$RΠΣ$中的细化伸缩算法--减少伸缩器度数的扩展
Refined telescoping algorithms in $RΠΣ$-extensions to reduce the degrees of the denominators
摘要：
我们提出了一个一般的框架，在设置的差环扩展，使人们能够找到改进的表示不定嵌套的总和，使所产生的内summands有减少的程度。底层的（参数化的）伸缩算法可以在建立在通用$ΠΣ$字段上的$RΠΣ$环扩展中执行。这个工具箱的一个重要应用是简化的达朗伯和Liouvillian的解决方案来自递归关系，其中所产生的总和的分解器没有很好的因素。
英文摘要：
We present a general framework in the setting of difference ring extensions that enables one to find improved representations of indefinite nested sums such that the arising denominators within the summands have reduced degrees. The underlying (parameterized) telescoping algorithms can be executed in $RΠΣ$-ring extensions that are built over general $ΠΣ$-fields. An important application of this toolbox is the simplification of d'Alembertian and Liouvillian solutions coming from recurrence relations where the denominators of the arising sums do not factor nicely.
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