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Background and Motivation
Background for Linear Systems
Buchberger's algorithm for polynomially nonlinear equations
Differential Algebra
Applications to linear overdetermined systems of PDE

Differential Elimination Completion Algorithms for PDE
The Standard Form Package for Linear Systems
The Reduced Involutive Form Algorithm for Nonlinear Systems

Determination of the Size and Structure of Invariance Groups of PDE
Finite parameter Lie groups of symmetries of PDEs
Infinite Lie pseudogroups

Solving PDEs
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Greg Reid 2003-11-24