A non-trivial symbolic machinery is presented that can rephrase algorithmically a finite set of nested hypergeometric products in appropriately designed difference rings. As a consequence, one obtains an alternative representation in terms of one single product defined over a root of unity and nested hypergeometric products which are algebraically independent among each other. In particular, one can solve the zero-recognition problem: the input expression of nested hypergeometric products evaluates to zero if and only if the output expression is the zero expression. Combined with available symbolic summation algorithms in the setting of difference rings, one obtains a general machinery that can represent (and simplify) nested sums defined over nested products.

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不同环中更高嵌套深度的超几何产品的表示

提出了一种非平凡的符号机制，它可以在算法上重新表述一组在适当设计的差分环中的嵌套超几何产品的有限集。因此，人们根据在统一根和嵌套超几何产品上定义的单个产品获得了替代表示，这些产品在代数上相互独立。特别是，可以解决零识别问题：当且仅当输出表达式是零表达式时，嵌套超几何乘积的输入表达式的计算结果为零。结合差分环设置中可用的符号求和算法，可以获得一种通用机制，可以表示（和简化）定义在嵌套乘积上的嵌套和。