Rational solutions of the mixed differential equation and its application to factorization of differential operators

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Rational solutions of the mixed differential equation and its application to factorization of differential operators

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1996 international symposium on Symbolic and algebraic computation table of contents

Zurich, Switzerland

Pages: 219 - 225

Year of Publication: 1996

ISBN:0-89791-796-0

Author

Mark van Hoeij

Department of mathematics, University of Nijmegen, 6525 ED Nijmegen, The Netherlands

Sponsors

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation
SIGNUM: ACM Special Interest Group on Numerical Mathematics

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 1, Downloads (12 Months): 6, Citation Count: 6

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	Sergei A. Abramov , Manuel Bronstein , Marko Petkovšek, On polynomial solutions of linear operator equations, Proceedings of the 1995 international symposium on Symbolic and algebraic computation, p.290-296, July 10-12, 1995, Montreal, Quebec, Canada [doi>10.1145/220346.220384]
	2	B. Beckermann, G. Labahn, A uniform approach for Hermite Padd and simultaneous Padd Approximants and their Matrix-type generalizations, Numerical Algorithms, 3 (1992), pp. 45-54
	3	Bernhard Beckermann , George Labahn, A Uniform Approach for the Fast Computation of Matrix-Type Pade Approximants, SIAM Journal on Matrix Analysis and Applications, v.15 n.3, p.804-823, July 1994 [doi>10.1137/S0895479892230031]
	4	E. Beke Die Irreduzibilitiit der homogenen linearen JDifferentialgleichungen, Math. Ann. 45, (1894), 278- 294.
	5	Manuel Bronstein, Linear ordinary differential equations: breaking through the order 2 barrier, Papers from the international symposium on Symbolic and algebraic computation, p.42-48, July 27-29, 1992, Berkeley, California, United States [doi>10.1145/143242.143264]
	6	H. Derksen An algorithm to compute generalized Padd-Hermite forms Manuscript. Available by ftp at daisy.math, unibas, ch in /pub/hderksen/pade. dvi
	7	Peter A. Hendriks , Marius van der Put, Galois action on solutions of a differential equation, Journal of Symbolic Computation, v.19 n.6, p.559-576, June 1995 [doi>10.1006/jsco.1995.1032]
	8	Mark Van Hoeij, Formal solutions and factorization of differential operators with power series coefficients, Journal of Symbolic Computation, v.24 n.1, p.1-30, July 1997 [doi>10.1006/jsco.1997.0110]
	9	Mark Van Hoeij, Factorization of differential operators with rational functions coefficients, Journal of Symbolic Computation, v.24 n.5, p.537-561, Nov. 1997 [doi>10.1006/jsco.1997.0151]
	10	A. Loewy, (rber vollstiindig reduzible lineare homogene Differentialgleichungen, Math. Ann., 62, (1906), 89- 117.
	11	O. Ore, Formale Theorie der linearen Differentialgleichungen (Zweiter Tell), J. ffir d. Reine u. angew. Math., 168, (1932), 233-252.
	12	O. Ore, Theory of non-commutative polynomial rings, Ann. of Math. 34 pp. 480-508 (1933)
	13	F. Schwarz, A factorization algorithm for linear ordinary differential equations, Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation, p.17-25, July 17-19, 1989, Portland, Oregon, United States [doi>10.1145/74540.74544]
	14	M.F. Singer, Testing Reducibility of Linear Differential Operators: A Group Theoretic Perspective, To appear in J. of Appl. Alg. in Eng. Comm. and Comp.
	15	S.P. Tsarev, On the problem of factorization of linear ordinary differential operators, Programming & computer software, 1994, v. 20, 1~ p. 27"-29.
	16	J.A. Weil, Constantes et polyn6mes de Darboux en alg~bre diffdrentieUe : application aux syst~mes diffdrentiels lindaires, PhD dissertation, t~cole Polytechnique, 1995.

CITED BY 6

	Sergei A. Abramov , Mark van Hoeij, A method for the integration of solutions of Ore equations, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.172-175, July 21-23, 1997, Kihei, Maui, Hawaii, United States
	S. P. Tsarev, Symbolic manipulation of integrodifferential expressions and factorization of linear ordinary differential operators over transcendental extensions of a differential field, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.310-315, July 21-23, 1997, Kihei, Maui, Hawaii, United States
	Thomas Cluzeau, Factorization of differential systems in characteristic p, Proceedings of the 2003 international symposium on Symbolic and algebraic computation, p.58-65, August 03-06, 2003, Philadelphia, PA, USA
	S. P. Tsarev, An algorithm for complete enumeration of all factorizations of a linear ordinary differential operator, Proceedings of the 1996 international symposium on Symbolic and algebraic computation, p.226-231, July 24-26, 1996, Zurich, Switzerland
	Mark Giesbrecht , Yang Zhang, Factoring and decomposing ore polynomials over F_q(t), Proceedings of the 2003 international symposium on Symbolic and algebraic computation, p.127-134, August 03-06, 2003, Philadelphia, PA, USA
	M. A. Barkatou , E. Pflügel, On the equivalence problem of linear differential systems and its application for factoring completely reducible systems, Proceedings of the 1998 international symposium on Symbolic and algebraic computation, p.268-275, August 13-15, 1998, Rostock, Germany