Deciding Ellipticity by Quantifier Elimination

Co-author(s): Andreas Weber

Reference: Computer Algebra in Scientific Computing - CASC 2003, V.G. Ghanza, E.W. Mayr, E.V. Vorozhtsov (eds.), TU München 2003, pp. 347-355

Description: We discuss how ellipticity of a (possibly overdetermined) linear system of partial differential equations can be decided using quantifier elimination. Our definition of ellipticity is based on the weighted principal symbol introduced by Douglis and Nirenberg. Thus part of the decision procedure is to check whether appropriate weights exist. We present a concrete implementation using MuPAD and Redlog (a quantifier elimination package for Reduce): in the computer algebra system MuPAD we generate a logical formula the truth of which is then decided by Redlog.

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