Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Drew Sills**, Rutgers University, asills {at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Holonomic Programs

Speaker: **Jacques Carette**, McMaster University

Date: Thursday, October 19, 2006 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

We want to add a third member to the holonomic family: after sequences and functions, programs. First, we review simple ways to transform recurrences into programs to compute terms, and thence from differential equations to programs to approximation solutions via Taylor series. These programs have a particularly simple structure. We then look at the inverse problem of taking programs from this family and find the appropriate 'holonomic object' to which it corresponds. One intriguing aspect of this work is that programs compute certain constants (such as exp(1)) fit within our scheme, so that from a way to compute exp(1) we can uncover which holonomic object it corresponds to, in a completely deterministic fashion. The underlying theory and 'live' examples of "reverse engineering" of holonomic information from programs will be shown.