Re: [sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
Dear category fans, Thanks everybody for your feedback in this discussion! Let me try to make a synthesis. (1) In the long run, Algebras(R) should match with Wikipedia's definition and not assume any axiom: an algebra A is an R-module with a binary multiplication which is bilinear. Note that this might not be the end of the discussion: at some point we will want to support R to be just a semiring and in this case `A` we would not necessarily need to require A to have additive inverses. But one problem at a time. (2) Point (1) is a backward incompatible change, which will take some work. There is already enough on our plate with #10963, so this change is postponed for later. For now we need a temporary name. The two current suggestions are: - NonAssociativeNonUnitalAlgebras - MagmaticAlgebras The former is actually technically correct in English (though not so nice). In any cases, there seems to be a preference of the latter (this means more work for me, but so be it). Note: MagmaAlgebras is not an option as it is confusing. Since we call group algebra the algebra of a group, a magma algebra stands naturally for the algebra of a magma. (3) For the related situation of a multiplicative magma that distributes over a magma, there are two suggestions currently: - DistributiveMagmasAndAdditiveMagmas - MagmaticRing The first one is ugly but rather explicit. The second one is consistent with MagmaticAlgebras, though we don't care so much since MagmaticAlgebras will eventually disappear. By default I'll stick with the former to save time, but I could bend under popular pressure. (4) There are way too many categories in the global name space. There is for example no reason to have FiniteDimensionalHopfAlgebrasWithBasis(QQ) there. Some people further said that there is actually no reason whatsoever to have any category in the global name space because categories are only for the programmer. I object to that part. The following are perfectly natural things a user would want to do with categories: sage: A in Fields() # Is A known to be a field? sage: Hom(F, G, Groups()) # Construct a homset in a given category sage: Groups? # What is a group? sage: Groups().example()# Give me an example sage: S = Semigroups().example(); S?? # Show me the code! sage: DivisionRings() Sets().Finite() # Please remind me about Wedderburn Category of finite fields sage: Fields().all_implementations()# All fields in Sage (Florent has some code toward this) sage: MatrixGroup(..., category = FiniteGroups()) # I promise that the result is actually finite In short, categories are about the mathematics in Sage and we want our user to use and explore this mathematics. Of course #10963 will allow to considerably reduce the number of entry points being actually imported by default since e.g.: FiniteGroups() can now be Groups().Finite(), GradedHopfAlgebrasWithBasis() can now be HopfAlgebras().Graded().WithBasis() I could possibly be convinced to further reduce the pollution by making the categories accessible as categories.Groups() instead of Groups(). In any cases, this will be for after #10963. (5) The docstring of many categories could take some love as it is an important entry point for users. Volunteers are welcome once #10963 will have been merged. Cheers, Nicolas -- Nicolas M. Thiéry Isil nthi...@users.sf.net http://Nicolas.Thiery.name/ -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
[sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
Dear all, While working on an implementation of finite algebras over fields (#12141) I was slightly annoyed by the fact that Algebras are currently assumed to be unital. I agree with Simon King's opinion: I don't really like magma algebra or magmatic algebra, but that's mainly because I never heard anyone using this notion before. I'd rather describe an algebra as a module over an appropriate operade than call it magma algebra. What I'd prefer is very simple: Just say algebra to an algebra. If any additional axiom holds, then the algebra should be called commutative, associative, unital, noetherian, lie, finite-dimensional, or whatever you like. But don't mention the *absence* of axioms! Best regards, Peter Bruin -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
[sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
On 2013-07-04, Volker Braun vbraun.n...@gmail.com wrote: --=_Part_6640_25172370.1372980267137 Content-Type: text/plain; charset=ISO-8859-1 +1 for switching Algebras to CommutativeUnitalAlgebras (or so) and the using Algebras for the most general algebra. ++ all these magma or generic are quite confusing. In fact, I don't understand why Algebras has to be in the global namespace. I've never once found it useful to start an interactive session by instantiating a new category. +1 (although full-time category theorists might disagree :)) The docstring isn't particularly useful either. Essentially, it is only is a trap for newcomers. Unless somebody has a really good use case I wouldn't mind removing all categories from the global namespace and implicitly making their name an implementation detail subject to change as the category hierarchy matures. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
[sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
