qFunctions - A Mathematica package for q-series and partition theory applications
qFunctions - A Mathematica package for q-series and partition theory applications
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DOI：
10.1016/j.jsc.2021.02.003
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发表时间：
2021-03-12
影响因子：
0.7
通讯作者：
Uncu, Ali Kemal
中科院分区：
文献类型：
--
作者：
Ablinger, Jakob;Uncu, Ali Kemal
我们描述了qFunctions Mathematica包的q系列和分区理论的应用。该软件包包括实验性和象征性工具。实验组的元素包括猜测的q-差分方程和递归给定的q-差分和拟合/发现显式表达式的多项式序列。这个软件包可以象征性地处理q-微分，q-差分方程和递归的形式操作，例如在这些形式之间切换，找到递归的最大公约数，以及形式替换。包qFunctions实现了自动创建加权单词方法的递归系统以及圆柱形分区的方案。我们还讨论了加权词的经典方法的一个轻微的扩展，并提出了一些新的和积恒等式。(C)2021爱思唯尔有限公司保留所有权利。
We describe the qFunctions Mathematica package for q-series and partition theory applications. This package includes both experimental and symbolic tools. The experimental set of elements includes guessers for q-difference equations and recurrences for given q-difference and fitting/finding explicit expressions for sequences of polynomials. This package can symbolically handle formal manipulations on q-differential, q-difference equations and recurrences, such as switching between these forms, finding the greatest common divisor of recurrences, and formal substitutions. The package qFunctions has implementations that automate the recurrence system creation of the weighted words approach as well as a scheme on cylindric partitions. We also discuss a slight extension of the classical method of weighed words and present some new sum-product identities. (C) 2021 Elsevier Ltd. All rights reserved.