Calculs d'invariants primitifs de groupes finis
Abdeljaouad, Ines
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 33 (1999), p. 59-77 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1999-01-01
@article{ITA_1999__33_1_59_0,
     author = {Abdeljaouad, Ines},
     title = {Calculs d'invariants primitifs de groupes finis},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     volume = {33},
     year = {1999},
     pages = {59-77},
     mrnumber = {1705856},
     zbl = {0937.13001},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/ITA_1999__33_1_59_0}
}

Abdeljaouad, Ines. Calculs d'invariants primitifs de groupes finis. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 33 (1999) pp. 59-77. http://gdmltest.u-ga.fr/item/ITA_1999__33_1_59_0/

[1] I. Abdeljaouad, Calculs d'invariants primitifs minimaux et implantation en Axiom, Mémoire de stage, DEA Algorithmique (1996). Disponible sur la page web du Projet Galois du GDR MEDICIS : http://rnedicis.polyteclinique.fr/medicis/projetGalois

[2] I. Abdeljaouad, Package PrimitiveInvariant sous GAP, (1997). Disponible sur la page web du Projet Galois du GDR MEDICIS : http://medicis.polytechnique.fr/medicis/projetGalois

[3] J. M. Arnaudiès and A. Valibouze, Lagrange resolvents. J. Pure Appl. Algebra (1997). | MR 1457831 | Zbl 0945.12004

[4] E. H. Berwick, The condition that a quintic equation should be soluble by radicals. Proc. London Math. Soc. 14 (1915) 301-307. | JFM 45.1227.04

[5] E. H. Berwick, On soluble sextic equations. Proc. London Math. Soc. 29 (1929) 1-28. | JFM 54.0125.03

[6] A. Cayley, On a new auxiliary equation in the theory of equation of fifth order. Philos. Trans. Roy. Soc. London, CLL (1861).

[7] A. Colin, Formal computation of Galois groups with relative resolvents, AAECC'95, Springer Verlag, Lecture Notes in Computer Science 948 (1995) 169-182. | MR 1448163 | Zbl 0887.12006

[8] A. Colin, Solving a System of algebraic equations with symmetries. J. Pure and Appl. Algebra (1996). | MR 1457839 | Zbl 0890.68079

[9] H. O. Foulkes, The resolvents of an equation of seventh degree. Quart. J. Math. Oxford Ser. (1931) 9-19. | Zbl 0001.11601

[10] G. A. P. Groups, algorithms and programming, Martin Schönert and others, Lehrstuhl D für Mathematik, Rheinisch-Westfälische Technische Hochoschule, Aachem, gap@samson.math.rwth-aachen.de (1993).

[11] K. Girstmair, On invariant polynomials and their application in field theory. Maths of Comp. 48 (1987) 781-797. | MR 878706 | Zbl 0637.12012

[12] C. Jordan, Traité des substitutions et des équations algébriques, Gauthier-Villard, Paris (1870). | Zbl 0828.01011

[13] G. Kemper, Calculating invariant rings of finite groups over arbitrary fields. J. Symbolic Commutation (1995). | MR 1400337 | Zbl 0889.13004

[14] F. Lehobey, Resolvent computation by resultants without extraneous powers. J. Pure Appl. Algebra (1999) à paraître.

[15] E. Luther, Ueber die factoren des algebraisch lôsbaren irreducible Gleichungen vom sechsten Grade und ihren Resolvanten. Journal für Math. 37 (1848) 193-220. | Zbl 037.1025cj

[16] N. Rennert and A. Valibouze, Modules de Cauchy, Rapport interne LIP6 (1997).

[17] L. Soicher, The computation of the Galois groups, Thesis in departement of computer science, Concordia University, Montreal, Quebec, Canada (1981).

[18] R. P. Stauduhar, The computation of Galois groups. Math. Cornp. 27 (1973) 981-996. | MR 327712 | Zbl 0282.12004

[19] B. Sturmfels, Algorithms in invariant theory, Wien, New-York: Springer Verlag (1993). | MR 1255980 | Zbl 0802.13002

[20] A. Valibouze, Groupes de Galois jusqu'en degré 7. Rapport interne LIP6 (1997).

[21] A. Vandermonde, Mémoire de l'Académie des Sciences de Paris (1771).

[22] R. L. Wilson, A method for the determination of the Galois group, Amer. Math. Soc. (1949). | MR 39689