E Y on Tue, 15 Mar 2016 22:42:30 +0100

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qPochhammer symbol and indefinite products in general

qPochhammer symbol and indefinite products in general


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:
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