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)
Algorithms for rational function arithmetic operations
STOC '72 Proceedings of the fourth annual ACM symposium on Theory of computing
Uniform closure properties of P-computable functions
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
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
Greatest common divisors of polynomials given by straight-line programs
Journal of the ACM (JACM)
Analysis of euclidean algorithms for polynomials over finite fields
Journal of Symbolic Computation
On computing determinants of matrices without divisions
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
A generalization of the binary GCD algorithm
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
Asymptotically fast solution of Toeplitz-like singular linear systems
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Faster solution of the key equation for decoding BCH error-correcting codes
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Fast polynomial factorization over high algebraic extensions of finite fields
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
An output-sensitive variant of the baby steps/giant steps determinant algorithm
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Acceleration of Euclidean algorithm and extensions
Proceedings of the 2002 international 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
The computational complexity of continued fractions
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
Half-GCD and fast rational recovery
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Fast rational function reconstruction
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Around the numeric-symbolic computation of differential Galois groups
Journal of Symbolic Computation
IEEE Transactions on Communications
Fast arithmetic in unramified p-adic fields
Finite Fields and Their Applications
New Techniques for the Computation of Linear Recurrence Coefficients
Finite Fields and Their Applications
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Journal of Symbolic Computation
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An integer greatest common divisor (GCD) algorithm due to Schönhage is generalized to hold in all euclidean domains which possess a fast multiplication algorithm. It is shown that if two N precision elements can be multiplied in O(N loga N), then their GCD can be computed in O(N loga+1 N). As a consequence, a new faster algorithm for multivariate polynomial GCD's can be derived and with that new bounds for rational function manipulation.