Geodesic
A Macsyma Implementation of Zeilberger's Fast Algorithm
Séminaire lotharingien de combinatoire, Tome 43 (1999-2000)

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We present the first implementation within the Macsyma computer algebra system of Zeilberger's fast algorithm for the definite summation problem for a very large class of sequences; i.e., given a hypergeometric sequence F(n,k), we want to represent f(n)=sum_{k=0}^{n} F(n,k) in a "simpler" form. We do this by finding a linear recurrence for the summand F(n,k), from which we can obtain a homogeneous k-free recurrence for f(n). The solution of this recurrence is left as a post-processing, and it will give the "simpler" form we were looking for.

Zeilberger's fast algorithm exploits a specialized version of Gosper's algorithm for the indefinite summation problem; i.e., given a hypergeometric sequence t(k), the problem of finding another sequence T(k) such that t(k)=\Deltak T(k)=T(k+1)- T(k). The implementation of this algorithm has been carried out in Macsyma, and its details are also briefly described in this paper. 

@article{SLC_1999-2000_43_a8,
     author = {Fabrizio Caruso},
     title = {A {Macsyma} {Implementation} of {Zeilberger's} {Fast} {Algorithm}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {43},
     year = {1999-2000},
     url = {http://geodesic.mathdoc.fr/item/SLC_1999-2000_43_a8/}
}
TY  - JOUR
AU  - Fabrizio Caruso
TI  - A Macsyma Implementation of Zeilberger's Fast Algorithm
JO  - Séminaire lotharingien de combinatoire
PY  - 1999-2000
VL  - 43
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_1999-2000_43_a8/
ID  - SLC_1999-2000_43_a8
ER  - 
%0 Journal Article
%A Fabrizio Caruso
%T A Macsyma Implementation of Zeilberger's Fast Algorithm
%J Séminaire lotharingien de combinatoire
%D 1999-2000
%V 43
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_1999-2000_43_a8/
%F SLC_1999-2000_43_a8
Fabrizio Caruso. A Macsyma Implementation of Zeilberger's Fast Algorithm. Séminaire lotharingien de combinatoire, Tome 43 (1999-2000). http://geodesic.mathdoc.fr/item/SLC_1999-2000_43_a8/