On computing isomorphisms of equation orders

Pohst, M.

doi:10.1090/S0025-5718-1987-0866116-2

On computing isomorphisms of equation orders

Author: M. Pohst
Journal: Math. Comp. 48 (1987), 309-314
MSC: Primary 11R09; Secondary 11-04, 11Y40
DOI: https://doi.org/10.1090/S0025-5718-1987-0866116-2
MathSciNet review: 866116
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A number-geometric method for computing isomorphisms of algebraic number fields (respectively, $\mathbb{Z}$ -orders of such fields) is developed. Its main advantage is its easy implementation and moderate computation time.

[1] F. Diaz y Diaz, Private communication to the author.
[2] U. Fincke and M. Pohst, Improved methods for calculating vectors of short length in a lattice, including a complexity analysis, Math. Comp. 44 (1985), no. 170, 463–471. MR 777278, https://doi.org/10.1090/S0025-5718-1985-0777278-8
[3] A. K. Lenstra, H. W. Lenstra Jr., and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982), no. 4, 515–534. MR 682664, https://doi.org/10.1007/BF01457454
[4] M. Pohst, The minimum discriminant of seventh degree totally real algebraic number fields, Number theory and algebra, Academic Press, New York, 1977, pp. 235–240. MR 0466069
[5] Michael Pohst, On the computation of number fields of small discriminants including the minimum discriminants of sixth degree fields, J. Number Theory 14 (1982), no. 1, 99–117. MR 644904, https://doi.org/10.1016/0022-314X(82)90061-0
[6] M. Pohst & H. Zassenhaus, Methods and Problems of Computational Algebraic Number Theory, Cambridge Univ. Press. (To appear.)
[7] H. Zassenhaus and J. Liang, On a problem of Hasse, Math. Comp. 23 (1969), 515–519. MR 246853, https://doi.org/10.1090/S0025-5718-1969-0246853-2
[8] Horst G. Zimmer, Computational problems, methods, and results in algebraic number theory, Lecture Notes in Mathematics, Vol. 262, Springer-Verlag, Berlin-New York, 1972. MR 0323751