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2011 | 9 | 4 | 897-904
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An algorithm for primary decomposition in polynomial rings over the integers

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EN
Abstrakty
EN
We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals, resp. over finite fields, and the idea of Shimoyama-Yokoyama, resp. Eisenbud-Hunecke-Vasconcelos, to extract primary ideals from pseudo-primary ideals. A parallelized version of the algorithm is implemented in Singular. Examples and timings are given at the end of the article.
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
4
Strony
897-904
Opis fizyczny
Daty
wydano
2011-08-01
online
2011-05-26
Twórcy
autor
Bibliografia
  • [1] Adams W.W., Loustaunau P., An Introduction to Gröbner Bases, Grad. Stud. Math., 3, American Mathematical Society, Providence, 1994
  • [2] Ayoub C.W., The decomposition theorem for ideals in polynomial rings over a domain, J. Algebra, 1982, 76(1), 99–110 http://dx.doi.org/10.1016/0021-8693(82)90239-3
  • [3] Boege W., Gebauer R., Kredel H., Some examples for solving systems of algebraic equations by calculating Groebner bases, J. Symbolic Comput, 1986, 2(1), 83–98 http://dx.doi.org/10.1016/S0747-7171(86)80014-1
  • [4] Decker W., Greuel G.-M., Pfister G., Primary decomposition: algorithms and comparisons, In: Algorithmic Algebra and Number Theory, Heidelberg, 1997, Springer, Berlin, 1999, 187–220
  • [5] Decker W., Greuel G.-M., Pfister G., Schönemann H., Sincular3-1-1 - A computer algebra system for polynomial computations, 2010, http://www.singular.uni-kl.de
  • [6] Eisenbud D., Huneke C., Vasconcelos W., Direct methods for primary decomposition, Invent. Math., 1992, 110(2), 207–235 http://dx.doi.org/10.1007/BF01231331
  • [7] Eisenbud D., Sturmfels B., Binomial ideals, Duke Math. J., 1996, 84(1), 1–45 http://dx.doi.org/10.1215/S0012-7094-96-08401-X
  • [8] Gianni P., Trager B., Zacharias G., Gröbner bases and primary decomposition of polynomial ideals, J. Symbolic Comput, 1988, 6(2–3), 149–167 http://dx.doi.org/10.1016/S0747-7171(88)80040-3
  • [9] Gräbe H.-G., The SymbolicData Project - Tools and Data for Testing Computer Algebra Software, 2010, http://www.symbolicdata.org
  • [10] Greuel G.-M., Pfister G., A Singular Introduction to Commutative Algebra, 2nd ed., Springer, Berlin, 2008
  • [11] Greuel C.-M., Seelisch F., Wienand O., The Gröbner basis of the ideal of vanishing polynomials, J. Symbolic Comput., 2011, 46(5), 561–570 http://dx.doi.org/10.1016/j.jsc.2010.10.006
  • [12] Seidenberg A., Constructions in a polynomial ring over the ring of integers, Amer. J. Math., 1978, 100(4), 685–703 http://dx.doi.org/10.2307/2373905
  • [13] Shimoyama T, Yokoyama K., Localization and primary decomposition of polynomial ideals, J. Symbolic Comput., 1996, 22(3), 247–277 http://dx.doi.org/10.1006/jsco.1996.0052
  • [14] Wienand O., Algorithms for Symbolic Computation and their Applications, Ph.D. thesis, Kaiserslautern, 2011
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0037-8
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