Séminaire du 22 février 2010, 14h00: Shaoshi Chen,
Complexity of the Creative Telescoping for Bivariate Rational Functions.
The long-term goal initiated in this work is to obtain fast algorithms and
implementations for definite integration in the framework, introduced by
Almkvist and Zeilberger, of (differential) creative telescoping. Our approach
bases on complexity analysis, by obtaining tight degree bounds on the
various differential operators and polynomials involved in the method.
To make the problem more tractable, we restrict in this work to the integration
of bivariate rational functions. By considering this constrained class of inputs,
we are able to blend the general method of creative telescoping with the
well-known Hermite reduction. We then study a family of combinatorial
applications encoded as diagonals of rational power series, themselves
expressible as integrals.
Last modified: Mon Jan 4 17:39:50 CET 2010