y1, ..., yn of E are called J-I-E antiderivatives if the derivatives of yi in E satisfies certain conditions. We will discuss a new proof for the Kolchin-Ostrowski theorem and generalize this theorem for a tower of extensions by J-I-E antiderivatives and use this generalized version of the theorem to classify the finitely differentially generated subfields of this tower. In the process, we will show that the J-I-E antiderivatives are algebraically independent over the ground differential field. An example of a J-I-E tower is extensions by iterated logarithms. We will discuss the normality of extensions by iterated logarithms and produce an algorithm to compute its finitely differentially generated subfields.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
