Calculs d'invariants primitifs de groupes finis

 Access to full text

 Full (PDF)

1. [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. [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. [3] J. M. Arnaudiès and A. Valibouze, Lagrange resolvents. J. Pure Appl. Algebra (1997). Zbl0945.12004MR1457831
4. [4] E. H. Berwick, The condition that a quintic equation should be soluble by radicals. Proc. London Math. Soc. 14 (1915) 301-307. Zbl45.0187.13JFM45.1227.04
5. [5] E. H. Berwick, On soluble sextic equations. Proc. London Math. Soc. 29 (1929) 1-28. Zbl54.0125.03JFM54.0125.03
6. [6] A. Cayley, On a new auxiliary equation in the theory of equation of fifth order. Philos. Trans. Roy. Soc. London, CLL (1861). 
7. [7] A. Colin, Formal computation of Galois groups with relative resolvents, AAECC'95, Springer Verlag, Lecture Notes in Computer Science 948 (1995) 169-182. Zbl0887.12006MR1448163
8. [8] A. Colin, Solving a System of algebraic equations with symmetries. J. Pure and Appl. Algebra (1996). Zbl0890.68079MR1457839
9. [9] H. O. Foulkes, The resolvents of an equation of seventh degree. Quart. J. Math. Oxford Ser. (1931) 9-19. Zbl0001.11601
10. [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. [11] K. Girstmair, On invariant polynomials and their application in field theory. Maths of Comp. 48 (1987) 781-797. Zbl0637.12012MR878706
12. [12] C. Jordan, Traité des substitutions et des équations algébriques, Gauthier-Villard, Paris (1870). Zbl0828.01011
13. [13] G. Kemper, Calculating invariant rings of finite groups over arbitrary fields. J. Symbolic Commutation (1995). Zbl0889.13004MR1400337
14. [14] F. Lehobey, Resolvent computation by resultants without extraneous powers. J. Pure Appl. Algebra (1999) à paraître. Zbl1113.12301
15. [15] E. Luther, Ueber die factoren des algebraisch lôsbaren irreducible Gleichungen vom sechsten Grade und ihren Resolvanten. Journal für Math. 37 (1848) 193-220. 
16. [16] N. Rennert and A. Valibouze, Modules de Cauchy, Rapport interne LIP6 (1997). 
17. [17] L. Soicher, The computation of the Galois groups, Thesis in departement of computer science, Concordia University, Montreal, Quebec, Canada (1981). 
18. [18] R. P. Stauduhar, The computation of Galois groups. Math. Cornp. 27 (1973) 981-996. Zbl0282.12004MR327712
19. [19] B. Sturmfels, Algorithms in invariant theory, Wien, New-York: Springer Verlag (1993). Zbl0802.13002MR1255980
20. [20] A. Valibouze, Groupes de Galois jusqu'en degré 7. Rapport interne LIP6 (1997). 
21. [21] A. Vandermonde, Mémoire de l'Académie des Sciences de Paris (1771). 
22. [22] R. L. Wilson, A method for the determination of the Galois group, Amer. Math. Soc. (1949). MR39689