A Generic Projection Operator for Partial Cylindrical Algebraic Decomposition

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

Volumn , Issue , 2003, Pages 240-247

  Seidl, Andreas ^a   Sturm, Thomas ^a  

^a UNIVERSITY OF PASSAU   (Germany)

Author keywords

Partial CAD; Projection Operator; REDLOG

Indexed keywords

ALGEBRA; ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; FORMAL LOGIC; MATHEMATICAL OPERATORS;

PARTIAL CAD; PROJECTION OPERATORS; REDLOG;

COMPUTER AIDED DESIGN;

EID: 1542270104     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/860854.860903     Document Type: Conference Paper

References (23)

1. ARNON, D. S., COLLINS, G. E., AND MCCALLUM, S. Cylindrical algebraic decomposition I: The basic algorithm. SIAM Journal on Computing 13, 4 (Nov. 1984), 865-877.
2. BROWN, C. W. Guaranteed solution formula construction. In Proceedings of the ISSAC 99, S. Dooley, Ed. ACM Press, New York, NY, July 1999, pp. 137-144.
3. BROWN, C. W. Improved projection for cylindrical algebraic decomposition. Journal of Symbolic Computation 32, 5 (Nov. 2001), 447-465.
4. CHOU, S.-C. Mechanical Geometry Theorem Proving. Mathematics and its applications. D. Reidel Publishing Company, Dordrecht, Boston, Lancaster, Tokyo, 1988.
5. COLLINS, G. E. Quantifier elimination for the elementary theory of real closed fields by cylindrical algebraic decomposition. In Automata Theory and Formal Languages. 2nd GI Conference, H. Brakhage, Ed., vol. 33 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, Heidelberg, New York, 1975, pp. 134-183.
6. COLLINS, G. E., AND HONG, H. Partial cylindrical algebraic decomposition for quantifier elimination. Journal of Symbolic Computation 12, 3 (Sept. 1991), 299-328.
7. DOLZMANN, A., AND STURM, T. Redlog: Computer algebra meets computer logic. ACM SIGSAM Bulletin 31, 2 (June 1997), 2-9.
8. DOLZMANN, A., AND STURM, T. Simplification of quantifier-free formulae over ordered fields. Journal of Symbolic Computation 24, 1 (Aug. 1997), 209-231.
9. DOLZMANN, A., STURM, T., AND WEISPFENNING, V. A new approach for automatic theorem proving in real geometry. Journal of Automated Reasoning 21, 3 (1998), 357-380.
10. HENNIG, E. Rechnergestützte Dimensionierung analoger Schaltungen auf der Basis symbolischer Analyseverfahren. Tech, rep., Zentrum für Mikroelektronik, Universität Kaiserslautern, Dec. 1995. Annual report on a research project.
11. HENNIG, E., AND HALFMANN, T. Analog Insydes tutorial. ITWM. Kaiserslautern, Germany, 1998.
12. HONG, H. An improvement of the projection operator in cylindrical algebraic decomposition. In Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 90), S. Watanabe and M. Nagata, Eds. ACM Press, New York, Aug. 1990, pp. 261-264.
13. HONG, H. Simple solution formula construction in cylindrical algebraic decomposition based quantifier elimination. In Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 92), P. S. Wang, Ed. ACM Press, New York, July 1992, pp. 177-188.
14. HONG, H. Quantifier elimination for formulas constrained by quadratic equations via slope resultants. THE Computer Journal 36, 5 (1993), 440-449. Special issue on computational quantifier elimination.
15. LAZARD, D. Quantifier elimination: Optimal solution for two classical examples. Journal of Symbolic Computation 5, 1&2 (Feb. 1988), 261-266.
16. MCCALLUM, S. Solving polynomial strict inequalities using cylindrical algebraic decomposition. THE Computer Journal 36, 5 (1993), 432-438. Special issue on computational quantifier elimination.
17. MCCALLUM, S. An improved projection operation for cylindrical algebraic decomposition. In Quantifier Elimination and Cylindrical Algebraic Decomposition, B. F. Caviness and J. R. Johnson, Eds. Springer-Verlag, Wien, 1998, pp. 242-268.
18. SEIDL, A. An efficient representation of algebraic numbers and polynomials for cylindrical algebraic decomposition (extendend abstract). In Proceedings of the 8th Rhine Workshop on Computer Algebra (Mannheim, Germany, 2002), pp. 167-172.
19. STRZEBOŃSKI, A. Solving systems of strict polynomial inequalities. Journal of Symbolic Computation 29, 3 (Mar. 2000), 471-480.
20. STURM, T. Real Quantifier Elimination in Geometry. Doctoral dissertation, Department of Mathematics and Computer Science. University of Passau, Germany, D-94030 Passau, Germany, Dec. 1999.
21. STURM, T. Reasoning over networks by symbolic methods. Applicable Algebra in Engineering, Communication and Computing 10, 1 (Sept. 1999), 79-96.
22. WEISPFENNING, V. The complexity of linear problems in fields. Journal of Symbolic Computation 5, 1&2 (Feb.-Apr. 1988), 3-27.
23. WEISPFENNING, V. Quantifier elimination for real algebra - the quadratic case and beyond. Applicable Algebra in Engineering Communication and Computing 8, 2 (Feb. 1997), 85-101.