On an installation of Buchberger's algorithm
Journal of Symbolic Computation
Gröbner bases computation using syzygies
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
A criterion for detecting unnecessary reductions in the construction of Groebner bases
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Gröbner-Bases, Gaussian elimination and resolution of systems of algebraic equations
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Computing in Algebraic Geometry: A Quick Start using SINGULAR (Algorithms and Computation in Mathematics)
PolyBoRi: A framework for Gröbner-basis computations with Boolean polynomials
Journal of Symbolic Computation
A Singular Introduction to Commutative Algebra
A Singular Introduction to Commutative Algebra
On efficient computation of grobner bases
On efficient computation of grobner bases
F5C: A variant of Faugère's F5 algorithm with reduced Gröbner bases
Journal of Symbolic Computation
MXL3: an efficient algorithm for computing gröbner bases of zero-dimensional ideals
ICISC'09 Proceedings of the 12th international conference on Information security and cryptology
A signature-based algorithm for computing Gröbner bases in solvable polynomial algebras
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
The termination of the F5 algorithm revisited
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Improving incremental signature-based Gröbner basis algorithms
ACM Communications in Computer Algebra
An analysis of inhomogeneous signature-based Gröbner basis computations
Journal of Symbolic Computation
Termination of the F5 algorithm
Programming and Computing Software
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The structure of the F5 algorithm to compute Gröbner bases makes it very efficient. However, it is not clear whether it terminates for all inputs, not even for "regular sequences". This paper has two major parts. In the first part, we describe in detail the difficulties related to a proof of termination. In the second part, we explore three variants that ensure termination. Two of these have appeared previously in dissertations, and ensure termination by checking for a Gröbner basis using traditional criteria. The third variant, F5+, identifies a degree bound using a distinction between "necessary" and "redundant" critical pairs that follows from the analysis in the first part. Experimental evidence suggests this third approach is the most efficient of the three.