I also would not use "ring" unless it had both a 0 and a 1. I have not looked at the rest of what has been done in any one detail. But I hope that all the functionality for abelian groups will be available for both additive and multiplicative groups, something which is certainly not the case at present.
John 2009/5/24 William Stein <wst...@gmail.com>: > > 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 -~----------~----~----~----~------~----~------~--~---
