On Jun 24, 12:23 am, "Nicolas M. Thiery" <nicolas.thi...@u-psud.fr> wrote: > On Wed, Jun 23, 2010 at 11:06:40PM -0700, John H Palmieri wrote: > > > If the grading is over NN/ZZ, or some naturally ordered monoid, I > > > would definitely argue for keeping degree for all elements. > > > That's not how I think of elements of a Z-graded algebra: in my > > experience, if they're not homogeneous, then they don't have a > > degree. It should probably be left as a case-by-case situation. > > Well, certainly not case by case, since for most of our graded > algebras (and we will have lots of them) we definitely want to have a > degree function for all elements. But maybe that should be just in a > subcategory (most of our algebras are actually graded connected over > NN). > > What makes you dislike having degree implemented for all elements? > > - That it could be accidently used on non homogeneous elements by the > caller, when not meant to, without an error raised?
Yes, or that mathematically, at least some people would view "degree" as being undefined except on homogeneous elements, and I would want Sage to reflect that. If someone tells me that an element of a graded algebra has degree d, then I expect it to be homogeneous: I expect it to give a well-defined action, raising degree by d, on any graded module over that graded algebra. If someone says that they have a "degree d polynomial", then I understand that this just means that the leading term is homogeneous of degree d, but if they say they have a "degree d element in the polynomial ring k[x,y,z] graded by ...", then I interpret this to be a homogeneous element. (By "if they say", I really mean, "if I read this in a paper dealing with graded algebras". For example, if X is a topological space and H^*(X) is its cohomology, then if someone talks about a "degree d element of H^*(X)", they are almost guaranteed, in my experience, to mean "a *homogeneous* element of degree d of H^*(X)".) I'm leaving my example as is: non-homogeneous elements don't have a well-defined degree. But I'm also including a comment about this choice in the docstring. > - That the specs might be ill-defined for non homogeneous elements > (e.g. if the order is not total)? > > - That there is a faster way to do it for homogeneous elements > (assuming we don't check for homogeneity)? > > > Because without forcing the list, the TestSuite fails. > Ah ok. Then that's just a bug that should be investigated and > fixed. Let me know when you have an updated patch on trac, and I'll > have a look. It's posted now: <http://trac.sagemath.org/sage_trac/ticket/9280> > It's great that we are having all those discussions. Once the example > will be finalized, we will have a sound basis to build upon. That's what I'm hoping. Thanks to everyone for all of your comments and suggestions. -- John -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To post to this group, send email to sage-combinat-de...@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.
