Timeline for What algorithm in algebraic geometry should I work on implementing?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| May 25, 2010 at 4:55 | comment | added | Junkie | I have heard that Allan Steel has a version of F5 in Magma, which works better than F4 in some specific examples, but it is not publically available. I definitely agree that GB algos are extremely tricky to implement well. My notion is that F4 has been tried by a few people (maybe 10 in all) to implement it, but only Faugere and Steel consistently can beat a souped-up version of the classical Buchberger. Another idea for GBs would be to take something already out there, and widen the set of base rings allowed. Inexact rings, are a real pain for correctness. but would be interesting. | |
| Mar 17, 2010 at 13:04 | comment | added | Jacques Carette | @Torsten: extremely efficient versions are tricky, moderately efficient versions are not. Picking a reasonable language (like O'Caml) for the task would make it easier than the usual suspects. | |
| Mar 17, 2010 at 12:53 | comment | added | Steven Gubkin | Cool. This does seem low enough to the ground that we could after a crash course in Groebner bases we could get started on it. If it is going to be really "gory" (as Torsten suggests) it might not be the best project though. @Kevin: That does seem doable! An option to keep in mind. | |
| Mar 17, 2010 at 7:42 | comment | added | Kevin Buzzard | If you want an "application of Grobner bases" (which unfortunately would mean calculating over Z_2 (the 2-adic integers) rather than a field) then I'll remark that as far as I know it's still an open problem as to whether every group scheme of order 4 is killed by 4, and this always seems to me to be in the general ballpark of accessibility, it just needs a good algebraic geometer and a good programmer ;-) The alg geometer needs to translate the question into a ring theory one, using the programmer to guide them as to which variables to use to make things most efficient. | |
| Mar 17, 2010 at 5:16 | comment | added | Torsten Ekedahl | I have the impression that Gröbner basis algortihms are very tricky to implement efficiently and if so this may put too much emphasis on gory details. | |
| Mar 16, 2010 at 23:32 | history | answered | Jacques Carette | CC BY-SA 2.5 |