<p>It is implemented in Maxima (<a href="http://maxima.sourceforge.net/docs/manual/de/maxima_77.html#SEC400">http://maxima.sourceforge.net/docs/manual/de/maxima_77.html#SEC400</a>), 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. </p>

CC BY-SA 3.0
2017-02-01T19:02:44.200Z
P.S. There is also a recent sage implementation which I just noticed but haven't tested: see the webpage http://arminstraub.com/teaching/specialfunctions-summer16
Vladimir Dotsenko
CC BY-SA 3.0
2017-02-02T13:00:19.400Z
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](https://trac.sagemath.org/ticket/21344).
Bruno
CC BY-SA 3.0
2017-02-02T13:05:27.993Z
@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...)
Vladimir Dotsenko
CC BY-SA 3.0
2017-03-03T15:57:14.647Z
@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.
Vladimir Dotsenko
CC BY-SA 3.0
2017-03-30T20:14:19.183Z
@Bruno : see https://sourceforge.net/p/maxima/mailman/message/35755540/
Vladimir Dotsenko
CC BY-SA 3.0
2017-02-01T16:42:02.797Z
2017-02-01T16:42:02.797Z
Vladimir Dotsenko
<p>The book <a href="http://www.math.upenn.edu/~wilf/AeqB.html">A=B</a> by Petkovsek, Wilf and Zeilberger describes algorithms to compute different sums of binomials. AFAIK, these algorithms are still being improved by different authors. </p>

<p>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 <a href="http://sagemath.org">Sage</a>?</p>

CC BY-SA 3.0
2012-04-18T17:30:01.660Z
Try mailing Doron Zeilberger [he codes](http://www.math.rutgers.edu/~zeilberg/Opinion37.html). [here](http://www.math.upenn.edu/~wilf/progs.html).
Pratik Deoghare
CC BY-SA 3.0
2012-04-18T18:41:24.863Z
@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.
Peter Taylor
CC BY-SA 3.0
2012-04-19T17:27:53.207Z
@PratikDeoghare: I actually knew those implementations, but they are pretty old now. But you are right about directly asking Doron Zeilberger, he might know some new implementations if they exist.
Bruno
CC BY-SA 3.0
2012-04-19T17:33:37.740Z
@PeterTaylor: Of course, I am not fully satisfied by Maple implementations since I'd prefer free alternatives. For Sage, I found [this page](http://wiki.sagemath.org/symbolics). It seems that it is not implemented yet.
Bruno
CC BY-SA 3.0
2012-04-19T22:27:34.917Z
Some further information regarding Sage may be found [here](http://www.mail-archive.com/sage-devel@googlegroups.com/msg25543.html)
Timothy Chow
CC BY-SA 3.0
2014-07-06T01:53:43.107Z
I've opened http://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.
kcrisman
CC BY-SA 3.0
2014-07-06T09:20:29.350Z
It's not my area either, though I might be closer to these questions than you are. Yet, I'll point your ticket to people that could possibly be interested in implementing this. I'd realy like to have such algorithms in Sage!
Bruno
<ds.algorithms><co.combinatorics><implementation>
Implementation of Wilf-Zeilberger and related methods
Bruno
# Implementation of Wilf-Zeilberger and related methods

(Asked by: username_0 on 2012-04-18)

The book [A=B](http://www.math.upenn.edu/~wilf/AeqB.html) 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](http://sagemath.org)?

**Tags:** ds.algorithms, co.combinatorics, implementation
> **Comments:**
> **username_1**: Try mailing Doron Zeilberger [he codes](http://www.math.rutgers.edu/~zeilberg/Opinion37.html). [here](http://www.math.upenn.edu/~wilf/progs.html).  
> **username_2**: @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.  
> **username_0**: @PratikDeoghare: I actually knew those implementations, but they are pretty old now. But you are right about directly asking Doron Zeilberger, he might know some new implementations if they exist.  
> **username_0**: @PeterTaylor: Of course, I am not fully satisfied by Maple implementations since I'd prefer free alternatives. For Sage, I found [this page](http://wiki.sagemath.org/symbolics). It seems that it is not implemented yet.  
> **username_3**: Some further information regarding Sage may be found [here](http://www.mail-archive.com/sage-devel@googlegroups.com/msg25543.html)  
> **username_4**: I've opened http://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.  
> **username_0**: It's not my area either, though I might be closer to these questions than you are. Yet, I'll point your ticket to people that could possibly be interested in implementing this. I'd realy like to have such algorithms in Sage!  

---

## 1 answers

### Answer by username_5 on 2017-02-01. Score: 7 | Accepted answer

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.

> **Comments:**
> **username_5**: P.S. There is also a recent sage implementation which I just noticed but haven't tested: see the webpage http://arminstraub.com/teaching/specialfunctions-summer16  
> **username_0**: 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](https://trac.sagemath.org/ticket/21344).  
> **username_5**: @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...)  
> **username_5**: @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.  
> **username_5**: @Bruno : see https://sourceforge.net/p/maxima/mailman/message/35755540/  

---

