Irreducible decomposition of polynomial ideals

In this paper we present some algorithms for computing an irreducible decomposition of an ideal in a polynomial ring R=K[x"1,...,x"n] where K is an arbitrary effective field.

[1]  E. Kunz.  Introduction to commutative algebra and algebraic geometry , 1984 .

[2]  Erich Kaltofen,et al.  On the complexity of computing grobner bases for zero-dimensional polynomial ideals , 1990 .

[3]  Craig Huneke.  Hyman Bass and Ubiquity: Gorenstein Rings , 2002 .

[4]  Hyman Bass,et al.  On the ubiquity of Gorenstein rings , 1963 .

[5]  G. Greuel,et al.  A Singular Introduction to Commutative Algebra , 2002 .

[6]  Marie-Françoise Roy,et al.  Multivariate Bezoutians, Kronecker symbol and Eisenbud-Levine formula , 1996 .

[7]  Maria Grazia Marinari,et al.  Gröbner bases of ideals defined by functionals with an application to ideals of projective points , 1993, Applicable Algebra in Engineering, Communication and Computing.

[8]  David A. Buchsbaum,et al.  Algebra Structures for Finite Free Resolutions, and Some Structure Theorems for Ideals of Codimension 3 , 1977 .

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

[10]  D. Eisenbud.  Commutative Algebra: with a View Toward Algebraic Geometry , 1995 .

[11]  W. Gröbner,et al.  Über irreduzible Ideale in kommutativen Ringen , 1935 .

[12]  G. B. M. Zerr,et al.  Algebra: 117-118 , 1900 .

[13]  B. Mourrain.  Isolated points, duality and residues , 1997 .

[14]  Patrizia M. Gianni,et al.  Gröbner Bases and Primary Decomposition of Polynomial Ideals , 1988, J. Symb. Comput..

[15]  Emmy Noether.  Idealtheorie in Ringbereichen , 1921 .

[16]  H. Michael Möller,et al.  Multivariate Polynomial System Solving Using Intersections of Eigenspaces , 2001, J. Symb. Comput..

[17]  Victor Y. Pan,et al.  Asymptotic acceleration of solving multivariate polynomial systems of equations , 1998, STOC '98.

[18]  Ulrich Oberst,et al.  On inverse systems and squarefree decomposition of zero-dimensional polynomial ideals , 2006, J. Symb. Comput..