Résolution du problème de l'ellipse et du cercle par l'algorithme de Hörmander

Annette Paugam

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (1990)

  • Volume: 24, Issue: 2, page 161-188
  • ISSN: 0988-3754

How to cite

top

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 24.2 (1990): 161-188. <http://eudml.org/doc/92354>.

@article{Paugam1990,
author = {Paugam, Annette},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {Kahan's problem; Hörmander’s proof of quantifier elimination},
language = {fre},
number = {2},
pages = {161-188},
publisher = {EDP-Sciences},
title = {Résolution du problème de l'ellipse et du cercle par l'algorithme de Hörmander},
url = {http://eudml.org/doc/92354},
volume = {24},
year = {1990},
}

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
PB - EDP-Sciences
VL - 24
IS - 2
SP - 161
EP - 188
LA - fre
KW - Kahan's problem; Hörmander’s proof of quantifier elimination
UR - http://eudml.org/doc/92354
ER -

References

top
  1. 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. Zbl0562.14001MR764184
  2. 2. D. S. ARNON, Towards Mechanical Solution of Kahan Ellipse Problem I, Computer Algebra, Lectures Notes, 162, Springer-Verlag, 1983. Zbl0553.68031MR774802
  3. 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. 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. Zbl0644.68051MR949121
  5. 5. J. BOCHNAK et M. COSTE, M.-F. ROY, Géométrie Algébrique Réelle, Ergebnisse der Mathematik, Springer-Verlag, 1987. Zbl0633.14016MR949442
  6. 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. Zbl0226.65041MR303684
  7. 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. Zbl0495.03016MR728966
  8. 8. G. E. COLLINSet R. LOOS, Real Zeros of Polynomials, Computer Algebra Symbolic and Algebraic Computation, Springer-Verlag, 1982-1983. Zbl0533.68038MR728967
  9. 9. HÖRMANDER, The Analysis of Linear Partiel Differential Operators, tome 2, Springer-Verlag, 1983. Zbl0521.35002
  10. 10. N. JACOBSON, Basic Algebra I, San Francisco, Freeman, 1974. Zbl0284.16001MR356989
  11. 11. W. KAHAN, « Problem=9: an Ellipse Problem », SIGSAM Bulletin of the Assoc. Comp. Math., vol. 9, 1975, p. 11. 
  12. 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. Zbl0401.51010
  13. 13. D. LAZARD, Quantifier Elimination: Optimal Solution for 2 Classical Examples, J. Symbolic Computation, vol. 5, 1988, p. 261-266. Zbl0647.03023MR949122
  14. 14. R. LOOS, Generalized Polynomial Remainder Sequences, Computer Algebra Symbolic and Algebraic Commutation, Springer-Verlag, 1982-1983. Zbl0577.13001MR728969
  15. 15. R. LOOS, Computing in Algebraic Extensions, Computer Algebra Symbolic and Algebraic Computation, Springer-Verlag, 1982-1983. Zbl0576.12001MR728972
  16. 16. M. MIGNOTTE, Solution au problème de Kahan (non publié). 
  17. 17. A. PAUGAM, Comparaison entre 3 algorithmes d'élimination des quantificateurs sur les corps réels clos, Thèse, 1986. 
  18. 18. A. SEIDENBERG, A New Decision Method for Elementary Algebra, Ann. of Math. 60, 1954, p, 365-374. Zbl0056.01804MR63994
  19. 19. A. TARSKI, A Decision Method for Elementary Algebra and Geometry, Prepared for publication by J. C. C. MacKinsey, Berkeley, 1951. Zbl0044.25102

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.