Details:
Title  Involutive method for computing Gr\"obner bases over $mathbb F_2$.  Author(s)  Vladimir P. Gerdt, M.V. Zinin  Type  Article in Journal  Abstract  In this paper, an involutive algorithm for computation of Gröbner bases for polynomial ideals in a ring of polynomials in many variables over the finite field 𝔽2 with the values of variables belonging of 𝔽2 is considered. The algorithm uses Janet division and is specialized for a graded reverse lexicographical order of monomials. We compare efficiency of this algorithm and its implementation in C++ with that of the Buchberger algorithm, as well as with the algorithms of computation of Gröbner bases that are built in the computer algebra systems Singular and CoCoA and in the FGb library for Maple. For the sake of comparison, we took widely used examples of computation of Gröbner bases over ℚ and adapted them for 𝔽2. Polynomial systems over 𝔽2 with the values of variables in 𝔽2 are of interest, in particular, for modeling quantum computation and a number of cryptanalysis problems.  ISSN  03617688; 16083261/e 
URL 
http://link.springer.com/article/10.1134%2FS0361768808040026 
Language  English  Journal  Program. Comput. Softw.  Volume  34  Number  4  Pages  191203  Publisher  Springer US, New York, NY; Pleiades Publishing, New York, NY; MAIK ``Nauka/Interperiodica  Year  2008  Edition  0  Translation 
No  Refereed 
No 