Hi Dima, On 2013-07-05, Dima Pasechnik dimp...@gmail.com wrote: In fact, I don't understand why Algebras has to be in the global namespace. I've never once found it useful to start an interactive session by instantiating a new category. +1 (although full-time category theorists might disagree :)) I think I am only part-time categorist. On the one hand, I too think that there is currently no need to insert categories into the global namespace. Categories do a lot of useful stuff in the background, but usually they do not show up in the foreground. On the other hand, this might actually change with Nicolas' upcoming functorial constructions patch. If Sage would be able to really do fancy constructions with categories, then it would certainly make sense to do/test these constructions in an interactive session. On the third hand (on the one foot??), if one wants to do arithmetics *on* categories (rather than just arithmetics *using* categories), then one can still do something like from sage.categories import * without too much effort. On the other foot, removing categories from the global namespace would probably break a lot of tests. How should this be organised? On the functorial constructions ticket, which already is big enough? On a later ticket? On an earlier ticket? Best regards, Simon -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
On Jul 5, 2013 7:13 AM, Simon King simon.k...@uni-jena.de wrote: Hi Dima, On 2013-07-05, Dima Pasechnik dimp...@gmail.com wrote: In fact, I don't understand why Algebras has to be in the global namespace. I've never once found it useful to start an interactive session by instantiating a new category. +1 (although full-time category theorists might disagree :)) I think I am only part-time categorist. On the one hand, I too think that there is currently no need to insert categories into the global namespace. Categories do a lot of useful stuff in the background, but usually they do not show up in the foreground. On the other hand, this might actually change with Nicolas' upcoming functorial constructions patch. If Sage would be able to really do fancy constructions with categories, then it would certainly make sense to do/test these constructions in an interactive session. On the third hand (on the one foot??), if one wants to do arithmetics *on* categories (rather than just arithmetics *using* categories), then one can still do something like from sage.categories import * without too much effort. I like the idea of being able to do categories.tab and seeing a list of the available categories (or some reasonable subset of). For the record, I like the term magmatic algebras. It is not standard/common terminology and would certainly invite the user to look at the documentation to figure out what it is. Franco On the other foot, removing categories from the global namespace would probably break a lot of tests. How should this be organised? On the functorial constructions ticket, which already is big enough? On a later ticket? On an earlier ticket? Best regards, Simon -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
[sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
Hi Franco, On 2013-07-05, Franco Saliola sali...@gmail.com wrote: I like the idea of being able to do categories.tab and seeing a list of the available categories (or some reasonable subset of). ... which would not require them being inserted into the global namespace, AFAIK. For the record, I like the term magmatic algebras. It is not standard/common terminology and would certainly invite the user to look at the documentation to figure out what it is. When do you ever see the category of a parent P? In addition, there currently is no non-associative algebra in Sage, hence, even if you do P.category(), you would not see Category of magmatic algebras. Best regards, Simon -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
On Friday, July 5, 2013 7:33:49 AM UTC-4, Franco Saliola wrote: categories.tab That would be nice, too. Then you don't get useless (for interactive use) categories showing up when you use tab-completion to search for non-category stuff but you can still write doctests without having to import stuff manually. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
On Jul 5, 2013 7:41 AM, Simon King simon.k...@uni-jena.de wrote: Hi Franco, On 2013-07-05, Franco Saliola sali...@gmail.com wrote: I like the idea of being able to do categories.tab and seeing a list of the available categories (or some reasonable subset of). ... which would not require them being inserted into the global namespace, AFAIK. For the record, I like the term magmatic algebras. It is not standard/common terminology and would certainly invite the user to look at the documentation to figure out what it is. When do you ever see the category of a parent P? In addition, there currently is no non-associative algebra in Sage, hence, even if you do P.category(), you would not see Category of magmatic algebras. Let me make my vote more precise: I like magmatic algebra as a temporary solution; otherwise I concur with Simon that we should redefine the current category Algebras. Franco -- -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
[sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
On 2013-07-05, Franco Saliola sali...@gmail.com wrote: --089e0112cf9a05cdd104e0c5e9eb Content-Type: text/plain; charset=ISO-8859-1 On Jul 5, 2013 7:41 AM, Simon King simon.k...@uni-jena.de wrote: Hi Franco, On 2013-07-05, Franco Saliola sali...@gmail.com wrote: I like the idea of being able to do categories.tab and seeing a list of the available categories (or some reasonable subset of). ... which would not require them being inserted into the global namespace, AFAIK. For the record, I like the term magmatic algebras. It is not standard/common terminology and would certainly invite the user to look at the documentation to figure out what it is. When do you ever see the category of a parent P? In addition, there currently is no non-associative algebra in Sage, hence, even if you do P.category(), you would not see Category of magmatic algebras. Let me make my vote more precise: I like magmatic algebra as a temporary solution; otherwise I concur with Simon that we should redefine the current category Algebras. IMHO there should also be some consistency here, e.g. then one should have magmatic rings... Dima Franco -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
