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We introduce a general algebraic setting for describing linear boundaryproblems in a symbolic computation context, with emphasis on the case ofpartial differential equations. The general setting is then applied to theCauchy problem for completely reducible partial differential equations withconstant coefficients. While we concentrate on the theoretical features in thispaper, the underlying operator ring is implemented and provides a sufficientbasis for all methods presented here.

A Symbolic Approach to Boundary Problems for Linear Partial Differential  Equations: Applications to the Completely Reducible Case of the Cauchy  Problem with Constant Coefficients