In the past two decades there has been rapid development
in methods for gaining insight into a given physical PDE by
formulating auxiliary overdetermined systems whose solutions
determine features of the given PDE.
The auxiliary overdetermined system of PDEs for the
infinitesimal Lie symmetries of a given PDE can be
automatically produced by many symbolic programs [34],
and may contain thousands of PDEs.
Other symbolic programs have been found
to be very useful for simplifying and often solving these
systems.
Applications of Lie symmetries include the
determination of invariant or similarity
solutions, Bäcklund transformations and soliton solutions.
We contributed to this area with our Standard Form
package [67].
There has been considerable activity
analysing properties of physical PDEs through generalizations
of Lie's methods [3,21].
Often the associated overdetermined systems
are nonlinear.
Thus systematic methods for simplifying large nonlinear systems are
needed. Few programs and methods have been developed
in this area compared to the well-developed theory, methods and
implemented algorithms for linear systems.
This motivated us to develop the *rif*
algorithm for simplifying and determining properties of such systems.

** Next:** Differential Elimination Completion Algorithms
** Up:** Background and Motivation
** Previous:** Differential Algebra
Greg Reid
2003-11-24