Hi, On Wed, Jul 03, 2013 at 08:43:06PM +, Simon King wrote: What I'd prefer is very simple: Just say algebra to an algebra. If any additional axiom holds, then the algebra should be called commutative, associative, unital, noetherian, lie, finite-dimensional, or whatever you like. But don't mention the *absence* of axioms! +1 for this proposal. I think this is not the role of Sage to change existing mathematical notations/definitions. In Lang, Algebra (3rd ed., page 121), it is stated that the restriction to associative and unital algebras is made for the book only. It is a pity that the name is already used for a more restrictive notion, but i think that this backward incompatible change is better that the other currently proposed solutions. Perhaps could we list and fix all similar misnamings or annoyances during a change of major version (e.g. Sage 6.0) and announce this clearly, so that we will suffer only once ? Ciao, Thierry The only problem is that this very simple solution is backward incompatible, because unfortunately Algebras() returns the category of *associative* *unital* algebras, in Sage. That's bad. And we would not want to deprecate the Algebras() command: Not the command itself should be deprecated, but its current semantic should be deprecated. So, how could a smooth transition be obtained? Best regards, Simon -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
[sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
+1 for switching Algebras to CommutativeUnitalAlgebras (or so) and the using Algebras for the most general algebra. In fact, I don't understand why Algebras has to be in the global namespace. I've never once found it useful to start an interactive session by instantiating a new category. The docstring isn't particularly useful either. Essentially, it is only is a trap for newcomers. Unless somebody has a really good use case I wouldn't mind removing all categories from the global namespace and implicitly making their name an implementation detail subject to change as the category hierarchy matures. -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
[sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
On Wed, Jul 03, 2013 at 03:21:34PM +0200, Nicolas M. Thiery wrote: One of the features introduced by the category patch #10963 is a new category for algebras that are not necessarily associative nor unital. This is a call for suggestions and votes for a good name for it. On a similar note: this ticket also introduces a category for sets (E,+,*) where (E,+) is an additive magma, (E,*) is a magma, and * distributes over +. In other words a ring with no axiom whatsoever but distributivity. In the current patch, this category is dubbed DistributiveMagmasAndAdditiveMagmas, by lack of creativity ... Better suggestions welcome! In the longer run, I'll also need a name for the same category, without the distributivity axiom. Cheers, Nicolas -- Nicolas M. Thiéry Isil nthi...@users.sf.net http://Nicolas.Thiery.name/ -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
[sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
Hey Nicolas, For the category of non-unital rings, how about Rngs? (I'm half joking.) Somewhat more serious, GeneralAlgebras/GeneralRings? I think overall we should be consistent between rings and algebras. On the math side of things, doesn't a ring in general has to be distributive; if so, then I think (distributive) non-* rings should be called *Rings and non-distributive things should be MultiplicativeAndAdditiveMagmas (or maybe AdditiveAndMultiplicativeMagmas). Also do we want/have a category for skew fields (a.k.a. division rings)? Best, Travis On Wednesday, July 3, 2013 3:38:00 PM UTC+2, Nicolas M. Thiery wrote: On Wed, Jul 03, 2013 at 03:21:34PM +0200, Nicolas M. Thiery wrote: One of the features introduced by the category patch #10963 is a new category for algebras that are not necessarily associative nor unital. This is a call for suggestions and votes for a good name for it. On a similar note: this ticket also introduces a category for sets (E,+,*) where (E,+) is an additive magma, (E,*) is a magma, and * distributes over +. In other words a ring with no axiom whatsoever but distributivity. In the current patch, this category is dubbed DistributiveMagmasAndAdditiveMagmas, by lack of creativity ... Better suggestions welcome! In the longer run, I'll also need a name for the same category, without the distributivity axiom. Cheers, Nicolas -- Nicolas M. Thi�ry Isil nth...@users.sf.net javascript: http://Nicolas.Thiery.name/ -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
[sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
On Wed, Jul 03, 2013 at 06:47:12AM -0700, Travis Scrimshaw wrote: For the category of non-unital rings, how about Rngs? (I'm half joking.) Actually that joke, for good or bad, is what's already been implemented in successively Axiom, MuPAD, and Sage :-) They even had Rigs. And Rgs. But here we want to go further and remove all other axioms (associativity, additive inverse, ...) but distributivity. Somewhat more serious, GeneralAlgebras/GeneralRings? I think overall we should be consistent between rings and algebras. That would be a plus indeed. On the math side of things, doesn't a ring in general has to be distributive; if so, then I think (distributive) non-* rings should be called *Rings and non-distributive things should be MultiplicativeAndAdditiveMagmas (or maybe AdditiveAndMultiplicativeMagmas). Thanks for your input. Also do we want/have a category for skew fields (a.k.a. division rings)? sage: Rings().Division() Category of division rings sage: Rings().Division().Commutative() Category of fields sage: Rings().Division().Finite() Category of finite fields :-) Cheers, Nicolas -- Nicolas M. Thiéry Isil nthi...@users.sf.net http://Nicolas.Thiery.name/ -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
