论文标题
S主要塔中的添加分解
An Additive Decomposition in S-Primitive Towers
论文作者
论文摘要
我们将原始塔中的添加剂分解问题考虑，并提出了一种算法将S-aprive塔中的功能分解为塔中的衍生物的总和，其余的则在某种意义上是最小的。 S主要塔的特殊实例包括有限的许多对数函数和对数积分产生的差分字段。当剩余等于零时，S-promitive塔中的功能在塔中可以集成在塔中。添加剂分解是通过将我们的塔而不是传统的扩展场链视为直接的某些子圈来实现的。此外，我们可以确定S-promitive塔中的功能是否具有基本积分，而无需求解任何微分方程。我们还表明，可以将一种称为对数塔的S主要塔嵌入到特定的扩展中，我们可以在其中获得剩余的剩余。
We consider the additive decomposition problem in primitive towers and present an algorithm to decompose a function in an S-primitive tower as a sum of a derivative in the tower and a remainder which is minimal in some sense. Special instances of S-primitive towers include differential fields generated by finitely many logarithmic functions and logarithmic integrals. A function in an S-primitive tower is integrable in the tower if and only if the remainder is equal to zero. The additive decomposition is achieved by viewing our towers not as a traditional chain of extension fields, but rather as a direct sum of certain subrings. Furthermore, we can determine whether or not a function in an S-primitive tower has an elementary integral without solving any differential equations. We also show that a kind of S-primitive towers, known as logarithmic towers, can be embedded into a particular extension where we can obtain a finer remainder.
