Lower bounds for zero-dimensional projections. (English) Zbl 1237.68253
May, John P. (ed.), ISSAC 2009. Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, Seoul, July 28–31, 2009. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-60558-609-0). 79-85 (2009).
For the entire collection see [Zbl 1236.00041].
MSC:
| 68W30 | Symbolic computation and algebraic computation |
References:
| [1] | J.-D. Boissonnat, D. Cohen-Steiner, B. Mourrain, G. Rote, and G. Vegter. Meshing of surfaces. In J.-D. Boissonnat and M. Teillaud, editors, Effective Computational Geometry for Curves and Surfaces. Springer, 2006. Chapter 5. |
| [2] | W. D. Brownawell. Bounds for the degrees in the Nullstellensatz. Annals of Math., 126:577-591, 1987. · Zbl 0641.14001 |
| [3] | W. D. Brownawell. Local Diophantine Nullstellen inequalities. Journal A.M.S., 1:311-322, 1988. · Zbl 0651.10022 |
| [4] | W. D. Brownawell and D. W. Masser. Multiplicity estimates for analytic functions, II. Duke Math. J., 47:273-295, 1980. · Zbl 0461.10027 |
| [5] | B. Buchberger, G. E. Collins, and R. Loos, editors. Computer Algebra. Springer-Verlag, Berlin, 2nd edition, 1983. |
| [6] | C. Burnikel, S. Funke, K. Mehlhorn, S. Schirra, and S. Schmitt. A separation bound for real algebraic expressions. In 9th ESA, volume 2161 of Lecture Notes in Computer Science, pages 254-265. Springer, 2001. To appear, Algorithmica. · Zbl 1006.68960 |
| [7] | M. Burr, S. Choi, B. Galehouse, and C. Yap. Complete subdivision algorithms, II: Isotopic meshing of singular algebraic curves. In Proc. Int’l Symp. Symbolic and Algebraic Computation (ISSAC’08), pages 87-94, 2008. Hagenberg, Austria. Jul 20-23, 2008. 10.1145/1390768.1390783 · Zbl 1487.65024 |
| [8] | J. F. Canny. Generalized characteristic polynomials. J. of Symbolic Computation, 9:241-250, 1990. 10.1016/S0747-7171(08)80012-0 · Zbl 0704.12004 |
| [9] | J.-S. Cheng, X.-S. Gao, and C.-K. Yap. Complete numerical isolation of real zeros in zero-dimensional triangular systems. J. of Symbolic Computation, 2008. In Press. Special Issue of JSC based on ISSAC 2007. Available online at JSC. 10.1016/j.jsc.2008.04.017 |
| [10] | H. Cohen. A Course in Computational Algebraic Number Theory. Springer, 1993. · Zbl 0786.11071 |
| [11] | G. E. Collins, J. R. Johnson, and W. Krandick. Interval arithmetic in cylindrical algebraic decomposition. J. of Symbolic Computation, 34:145-157, 2002. 10.1006/jsco.2002.0547 · Zbl 1007.68210 |
| [12] | Z. Du. Guaranteed Precision for Transcendental and Algebraic Computation made Easy. Ph.D. thesis, New York University, Department of Computer Science, Courant Institute, May 2006. From http://cs.nyu.edu/exact/doc/. |
| [13] | A. Fabri, E. Fogel, B. Gärtner, M. Hoffmann, L. Kettner, S. Pion, M. Teillaud, R. Veltkamp, and M. Yvinec. The CGAL manual. 2003. Release 3.0. |
| [14] | A. Gel’fond. Algebraic and Transcendental Numbers. Dover Publications, 1934. |
| [15] | J. Harris. Algebraic Geometry. Springer-Verlag, New York, 1992. · Zbl 0779.14001 |
| [16] | W. Hodge and D. Pedoe. Methods of Algebraic Geometry, volume 1-3. Cambridge University Press, 1994. · Zbl 0796.14001 |
| [17] | H. Hong. An efficient method for analyzing the topology of plane real algebraic curves. Mathematics and Computers in Simulation, 42:571-582, 1996. 10.1016/S0378-4754(96)00034-1 · Zbl 1037.14503 |
| [18] | V. Karamcheti, C. Li, I. Pechtchanski, and C. Yap. A Core library for robust numerical and geometric computation. In 15th ACM Symp. Computational Geometry {19}, pages 351-359. 10.1145/304893.304989 |
| [19] | V. Karamcheti, C. Li, I. Pechtchanski, and C. Yap. A Core library for robust numerical and geometric computation. In 15th ACM Symp. Computational Geometry, pages 351-359, 1999. 10.1145/304893.304989 |
| [20] | C. Li, S. Pion, and C. Yap. Recent progress in Exact Geometric Computation. J. of Logic and Algebraic Programming, 64(1):85-111, 2004. Special issue on “Practical Development of Exact Real Number Computation”. · Zbl 1080.68106 |
| [21] | C. Li and C. Yap. A new constructive root bound for algebraic expressions. In 12th SODA, pages 496-505, Jan. 2001. · Zbl 0988.65037 |
| [22] | D. W. Masser and G. Wüstholz. Fields of large transcendence degree generated by values of elliptic functions. Inventiones Math., 72:407-464, 1983. · Zbl 0516.10027 |
| [23] | K. Mehlhorn and S. Näher. LEDA: a platform for combinatorial and geometric computing. volume 38, pages 96-102, 1995. 10.1145/204865.204889 |
| [24] | M. Mignotte. Identification of algebraic numbers. J. of Algorithms, 3:197-204, 1982. · Zbl 0498.12004 |
| [25] | Y. V. Nesterenko. Bounds for the characteristic function of a prime ideal. Math. USSR Sbronik, 51:9-32, 1985. Transl. of Mat. Sbornik 123(165) No. 1:11-34, 1984. · Zbl 0579.10030 |
| [26] | Y. V. Nesterenko. On the algebraic independence of algebraic powers of algebraic numbers. Math. USSR Sbornik, 51:429-454, 1985. Transl. of Mat. Sbornik 123(165), No. 4:435-459, 1984. · Zbl 0549.10023 |
| [27] | D. Richardson. How to recognize zero. J. of Symbolic Computation, 24:627-645, 1997. 10.1006/jsco.1997.0157 · Zbl 0917.11062 |
| [28] | R. Seidel and N. Wolpert. On the exact computation of the topology of real algebraic curves. In Proc. 21st ACM Symp. on Comp. Geometry, pages 107-116, 2005. Pisa, Italy. 10.1145/1064092.1064111 · Zbl 1387.68276 |
| [29] | H. H. Stetter. Numerical Polynomial Algebra. SIAM, 2004. · Zbl 1058.65054 |
| [30] | C. K. Yap. Fundamental Problems of Algorithmic Algebra. Oxford University Press, 2000. · Zbl 0999.68261 |
| [31] | C. K. Yap. Robust geometric computation. In J. E. Goodman and J. O’Rourke, editors, Handbook of Discrete and Computational Geometry, chapter 41, pages 927-952. Chapman & Hall/CRC, Boca Raton, FL, 2nd edition, 2004. |
| [32] | C. K. Yap. Complete subdivision algorithms, I: Intersection of Bezier curves. In 22nd ACM Symp. on Comp. Geometry, pages 217-226, July 2006. 10.1145/1137856.1137890 · Zbl 1153.65324 |
| [33] | C. K. Yap and T. Dubé. The exact computation paradigm. In D.-Z. Du and F. K. Hwang, editors, Computing in Euclidean Geometry, pages 452-492. World Scientific Press, Singapore, 2nd edition, 1995. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