Le 03/07/2013 15:38, Nicolas M. Thiery a écrit : On Wed, Jul 03, 2013 at 03:21:34PM +0200, Nicolas M. Thiery wrote: One of the features introduced by the category patch #10963 is a new category for algebras that are not necessarily associative nor unital. This is a call for suggestions and votes for a good name for it. On a similar note: this ticket also introduces a category for sets (E,+,*) where (E,+) is an additive magma, (E,*) is a magma, and * distributes over +. In other words a ring with no axiom whatsoever but distributivity. In the current patch, this category is dubbed DistributiveMagmasAndAdditiveMagmas, by lack of creativity ... DistributiveDoubleMagma? Better suggestions welcome! In the longer run, I'll also need a name for the same category, without the distributivity axiom. DoubleMagma? Snark on #sagemath -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
On 7/3/13 6:21 AM, Nicolas M. Thiery wrote: Dear category fans, One of the features introduced by the category patch #10963 is a new category for algebras that are not necessarily associative nor unital. This is a call for suggestions and votes for a good name for it. - ``Algebras``: that's wikipedia's choice [1]. However using this name would be backward incompatible, since ``Algebras'' in Sage currently refers to associative unital algebras. At this point in time, I don't want to open another can of worm on a ticket that is already way too big. But we could think about it in a later ticket. Note: many textbooks/papers use algebra as a short hand for associative unital (and sometimes commutative) algebras; but they usually specify this explicitly at the beginning, and they are each in a smaller context than Sage's. - ``NonAssociativeNonUnitalAlgebras``: that's what's currently used in the patch. Of course this terminology is not great because an associative algebra would then be a special case of a non associative algebra ... Note: I remember someone mentioning once that there was a tiny difference between ``non-associative'' and ``not associative'' that could possibly make this acceptable but I have no informed opinion myself. - ``MagmaticAlgebras``: this was suggested by Florent, referring to the terminology used in the operad community; see e.g. 13.8 of LodayValette [2] - Something else? MagmaticAlgebras or perhaps AlgebrasOverMagmas or Magma-Algebras (in analogy to an R-module) seems to be what you want? See https://en.wikipedia.org/wiki/Magma_%28algebra%29 Otherwise, Travis' suggestion of GeneralAlgebras and GeneralRings would also be good (if it is explained in the documentation why this name was chosen)! Best, Anne -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
[sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
Hi! On 2013-07-03, anne1.schill...@gmail.com anne1.schill...@gmail.com wrote: MagmaticAlgebras or perhaps AlgebrasOverMagmas or Magma-Algebras (in analogy to an R-module) seems to be what you want? See https://en.wikipedia.org/wiki/Magma_%28algebra%29 Otherwise, Travis' suggestion of GeneralAlgebras and GeneralRings would also be good (if it is explained in the documentation why this name was chosen)! I don't really like magma algebra or magmatic algebra, but that's mainly because I never heard anyone using this notion before. I'd rather describe an algebra as a module over an appropriate operade than call it magma algebra. What I'd prefer is very simple: Just say algebra to an algebra. If any additional axiom holds, then the algebra should be called commutative, associative, unital, noetherian, lie, finite-dimensional, or whatever you like. But don't mention the *absence* of axioms! The only problem is that this very simple solution is backward incompatible, because unfortunately Algebras() returns the category of *associative* *unital* algebras, in Sage. That's bad. And we would not want to deprecate the Algebras() command: Not the command itself should be deprecated, but its current semantic should be deprecated. So, how could a smooth transition be obtained? Best regards, Simon -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
[sage-devel] Re: RFC: a good name the category of algebras that are not necessarily associative nor unital
Hi Simon, I don't really like magma algebra or magmatic algebra, but that's mainly because I never heard anyone using this notion before. I'd rather describe an algebra as a module over an appropriate operade than call it magma algebra. What I'd prefer is very simple: Just say algebra to an algebra. If any additional axiom holds, then the algebra should be called commutative, associative, unital, noetherian, lie, finite-dimensional, or whatever you like. But don't mention the *absence* of axioms! The only problem is that this very simple solution is backward incompatible, because unfortunately Algebras() returns the category of *associative* *unital* algebras, in Sage. That's bad. And we would not want to deprecate the Algebras() command: Not the command itself should be deprecated, but its current semantic should be deprecated. So, how could a smooth transition be obtained? I understand your point and think just Algebras would also be perfect (if it was not for the backward incompatibilty). How about GeneralAlgebras for now and then a deprecation/switch in a later patch? Best, Anne -- You received this message because you are subscribed to the Google Groups sage-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
