Rankings of partial derivatives

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Rankings of partial derivatives

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1997 international symposium on Symbolic and algebraic computation table of contents

Kihei, Maui, Hawaii, United States

Pages: 9 - 16

Year of Publication: 1997

ISBN:0-89791-875-4

Authors

C. J. Rust	Department of Mathematics, University of Chicago, Chicago, IL
G. J. Reid	Centre for Experimental and Constructive Mathematics, Simon Fraser University, Burnaby, BC, Canada V5A 1S6

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): 3, Downloads (12 Months): 21, Citation Count: 8

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references cited by index terms collaborative colleagues

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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	Becket, T. and Weispfenning, V. with H. Kredel (1993), GrSbner Bases, GTM Vol. 141, Springer-Verlag.
	2	F. Boulier , D. Lazard , F. Ollivier , M. Petitot, Representation for the radical of a finitely generated differential ideal, Proceedings of the 1995 international symposium on Symbolic and algebraic computation, p.158-166, July 10-12, 1995, Montreal, Quebec, Canada [doi>10.1145/220346.220367]
	3	Buchberger, B. (1965), An Algorithm .for Finding a Basis for the Residue Class Ring of a Zero-Dimensional Polynomial Ideal, Ph.D. Thesis, Univ. of Innsbruck.
	4	Caboara, M. and Silvestri, M. (1996), "Compatible module orderings", ISSA C'96 Poster Session, 17-22.
	5	Carr~-Ferro, G. and W. Y. Sit (1993), On Term. Orderinys and Rankings, Lecture Notes in Pure and Applied Math., Computational Algebra, Dekker, 151.
	6	Eisenbud, D. (1995), Commutative Algebra with a View Toward Algebraic Geometry, GTM Vol. 150, Springer.
	7	Janet, M. (1920), "Sur les Systbmes d'6quations aux d6riv6es partielles", J. de Math. (8), Volume 3, 65-151.
	8	Kolchin, E. R. (1973), Differential Algebra and Algebraic Groups, (Academic Press).
	9	Mansfield, E. (1991), Differential GrSbner Bases, Ph.D Thesis, University of Sydney.
	10	Reid, G.J. and Wittkopf, A.D. (1993), The long guide to the Standard Form package, ftp:math.ubc, ca in directory/pub/re id/s tandaxdform.
	11	Reid, G.J. and Wittkopf, A.D. and A. Boulton, Reduction of systems of nonlinear partial differential equations to simplified involutive forms. To appear in the Eur. j. of Appl. Math.
	12	Riquier, C. (1910), Les syst~mes d'dquations aux ddrivdes partielles, (Gauthier-Villars, Paris).
	13	Ritt, J. F. (1950), Differential Algebra, (Dover).
	14	Lorenzo Robbiano, Term Orderings on the Polynominal Ring, Research Contributions from the European Conference on Computer Algebra-Volume 2, p.513-517, April 01-03, 1985
	15	Rust, C. (1995), On the Classification of Rankings of Partial Derivatives, available on http : //www. math. uchi cago. edu/~rust/orderings, ps.
	16	Rust, C. (in prep.), The Classification of Rankings of Partial Derivatives, Ph.D. Thesis, Univ. of Chicago.
	17	Fritz Schwarz, Monomial orderings and Gro¨bner bases, ACM SIGSAM Bulletin, v.25 n.1, p.10-23, Jan. 1991 [doi>10.1145/122525.122526]
	18	Fritz Schwarz, Reduction and completion algorithms for partial differential equations, Papers from the international symposium on Symbolic and algebraic computation, p.49-56, July 27-29, 1992, Berkeley, California, United States [doi>10.1145/143242.143265]
	19	Stormark, O. (1989), Formal and Local Solvability of Partial Differential Equation's, Dept. of Math., Royal Inst. of Technology, Stockholm, TRITA-MAT-1989-11.
	20	Thomas, J. M. (1931), "Matrices of Integers Ordering Derivatives", Trans. Amer. Math. Soc. 33,389-410.
	21	Trevisan, G. (1953), "Classificazione dei semplici ordinamenti di un gruppo libero commutativo con N generatori", Rend. Sere. Mat. Univ. Padova 22, 143-156.
	22	Alan Tucker, Applied combinatorics (3rd ed.), John Wiley & Sons, Inc., New York, NY, 1994
	23	Volker Weispfenning, Admissible orders and linear forms, ACM SIGSAM Bulletin, v.21 n.2, p.16-18, May 1987 [doi>10.1145/24554.24557]
	24	Volker Weispfenning, Differential term-orders, Proceedings of the 1993 international symposium on Symbolic and algebraic computation, p.245-253, July 06-08, 1993, Kiev, Ukraine [doi>10.1145/164081.164138]
	25	Zai'ceva, M. (1953), "On the set of orderings of Abelian groups" (in Russian), Math. USSR Doklady, 8,135-137.

CITED BY 8

	C. J. Rust , G. J. Reid , A. D. Wittkopf, Existence and uniqueness theorems for formal power series solutions of analytic differential systems, Proceedings of the 1999 international symposium on Symbolic and algebraic computation, p.105-112, July 28-31, 1999, Vancouver, British Columbia, Canada
	Gregory J. Reid , Allan D. Wittkopf, Determination of maximal symmetry groups of classes of differential equations, Proceedings of the 2000 international symposium on Symbolic and algebraic computation, p.272-280, July 2000, St. Andrews, Scotland
	François Lemaire, An orderly linear PDE system with analytic initial conditions with a non-analytic solution, Journal of Symbolic Computation, v.35 n.5, p.487-498, May 2003
	Johannes Grabmeier , Erich Kaltofen , Volker Weispfenning, Cited References, Computer algebra handbook, Springer-Verlag New York, Inc., New York, NY, 2003
	Aleksey Zobnin, Admissible orderings and finiteness criteria for differential standard bases, Proceedings of the 2005 international symposium on Symbolic and algebraic computation, p.365-372, July 24-27, 2005, Beijing, China
	Oleg Golubitsky, Construction of rankings on partial derivatives, ACM Communications in Computer Algebra, v.40 n.2, June 2006
	A. I. Zobnin, Generalized Reduction in Rings of Differential Polynomials, Programming and Computing Software, v.30 n.2, p.88-94, March-April 2004
	Oleg Golubitsky, Universal characteristic decomposition of radical differential ideals, Journal of Symbolic Computation, v.43 n.1, p.27-45, January, 2008