Term rewriting and all that
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
On efficient computation of grobner bases
On efficient computation of grobner bases
Generalization of the F5 algorithm for calculating Gröbner bases for polynomial ideals
Programming and Computing Software
A new incremental algorithm for computing Groebner bases
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Journal of Symbolic Computation
F5C: A variant of Faugère's F5 algorithm with reduced Gröbner bases
Journal of Symbolic Computation
Modifying Faugère's F5 algorithm to ensure termination
ACM Communications in Computer Algebra
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The F5 algorithm, which calculates the Gr枚bner basis of an ideal generated by homogeneous polynomials, was proposed by Faug猫re in 2002; simultaneously, the correctness of this algorithm was proved under the condition of termination. However, termination itself was demonstrated only for a regular sequence of polynomials. In this paper, it is proved that the algorithm terminates for any input data. First, it is shown that if the algorithm does not terminate, it eventually generates two polynomials where the first is a reductor for the second. However, it is not argued that such a reduction is permitted by all the criteria introduced in F5. Next, it is shown that if such a pair exists, then there exists another pair for which the reduction is permitted by all the criteria, which is impossible.