Generic asymptotic expansions

Applicable Algebra in Engineering, Communications and Computing

Volumn 9, Issue 1, 1998, Pages 25-44

  Van Der Hoeven, Joris ^a  

^a ÉCOLE POLYTECHNIQUE   (France)

Author keywords

Algorithm; Asymptotic expansion; Exp log function; Genericity

Indexed keywords

COMPUTATIONAL COMPLEXITY; FUNCTIONS; PROBLEM SOLVING;

ASYMPTOTIC EXPANSIONS; SCHANUEL'S CONJECTURE;

ALGORITHMS;

EID: 0031678151     PISSN: 09381279     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002000050094     Document Type: Article

References (30)

1. 3/2) algorithms for composition and reversion of power series. In J. F Traub, (ed), Analytic Computational Complexity, 1975. Proc. of symposium on analytic computational complexity held by Carnegie-Mellon University
2. Brent, R. P., Kung, H. T.: Fast algorithms for manipulating formal power series. Journal of the ACM 25, 581-595 (1978)
3. Collins, G. E.: Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In Proc. 2-nd conf. on automata theory and formal languages, Vol. 33 of Lect. Notes in Comput. Sci., pp 134-183. Berlin Heidelberg New York: Springer, 1975
4. Dahn B. I., Göring P.: Notes on exponential-logarithmic terms. Fundam. Math. 127, 45-50 (1986)
5. Della Dora, J., Dicrescenzo, C., Duval, D.: A new method for computing in algebraic number fields. In G. Goos and J. Hartmanis (eds) Eurocal'85 (2), Vol. 174 of Lect. Notes in Comput. Sci., pp 321-326. Berlin Heidelberg New York Springer, 1985
6. Denef, J., Lipshitz, L.: Decision problems for differential equations. J. Symb. Log. 55 (3), 941-950 (1989)
7. Écalle, J.: Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac. Hermann, collection: Actualités mathématiques, 1992
8. Geddes, K. O., Gonnet, G. H.: A new algorithm for computing symbolic limits using hierarchical series. In Proc. ISSAC '88, Vol. 358 of Lect. Notes Comput. Sci., pp 490-495. Berlin Heidelberg New York: Springer, 1988
9. Gomez-Diaz, T.: Quelques applications de l'évaluation dynamique. PhD thesis, Univ. of Limoges, France, 1994
10. Gonnet, G. H., Gruntz, D.: Limit computation in computer algebra. Technical Report 187, ETH, Zürich, 1992
11. Hardy, G. H.: Orders of infinity. Cambridge University Press, 1910
12. Hardy, G. H.: Properties of logarithmico-exponential functions. Proc. Lond. Math. Soc., 10 (2), 54-90 (1911)
13. van der Hoeven, J.: General algorithms in asymptotics I: Gonnet and Gruntz' algorithm. Technical Report LIX/RR/94/10, LIX, École polytechnique, France, 1994
14. van der Hoeven, J.: Outils effectifs en asymptotique et applications. Technical Report LIX/RR/94/09, LIX, École polytechnique, France, 1994
15. van der Hoeven, J.: Automatic numerical expansions. In J.-C. Bajard, D. Michelucci, J.-M. Moreau, J.-M. Müller (eds) Proc. of the conference "Real numbers and computers", Saint-Étienne, France, pp 261-274, 1995
16. van der Hoeven, J.: Automatic asymptotics. PhD thesis, École polytechnique, France, 1997
17. van der Hoeven, J.: Lazy multiplication of formal power series. In W. W. Küchlin, (ed) Proc. ISSAC '97 pp 17-20, Maui. Hawaii, July 1997
18. Knuth, D. E.: The art of computer programming, Vol. 2: Seminumerical algorithms. Reading, MA: Addision-Wesley, 2-nd edn, 1981
19. König. D.: Theorie der endlichen und unendlichen Graphen. New York: Chelsea, 1950
20. Péladan-Germa, A.: Testing identities of series defined by algebraic partial differential equations. In G. Cohen, M. Giusti, T. Mora, (eds.) Proc. of AAECC-11, Vol. 948 of Lect. Notes Comput. Sci., pp 393-407. Paris: Springer, 1995
21. Péladan-Germa, A.: Tests effectifs de nullité dans des extensions d'anneaux différentiels. PhD thesis, Gage, École Polytechnique, Palaiseau, France, 1997
22. Richardson, D.: The elementary constant problem. In Proc. ISSAC '92, pp 108-116, 1992
23. Richardson, D.: A simplified method for recognizing zero among elementary constants. In Proc. ISSAC '95, pp 104-109, 1995. See also "How to recognize zero", accepted for publication in JSC
24. Richardson, D.: A simplified method for recognizing zero among elementary constants. In Proc. ISSAC '95, pp 104-109, 1995. See also "How to recognize zero", accepted for publication in JSC
25. Richardson, D., Salvy, B., Shackell, J., van der Hoeven, J.: Expansions of exp-log functions. In Y. N. Lakshman (ed.) Proc. ISSAC '96, pp 309-313. Zürich, Switzerland, July 1996
26. Risch, R. H.: Algebraic properties of elementary functions in analysis. Am. J. Math. 4, 743-759 (1975)
27. Salvy, B.: Asymptotique automatique et fonctions génératices. PhD thesis, École Polytechnique, France, 1991
28. Shackell, J.: A differential-equations approach to functional equivalence. In Proc. ISSAC '89, pp 7-10, Portland, Oregon, A.C.M., New York, 1989
29. Shackell, J.: Growth estimates for exp-log functions. J. Symb. Comput. 10, 611-632 (1990)
30. Shackell, J.: Limits of Liouvillian functions. Proc. Lond. Math. Soc. 72, 124-156, 1996. Appeared in 1991 as a technical report at the Univ. of Kent, Canterbury.