The F4-algorithm for Euclidean rings

• Autorzy: Afshan Sadiq
• Języki publikacji: EN

Abstrakty

EN

In this short note, we extend Faugére’s F4-algorithm for computing Gröbner bases to polynomial rings with coefficients in an Euclidean ring. Instead of successively reducing single S-polynomials as in Buchberger’s algorithm, the F4-algorithm is based on the simultaneous reduction of several polynomials.

Słowa kluczowe

EN

Global ordering; Gröbner bases

Kategorie tematyczne

• 13P25: Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
• 13P10: Gr\"obner bases; other bases for ideals and modules (e.g., Janet and border bases)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 6
• Strony: 1156-1159

Daty

wydano

2010-12-01

online

2010-10-30

Twórcy

autor

Afshan Sadiq

• GC University

Bibliografia

• [1] Adams W.W., Loustaunau P., An Introduction to Gröbner Bases, Grad. Stud. Math., 3, American Mathematical Scociety, Providence, 2003
• [2] Buchberger B., Bruno BuchbergerŠs PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal, J. Symbolic Comput., 2006, 41(3–4), 475–511 http://dx.doi.org/10.1016/j.jsc.2005.09.007
• [3] Cox D.A., Little J., O’shea D., Using Algebraic Geometry, 2nd ed., Grad. Texts in Math., 185, Springer, New York, 2005
• [4] Faugére J.-Ch., A new efficient algorithm for computing Gröbner bases (F 4), J. Pure Appl. Algebra, 1999, 139(1–3), 61–88 http://dx.doi.org/10.1016/S0022-4049(99)00005-5
• [5] Greuel G.-M., Pfister G., A Singular Introduction to Commutative Algebra, 2nd ed., Springer, Berlin, 2008
• [6] Greuel G.-M., Pfister G., Schönemann H., Singular - A Computer Algebra System for Polynomial Computations, free software under GNU General Public Licence (1990-to date), available at http://www.singular.uni-kl.de

Identyfikatory

DOI

10.2478/s11533-010-0064-x