Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Parameterized telescoping (including telescoping and creative telescoping) and refined versions of it play a central role in the research area of symbolic summation. Karr introduced 1981 $\Pi\Sigma$-fields, a general class of difference fields, that enables one to consider this problem for indefinite nested sums and products covering as special cases, e.g., the ($q$--)hypergeometric case and their mixed versions. This survey article presents the available algorithms in the framework of $\Pi\Sigma$-extensions and elaborates new results concerning efficiency.
['Carsten Schneider']
I am writing a research paper on a idea Fast Algorithms for Refined Parameterized Telescoping in Difference Fields
[{"from": "human", "value": "I am writing a research paper on a idea Fast Algorithms for Refined Parameterized Telescoping in Difference Fields"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Parameterized telescoping (including telescoping and creative telescoping) and refined versions of it play a central role in the research area of symbolic summation. Karr introduced 1981 $\\Pi\\Sigma$-fields, a general class of difference fields, that enables one to consider this problem for indefinite nested sums and products covering as special cases, e.g., the ($q$--)hypergeometric case and their mixed versions. This survey article presents the available algorithms in the framework of $\\Pi\\Sigma$-extensions and elaborates new results concerning efficiency."}]