Termination of the F5 algorithm

Galkin, V. V.

doi:10.1134/s0361768814020042

Cited by 3 publications

(1 citation statement)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proving termination of F5 had been an open problem for a decade before it was settled by Galkin [6]. PHW later proved that F5GEN (and hence RB) terminates [8], which implies that F5 terminates.…”

Section: Termination Of Rb and Hence F5mentioning

confidence: 99%

Signature rewriting in gröbner basis computation

Eder

Roune

2013

Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation

View full text Add to dashboard Cite

We introduce the RB algorithm for Gröbner basis computation, a simpler yet equivalent algorithm to F5GEN. RB contains the original unmodified F5 algorithm as a special case, so it is possible to study and understand F5 by considering the simpler RB. We present simple yet complete proofs of this fact and of F5's termination and correctness.RB is parametrized by a rewrite order and it contains many published algorithms as special cases, including SB. We prove that SB is the best possible instantiation of RB in the following sense. Let X be any instantiation of RB (such as F5). Then the S-pairs reduced by SB are always a subset of the S-pairs reduced by X and the basis computed by SB is always a subset of the basis computed by X.

show abstract

Section: Termination Of Rb and Hence F5mentioning

confidence: 99%

Signature rewriting in gröbner basis computation

Eder

Roune

2013

Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation

View full text Add to dashboard Cite

show abstract

A survey on signature-based algorithms for computing Gröbner bases

Eder

Faugère

2017

Journal of Symbolic Computation

View full text Add to dashboard Cite

This paper is a survey on the area of signature-based Gröbner basis algorithms that was initiated by Faugère's F5 algorithm in 2002. We explain the general ideas behind the usage of signatures. We show how to classify the various known variants by 3 different orderings. For this we give translations between different notations and show that besides notations many approaches are just the same. Moreover, we give a general description of how the idea of signatures is quite natural when performing the reduction process using linear algebra. This survey shall help to outline this field of active research. At the moment the area of signature-based Gröbner basis algorithms is confusing and vast. More and more papers are published proving statements already proven before, and even more publications can be found on "new" variants that boil down to be a known one just with a different notation. In this paper we try to give a rigorous survey on signature-based Gröbner basis theory, including all variants known up to now. We lay an emphasis on understanding and we show how the variants presented over the last years are mostly differ in small parts only. Moreover, we give the reader a vocabulary book at hand which helps to understand how notations, varying for different authors, coincide. Since this is a survey, we do not give proofs if they are long, complex, or do not help in understanding the topic. We always explain the idea behind the proofs and refer to the related publication which includes a complete proof. There the reader is then, with our descriptions and explanations, able to understand the

show abstract

Axioms for a theory of signature bases

Lairez

2024

Journal of Symbolic Computation

View full text Add to dashboard Cite

Termination of the F5 algorithm

Cited by 3 publications

References 9 publications

Signature rewriting in gröbner basis computation

Signature rewriting in gröbner basis computation

A survey on signature-based algorithms for computing Gröbner bases

Axioms for a theory of signature bases

Contact Info

Product

Resources

About