no. 2
Résolution du problème de l'ellipse et du cercle par l'algorithme de Hörmander
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 24 (1990) no. 2, pp. 161-188. 
@article{ITA_1990__24_2_161_0,
     author = {Paugam, Annette},
     title = {R\'esolution du probl\`eme de l'ellipse et du cercle par l'algorithme de {H\"ormander}},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {161--188},
     publisher = {EDP-Sciences},
     volume = {24},
     number = {2},
     year = {1990},
     mrnumber = {1073532},
     zbl = {0701.68055},
     language = {fr},
     url = {http://www.numdam.org/item/ITA_1990__24_2_161_0/}
}
TY  - JOUR
AU  - Paugam, Annette
TI  - Résolution du problème de l'ellipse et du cercle par l'algorithme de Hörmander
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 1990
SP  - 161
EP  - 188
VL  - 24
IS  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/ITA_1990__24_2_161_0/
LA  - fr
ID  - ITA_1990__24_2_161_0
ER  - 
%0 Journal Article
%A Paugam, Annette
%T Résolution du problème de l'ellipse et du cercle par l'algorithme de Hörmander
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 1990
%P 161-188
%V 24
%N 2
%I EDP-Sciences
%U http://www.numdam.org/item/ITA_1990__24_2_161_0/
%G fr
%F ITA_1990__24_2_161_0
Paugam, Annette. Résolution du problème de l'ellipse et du cercle par l'algorithme de Hörmander. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 24 (1990) no. 2, pp. 161-188. http://www.numdam.org/item/ITA_1990__24_2_161_0/

1. D. S. Arnon, G. E. Collins et S. Mccallum, Cylindrical Algebraic Decomposition I and II: the Basic Algorithm, Siam J. Comput., vol. 13, n° 4, nov. 84, p.865-889. | MR

2. D. S. Arnon, Towards Mechanical Solution of Kahan Ellipse Problem I, Computer Algebra, Lectures Notes, 162, Springer-Verlag, 1983. | MR | Zbl

3. D. S. Arnon, On Mechanical Quantifier Elimination For Elementary. Algebra and Geometry: Solution of a non Trivial Problem, Eurocal 85, Lectures Notes 204, p. 270-271, Springer-Verlag, 1985.

4. D. S. Arnon et M. Mignotte, On Mechanical Quantifier Elimination For Elementary Algebra and Geometry, J. Symbolic Computation, Vol. 5, 1988, p. 237-259. | MR | Zbl

5. J. Bochnak et M. Coste, M.-F. Roy, Géométrie Algébrique Réelle, Ergebnisse der Mathematik, Springer-Verlag, 1987. | MR | Zbl

6. W. S. Brown et J.-F. Traub, On Euclid's Algorithm and the Theory of Subresultants, J. Assoc. Comput. Math., vol. 18, n° 4, 1971, p. 505-514. | MR | Zbl

7. G. E. Collins, Quantifier Elimination for Real Closed Fields: a Guide to the Litterature, Computer Algebra Symbolic and Algebraic Computation, Springer-Verlag, 1982-1983. | MR | Zbl

8. G. E. Collinset R. Loos, Real Zeros of Polynomials, Computer Algebra Symbolic and Algebraic Computation, Springer-Verlag, 1982-1983. | MR | Zbl

9. Hörmander , The Analysis of Linear Partiel Differential Operators, tome 2, Springer-Verlag, 1983.

10. N. Jacobson, Basic Algebra I, San Francisco, Freeman, 1974. | MR | Zbl

11. W. Kahan, « Problem=9: an Ellipse Problem », SIGSAM Bulletin of the Assoc. Comp. Math., vol. 9, 1975, p. 11.

12. M. Lauer, A solution to Kahan's problem (SIGSAM problem n° 9); SIGSAM Bulletin of the Ass. Com. Math., vol. 11, 1977, p. 16-20. | Zbl

13. D. Lazard, Quantifier Elimination: Optimal Solution for 2 Classical Examples, J. Symbolic Computation, vol. 5, 1988, p. 261-266. | MR | Zbl

14. R. Loos, Generalized Polynomial Remainder Sequences, Computer Algebra Symbolic and Algebraic Commutation, Springer-Verlag, 1982-1983. | MR | Zbl

15. R. Loos, Computing in Algebraic Extensions, Computer Algebra Symbolic and Algebraic Computation, Springer-Verlag, 1982-1983. | MR | Zbl

16. M. Mignotte, Solution au problème de Kahan (non publié).

17. A. Paugam, Comparaison entre 3 algorithmes d'élimination des quantificateurs sur les corps réels clos, Thèse, 1986.

18. A. Seidenberg, A New Decision Method for Elementary Algebra, Ann. of Math. 60, 1954, p, 365-374. | MR | Zbl

19. A. Tarski, A Decision Method for Elementary Algebra and Geometry, Prepared for publication by J. C. C. MacKinsey, Berkeley, 1951. | Zbl