The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
On Euclid's Algorithm and the Theory of Subresultants
Journal of the ACM (JACM)
The Calculation of Multivariate Polynomial Resultants
Journal of the ACM (JACM)
Towards a general theory of special functions
Communications of the ACM
Algorithms for polynomial factorization.
Algorithms for polynomial factorization.
Computer Algebra: Past and Future
Journal of Symbolic Computation
Computing with polynomials given by straight-line programs I: greatest common divisors
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Greatest common divisors of polynomials given by straight-line programs
Journal of the ACM (JACM)
A p-adic approach to the computation ofGröbner bases
Journal of Symbolic Computation
GCDHEU: Heuristic polynomial GCD algorithm based on integer GCD computation
Journal of Symbolic Computation
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
Three new algorithms for multivariate polynomial GCD
Journal of Symbolic Computation
Parallel univariate p-adic lifting on shared-memory multiprocessors
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
On computing greatest common divisors with polynomials given by black boxes for their evaluations
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
The Subresultant PRS Algorithm
ACM Transactions on Mathematical Software (TOMS)
On square-free decomposition algorithms
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Algebraic algorithms using p-adic constructions
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
On the subresultant PRS algorithm
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Newton's iteration and the sparse Hensel algorithm (Extended Abstract)
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
Factorization of multivariate polynomials by extended Hensel construction
ACM SIGSAM Bulletin
On algorithms for solving systems of polynomial equations
ACM SIGSAM Bulletin
On computing with factored rational expressions
ACM SIGSAM Bulletin
ACM SIGSAM Bulletin
Factoring larger multivariate polynomials
ACM SIGSAM Bulletin
A p-adic division with remainder algorithm
ACM SIGSAM Bulletin
Course outline: Yale University, New Haven
ACM SIGSAM Bulletin
ACM SIGSAM Bulletin
Symbolic mathematical computation: a survey
ACM SIGSAM Bulletin
An improved EZ-GCD algorithm for multivariate polynomials
Journal of Symbolic Computation
Computing multivariate approximate GCD based on Barnett's theorem
Proceedings of the 2009 conference on Symbolic numeric computation
Editorial: Macsyma: A personal history
Journal of Symbolic Computation
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This paper presents a preliminary report on a new algorithm for computing the Greatest Common Divisor (GCD) of two multivariate polynomials over the integers. The algorithm is strongly influenced by the method used for factoring multivariate polynomials over the integers. It uses an extension of the Hensel lemma approach originally suggested by Zassenhaus for factoring univariate polynomials over the integers. We point out that the cost of the Modular GCD algorithm applied to sparse multivariate polynomials grows at least exponentially in the number of variables appearing in the GCD. This growth is largely independent of the number of terms in the GCD. The new algorithm, called the EZ (Extended Zassenhaus) GCD Algorithm, appears to have a computing bound which in most cases is a polynomial function of the number of terms in the original polynomials and the sum of the degrees of the variables in them. Especially difficult cases for the EZ GCD Algorithm are described. Applications of the algorithm to the computation of contents and square-free decompositions of polynomials are indicated.