Skip to main content
Log in

Computation of the Decomposition Group of a Triangular Ideal

  • Published:
Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

This article describes two algorithms in order to search decomposition groups of ideals of polynomials with coefficients in a perfect field when those ideals are generated by a triangular system of generators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Anai, H., Noro, M., Yokoyama, K.: Computation of the splitting fields and the Galois groups of polynomials. In: Algorithms in algebraic geometry and applications (Santander, 1994), volume 143 of Progr. Math. Birkhäuser, Basel, 1996, pp. 29–50

  2. Aubry, P., Valibouze, A.: Using Galois ideals for computing relative resolvents. J. Symbolic Comput. 30(6), 635–651 (2000). Algorithmic methods in Galois theory

    Article  MATH  Google Scholar 

  3. Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. The user language. J. Symbolic Comput. 24(3–4), 235–265 (1997). Computational algebra and number theory (London, 1993)

  4. Bourbaki, N.: Algèbre Commutative. Chapitres 5 à 7. Éléments de mathématiques. Masson, 1985

  5. Butler, G.: Fundamental algorithms for permutation groups, volume 559 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1991

  6. Butler, G., McKay, J.: The transitive groups of degree up to eleven. Comm. Algebra 11(8), 863–911 (1983)

    MATH  Google Scholar 

  7. Cox, D., Little, J., O’Shea, D.: Ideals, varieties, and algorithms. Undergraduate Texts in Mathematics. Springer-Verlag, New York, second edition, 1997. An introduction to computational algebraic geometry and commutative algebra

  8. Orange, S., Renault, G., Valibouze, A.: Calcul efficace d’un corps de décomposition. LIP6 Research Report 2003.005, LIP6, Université Pierre et Marie Curie, France, 2003

  9. Valibouze, A.: Étude des relations algébriques entre les racines d’un polynôme d’une variable. Bull. Belg. Math. Soc. Simon Stevin 6(4), 507–535 (1999)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to I. Abdeljaouad-Tej.

Additional information

Acknowledgement The authors would like to thank the anonymous referees for extensive comments on clarifying and improving the exposition of this paper and Laurence Bessis for her helpful suggestions and comments.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Abdeljaouad-Tej, I., Orange, S., Renault, G. et al. Computation of the Decomposition Group of a Triangular Ideal. AAECC 15, 279–294 (2004). https://doi.org/10.1007/s00200-004-0160-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00200-004-0160-x

Key words

Navigation