QFunctions – A Mathematica package for q-series and partition theory applications. (November 2021)

• Record Type: Journal Article
• Authors: Ablinger, Jakob; Uncu, Ali Kemal
• Is Part Of: Journal of symbolic computation. Volume 107(2021)
• Page Start: 145
• Page End: 166
• Publication Date: 2021-11
• Subjects: 05A15 -- 05A17 -- 05A19 -- 11P81 -- 33D15 -- 68-01 -- 68R05; Integer partitions -- q-Series -- q-Difference equations -- Recurrences -- Method of weighted words -- Cylindric partitions; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2021.02.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: 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.