On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
Polynomial Gcd Computations over Towers of Algebraic Extensions
AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Early detection of true factors in univariate polynominal factorization
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
A modular GCD algorithm over number fields presented with multiple extensions
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Maximal quotient rational reconstruction: an almost optimal algorithm for rational reconstruction
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Algorithms for polynomial GCD computation over algebraic function fields
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Lifting techniques for triangular decompositions
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Algorithms for the non-monic case of the sparse modular GCD algorithm
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
On factorization of multivariate polynomials over algebraic number and function fields
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Parallel sparse polynomial interpolation over finite fields
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
On sparse interpolation over finite fields
ACM Communications in Computer Algebra
Diversification improves interpolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
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We present a first sparse modular algorithm for computing a greatest common divisor of two polynomials f1, f2 ε L[x] where L is an algebraic function field in k ≥ 0 parameters with r ≥ 0 field extensions. Our algorithm extends the dense algorithm of Monagan and van Hoeij from 2004 to support multiple field extensions and to be efficient when the gcd is sparse. Our algorithm is an output sensitive Las Vegas algorithm. We have implemented our algorithm in Maple. We provide timings demonstrating the efficiency of our algorithm compared to that of Monagan and van Hoeij and with a primitive fraction-free Euclidean algorithm for both dense and sparse gcd problems.