Sparse Hensel lifting. (English) Zbl 0605.12011
Computer algebra, EUROCAL ’85, Proc. Eur. Conf., Linz/Austria 1985, Vol. 2, Lect. Notes Comput. Sci. 204, 4-17 (1985).
[For the entire collection see Zbl 0568.00019.]
A new algorithm is introduced which computes the multivariate leading coefficients of polynomial factors from their univariate images. This algorithm is incorporated into a sparse Hensel lifting scheme and only requires the factorization of a single univariate image. The algorithm also provides the content of the input polynomial in the main variable as a by-product. We show how we can take advantage of this property when computing the GCD of multivariate polynomials by sparse Hensel lifting.
A new algorithm is introduced which computes the multivariate leading coefficients of polynomial factors from their univariate images. This algorithm is incorporated into a sparse Hensel lifting scheme and only requires the factorization of a single univariate image. The algorithm also provides the content of the input polynomial in the main variable as a by-product. We show how we can take advantage of this property when computing the GCD of multivariate polynomials by sparse Hensel lifting.
MSC:
| 12E05 | Polynomials in general fields (irreducibility, etc.) |
| 12Y05 | Computational aspects of field theory and polynomials (MSC2010) |
| 68W30 | Symbolic computation and algebraic computation |
| 12D05 | Polynomials in real and complex fields: factorization |
| 13B25 | Polynomials over commutative rings |
