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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Absolute factoring of nonholonomic ideals in the plane
 Watt, S.M. ; Association for Computing Machinery ACM, Special Interest Goup on Symbolic and Algebraic Manipulation SIGSAM: Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010 : Munich, Germany, July 25  28, 2010 New York: ACM, 2010 ISBN: 9781450301503 S.9397 
 International Symposium on Symbolic and Algebraic Computation (ISSAC) <35, 2010, Munich> 

 Englisch 
 Konferenzbeitrag 
 Fraunhofer SCAI () 
Abstract
We study nonholonomic overideals of a left differential ideal J ( F[8x, 8y] in two variables where F is a differentially closed field of characteristic zero. One can treat the problem of finding nonholonomic overideals as a generalization of the problem of factoring a linear partial differential operator. The main result states that a principal ideal J = <P> generated by an operator P with a separable symbol symb(P) has a finite number of maximal nonholonomic overideals; the symbol is an algebraic polynomial in two variables. This statement is extended to nonholonomic ideals J with a separable symbol. As an application we show that in case of a secondorder operator P the ideal <P> has an infinite number of maximal nonholonomic overideals iff <P> is essentially ordinary. In case of a thirdorder operator P we give sufficient conditions on <P> in order to have a finite number of maximal nonholonomic overideals. In the Appendix we study the problem of finding nonholonomic overideals of a principal ideal generated by a second order operator, the latter being equivalent to the Laplace problem. The possible application of some of these results for concrete factorization problems is pointed out.