Joerg Arndt on Thu, 17 Mar 2016 09:00:39 +0100 |
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Re: qPochhammer symbol and indefinite products in general |
Some of the files under http://jjj.de/pari/ might be useful. Especially eta.gpi for computation of q-pochhammer. Best regards, Joerg Arndt * E Y <ernestyalumni@gmail.com> [Mar 16. 2016 12:14]: > qPochhammer symbol and indefinite products in general > > Pari-users, > > Hi, I’m Ernest Yeung, and I’m writing to the users list because I saw a question about the qPochhammer symbol for Pari/GP in the mailing list, but it was too old to reply to (I also joined the mailing list just now and so haven’t gotten used to interacting with the list; any advice on etiquette would help). > > Is there a way to implement the qPochhammer symbol in Pari/GP for arbitrary variables (i.e. an “indefinite product”, with variables in the ending number you multiply up to?)? How would I implement such a symbol? A function returning a function? Any suggestions would help since I’m starting out. > > Ultimately, I’d want to implement this paper/algorithms for q-analogues of the Wilf-Zeilberger algorithm, for proving q-hypergeometric multisum identities: > http://www.risc.jku.at/research/combinat/software/ergosum/RISC/qMultiSum.html > but in Pari/GP because > -I’ve used qMultiSum.m before, but there were serious slowdowns due to using Mathematica; would like to see speed up for my needs; hopefully Pari/GP based on C,C++ can help speed up computation > -would like an open-source alternative so to develop directly for my needs in implementing q-hypergeometric summations > > Any thoughts on implementing recursion algorithms of the such (Wilf-Zeilberger, Gosper’s algorithm, etc.), or even in general doing symbolic computation and writing scripts for Pari/GP AND how indefinite summation and INDEFINITE products (i.e. NOT specifying the bounds before with numbers) are to be implemented in Pari/GP would help. Thanks, -Ernest Yeung > >