The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Algorithms for polynomial factorization.
Algorithms for polynomial factorization.
LISP 1.5 Programmer's Manual
Multivariate Polynomial Factorization
Journal of the ACM (JACM)
Corrigendum: `` Allocating Storage for Extendible Arrays''
Journal of the ACM (JACM)
Restructuring of Arithmetic Expressions For Parallel Evaluation
Journal of the ACM (JACM)
Journal of the ACM (JACM)
On the Generation of Binary Trees
Journal of the ACM (JACM)
Theorem Proving via General Matings
Journal of the ACM (JACM)
Solution to problem #7 using MACSYMA
ACM SIGSAM Bulletin
On computing with factored rational expressions
ACM SIGSAM Bulletin
ACM SIGSAM Bulletin
A p-adic division with remainder algorithm
ACM SIGSAM Bulletin
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This paper gives an algorithm for finding the irreducible factors of any multivariate polynomial with integer coefficients. The algorithm begins by making substitutions for all but one of the variable. This univariate polynomial is then factored by a known method, which uses an algorithm of Berlekamp for factoring univariate polynomials over finite fields. After this factorization is done, the multivariate factors are recovered from the univariate ones by a kind of Hensel algorithm. A number of ideas are given which greatly speed the computation in some special cases.