This talk gives an introduction to the method of
Thomas decomposition for systems of nonlinear partial
differential equations, which is fundamental for solving
tasks like determining all power series solutions of the
PDE system (around sufficiently generic points), deciding
membership of a differential equation to the corresponding
radical differential ideal, determining all consequences
of the system that involve only certain specified unknown
functions. The algorithms have been implemented and are
now available as a package in the standard distribution
of Maple. Among the various applications of the method
are: finding singular solutions, differential elimination,
nonlinear control theory.
Forschungs-