Computations with parametric equations

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	Arnon, D. and Sederberg, T (1984), Implicit Equation for a Parametric Surface by GrSbner Bases, Proc. of 198~ MACSYMA User's Conference (V.E. Golden ed.), GE, Schenectady, New York, 431-436.
	2	Artin, M. and Mumford, D. (1972), Some Elementary Examples of Unirational Varieties Which Are Non-r~tional, Proc. London Math. Soc., (3) 25, pp. 75-95.
	3	B. Buchberger, Applications of Gro¨bner bases in non-linear computational geometry, Trends in computer algebra, Springer-Verlag New York, Inc., New York, NY, 1988
	4	Castelnuovo, (1894), Sulla rationalita della involuzioni pinae, Math. Ann., 44, pp. 125-155.
	5	Shang-Ching Chou , Xiao-Shan Gao, Ritt-Wu's decomposition algorithm and geometry theorem proving, Proceedings of the tenth international conference on Automated deduction, p.207-220, July 1990, Kaiserslautern, Germany
	6	Chou, S.C., Schelter W.F., and Yang, J.G. (1990), An Algorithm for Constructing GrSbner Bases from Characteristic Sets, Algorithmic, 5, 147-154.
	7	J. H. Chuang , C. M. Hoffmann, On local implicit approximation and its applications, ACM Transactions on Graphics (TOG), v.8 n.4, p.298-324, Oct. 1989 [doi>10.1145/77269.77272]
	8	Xiao Gao , Shang Chou, Independent Parameters, Inversions and Proper Parameterization, University of Texas at Austin, Austin, TX, 1990
	9	Xiao Gao , Shang Chou, Implicitization of Rational Parametric Equations, University of Texas at Austin, Austin, TX, 1990
	10	Michael Kalkbrenner, Implicitization of Rational Parametric Curves and Surfaces, Proceedings of the 8th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, p.249-259, August 20-24, 1990
	11	Kalkbrener, M.(1990b), Implicitization by Using GrSbner Bases, RISC-Linz, 90-27.0, November, 1990.
	12	Li, Z.M. (1989), Automatic Implicitization of P~rametric Objects, MM Research Preprints, No.4, ins. of Systems Science, Academia Sinica.
	13	Dinesh Manocha , John F. Canny, Implicitizing Rational Parametric Surfaces, University of California at Berkeley, Berkeley, CA, 1990
	14	T W Sederberg, Improperly parametrized rational curves, Computer Aided Geometric Design, v.3 n.1, p.67-75, May 1986 [doi>10.1016/0167-8396(86)90025-7]
	15	Sederberg, T.W., Anderson, D.C., and Goldman, R. (1984), Implicit Representation of Parametric Curves and Surfaces, Computer Vision, Graph, Image Proc., vol28 pp 72-84. Segre, B. (1951), Sull Esistenza, Sia Nel Campo Rationale chenel Campo ReaIe, Rend. Accad. Naz. Lincei (8) 10, pp. 564-57o.
	16	David Shannon , Moss Sweedler, Using Gro¨bner bases to determine algebra membership, split surjective algebra homomorphisms determine birational equivalence, Journal of Symbolic Computation, v.6 n.2-3, p.267-273, Oct./Dec. 1988 [doi>10.1016/S0747-7171(88)80047-6]
	17	Shannon, D. and Sweedler, M. (1989), Using GrSbner bases to determine the algebraic and transcendental nature of field extensions within the field of rational functions, Preprint.
	18	Tarski, A. (1951), A Decision Method for Elementary Algebra and Geometry, University of California Press, Berkeley, Calif., 1951.
	19	Walker, R. (1950), Algebraic Curves, Princeton University Press.
	20	Wen-Tsun Wu, Basic principles of mechanical theorem proving in elementary geometrics, Journal of Automated Reasoning, v.2 n.3, p.221-252, Aug. 1987 [doi>10.1007/BF02328447]
	21	Wu, W.T. (1989), On a Projection Theorem of Quasi-Varieties in Elimination Theory MM Preprints, No. 4, Ins. of Systems Science, Academia Sinica.