Diophantine linear system solving

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Diophantine linear system solving

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1999 international symposium on Symbolic and algebraic computation table of contents

Vancouver, British Columbia, Canada

Pages: 181 - 188

Year of Publication: 1999

ISBN:1-58113-073-2

Authors

Thom Mulders	Institute of Scientific Computing, ETH Zurich, Switzerland
Arne Storjohann	Institute of Scientific Computing, ETH Zurich, Switzerland

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): 25, Citation Count: 8

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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	ABt3o'r'r, J., BRONSTEIN, M., AND ~IUIJI)ERS. T. Fast deterministic computation of determinants of dense ,hatrices. These proceedings.
	2	Eric Bach , Jeffrey Shallit, Algorithmic number theory, MIT Press, Cambridge, MA, 1996
	3	George E. Collins , Mark J. Encarnación, Efficient rational number reconstruction, Journal of Symbolic Computation, v.20 n.3, p.287-297, Sept. 1995 [doi>10.1006/jsco.1995.1051]
	4	DIXOX, J. Exact solution of linear equations using padic expansions. Numer. Math. ~0 (1982), 137-141.
	5	Wayne Eberly, Processor-efficient parallel matrix inversion over abstract fields: two extensions, Proceedings of the second international symposium on Parallel symbolic computation, p.38-45, July 20-22, 1997, Maui, Hawaii, United States [doi>10.1145/266670.266684]
	6	Keith O. Geddes , Stephen R. Czapor , George Labahn, Algorithms for computer algebra, Kluwer Academic Publishers, Norwell, MA, 1992
	7	Mark Giesbrecht, Efficient parallel solution of sparse systems of linear diophantine equations, Proceedings of the second international symposium on Parallel symbolic computation, p.1-10, July 20-22, 1997, Maui, Hawaii, United States [doi>10.1145/266670.266678]
	8	M. Giesbrecht , A. Lobo , B. D. Saunders, Certifying inconsistency of sparse linear systems, Proceedings of the 1998 international symposium on Symbolic and algebraic computation, p.113-119, August 13-15, 1998, Rostock, Germany [doi>10.1145/281508.281591]
	9	KALTOFEN, E., AND PAN. V. Processor-rfficieilt parallel solution of linear systems II' The general case. In Proc. 33rd IEEE Symposium on Foundations of Computer Science (Pittsburgh, USA, 1992), pp. 714-723.
	10	LIDL, R... AND NIEDli:RP~EITER., H. Finite Fields. / ,R , , Addison-We..'ley. 1983.
	11	NEWMAN. M. Integral Matrices. Academic Press, 1972.
	12	ROSSElt. J. B., A.','D SCttOENFELr), L. Approximate formulas for some flmctions of prime Immbers. Ill. J. Math. 6 (1962), 64--94.
	13	VILLARI), G. Calcul Formel et Paralldlisrn.e: Resolution de. Systemes Line.aires. PhD thesis, L. Institut, National Polytechnique de Grenoble, 1988.
	14	D H Wiedemann, Solving sparse linear equations over finite fields, IEEE Transactions on Information Theory, v.32 n.1, p.54-62, Jan. 1986 [doi>10.1109/TIT.1986.1057137]

CITED BY 8

	Arne Storjohann, High-order lifting, Proceedings of the 2002 international symposium on Symbolic and algebraic computation, p.246-254, July 07-10, 2002, Lille, France
	John Abbott , Manuel Bronstein , Thom Mulders, Fast deterministic computation of determinants of dense matrices, Proceedings of the 1999 international symposium on Symbolic and algebraic computation, p.197-204, July 28-31, 1999, Vancouver, British Columbia, Canada
	Daniele Micciancio , Bogdan Warinschi, A linear space algorithm for computing the hermite normal form, Proceedings of the 2001 international symposium on Symbolic and algebraic computation, p.231-236, July 2001, London, Ontario, Canada
	Jean-Guillaume Dumas , B. David Saunders , Gilles Villard, Integer Smith form via the valence: experience with large sparse matrices from homology, Proceedings of the 2000 international symposium on Symbolic and algebraic computation, p.95-105, July 2000, St. Andrews, Scotland
	Thom Mulders , Arne Storjohann, Rational solutions of singular linear systems, Proceedings of the 2000 international symposium on Symbolic and algebraic computation, p.242-249, July 2000, St. Andrews, Scotland
	Arne Storjohann, High-order lifting and integrality certification, Journal of Symbolic Computation, v.36 n.3-4, p.613-648, September 2003
	Zhuliang Chen , Arne Storjohann, A BLAS based C library for exact linear algebra on integer matrices, Proceedings of the 2005 international symposium on Symbolic and algebraic computation, p.92-99, July 24-27, 2005, Beijing, China
	Wayne Eberly , Mark Giesbrecht , Pascal Giorgi , Arne Storjohann , Gilles Villard, Solving sparse rational linear systems, Proceedings of the 2006 international symposium on Symbolic and algebraic computation, July 09-12, 2006, Genoa, Italy