= F5 Project at Sage Days 12 =

== Participants ==
 * Martin Albrecht
 * John Perry

== Questions/Tasks ==
 * Does F5 terminate for all inputs and can it be proven? What adaptations are necessary if not.
 * What is the relationship between the F5 criteria and the Buchberger criteria?
 * Come up with an F4-style F5.

== Literature ==
 * Faugere's [[http://www-spaces.lip6.fr/%40papers/F02a.pdf|original paper]]
 * Till Stegers' [[http://eprint.iacr.org/2006/404|Diplom thesis]]
 * Justin Gash's [[attachment:gash-phd.pdf|PhD thesis on F5]]
 * Christian Eder: [[http://arxiv.org/abs/0804.2033|On The Criteria Of The F5 Algorithm]]
 * Christian Eder: [[http://arxiv.org/abs/0810.5335|The Algorithmic Behaviour of the F5 Algorithm]]

== Code ==
 * John Perry's Singular [[http://www.math.usm.edu/perry/Research/|implementation]] of F5 (three variants)
 * Till Stegers' Magma [[http://wwwcsif.cs.ucdavis.edu/~stegers/f5_magma.tar.gz|implementation]] of F5
 * Simon King's Sage/Cython [[days10/CodingSprint|implementation]] of F5
 * Martin Albrecht's Sage/Python [[http://www.bitbucket.org/malb/algebraic_attacks/src/tip/f5.py|implementation]] of F5 (three variants)
 * Martin Albrecht's Sage/Python [[http://www.bitbucket.org/malb/algebraic_attacks/src/tip/f5matrix.py|implementation]] of Matrix F5