Sun, 25. Jan 2009

F4-Style F5

When I asked Jean-Charles Faugère a while back why he doesn’t publish his F4-style F5 he answered that there would be nothing to publish since it is straight forward. I don’t know about that but I was actually quite surprised how quickly John Perry and I could come up with an F4-style F5 here at Sage Days 12 (pictures). Btw. Till Stegers calls this F4.5 but I don’t know how Jean-Charles Faugère refers it.

I’ve uploaded the toy implementation to bitbucket. It seems to behave like the polynomial F5 implementation in the same file, so at least it is bug by bug compatible with that. Speaking of behaviour: When computing Cyclic-6 over $\mathbb{F}_{32003}$ w.r.t. degrevlex I noticed that my F4 implementation only goes up to degree 16 while my F5 implementations need to consider degree 18. Although no matrix is constructed for degree 18, the F4-style F5 does construct and eliminate a matrix for degree 17 … puzzling.

posted at: 22:45 :: permanent link

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F4-Style F5