Representations and parallel computations for rational functions
SIAM Journal on Computing
Sums of divisors, perfect numbers and factoring
SIAM Journal on Computing
ISSAC '88: proceedings of the international symposium on Symbolic and algebraic computation
ISSAC '88: proceedings of the international symposium on Symbolic and algebraic computation
Algorithmic algebraic number theory
Algorithmic algebraic number theory
Proceedings of the international symposium on Symbolic and algebraic computation
ISSAC'90 Int'l Symposium on Symbolic Algebraic Computation
Detecting algebraic dependencies between unnested radicals (extended abstract)
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Journal of Algorithms
Recognizing units in number fields
Mathematics of Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Subquadratic-time factoring of polynomials over finite fields
Mathematics of Computation
Detecting perfect powers in essentially linear time
Mathematics of Computation
On factor refinement in number fields
Mathematics of Computation
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Algebraic Algorithms and Error-Correcting Codes
Algebraic Algorithms and Error-Correcting Codes
Proceedings of the Second International Symposium on Algorithmic Number Theory
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
On a Little but Useful Algorithm
AAECC-3 Proceedings of the 3rd International Conference on Algebraic Algorithms and Error-Correcting Codes
On the Computational Complexity of the Resolution of Plane Curve Singularities
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
About a New Method for Computing in Algebraic Number Fields
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Fast Ideal Artithmetic via Lazy Localization
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Proceedings of the sixteenth annual ACM symposium on Theory of computing
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Sums of divisors, perfect numbers, and factoring
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Smith normal form of dense integer matrices fast algorithms into practice
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Query-efficient algorithms for polynomial interpolation over composites
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the complexity of the D5 principle
ACM SIGSAM Bulletin
Solving structured linear systems with large displacement rank
Theoretical Computer Science
Comprehensive triangular decomposition
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
Testing set proportionality and the Ádám isomorphism of circulant graphs
Journal of Discrete Algorithms
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Let S be a finite set of positive integers. A "coprime base for S" means a set P of positive integers such that (1) each element of P is coprime to every other element of P and (2) each element of S is a product of powers of elements of P. There is a natural coprime base for S. This paper introduces an algorithm that computes the natural coprime base for S in essentially linear time. The best previous result was a quadratic-time algorithm of Bach, Driscoll, and Shallit. This paper also shows how to factor S into elements of P in essentially linear time. The algorithms use solely multiplication, exact division, gcd, and equality testing, so they apply to any free commutative monoid with fast algorithms for those four operations; for example, given a finite set S of monic polynomials over a finite field, the algorithms factor S into coprimes in essentially linear time. These algorithms can be used as a substitute for prime factorization in many applications.