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The book A=B by Petkovsek, Wilf and Zeilberger describes algorithms to compute different sums of binomials. AFAIK, these algorithms are still being improved by different authors.

Do you know where we can find the most up-to-date implementations of these algorithms? And do you know if there exist implementations in some free softwares such as Sage?

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  • $\begingroup$ Try mailing Doron Zeilberger he codes. here. $\endgroup$ – Pratik Deoghare Apr 18 '12 at 17:30
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    $\begingroup$ @PratikDeoghare, he writes in Maple, which isn't free. If you know of a tool to automatically port Maple code to e.g. Sage then that would constitute an answer. $\endgroup$ – Peter Taylor Apr 18 '12 at 18:41
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    $\begingroup$ @PeterTaylor: Of course, I am not fully satisfied by Maple implementations since I'd prefer free alternatives. For Sage, I found this page. It seems that it is not implemented yet. $\endgroup$ – Bruno Apr 19 '12 at 17:33
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    $\begingroup$ Some further information regarding Sage may be found here $\endgroup$ – Timothy Chow Apr 19 '12 at 22:27
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    $\begingroup$ I've opened trac.sagemath.org/ticket/16619 for implementing W-Z (or any more recent research - this is not my area at all) in Sage, if anyone is interested. $\endgroup$ – kcrisman Jul 6 '14 at 1:53
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It is implemented in Maxima (http://maxima.sourceforge.net/docs/manual/de/maxima_77.html#SEC400), to which Sage has interface. A few dozens of examples (ranging from very easy to very difficult) I tested today work in the exact same way as in Maple.

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    $\begingroup$ P.S. There is also a recent sage implementation which I just noticed but haven't tested: see the webpage arminstraub.com/teaching/specialfunctions-summer16 $\endgroup$ – Vladimir Dotsenko Feb 1 '17 at 19:02
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    $\begingroup$ Thanks Vladimir. There is a problem with the implementation you mention in the comment is that it relies on Kauers' package Ore algebra with is currently broken. $\endgroup$ – Bruno Feb 2 '17 at 13:00
  • $\begingroup$ @Bruno : thank you for letting me know! I did not realise that, noted. Thankfully, the Maxima implementation seems to meet my needs. (I found your question completely by accident in the process of hunting for free software implementations myself...) $\endgroup$ – Vladimir Dotsenko Feb 2 '17 at 13:05
  • $\begingroup$ @Bruno : I have to say that I found a bizarre bug in the Maxima implementation, so maybe you should un-accept this answer. I'll file a bug report to the developers over the weekend. $\endgroup$ – Vladimir Dotsenko Mar 3 '17 at 15:57
  • $\begingroup$ @Bruno : see sourceforge.net/p/maxima/mailman/message/35755540 $\endgroup$ – Vladimir Dotsenko Mar 30 '17 at 20:14

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