On the Computation of the Radical of Polynomial Complete Intersection Ideals

This paper deals with the effective computation of the radical of certain polynomial ideals. Let k be a characteristic zero field, f1,..., fn−r e k[X1,..., X n ] a regular sequence with d:=maxj deg fj, the generated ideal, its radical, and suppose that the factor ring k[X1,...,X n ]/ is a Cohen-Macaulay ring. Under these assumptions we exhibit a single exponential algorithm which computes a system of generators of .

[1]  A. Grothendieck,et al.  Éléments de géométrie algébrique , 1960 .

[2]  C. Berenstein,et al.  Recent improvements in the complexity of the effective Nullstellensatz , 1991 .

[3]  Joos Heintz,et al.  Corrigendum: Definability and Fast Quantifier Elimination in Algebraically Closed Fields , 1983, Theor. Comput. Sci..

[4]  A. Meyer,et al.  The complexity of the word problems for commutative semigroups and polynomial ideals , 1982 .

[5]  D. Eisenbud,et al.  Direct methods for primary decomposition , 1992 .

[6]  Alicia Dickenstein,et al.  Duality methods for the membership problem , 1991 .

[7]  Fabio Rossi,et al.  Some Effective Methods in the Openness of Loci for Cohen-Macaulay and Gorenstein Properties , 1991 .

[8]  M. Reid,et al.  Commutative ring theory: Regular rings , 1987 .

[9]  Alicia Dickenstein,et al.  The membership problem for unmixed polynomial ideals is solvable in single exponential time , 1991, Discret. Appl. Math..

[10]  Tsit Yuen Lam,et al.  Serre's Conjecture , 1978 .

[11]  Stuart J. Berkowitz,et al.  On Computing the Determinant in Small Parallel Time Using a Small Number of Processors , 1984, Inf. Process. Lett..

[12]  Robert Lazarsfeld,et al.  On a theorem of Castelnuovo, and the equations defining space curves , 1983 .

[13]  Birger Iversen,et al.  Generic Local Structure of the Morphisms in Commutative Algebra , 1973 .

[14]  Teresa Krick,et al.  An Algorithm for the Computation of the Radical of an Ideal in the Ring of Polynomials , 1991, AAECC.

[15]  André Galligo,et al.  Some New Effectivity Bounds in Computational Geometry , 1988, AAECC.

[16]  Bernard Teissier,et al.  Résultats récents d'algèbre commutative effective , 1990 .

[17]  Jean-Pierre Serre,et al.  Algèbre locale : multiplicités , 1957 .

[18]  Teo Mora,et al.  Local Decomposition Algorithms , 1990, AAECC.

[19]  David Mumford,et al.  What Can Be Computed in Algebraic Geometry , 1993, alg-geom/9304003.