The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Multivariate Polynomial Factorization
Journal of the ACM (JACM)
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
ACM '73 Proceedings of the ACM annual conference
A system for manipulating polynomials given by straight-line programs
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
On the power series solution of a system of algebraic equations
ACM SIGSAM Bulletin
Interpolating polynomials from their values
Journal of Symbolic Computation - Special issue on computational algebraic complexity
On the multi-threaded computation of integral polynomial greatest common divisors
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Dagwood: a system for manipulating polynomials given by straight-line programs
ACM Transactions on Mathematical Software (TOMS)
Checking polynomial identities over any field: towards a derandomization?
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A polynomial reduction from multivariate to bivariate integral polynomial factorization.
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Polynomial factorization: a success story
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
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This paper presents an organization of the p-adic lifting (or Hensel) algorithm that differs from the organization previously presented by Zassenhaus [Zas69] and currently used in algebraic manipulation circles [Mos73, Yun74, Wan75, Mus75]. Our organization is somewhat more general than the earlier one and admits the improvements that yielded the “sparse modular” algorithm [Zip79] more easily than the Zassenhaus algorithm. From a pedagogical point of view, the relationship between Newton's iteration and the p-adic algorithms is clearer in our formulation than with the Zassenhaus algorithm.