Efficient projection orders for CAD

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Volumn , Issue , 2004, Pages 111-115

  Dolzmann, Andreas ^a   Seidl, Andreas ^b   Sturm, Thomas ^a  

^a UNIVERSITY OF PASSAU   (Germany)

^b UNIVERSITY OF CANTABRIA   (Spain)

Author keywords

Partial CAD; Projection Operator; REDLOG

Indexed keywords

ALGEBRA; ALGORITHMS; COMPUTATIONAL METHODS; DATA ACQUISITION; STATISTICAL METHODS;

PARTIAL CAD; PROJECTION OPERATOR; PROJECTION SETS; REDLOG;

COMPUTER AIDED DESIGN;

EID: 9444281527     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1005285.1005303     Document Type: Conference Paper

References (16)

1. D. S. Arnon, G. E. Collins, and S. McCallum. Cylindrical algebraic decomposition I: The basic algorithm. SIAM Journal on Computing, 13(4):865-877, Nov. 1984.
2. D. S. Arnon, G. E. Collins, and S. McCallum. Cylindrical algebraic decomposition II: An adjacency algorithm for the plane. SIAM Journal on Computing, 13(4):878-889, Nov. 1984.
3. C. W. Brown. Improved projection for cylindrical algebraic decomposition. Journal of Symbolic Computation, 32(5):447-465, Nov. 2001.
4. G. E. Collins. Quantifier elimination for the elementary theory of rcal closed fields by cylindrical algebraic decomposition. In H. Brakhage, editor, Automata Theory and Formal Languages. 2nd GI Conference, volume 33 of Lecture Notes in Computer Science, pages 134-183. Springer-Verlag, Berlin, Heidelberg, New York, 1975.
5. G. E. Collins and H. Hong. Partial cylindrical algebraic decomposition for quantifier elimination. Journal of Symbolic Computation, 12(3):299-328, Sept. 1991.
6. D. Cox, J. Little, and D. O'Shea. Ideals, Varieties and Algorithms. Undergraduate Texts in Mathematics. Springer-Verlag, New York, Berlin, Heidelberg, 1992.
7. A. Dolzmann and T. Sturm. Redlog: Computer algebra meets computer logic. ACM SIGSAM Bulletin, 31(2):2-9, June 1997.
8. H. Hong, An improvement of the projection operator in cylindrical algebraic decomposition. In S. Watanabe and M. Nagata, editors, Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 90), pages 261-264. ACM Press, New York, Aug. 1990.
9. W. Kahan. An ellipse problem. ACM SIGSAM Bulletin, 9(3):11, Aug. 1975. SIGSAM Problem #9.
10. D. Lazard. Quantifier elimination: Optimal solution for two classical examples. Journal of Symbolic Computation, 5(1&2):261-266, Feb. 1988.
11. D. Lazard. An improved projection for cylindrical algebraic decomposition. In C. L. Bajaj, editor, Algebraic Geometry and its Applications: Collections of Papers from Shreeram S. Abhyankar's 60th Birthday Conference. Springer, Berlin, 1994.
12. S. McCallum. An Improved Projection Operation for Cylindrical Algebraic Decomposition. Ph.D. dissertation, Computer Sciences Department, University of Wisconsin, Madison, 1984.
13. S. McCallum. Solving polynomial strict inequalities using cylindrical algebraic decomposition. Technical Report 87-25.0, RISC, Johannes Kepler University, Linz, Austria, 1987.
14. S. McCallum. An improved projection operation for cylindrical algebraic decomposition of three-dimensional space. Journal of Symbolic Computation, 5(1-2):141-161, Feb.-Apr. 1988.
15. J. T. Schwartz and M. Sharir. On the piano movers' problem. II. General techniques for computing topological properties of real algebraic manifolds. Advances in Applied Mathematics, 4:298-351, 1983.
16. A. Seidl and T. Sturm. A generic projection operator for partial cylindrical algebraic decomposition. In R. Sondra, editor, Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation (ISSAC 03), Philadelphia, Pennsylvania, pages 240-247. ACM Press, New York, NY, 2003.