On Jan 19, 6:28 am, Pierre <pierre.guil...@gmail.com> wrote: > hi all > > I've just realized that SAGE knows about the Steenrod algebra now. > Does it know about unstable modules, too ?
No, it doesn't, unfortunately. (Sage doesn't know about tensor products, which has delayed me from implementing various things, like the coproduct, and I suppose modules.) > I have another, related question. I have computed the unstable module > structure on the mod 2 cohomology rings of quite a bunch of finite > groups, see > > http://www-irma.u-strasbg.fr/~guillot/research/cohomology_of_groups/i... This looks very nice. > I was thinking that I should, somehow, provide a file readable by SAGE > so that people could use these algebras. Sure. > For one thing it would > provide many examples of unstable modules, which is always good to > test ideas about the Steenrod algebra. And regardless of the steenrod > operations, even the cohomology rings, as computed by Carlson and > others, are not available in SAGE yet (they're there as Magma files). > At this point I can relatively easily provide a partial translation > into SAGE. I think Simon King does some group cohomology computations with Sage, but I don't know exactly how he does it. > However I was wondering about the best "format" for this: assuming the > unstable algebra class does not exist, shall I present the algebras as > quotients of polynomial rings ? or just give a couple of SAGE lists > with the generators and relations, possibly just members of the formal > ring ? or something pickled perhaps ? I really don't know. Note that > I've got more information on these algebras yet (Stiefel-Whitney > classes...) It sounds to me as though you should create a new class, the UnstableAlgebra class, or the ModularGroupCohomology class, or something, which should derive from the class of quotients of polynomial algebras (so you can define at least part of the structure by specifying such a quotient), and then there should be extra structure: the Steenrod operations and Stiefel-Whitney classes and whatever else you have. > And shall I think of a mechanism for people to download ALL the > examples at once rather than separately ? (perhaps useful to try a > conjecture about unstable modules ?) You might have two files: one which defines the class, and another which presents all of the examples. I haven't used databases in Sage, but perhaps the examples could be a dictionary indexed by the group, or something like that? I'm looking forward to whatever you come up with. John Palmieri > suggestions most welcome. > Thanks, > > pierre --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
