A system for manipulating polynomials given by straight-line programs
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
The Bath algebraic number package
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
Factoring Polynomials Over Algebraic Number Fields
ACM Transactions on Mathematical Software (TOMS)
Lattices and Factorization of Polynomials over Algebraic Number Fields
EUROCAM '82 Proceedings of the European Computer Algebra Conference on Computer Algebra
Factoring polynominals over algebraic number fields
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
A generalized class of polynomials that are hard to factor
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
P-adic reconstruction of rational numbers
ACM SIGSAM Bulletin
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We describe three ways to generalize Lenstra's algebraic integer recovery method. One direction adapts the algorithm so that rational numbers are automatically produced given only upper bounds on the sizes of the numerators and denominators. Another direction produces a variant which recovers algebraic numbers as elements of multiple generator algebraic number fields. The third direction explains how the method can work if a reducible minimal polynomial had been given for an algebraic generator. Any two or all three of the generalizations may be employed simultaneously.