Abstract

Recently, it has been shown constructively how a finite set of hypergeometric products, multibasic hypergeometric products or their mixed versions can be modeled properly in the setting of formal difference rings. Here special emphasis is put on robust constructions: whenever further products have to be considered, one can reuse –up to some mild modifications – the already existing difference ring. In this article we relax this robustness criteria and seek for another form of optimality. We will elaborate a general framework to represent a finite set of products in a formal difference ring where the number of transcendental product generators is minimal. As a bonus we are able to describe explicitly all relations among the given input products.

中文翻译：

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单个嵌套产品的最小表示形式和代数关系

摘要

最近，建设性地显示了如何在形式差环的设置中正确地建模有限组的超几何积，多元超几何积或它们的混合形式。这里特别强调的是坚固的结构：每当需要考虑进一步的产品时，就可以重复使用-进行一些轻微的修改-已经存在的差动环。在本文中，我们放宽了这种鲁棒性标准，并寻求另一种形式的最优性。我们将详细阐述一个通用框架，用一个形式上的差异环表示有限的一组产品，其中先验乘积生成器的数量最少。另外，我们能够明确描述给定输入产品之间的所有关系。