On Oct 5, 2:41 pm, Niles <[email protected]> wrote: > Hello all, > > I'm interested in implementing some computational algebraic topology > using Hopf algebroids. As a warm-up, I thought I would see what > functionality exists in Sage for coalgebras, comodules, Hopf algebras, > etc. What currently exists seems to be placeholder categories (e.g. > [1], [2]), and some implementation for group algebras (see [3]). I've > read through the Category Theory Primer (Draft) [4] and the Categories > Tutorial (Draft) [5], but none of this leaves me with a good sense of > how to proceed. It's clear that someone has a vision of how new > functionality (like computations with Hopf algebroids) should be added > to Sage, but it's not clear to me what that vision is (beyond step > one, which seems to be "make a placeholder category for it"). > > If I just want to extend Sage's capabilities for, say, Hopf algebras > (build some new classes for Hopf algebras other than group algebras, > and add some new generic functionality), what would be the right place > to start? Or the right example to follow? Or is there another source > I should be looking at? Whatever answer you give me, does the same > answer hold for comodules over coalgebras, and the like?
First, you might want to post this on sage-combinat-devel and/or sage- algebra, as well as sage-devel. Second, I think having something with Hopf algebroids would be great! Please cc me on any ticket. Third, the file devel/sage/sage/categories/examples/ hopf_algebras_with_basis.py is an instructive, although brief, application of the basic Hopf algebra structure. At least you can see how to use CombinatorialFreeModule combined with a method like "antipode_on_basis" to define an antipode. Fourth, if you want to review <http://trac.sagemath.org/sage_trac/ ticket/10052>, you'll see how I used the Hopf algebra stuff in Sage to rewrite the implementation of the Steenrod algebra. (Don't feel any obligation, but I'm not sure who else to ask to do this...) A while ago, I polled people about topological ideas that might get added to Sage: see <http://wiki.sagemath.org/topology>. Unfortunately there seems to be nothing about Hopf algebroids (although formal group laws were mentioned). If you feel like adding to that page, please do. -- John -- To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
