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TitleHolonomic Systems and Automatic Proofs of Identities
Author(s) Frederic Chyzak
TypeTechnical Report, Misc
AbstractThis report presents three computer algebra packages in the Maple
language for the symbolic manipulation of linear systems of differential and recurrence equations. They are especially designed to deal with so-called holonomic systems. We also give a theoretical justification to our implementation. The set of holonomic functions and sequences is a large class of objects. It forms an algebra and is closed under algebraic substitution and diagonal. An implementation of these properties makes it possible to perform computer assisted proofs of holonomic identities in
a simple way, since any holonomic system has a normal form obtained
by an extension of the Grobner basis algorithm. For instance, combinatorial problems often lead to holonomic systems and to identities involving binomial coefficients. Many identities involving special
functions are also captured by the theory of holonomy. Examples are
given to show how some interesting identities are proved by our system.
Translation No
Refereed No
Institution INRIA