Journal of Symbolic Computation ( IF 0.7 ) Pub Date : 2021-03-01 , DOI: 10.1016/j.jsc.2021.02.003 Jakob Ablinger , Ali Kemal Uncu
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.
中文翻译:
qFunctions –用于q系列和分区理论应用程序的Mathematica软件包
我们描述了用于q系列和分区理论应用的qFunctions Mathematica软件包。该软件包包括实验和符号工具。实验元素集包括q差分方程的猜测器和给定q差分的递归,以及多项式序列的拟合/查找显式表达式。该软件包可以象征性地处理正式操作q -示差,q -difference方程和复发,如这些形式之间进行切换,寻找复发的最大公约数,并且正式取代。包qFunctions具有实现加权单词方法的递归系统创建以及圆柱分区方案的自动化的实现。我们还讨论了传统的加权词方法的略微扩展,并提出了一些新的求和积恒等式。