|
|
|
References
|
|
|
1. |
N. Burbaki, Kommutativnaya algebra, Mir, M., 1971 |
2. |
A. L. Chistov, “Algoritm polinomialnoi slozhnosti dlya razlozheniya mnogochlenov na neprivodimye mnozhiteli i nakhozhdenie komponent mnogoobraziya v subeksponentsialnoe vremya”, Zap. nauchn. semin. LOMI, 137, 1984, 124–188 |
3. |
A. L. Chistov, “Uluchshenie otsenki slozhnosti dlya resheniya sistem algebraicheskikh uravnenii”, Zap. nauchn. semin. POMI, 390, 2011, 299–306 |
4. |
A. L. Chistov, “Sistemy s parametrami, ili effektivnoe reshenie sistem polinomialnykh uravnenii $33$ goda spustya. I”, Zap. nauchn. semin. POMI, 462, 2017, 122–166 |
5. |
A. L. Chistov, “Sistemy s parametrami, ili effektivnoe reshenie sistem polinomialnykh uravnenii $33$ goda spustya. II”, Zap. nauchn. semin. POMI, 468, 2018, 138–176 |
6. |
A. L. Chistov, “Sistemy s parametrami, ili effektivnoe reshenie sistem polinomialnykh uravnenii $33$ goda spustya. III”, Zap. nauchn. semin. POMI, 481, 2018, 146–177 |
7. |
A. L. Chistov, “Neravenstva dlya funktsii Gilberta i primarnye razlozheniya”, Algebra i analiz, 19:6 (2007), 143–172 |
8. |
A. L. Chistov, “Dvazhdy eksponentsialnaya nizhnyaya otsenka na stepen sistemy obrazuyuschikh polinomialnogo prostogo ideala”, Algebra i analiz, 20:6 (2008), 186–213 |
9. |
W. Decker, G. M. Greuel, G. Pfister, “Primary decomposition: algorithms and comparisons”, Algorithmic Algebra and Number Theory, eds. B. H. Matzat, G. M. Greuel, G. Hiss, Springer, Berlin–Heidelberg, 1999, 187–220 |
10. |
G. Hermann, “Die Frage der endlich vielen Schritte in der Theorie der Polynomideale”, Math. Ann., 95 (1926), 736–788 |
11. |
E. Lasker, “Zur Theorie der Moduln und Ideale”, Math. Ann., 60 (1905), 19–116 |
12. |
D. Lazard, “Résolution des systèmes d'équations algébriques”, Theoret. Comput. Sci., 15 (1981), 77–110 |
13. |
N. Masayuki, “New algorithms for computing primary decomposition of polynomial ideals”, Mathematical Software – ICMS 2010, Lect. Notes Comput. Sci., 6327, eds. K. Fukuda, J. van der Hoeven, M. Joswig, N. Takayama, Springer, Berlin–Heidelberg, 2010, 233–244 |
14. |
E. Noether, “Idealtheorie in Ringbereichen”, Math. Ann., 83:1 (1921), 24–66 |
15. |
V. Ortiz, “Sur une certaine décomposition canonique d'un idéal en intersection d'idéaux primaires dans un anneau noethérien commutatif”, C. R. Acad. Sci. Paris, 248 (1959), 3385–3387 |
16. |
A. Seidenberg, “Constructions in algebra”, Trans. Amer. Math. Soc., 197 (1974), 273–313 |
17. |
T. Shimoyama, K. Yokoyama, “Localization and primary decomposition of polynomial ideals”, J. Symbolic Comput., 22 (1996), 247–277 |
18. |
Y. Yao, “Primary decomposition: compatibility, independence and linear growth”, Proc. Amer. Math. Soc., 130:6 (2002), 1629–1637 |