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)
Fast parallel absolute irreducibility testing
Journal of Symbolic Computation
A fast parallel algorithm for determining all roots of a polynomial with real roots
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
The complexity of elementary algebra and geometry
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
On a generalization of Stickelberger's Theorem
Journal of Symbolic Computation
Parallel modular exponentiation using load balancing without precomputation
Journal of Computer and System Sciences
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In Borodin-von zur Gathen-Hopcroft[82] the following program is laid out: obtain a “theory package for parallel algebraic computations”, i.e. fast parallel computations for the widely used problems of symbolic manipulation in an algebraic context. In that paper, two basic problems were considered: solving systems of linear equations and computing the gcd of two polynomials, both over arbitrary ground fields. The present paper continues this program, and fast parallel solutions to the following algebraic problems are given: computing all entries of the Extended Euclidean Scheme of two polynomials over an arbitrary field, gcd and lcm of many polynomials, factoring polynomials over finite fields, and the squarefree decomposition of polynomials over fields of characteristic zero and over finite fields.