On the computation of the radical of polynomial complete intersection ideals. (English) Zbl 0896.13022
Cohen, Gérard (ed.) et al., Applied algebra, algebraic algorithms and error-correcting codes. 11th international symposium, AAECC-11, Paris, France, July 17-22, 1995. Proceedings. Berlin: Springer-Verlag. Lect. Notes Comput. Sci. 948, 106-119 (1995).
Summary: This paper deals with the effective computation of the radical of certain polynomial ideals. Let \(k\) be a characteristic zero field, \(f_1,\dots,f_{n-r}\in k[X_1,\dots,X_n]\) a regular sequence with \(d:= \max_j \deg f_j\), \({\mathfrak I}\) the generated ideal, \(\sqrt {\mathfrak I}\) its radical, and suppose that the factor ring \(k[X_1, \dots, X_n]/ \sqrt {\mathfrak I}\) is a Cohen-Macaulay ring. Under these assumptions we exhibit a single exponential algorithm which computes a system of generators of \(\sqrt {\mathfrak I}\).
For the entire collection see [Zbl 0847.00060].
For the entire collection see [Zbl 0847.00060].
MSC:
| 13P10 | Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |
| 13A10 | Radical theory on commutative rings (MSC2000) |
| 13F20 | Polynomial rings and ideals; rings of integer-valued polynomials |
