Calculs d'invariants primitifs de groupes finis

Ines Abdeljaouad

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 33, Issue: 1, page 59-77
  • ISSN: 0988-3754

Abstract

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We introduce in this article a new method to calculate all absolute and relatif primitive invariants of finite groups. This method is inspired from K. Girstmair which calculate an absolute primitive invariant of minimal degree. Are presented two algorithms, the first one enable us to calculate all primitive invariants of minimal degree, and the second one calculate all absolute or relative primitive invariants with distincts coefficients. This work take place in Galois Theory and Invariant Theory.

How to cite

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Abdeljaouad, Ines. "Calculs d'invariants primitifs de groupes finis." RAIRO - Theoretical Informatics and Applications 33.1 (2010): 59-77. <http://eudml.org/doc/222095>.

@article{Abdeljaouad2010,
abstract = { We introduce in this article a new method to calculate all absolute and relatif primitive invariants of finite groups. This method is inspired from K. Girstmair which calculate an absolute primitive invariant of minimal degree. Are presented two algorithms, the first one enable us to calculate all primitive invariants of minimal degree, and the second one calculate all absolute or relative primitive invariants with distincts coefficients. This work take place in Galois Theory and Invariant Theory. },
author = {Abdeljaouad, Ines},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {permutation groups; invariant polynomial ring; algorithm},
language = {eng},
month = {3},
number = {1},
pages = {59-77},
publisher = {EDP Sciences},
title = {Calculs d'invariants primitifs de groupes finis},
url = {http://eudml.org/doc/222095},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Abdeljaouad, Ines
TI - Calculs d'invariants primitifs de groupes finis
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 1
SP - 59
EP - 77
AB - We introduce in this article a new method to calculate all absolute and relatif primitive invariants of finite groups. This method is inspired from K. Girstmair which calculate an absolute primitive invariant of minimal degree. Are presented two algorithms, the first one enable us to calculate all primitive invariants of minimal degree, and the second one calculate all absolute or relative primitive invariants with distincts coefficients. This work take place in Galois Theory and Invariant Theory.
LA - eng
KW - permutation groups; invariant polynomial ring; algorithm
UR - http://eudml.org/doc/222095
ER -

References

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  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://medicis.polytechnique.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  
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  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.  
  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. Comp.27 (1973) 981-996.  
  19. B. Sturmfels, Algorithms in invariant theory, Wien, New-York: Springer Verlag (1993).  
  20. A. Valibouze, Groupes de Galois jusqu'en degré 7. Rapport interne LIP6 (1997).  
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