Speaker:  Michael Nivala, Applied Mathematics

Date:  11/11/05

Title: Symbolic integration and summation using homotopy methods

Abstract:

Homotopy methods are powerful tools originating in differential geometry
and the calculus of variations for the integration of exact expressions.
In one spatial dimensions, this amounts to integrating total derivatives
of expressions containing unknown functions and their derivatives. Such
calculations occur frequently when dealing with soliton equations, for
instance when determining the functional form of consecutive conserved
densities and their fluxes.

The current version of mathematica fails at even simple examples. Both
maple and mathematica refuse to integrate expressions that are sums of
derivative and nonderivative terms, even when the vast majority of the
terms may be integrated. Combining an optimization approach with the
homotopy method we present an algorithm for the integration of expressions
that are not total derivatives, but contain many terms that are.