Computer algebra: symbolic and algebraic computation (2nd ed.)
Computer algebra: symbolic and algebraic computation (2nd ed.)
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
The Calculation of Multivariate Polynomial Resultants
Journal of the ACM (JACM)
Hankel Matrices and Polynomials
AAECC-5 Proceedings of the 5th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Symmetric subresultants and applications
Journal of Symbolic Computation
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In this paper we show some results concerning symbolic manipulation of Hankel matrices, as well as some applications of these matrices to Computer Algebra. We present algorithmic approaches, based on Hankel matrices, to the calculation of multivariate polynomial resultants, to polynomial gcd computations including the extended polynomial gcd problem, to modular factorization and to the determination of the number of distinct real roots of a real polynomial. The computing time analysis shows that the three first applications have the same asymptotic complexity as the currently fastest algorithm for these problems, and that the last one runs in O(n5 log2 L) where n is the degree of the polynomial, and L its norm.