=ADD=
=reftype=
14
=number=
00-12
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/2000/00-12.ps.gz
=year=
2000
=month=
04
=author=
Chyzak; Fr\'ed\'eric
=title=
About the Non-Minimality of the Outputs of Zeilberger's Algorithm
=abstract=
We report on case studies where Zeilberger's fast algorithm and the
other holonomy-based algorithms known so far for definite
hypergeometric summation fail to find the minimal annihilating
recurrence satisfied by the sum.  To explain the phenomenon we propose
a new elimination paradigm, together with a promising heuristic method
which we hope to turn into an algorithm in the future.  The approach
applies to $\partial$-finite functions as well and extends to the
related algorithms.
=sponsor=
SFB grant F1305 of the Austrian Science Foundation (FWF)
=keywords=
computer algebra, holonomic functions, special functions, symbolic summation