Algorithms for computer algebra
Algorithms for computer algebra
On the generation of multivariate polynomials which are hard to factor
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Factoring modular polynomials (extended abstract)
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
Fraction-Free Computation of Matrix Rational Interpolants and Matrix GCDs
SIAM Journal on Matrix Analysis and Applications
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We present a new algorithm for determining all factorizations of a polynomial f in the domain ZN[x], a non-unique factorization domain, given in terms of parameters. From the prime factorization of N, the problem is reduced to factorization in Zph[x] where p is a prime and k ⪈ 1. If pk does not divide the discriminant of f and one factorization is given, our algorithm determines all factorizations with complexity &Ogr;(n3 M(k log p)) where n denotes the degree of the input polynomial and M(t) denotes the complexity of multiplication of two t-bit numbers. Our algorithm improves on the method of von zur Gathen and Hartlieb, which has complexity &Ogr;(n7 k(klog p + log n2). The improvement is achieved by processing all factors at the same time instead of one at a time and by computing the kernels and determinants of matrices over Zpk in an efficient manner.