Added Jan. 10, 2004: Most of the stuff that EKHAD below can do is now built-in in Maple 8 and above, in the package SumTools.
The packages accompanying the book A=B, by Marko Petkovsek, Herb Wilf and Doron Zeilberger , are:
EKHAD (Added Jan. 3, 2003: If you use Maple 8, then you need EKHAD8), a Maple package for proving binomial coefficients and other types of identities. To use it, download it as EKHAD, go into Maple, type `read EKHAD:`, and follow the instructions given there. Version of Sept. 13, 2000, to adapt to Maple 6. The previous version Feb. 25, 1999. benefited from a GREAT SUGGESTION of Frederic CHYZAK (whom we thank so much!), and now is roughly four times as fast. It may not work on very early versions of Maple, in which case you still use the Old Version of EKHAD.
qEKHAD , a Maple package for proving q-binomial coefficients (a.k.a. basic-hypergeometric, and q-) identities. To use it, download it as qEKHAD, go into Maple, type `read qEKHAD:`, and follow the instructions given there. Version of Sept. 14, 2000, to adapt to Maple 6. The previous version implemented the above suggestion of Frederic CHYZAK, but the speed-up is not so dramatic. If you have a very early versions of Maple, you may need the Old Version of qEKHAD
Also mentioned in A=B are the following two programs, that are still prototypes, and are harder to use.
DOUBLE_SUM_SINGLE_INTEGRAL , A Maple programs that performs the algorithm described in my paper with Herb Wilf (Inv. Math. 108(1992), 575-633) for the case of two discrete and one continuous variables. To use it, download it, separate the input from the program files and follow the instructions given there. For example, try the input file for DOUBLE_SUM_SINGLE_INTEGRAL .
WZtriple , (with its sample input file inWZtriple , that should yield the output file oWZtriple), A Maple package that performs the algorithm described in my paper with Herb Wilf (Inv. Math. 108(1992), 575-633) for the case of two or three continuous variables. To use it, download WZtriple and follow the instructions given there.
Note: My brilliant student, Akalu Tefera has written a program for Multi-Inetgrals for ANY dimension. He also wrote another program, SMint , that only works for symmetric integrands, and takes advantage of the symmetry to get beautiful certificates.
Of theoretical interest only, is CCEL, a very short program that can find the recurrence satisfied by ANY hypergeometrix integral. Alas, it usually takes (almost) for ever.
zeilWZP , A single program, that uses EKHAD (you must have EKHAD in the same directory), that generalizes the so-called Zeilberger algorithm (a.k.a. as Gosper-Zeilberger, and Creative Telescoping) to the case where the summand is not just plain Closed Form but Closed Form times the Potential function of a WZ pair. It is described in English in Doron Zeilberger's artice in Contemporary Math v. 143, pp. 600 ff. To use it, download it as zeilWZP, make sure you have the package EKHAD (see above) in the same directory, go into maple, and type: read zeilWZP; Then follow the on-line instructions.
Of related interest is the package SYND , that accompanies the paper Curing The Andrews Syndrome .