Some cooking recipes for DE systems

Edgardo Cheb-Terrab, CECM/MITACS

When computing exact solutions to PDE systems, a crucial step is to
compute - first of all - what is frequently called a "differential
Grobner basis using lexicographical ordering" for it. In simple words
this amounts to triangularizing the PDE system, permiting one to
solve it by sequentially solving subsets of PDEs involving a single 
unknown at a time.

In many situations, however, before computing a differential Grobner
basis, it is possible and convenient to start by eliminating some of
the unknowns of the system. In various cases the whole PDE system can be
solved without computing any integrability conditions - resulting in a
relevant saving e.g. in the presence of nonlinear PDEs. More importantly:
in the "current Computer Algebra Systems" framework, even some linear 
PDE systems can *only* be solved when we start eliminating variables 
before computing any differential Groebner basis.

This talk presents some details of the problem and a new Maple
implementation of a mixed strategy, where elimination-in-advance and
DGB are both used.