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
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
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
A Singular Introduction to Commutative Algebra
A Singular Introduction to Commutative Algebra
CT-RSA'11 Proceedings of the 11th international conference on Topics in cryptology: CT-RSA 2011
Linear algebra to compute syzygies and Gröbner bases
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Signature-based algorithms to compute Gröbner bases
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Computing a structured Gröbner basis approximately
Proceedings of the 36th international symposium on Symbolic and algebraic computation
A generalized criterion for signature related Gröbner basis algorithms
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Modifying Faugère's F5 algorithm to ensure termination
ACM Communications in Computer Algebra
A signature-based algorithm for computing Gröbner bases in solvable polynomial algebras
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
On the use of Buchberger criteria in G2V algorithm for calculating Gröbner bases
Programming and Computing Software
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
Involutive bases algorithm incorporating F5 criterion
Journal of Symbolic Computation
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 F5 algorithm for computing Grobner bases achieves a high level of efficiency through the careful analysis of signatures assigned to each computed polynomial. However, it computes and uses many polynomials that turn out to be redundant. Eliminating these redundant polynomials is a non-trivial task, because they correspond to signatures required for reduction. This paper revisits the theory underlying F5 and describes F5C, a new variant that prunes redundant polynomials, then re-computes signatures to preserve correctness. This strategy successfully reduces both overhead and execution time.