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# Generalized loewy decomposition of D-modules

: Grigoriev, D.

 Kauers, M. ; Association for Computing Machinery -ACM-:ISSAC 2005, International Symposium on Symbolic and Algebraic Computation. Proceedings. CD-ROM : July 24 - 27, Beijing, ChinaNew York: ACM, 2005ISBN: 1-595-93191-0 International Symposium on Symbolic and Algebraic Computation (ISSAC) <30, 2005, Beijing> Englisch Konferenzbeitrag Fraunhofer SCAI () partial differential equation

Abstract
Starting from the well-known factorization of linear ordinary differential equations, we define the generalized Loewy decomposition for a ${\\cal D}$-module. To this end, for any module $I$, overmodules $J\\supseteq I$ are constructed. They subsume the conventional factorization as special cases.
Furthermore, the new concept of the module of relative syzygies $Syz(I,J)$ is introduced. The invariance of this module and its solution space w.r.t. the set of generators is shown. We design an algorithm which constructs the Loewy-decomposition for finite-dimensional and some kinds of general ${\\cal D}$-modules. These results are applied for solving various second-and third-order linear partial differential equations.

: http://publica.fraunhofer.de/dokumente/N-39162.html