Equality in computer algebra and beyond

Journal of Symbolic Computation

Volumn 34, Issue 4, 2002, Pages 259-270

  Davenport, James H ^a  

^a University of Bath   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036799942     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.2002.0551     Document Type: Article

References (41)

1. Abramowitz, M., Stegun, I. (1964). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, US Government Printing Office, 10th Printing December 1972.
2. Boehm, H.-J., Cartwright, R., Riggle, M., O'Donnell, M. J. (1986). Exact real arithmetic: a case study in higher order programming. In Proceedings of the LISP & Functional Programming, pp. 162-173. New York, ACM.
3. Bogen, R. A. et al. (1977). MACSYMA Reference Manual, version 9, Cambridge, MA, MIT Laboratory for Computer Science.
4. Bosma, W., Cannon, J., Matthews, G. (1994). Programming with algebraic structures: design of the Magma language. In Proceedings of the ISSAC 1994, pp. 52-57. New York, ACM.
5. Bosma, W., Cannon, J., Playoust, C. (1997). The Magma algebra system. I: the user language. J. Symb. Comput., 24, 235-265. Zbl. 898.68039.
6. Brown, W. S. (1969). Rational exponential expressions, and a conjecture concerning π and e. Am. Math. Monthly, 76, 28-34.
7. Caprotti, O., Oostdijk, M. (2001). Formal and efficient primality proofs by use of computer algebra oracles. J. Symb. Comput., 32, 55-70.
8. Char, B. W., Geddes, K. O., Gentleman, M. W., Gonnet, G. H. (1983). The design of MAPLE: a compact, portable and powerful computer algebra system. In Proceedings of the EUROCAL 83, volume 162 of Springer Lecture Notes in Computer Science, pp. 101-115. Springer.
9. Corless, R. M., Davenport, J. H., Jeffrey, D. J., Watt, S. M. (2000). According to Abramowitz and Stegun. ACM SIGSAM Bull., 30, 58-65.
10. Damgård, I., Landrock, P. (1993). Improved bounds for the Rabin primality test. In Ganley, M. ed., Proceedings of the 3rd IMA Conference on Coding and Cryptography, pp. 117-128. OUP, MR 95d:11171.
11. Davenport, J. H. (2000). Abstract data types in computer algebra. In Nielsen, M., Rovan, B. eds, Proceedings of the MFCS 2000, volume 1893 of Springer Lecture Notes in Computer Science, pp. 21-35. Springer.
12. Davenport, J. H., Fischer, H.-C. (1990). Manipulation of expressions. In Wallis, P. J. L. ed., Improving Floating-Point Programming, pp. 149-167. Wiley.
13. Davenport, J. H., Trager, B. M. (1990). Scratchpad's view of algebra I: basic commutative algebra. In Miola, A. ed., Proceedings of the DISCO '90, volume 429 of Springer Lecture Notes in Computer Science, pp. 40-54. Springer, A revised version is in Axiom Technical Report. ATR/1, Nag Ltd., December 1992.
14. Davenport, J. H., Siret, Y., Tournier, E. (1993). Computer Algebra, 2nd edn, London, Academic Press.
15. Dunstan, M. N. (1999). Larch/Aldor-a Larch BISL for AXIOM and Aldor. Ph.D. Thesis, University of St. Andrews.
16. Dunstan, M., Kelsey, T., Linton, S., Martin, U. (1998). Lightweight formal methods for computer algebra methods. In Gloor, O. ed., Proceedings of the ISSAC 1998, pp. 80-87. New York, ACM.
17. Dunstan, M., Kelsey, T., Linton, S., Martin, U. (1999). Formal methods for extensions to CAS. In Wing, J. W. J., Woodcock, J., Davies, J. eds, FM '99, volume II, volume 1709 of Springer Lecture Notes in Computer Science, pp. 1758-1777. Springer.
18. Edalat, A., Potts, P. J., Escardó, M. H. (1997). Semantics of exact computer arithmetic. In Proceedings of the 12th IEEE Symp. Logic in Computer Science, pp. 248-257. IEEE Computer Society Press.
19. Freeman, T., Imirzian, G., Kaltofen, E. (1986). A system for manipulating polynomials given by straight-line programs. In Proceedings of the SYMSAC 86, pp. 169-175. New York, ACM.
20. Gonnet, G. H. (1984). Determining equivalence of expressions in random polynomial time. In Proceedings of the 16th Symp. Theory of Computing, pp. 334-341. New York, ACM.
21. Gosper, R. W. Jr (1972). Item 101b: continued fraction arithmetic. HAKMEM, M.I.T. A.I. Memo 232. 39-44.
22. Guttag, J. V., Horning, J. J. (1993). Larch: languages and tools for formal specification, Texts and Monographs in Computer Science, Springer.
23. Harrington, S. J. (1980). Infinite power series. Softw., Practice Experience, 10, 835-848.
24. Hearn, A. C. (1991). REDUCE User's Manual, version 3.4, RAND Corporation Publication CP-78.
25. Hur, N. (2001). A symbolic and numeric approach to real number computation. Ph.D. Thesis, University of Bath.
26. Hur, N., Davenport, J. H. (2000). An exact real algebraic arithmetic with equality determination. In Traverso, C. ed., Proceedings of the ISSAC 2000, pp. 169-174.
27. IBM Corporation (1984). LISP/VM Reference Manual, SH20-6477-0, IBM.
28. Jenks, R. D., Sutor, R. S. (1992). AXIOM: The Scientific Computation System, New York, Springer.
29. Kaltofen, E., Trager, B. M. (1990). Computing with polynomials given by black boxes for their evaluations: greatest common divisors, factorization, separation of numerators and denominators. J. Symb. Comput., 9, 301-320.
30. Kelsey, T. W. (2000). Formal methods and computer algebra: a Larch specification of Axiom categories and functors. Ph.D. Thesis, St. Andrews.
31. Klüners, J., Malle, G. (2000). Explicit Galois realization of transitive groups of degree up to 15. J. Symb. Comput., 30, 675-716.
32. Ménissier-Morain, V. (1994). Arithmétique exacte, conception, algorithmique et performances d'une implémentation informatique en précision arbitraire. Thèse, Université Paris 7.
33. Naylor, W. A. (2000). Polynomial GCD using straight line program representation. Ph.D. Thesis, University of Bath.
34. Norman, A. C. (1975). Computing with formal power series. ACM Trans. Math. Softw., 1, 346-356.
35. Rabin, M. O. (1980). Probabilistic algorithm for testing primality. J. Number Theory, 12, 128-138.
36. Rioboo, R. (1992). Real algebraic closure of an ordered field, implementation in Axiom. In Proceedings of the ISSAC '92, pp. 206-215. New York, ACM.
37. Rotman, J. J. (1995). An Introduction to the Theory of Groups, volume 148 of Springer Graduate Texts in Mathematics, Springer.
38. Schönert, M. (together with, Bessche, H. U. et al.), (1997). updated by S. A. Linton, GAP: Groups Algorithms and Programming v. 3.4.4. Distributed Electronically with GAP, 18 April 1997.
39. Steel, A. (2002). A new scheme for computing with algebraically closed fields. In Proceedings of the Algorithmic Number Theory, to appear.
40. Steele, G. L. Jr (1990). Common LISP: The Language, 2nd edn, Digital Press.
41. Vuillemin, J. E. (1990). Exact real computer arithmetic with continued fractions. IEEE Trans. Comput., 39, 1087-1105.