Border bases and kernels of homomorphisms and of derivations

• Autorzy: Janusz Zieliński
• Języki publikacji: EN

Abstrakty

EN

Border bases are an alternative to Gröbner bases. The former have several more desirable properties. In this paper some constructions and operations on border bases are presented. Namely; the case of a restriction of an ideal to a polynomial ring (in a smaller number of variables), the case of the intersection of two ideals, and the case of the kernel of a homomorphism of polynomial rings. These constructions are applied to the ideal of relations and to factorizable derivations.

Słowa kluczowe

EN

Border basis; Gröbner basis; Factorizable derivation; Ideal of relations

Kategorie tematyczne

• 12H05: Differential algebra
• 12Y05: Computational aspects of field theory and polynomials
• 13P10: Gr\"obner bases; other bases for ideals and modules (e.g., Janet and border bases)
• 13N15: Derivations
• 68W30: Symbolic computation and algebraic computation

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 4
• Strony: 780-785

Daty

wydano

2010-08-01

online

2010-07-24

Twórcy

autor

Janusz Zieliński

• Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Toruń, Poland

Bibliografia

• [1] Chen Y.F., Meng X.H., Border bases of positive dimensional polynomial ideals, In: Proceedings of the 2007 International Workshop on Symbolic-Numeric Computation, London, Ontario, July 25–27, ACM, New York, 2007, 65–71
• [2] 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[Crossref]
• [3] Kehrein A., Kreuzer M., Characterizations of border bases, J. Pure Appl. Algebra, 2005, 196(2–3), 251–270 http://dx.doi.org/10.1016/j.jpaa.2004.08.028[Crossref]
• [4] Kehrein A., Kreuzer M., Computing border bases, J. Pure Appl. Algebra, 2006, 205(2), 279–295 http://dx.doi.org/10.1016/j.jpaa.2005.07.006[Crossref]
• [5] Kehrein A., Kreuzer M., Robbiano L., An algebraist’s view on border bases, In: Solving polynomial equations, Algorithms Comput. Math., 14, Springer, Berlin, 2005, 169–202 http://dx.doi.org/10.1007/3-540-27357-3_4[Crossref]
• [6] Kreuzer M., Robbiano L., Computational Commutative Algebra, 1&2, Springer, Berlin, 2000&2005 http://dx.doi.org/10.1007/978-3-540-70628-1[Crossref]
• [7] Nowicki A., Zielinski J., Rational constants of monomial derivations, J. Algebra, 2006, 302(1), 387–418 http://dx.doi.org/10.1016/j.jalgebra.2006.02.034[Crossref]
• [8] Zieliński J., Factorizable derivations and ideals of relations, Comm. Algebra, 2007, 35(3), 983–997 http://dx.doi.org/10.1080/00927870601117639[WoS][Crossref]

Identyfikatory

DOI

10.2478/s11533-010-0045-0