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Recovery of algebraic numbers from their p-adic approximations
Abbott J.  Symbolic and algebraic computation (Proceedings of the ACM-SIGSAM 1989 international symposium, Portland, Oregon, United States, Jul 17-19, 1989)112-120.1989.Type:Proceedings
Date Reviewed: Apr 1 1991

Recovering an algebraic number from its residue modulo an ideal is not difficult if this ideal is generated by a rational integer. Often, however, one needs to work with a prime ideal not of this form. When the algebraic number is an integral linear combination of powers of a root &agr; of a monic irreducible polynomial over &ZZ;, this problem has been treated by Lenstra using an algorithm for finding short vectors in lattices [1]. This paper extends Lenstra’s method by treating the general case of a rational linear combination of powers of &agr;. The author also extends this method to the situation where the number field is generated by several generators &agr;. Finally, he explains how the method can work if a reducible polynomial is given for an algebraic generator.

Reviewer:  Jan Denef Review #: CR114323
1) Lenstra, A. K. Lattices and factorization of polynomials over algebraic number fields. In Proceedings of EUROCAM 1982 (Marseille), Springer-Verlag, New York, 1982, 32–39.
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Approximation (G.1.2 )
 
 
Algebraic Algorithms (I.1.2 ... )
 
 
Computations On Polynomials (F.2.1 ... )
 
 
Algorithms (I.1.2 )
 
 
Numerical Algorithms And Problems (F.2.1 )
 
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