# The F4-algorithm for Euclidean rings

Open Mathematics (2010)

- Volume: 8, Issue: 6, page 1156-1159
- ISSN: 2391-5455

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topAfshan Sadiq. "The F4-algorithm for Euclidean rings." Open Mathematics 8.6 (2010): 1156-1159. <http://eudml.org/doc/269019>.

@article{AfshanSadiq2010,

abstract = {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.},

author = {Afshan Sadiq},

journal = {Open Mathematics},

keywords = {Global ordering; Gröbner bases; global ordering},

language = {eng},

number = {6},

pages = {1156-1159},

title = {The F4-algorithm for Euclidean rings},

url = {http://eudml.org/doc/269019},

volume = {8},

year = {2010},

}

TY - JOUR

AU - Afshan Sadiq

TI - The F4-algorithm for Euclidean rings

JO - Open Mathematics

PY - 2010

VL - 8

IS - 6

SP - 1156

EP - 1159

AB - 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.

LA - eng

KW - Global ordering; Gröbner bases; global ordering

UR - http://eudml.org/doc/269019

ER -

## References

top- [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

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