Semi-algebraic complexity of quotients and sign determination of remainders

Journal of Complexity

Volumn 12, Issue 4, 1996, Pages 545-571

  Lickteig, Thomas ^a   Marie Françoise, Roy ^b  

^a UNIVERSITY OF BONN   (Germany)

^b UNIVERSITÉ DE RENNES 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030524809     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcom.1996.0033     Document Type: Article

References (22)

1. [BS] BAUR, W., AND STRASSEN, V. (1983), The complexity of partial derivatives, Theoret. Comput. Sci. 22, 317-330.
2. [Be] BECKER, E. (1986), On the real spectrum of a ring and its applications to semialgebraic geometry, Bull. Am. Math. Soc. (N.S.) 15, 19-60.
3. [BCR] BOCHNAK, J., COSTE, M., AND ROY, M.-F. (1987), Géométrie algébrique réelle, "Ergebnisse der Mathematik und ihrer Grenzgebiete, 3," Vol. 12, Springer-Verlag, New York/Berlin.
4. [Br] BRUMFIEL, G. W. (1984), Witt rings and K-theory, Rocky Mountain J. Math. 17, 733-765.
5. [CR] COSTE, M., AND ROY, M.-F. (1992), La Topologie du Spectre Réel, Contemporary Math. 8, 27-59.
6. [CL] CUCKER, F., AND LICKTEIG, T. (to appear), Nash trees and Nash complexity, in "Proceedings, Mathematics of Numerical Analysis: Real Number Algorithms, Park City, 1995.
7. [KS] KNEBUSCH, M., AND SCHEIDERER, C. (1989), Einführung in die reelle Algebra, in "Vieweg-Studium 63: Aufbaukurs Mathematik, Vieweg."
8. [Kn] KNUTH, D. E. (1970), The analysis of algorithms, in "Proceedings, ICM Nice, Vol. 3, pp. 269-274.
9. [Li] LICKTEIG, T. (1996), Semi-algebraic decision complexity, the real spectrum, and degree, J. Pure Appl. Algebra 110(2), 131-184.
10. [LM] LICKTEIG, T., AND MEER, K. (to appear), Semi-algebraic complexity-Additive complexity of matrix computational tasks, Festschrift on the occasion of Shmuel Winograd's 60th birthday, J. Complexity. submitted (1996).
11. [Lin] LINNAINMAA, S. (1976), Taylor expansion of the accumulated rounding error, BIT 16, 146-160.
12. [Ma] MATSUMURA, H. (1986), Commutative ring theory, in "Cambridge Studies in Advanced Mathematics," Vol. 8, Cambridge Univ. Press, Cambridge, UK.
13. [MO] MOENCK, R. T. (1973), Fast computation of GCDs, in "Proceedings, STOC'73," pp. 142-151.
14. [RO] ROY, M.-F. (1982), Faisceau structural sur le spectre réel et fonctions de Nash, in "Géométrie algébrique réelle et formes quadratiques," pp. 406-432, Lecture Notes Mathematics, Vol. 959, Springer-Verlag, New York/Berlin.
15. [RO1] ROY, M.-F. (to appear), Basic algorithms in real algebraic geometry: From Sturm's theorem to the existential theory of reals, in "Lectures on Real Geometry in memoriam of Mario Raimondo," de Gruyter Expositions in Mathematics.
16. [RV] ROY, M.-F., AND VOROBJOV, N. (to appear), Computing the complexification of a semi-algebraic set," ISSAC 1996.
17. [Schö] SCHöNHAGE, A. (1971), Schnelle Berechnung von Kettenbruchentwicklungen, Acta Inform. 1, 139-144.
18. [Schu] SCHUSTER, P. (1980), "Interpolation und Kettenbruchentwicklung. Die Komplexität einiger Berechnungsaufgaben," Dissertation, Universität Zürich.
19. [Schw] SCHWARTZ, N. (1989), The basic theory of real closed spaces, Mem. Am. Math. Soc. 397.
20. [Str] STRASSEN, V. (1973), Die Berechnungskomplexität von elementarsymmetrischen Funktionen und Interpolationskoeffizienten, Numer. Math. 20(3), 238-251.
21. [St] STRASSEN, V. (1983), The computational complexity of continued fractions, SIAM J. Comput. 12(1), 1-27.
22. [Y] YAO, A. C. C. (1994), Decision tree complexity and Betti numbers, in "Proceedings, STOC'94," pp. 615-624.