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Factorization of overdetermined systems of linear partial differential equations with finite-dimensional solution space. (English) Zbl 0999.35062

Ganzha, Victor G. (ed.) et al., Computer algebra in scientific computing, CASC 2001. Proceedings of the 4th international workshop, Konstanz, Germany, September 22-26, 2001. Berlin: Springer. 529-539 (2001).
The paper concerns linear overdetermined systems (LOS) of partial differential equations with finite-dimensional solution space. Such systems typically arise during computation of infinitesimal symmetries and conservation laws of nonlinear systems of PDEs. Combining the Riquier-Janet theory, the improved Beke algorithm [M. Bronstein, in: Proc. of the ISSAC ’94, 336-340 (1994; Zbl 0964.68583)], and the Li-Schwarz algorithm [Z. Li and F. Schwarz, J. Symb. Comput. 31, No. 6, 691-716 (2001; Zbl 0985.34007)], the author gives a theoretical background for LOS and derives an algorithm to find right factors of a LOS. The results are relevant to machine computation of closed-form solutions of a LOS, with the important task of improving the efficiency of the algorithm still ahead.
For the entire collection see [Zbl 0970.00027].

MSC:

35N10 Overdetermined systems of PDEs with variable coefficients
68W30 Symbolic computation and algebraic computation
58J72 Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds
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