Localization and primary decomposition of polynomial ideals

Journal of Symbolic Computation

Volumn 22, Issue 3, 1996, Pages 247-277

  Shimoyama, Takeshi ^a   Yokoyama, Kazuhiro ^a  

^a FUJITSU LABORATORIES LTD   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030096538     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1996.0052     Document Type: Article

References (24)

1. Aho, A.V., Hopcroft, J.E., Ullman, J.D. (1974). The Design and Analysis of Computer Algorithms. Reading, MA: Addison-Wesley.
2. Atiyah, M.F., MacDonald, I.G. (1969). Introduction to Commutative Algebra. Reading, MA: Addison-Wesley.
3. Alonso, M.E., Mora, T., Raimondo, M. (1990). Local decomposition algorithms. AAECC-8, Springer LNCS 508, 208-221.
4. Backelin, J., Fröberg, R. (1991). How we prove that there are exactly 924 cyclic 7-roots. Proc. of ISSAC'91, ACM Press, 103-111.
5. Becker, T., Weispfenning, V. (1993). Gröbner Bases. New York: Springer-Verlag.
6. Boege, W., Gebauer, R., Kredel, H. (1986). Some examples for solving systems of algebraic equations by calculating Gröbner bases. J. Symbolic Computation 1, 83-98.
7. Buchberger, B. (1965). Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. Doctoral Dissertation Math. Inst. University of Innsbruck, Austria.
8. Buchberger, B. (1985) Gröbner bases: An algorithmic method in polynomial ideal theory. In: Bose, N.K. (ed.), Multidimensional Systems Theory, Dordrecht: Reidel, 184-232.
9. Eisenbud, D., Huneke, C., Vasconcelos, W. (1992). Direct methods for primary decomposition. Inventiones Mathematicae 110, 207-235.
10. Gianni, P., Trager, B., Zacharias, G. (1988). Gröbner bases and primary decomposition of polynomial ideals. J. Symbolic Computation 6, 149-167.
11. Gräbe H.G. (1994). On factorized Gröbner bases. To appear in Proc. Computer Algebra in Science and Engineering.
12. Gräbe H.G. (1995a). CALI-A REDUCE package for constructive commutative algebra, Version 2.2.1. (anonymous ftp from aix550.informatik.uni-leipzig.de)
13. Gräbe H.G. (1995b). Minimal primary decomposition and factorized Gröbner bases. To appear in Journal of Appl. Alg. in Eng. Comm. and Comp.
14. Kalkbrener, M., Sturmfels, B. (1993). Initial complexes of prime ideals. To appear in Advances in Mathematics.
15. Kredel, H. (1987). Primary ideal decomposition. EUROCAL '87, Springer LNCS 378, 270-281.
16. Kredel, H., Weispfenning, V. (1988). Computing dimension and independent sets for polynomial ideals. J. Symbolic Computation 6, 231-247.
17. Lazard, D. (1985). Ideal bases and primary decomposition: case of two variables. J. Symbolic Computation 1, 261-270.
18. Nagata, M. (1962). Local Rings. Tracts in Mathematics Number 13, New York: Interscience Publishers.
19. Noro, M., Takeshima, T. (1992). Risa/Asir - a computer algebra system. Proc. of ISSAC'92, ACM Press, 387-396. (anonymous ftp from (164.71.1.131) endeavor.fujitsu.co.jp, directory /pub/isis/asir)
20. Oaku, T. (1994). Computation of the characteristic variety and the singular locus of a system of differential equations with polynomial coefficients. Japan J. Indust. Appl. Math. 11, 485-497.
21. Rutman, E.W. (1992). Gröbner bases and primary decomposition of modules. J. Symbolic Computation 14, 483-503.
22. Shimoyama, T., Yokoyama, K. (1994). Localization and primary decomposition of polynomial ideals. FUJITSU ISIS Research Report, ISIS-RR-94-10E.
23. Wang, D. (1992). Irreducible decomposition of algebraic varieties via characteristic sets and Gröbner bases. Computer Aided Geometric Design 9, 471-484.
24. Zariski, O., Samuel, P. (1958/60). Commutative Algebra, vols. I, II. Princeton, NJ, Van Nostrand. Reprint New York: Springer-Verlag, 1975/79.