no. 2
Isomorphisms of algebraic number fields
van Hoeij, Mark1 ; Pal, Vivek2
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
Journal de théorie des nombres de Bordeaux, Tome 24 (2012) no. 2, pp. 293-305.

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

Let ℚ(α) and ℚ(β) be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, ℚ(β)→ℚ(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 :