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Cet article présente la correspondance entre les groupes finis et les resolvantes de Lagrange et montre comment elle est utilisée pour les problèmes de Galois direct et inverse.
Valibouze, Annick 1
@article{RFM_1997__2__45_0, author = {Valibouze, Annick}, title = {Theorie de {Galois} constructive}, journal = {Femmes & math}, pages = {45--55}, publisher = {Association femmes et math\'ematiques}, volume = {2}, year = {1997}, language = {fr}, url = {http://geodesic.mathdoc.fr/item/RFM_1997__2__45_0/} }
Valibouze, Annick. Theorie de Galois constructive. Femmes & math, Tome 2 (1997), pp. 45-55. http://geodesic.mathdoc.fr/item/RFM_1997__2__45_0/
[1] H. Anai, M. Noro, K. Yokoyama, Computation of the splitting field and the Galois groups of polynomials, présentation orale à MEGA94 | Zbl
[2] J.-M. Arnaudiès, A. Valibouze, Lagrange resolvents, MEGA 96,à paraitre au J.P.A.A., eds. A. Cohen et M.-F. Roy (Rapport interne LITP 93-61). | MR
[3] J.-M. Arnaudiès, A. Valibouze Groupes de Galois de polynômes en degré 4 à 11, Rapports internes LITP 94.25, 94.30, 94.48, 94.49, 94.50.
[4] AXIOM The Scientific Computation System, R. Jenks, R. Sutor, Springer-Verlag 1992,ISBN 0-387-97855-0 | MR | Zbl
[5] E.H. Berwick On soluble sextic equations, Proc. London Math. Soc. (2) 29, 1-28 (1929). | MR | JFM
[6] G. Butler, J. McKay, The transitive groups of degree up to 11, Comm. Algebra 11, 863-911 (1983). | MR | Zbl
[7] D. Casperson, J. McKay, Symmetric functions, -sets, and Galois groups, à paraitre dans Math. Comp.(1994). | MR | Zbl
[8] A. Cayley, On a new auxiliary equation in the theory of equation of the fifth order, Philosophical Transactions of the Royal Society of London, CLL (1861).
[9] C. J. Williamson, On algebraic construction of tri-Diagonal matrices, soumis aux Proceedings of CNTA-4 (Canadian Number Theory Association) (1994).
[10] H. Cohen, A Course in Computational Algebraic Number Theory, Graduate Texts in Mathematics 138, Springer Verlag, 1993. | MR | Zbl
[11] A. Colin, Théorie de Galois effective et implantation en AXIOM, Mémoire de DEA
[12] A. Colin, Formal Computation of Galois groups using relative resolvent poly-nomials, AAECC’95 (Paris, Juillet 1995), LNCS 948. | MR
[13] H.O. Foulkes, The resolvents of an equation of seventh degree, Quart. J. Math. Oxford Ser. (2), 9-19 (1931). | Zbl
[14] K. Girstmair, On invariant polynomials and their application in field theory Maths of Comp., vol. 48, no 178, 1987 (781-797). | MR | Zbl
[15] E. Galois, Oeuvres Mathématiques, publiées sous les auspices de la SMF, Gauthier-Villars, 1897. | JFM
[16] G.A.P. Groups, Algorithms and Programming, Martin Schönert and others, Lehrstuhl D für Mathematik, Rheinisch-Westfälische Technische Hochschule, Aachen, 93, gap@samson.math.rwth-aachen.de
[17] I. Gil-Delessalle, A. Valibouze, Galois inverse problem for some subgroups of degree 12, prépublication LITP 1996.
[18] J.-C. Lagarios, A.M. Odlyzko, Effective versions of the Chebotarev density theorem, Algebraic Number Fields (L-functions and Galois Theory), A. Frolich, ed., Academic Press, 1977, pp. 409-464. | MR | Zbl
[19] J.-L. Lagrange, Réflexions sur la résolution algébrique des équations, Mémoires de l’Académie de Berlin, (Oeuvres de Lagrange tome IV, 205-421). | MR
[20] F. Lehobey, Algorithmic methods and practical issues in the computation of Galois groups of polynomials, Mémoire de DEA, Université de Rennes I, (1994).
[21] MAPLE 3 volumes : Maple V - Maple Language Reference Manual, Maple V - Maple Library Reference Manual, Maple V - First Leaves : A Tutorial Introduction to Maple, Springer-Verlag.
[22] MAXIMA Maxima DOE maintenu par W. Schelter.
[23] J. McKay, Some remarks on computing Galois groups, SIAM J. Comput. 8, 344-347 (1979). | MR | Zbl
[24] J. McKay, E.Regener, Actions of permutation groups on -sets, Communica-tions in Algebra, 13(3), 619-630 (1985). | MR | Zbl
[25] J. McKay, L. Soicher, Computing Galois Groups over the rationals, Journal of number theory 20, 273-281 (1985). | MR | Zbl
[26] L. Soicher, The computation of the Galois groups, Thèse du Department of Computer Science, Concordia University, Montreal, Quebec, Canada, (1981).
[27] L. Soicher, An Algorithm for Computing Galois Groups, Computational Group Theory, Academic Press, London, 291-296 (1984) | MR | Zbl
[28] R.P. Stauduhar, The determination of Galois groups, Math. Comp. 27, 981-996 (1973). | MR | Zbl
[29] Extension SYM de MACSYMA, manuel de l’utilisateur, A. Valibouze A.
[30] N. Tchebotarev, Grundzüge des Galois’schen Theorie, P. Noordhoff (1950 ).
[31] B.L. Van der Waerden, Modern Algebra, Vol. 1 Ungar New York (1953). | MR | Zbl
[32] A. Valibouze, Mémoire d’habilitation à diriger les recherches, Université Paris 6, 1994.
[33] A. Valibouze, Computation of the Galois group of the resolvent factors for the direct and inverse Galois problems, Conference AAECC’95 (Paris, juillet 1995), LNCS 948. | MR | Zbl
[34] A. Valibouze, Modules de Cauchy, polynômes caractéristiques et résolvantes, Rapport interne LITP 95-62.