I am trying to prove the q-combinatorial identity
$$\sum_{s=0}^r(-1)^sq^{\frac{s(s+1)}{2}}{n-2r+s\brack n-2r}_q{n\brack r-s}_q=\sum_{s=0}^{r-1}(-1)^{s+1}q^{\frac{s(s+1)}{2}}{n-2r+s\brack n-2r}_q{n\brack r-s-1}_q,$$
where ${r\brack s}_q$ denotes q-binomial coefficients.
There is an algorithm called Wilf-Zeilberger algorithm which can used to prove such identities. Also Doron Zeilberger has written a Maple code that complete this task. Since I have never use Maple, I am looking for a Mathematica code that do the same job. Is there any such Mathematica code?
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J. M.'s missing motivation
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4Take a look here, ping Peter Paule for access... – ciao Jan 28 '17 at 01:45
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@ciao: Thank you for your extremely helpful comment. If you wish I would like to accept this as the answer for my question. – Bumblebee Jan 28 '17 at 04:28
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3Also check here. – Daniel Lichtblau Jan 28 '17 at 17:09
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1@Nil : thanks for sentiment, but seems a bit silly to get points for that. Hope it provides what you're looking for! – ciao Jan 29 '17 at 01:17
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Even though the title of these two question are same, they not same. In fact my question is about the q- analogy of Wilf-Zeilberger algorithm. Also both underline Maple codes are very different – Bumblebee Jan 30 '17 at 03:53