A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)

@inproceedings{Faug232re2002ANE,
title={A new efficient algorithm for computing Gr{\"o}bner bases without reduction to zero (F5)},
author={Jean Charles Faug232re},
booktitle={ISSAC '02},
year={2002}
}

This paper introduces a new efficient algorithm for computing Gröbner bases. We replace the Buchberger criteria by an optimal criteria. We give a proof that the resulting algorithm (called F5) generates no useless critical pairs if the input is a regular sequence. This a new result by itself but a first implementation of the algorithm F5 shows that it is also very efficient in practice: for instance previously untractable problems can be solved (cyclic 10). In practice for most examples there… CONTINUE READING