Isomorphisms of algebraic number fields
Journal de théorie des nombres de Bordeaux, Tome 24 (2012) no. 2, pp. 293-305.

Soient (α) et (β) des corps de nombres. Nous décrivons une nouvelle méthode permettant de déterminer (s’il en existe) tous les isomorphismes (β)(α). L’algorithme est particulièrement efficace lorsqu’il existe un unique isomorphisme.

Let (α) and (β) be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, (β)(α). The algorithm is particularly efficient if there is only one isomorphism.

DOI : 10.5802/jtnb.797
van Hoeij, Mark 1 ; Pal, Vivek 2

1 Florida State University 211 Love Building Tallahassee, Fl 32306-3027, USA
2 Columbia University Room 509, MC 4406 2990 Broadway New York, NY 10027, USA
@article{JTNB_2012__24_2_293_0,
     author = {van Hoeij, Mark and Pal, Vivek},
     title = {Isomorphisms of algebraic number fields},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {293--305},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {24},
     number = {2},
     year = {2012},
     doi = {10.5802/jtnb.797},
     zbl = {1282.11142},
     mrnumber = {2950693},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/jtnb.797/}
}
TY  - JOUR
AU  - van Hoeij, Mark
AU  - Pal, Vivek
TI  - Isomorphisms of algebraic number fields
JO  - Journal de théorie des nombres de Bordeaux
PY  - 2012
SP  - 293
EP  - 305
VL  - 24
IS  - 2
PB  - Société Arithmétique de Bordeaux
UR  - http://www.numdam.org/articles/10.5802/jtnb.797/
DO  - 10.5802/jtnb.797
LA  - en
ID  - JTNB_2012__24_2_293_0
ER  - 
%0 Journal Article
%A van Hoeij, Mark
%A Pal, Vivek
%T Isomorphisms of algebraic number fields
%J Journal de théorie des nombres de Bordeaux
%D 2012
%P 293-305
%V 24
%N 2
%I Société Arithmétique de Bordeaux
%U http://www.numdam.org/articles/10.5802/jtnb.797/
%R 10.5802/jtnb.797
%G en
%F JTNB_2012__24_2_293_0
van Hoeij, Mark; Pal, Vivek. Isomorphisms of algebraic number fields. Journal de théorie des nombres de Bordeaux, Tome 24 (2012) no. 2, pp. 293-305. doi : 10.5802/jtnb.797. http://www.numdam.org/articles/10.5802/jtnb.797/

[1] Granville, A., “Bounding the coefficients of a divisor of a given polynomial". Monatsh. Math. 109 (1990), 271–277. | MR | Zbl

[2] Conrad, Kieth., “The different ideal". Expository papers/Lecture notes. Available at: http://www.math.uconn.edu/kconrad/blurbs/gradnumthy/different.pdf

[3] Monagan, M. B., “A Heuristic Irreducibility Test for Univariate Polynomials". J. of Symbolic Comp., 13, No. 1, Academic Press (1992) 47–57. | MR | Zbl

[4] Dahan, X. and Schost, É., “Sharp estimates for triangular sets". In Proceedings of the 2004 international Symposium on Symbolic and Algebraic Computation (Santander, Spain, July 04 – 07, 2004). ISSAC ’04. ACM, New York, NY, 103–110. | MR

[5] Database by Jürgen Klüners and Gunter Malle, located at: http://www.math.uni-duesseldorf.de/klueners/minimum/minimum.html

[6] Belabas, Karim., “A relative van Hoeij algorithm over number fields". J. Symbolic Computation, Vol. 37 (2004), no. 5, pp. 641–668. | MR

[7] Website with implementations and Degree 81 examples: http://www.math.fsu.edu/vpal/Iso/

[8] van Hoeij, Mark., “Factoring Polynomials and the Knapsack Problem." J. Number Th. 95 (2002), 167–189. | MR

[9] Lenstra, A. K.; Lenstra, H. W., Jr.; Lovász, L., “Factoring polynomials with rational coefficients". Mathematische Annalen 261 (4) (1982), 515–534. | MR | Zbl

[10] M. van Hoeij and A. Novocin, “ Gradual sub-lattice reduction and a new complexity for factoring polynomials", accepted for proceedings of LATIN 2010. | MR

[11] Cohen, Henri, A Course in Computational Algebraic Number Theory. Graduate Texts in Mathematics 138, Springer-Verlag, 1993. | MR | Zbl

Cité par Sources :