On 5/23/09, Nicolas M. Thiery <nicolas.thi...@u-psud.fr> wrote: > > Dear Sage developers, > > The point below was discussed during Sage Days 15, > > On Sun, Nov 09, 2008 at 04:31:52PM +0100, Nicolas Thiéry wrote: >> >> ... About naming conventions for categories: >> >> - Do we want to stick to the (possibly questionable) Axiom/MuPAD >> convention to distinguish between monoids (or groups/...) written >> additively or multiplicatively: >> >> - AbelianGroups, AbelianMonoids, ...: structure for the + >> operation >> - Monoids, Groups, CommutativeGroups, ...: structure for the * >> operation >> >> With this convention, a Ring is both an AbelianGroup and a Monoid >> >> Alternatively, one could use the more verbose AdditiveMonoid >> w.r.t. MultiplicativeMonoid; other suggestions are welcome. >> >> Part of the question is whether we will ever want to have a >> category for non abelian monoids written additively (I would >> personnaly frown upon this, as much as I dislike using + for >> concatenation of lists and strings; but that might be just me). > > We discussed this point at Sage Days 15, and apparently the consensus > was to go for the more explicit, at the price of breaking with > historical conventions in Axiom and MuPAD (and actually also in Sage: > before the category patch, Rings inherits from AbelianGroups!). > > Since this was not debated on the list, this e-mail is a last call for > comments before the things get set in stone. > > So: is there a reasonable consensus on the following naming scheme: > > - Structure for the + operation: > AdditiveMonoids, AdditiveGroups, CommutativeAdditiveMonoids, ... > > - Structure for the * operation: > Monoids, Groups, CommutativeMonoids, CommutativeGroups > > Then, a Ring would be a CommutativeAdditiveGroup and a Monoid. > > > Note: I personally vote against specifying Multiplicative. > CommutativeMultiplicativeGroups is unnecessary long and cumbersome. > The convention above readily breaks any ambiguity. > > On a similar note, we will need conventions at some point for rings > without 1 or without 0. Here I am a totally in favor of breaking with > the historical hack which was certainly fun but not quite reasonable: > `i` stands for `identity`, and n for neutral. So: > > - Ring: usual ring > - Rig: Ring without 0 > - Rng: Ring without 1 > - Rg: Ring without 1 and 0 > > Suggestions?
For me rings always have both 1 and 0. I would call a "ring without 1" an algebra. > > Cheers, > Nicolas > -- > Nicolas M. Thiéry "Isil" <nthi...@users.sf.net> > http://Nicolas.Thiery.name/ > > > > -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
