A poly-algorithmic approach to simplifying elementary functions

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

Volumn , Issue , 2004, Pages 27-34

  Beaumont, James C ^a   Bradford, Russell J ^a   Davenport, James H ^a   Phisanbut, Nalina ^a  

^a University of Bath   (United Kingdom)

Author keywords

Branch Cuts; Simplification

Indexed keywords

ALGORITHMS; FUNCTIONS; MATHEMATICAL MODELS; PROBLEM SOLVING;

BRANCH CUTS; COMPUTER ALGEBRA; FUNDAMENTAL PROBLEM; SIMPLIFICATION;

ALGEBRA;

EID: 27644494190     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1005285.1005292     Document Type: Conference Paper

References (22)

1. BEAUMONT, J., BRADFORD, R., AND DAVENPORT, J. Towards Better Simplification of Elementary Functions. Pre-print, University of Bath, England. (2002). http://www.cs.bath.ac.uk/~cspnp/simplification/mvfunc.html
2. BEAUMONT, J., BRADFORD, R., AND DAVENPORT, J. Better Simplification of Elementary Functions Through Power Series. In Proceedings ISSAC 2003 (2003), J.R. Sendra, Ed., ACM, New York, pp. 30-36.
3. BRADFORD, R., CORLESS, R., DAVENPORT, J., JEFFREY, D., AND WATT, S. Reasoning about the Elementary Functions of Complex Analysis. Ann. Mathematics and Artificial Intelligence 36, (2002).
4. BRADFORD, R., AND DAVENPORT, J. Towards Better Simplification of Elementary Functions. In Proceedings ISSAC 2002 (2002), T. Mora, Ed., ACM, New York, pp. 15-22.
5. BROWN, C. W., Simple CAD Construction and its Applications. J. Symbolic Computation, (31):521-547, 2001.
6. COLLINS, G. Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition. In Proceedings 2nd. GI Conference Automata Theory & Formal Languages (1975), vol. 33 of LNCS, Springer-Verlag, pp. 134-183.
7. G. E. COLLINS AND H. HONG, Partial Cylindrical Algebraic Decomposition for Quantifier Elimination. J. Symbolic Computation, 12(3):299-328, 1991.
8. CORLESS, R., DAVENPORT, J., JEFFREY, D., AND WATT, S. According to Abramowitz and Stegun. SIGSAM Bulletin 34, 2 (2000), 58-65.
9. CORLESS, R. M. & JEFFREY, D. J. The Unwinding Number. SIGSAM Bulletin 30 (1996) 2, issue 116, pp. 28-35.
10. DAVENPORT, J., AND HEINTZ, J. Real Quantifier Elimination is Doubly Exponential. J. Symbolic Computation 5, (1988), 29-35.
11. FATEMAN, R. J. & DINGLE, A. Branch Cuts in Computer Algebra. In Proc. ISSAC 1994, ACM Press, New York, 1994, pp. 250-257.
12. GRIGORIEV, D. YU. & VOROBJOV, N. N. JR. Counting connected components of a semi-algebraic set in subexponential time. Computational Complexity 2 (1992) pp. 133-184.
13. GABRIELOV, A., AND VOROBJOV, N. Complexity of cylindrical decompositions of sub-Pfaffian sets. J. Pure Appl. Algebra 164 (2001), 179-197.
14. HENRICI, P. Applied and Computational Complex Analysis. Vol.1, Wiley and Sons, (1974).
15. KAHAN, W. Branch Cuts for Complex Elementary Functions. The State of Art in Numerical Analysis (1987), 165-211.
16. MANSFIELD, E. L. Differential Gröbner Bases. Ph.D. Thesis, University of Sydney, 1992.
17. MOSES, J. Algebraic Simplification, a Guide for the Perplexed. In Advances in Computational Mathematics 14, no.8 (1971).
18. PATTON, C. M. A Representation of Branch-Cut Information SIGSAM Bulletin 116(1996), pp. 21-24.
19. H. HONG et al. Quantifier Elimination by Partial Cylindrical Algebraic Decomposition. http://www.cs.usna.edu/~qepcad/B/QEPCAD.html
20. RICHARDSON, D. Some Unsolvable Problems Involving Elementary Functions of a Real Variable. Journal of Symbolic Logic 33(1968), pp. 514-520.
21. RICHARDSON, D. How to Recognize Zero. In Journal of Symbolic Computation (1994), 24(6), 627-646.
22. VAN DER HOEVEN, J. A new Zero-test for Formal Power Series. In Proceedings ISSAC 2002 (2002), T. Mora, Ed., ACM, New York, pp. 117-122.