F₅ – Gröbner bases using signatures

Ferdinand motivates and introduces the concepts used in signature based Gröbner basis computation algorithms, like the widely celebrated F₅. Omitted proofs can be found in the literature mentioned in the video and listed below. If you have questions, feel free to write him at ferdinand (at) asdm (dot) gmbh.

[Bibliography]
Faugère, J.C.: A new efficient algorithm for computing Gröbner bases without reduction to zero (F₅). In: Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation. pp. 75–83 (2002)

Cox, D.A., Little, J., O’Shea, D.: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer Science & Business Media (2013)

Eder, C., Faugère, J.C.: A survey on signature-based algorithms for computing Gröbner bases. Journal of Symbolic Computation 80, 719–784 (2017)