John, On Sunday, July 19, 2020 at 1:00:21 AM UTC+2 John H Palmieri wrote:
> Can you give a specific example of a computation in which you care about > the degree where your zero element lives? Or where you can't just recover > it from its component elements (if ab=0, then you have an element in degree > = deg(a) + deg(b)). I'm struggling to understand this. > It's more that I would like to avoid checking for the special case 0. The case we are discussing is similar to the use of pointers vs. references in C++: If a function returns a pointer to an object, the recipient have to check that it is not NULL before dereferencing it. On the other hand, if the function returns a reference to an object, you don't have to. The latter leads to cleaner code, and is preferred if one has a choice since it relieves the user from the responsibility of guarding against the null case. This is what Christian mentions too: > In practical terms this just shifts the responsibilities a bit: the result of a computation (e.g. multiplication) will not in general know its degree; therefore the piece of user code that triggered the multiplication must keep a memory of the grading that it's workign at. If we treated graded objects like Bob suggests, we would relieve the user of this responsibility. At this point I think it's clear that what I would like requires some work to get done right, so I guess I will let this rest for now. Thanks so much to all for your input! Best regards, Sverre > > If you are doing the same check repeatedly, then write a little function > to do it and then you have a one-line call to that function scattered > around your code, which doesn't seem like that big a deal to me. > Alternatively, and I know this isn't how we like to think about these > things, but what goes wrong if you allow nonhomogeneous elements? That > could be another way to simplify things. > > - John > > > > > On Saturday, July 18, 2020 at 3:28:56 PM UTC-7, Sverre Lunøe-Nielsen wrote: >> >> >> On Saturday, July 18, 2020 at 11:31:43 PM UTC+2, John H Palmieri wrote: >>> >>> In any case where the degree matters, you should first test whether an >>> element is zero (in which case it won't have a degree) and then perhaps >>> whether it is homogeneous. If not, you can raise an error (to keep someone >>> from multiplying a module element by Sq(1) + Sq(2), for example). If it is >>> homogeneous, you can proceed the way you want. >>> >> >> This is indeed what we do in the current version. However, I have come >> to think of this as some kind of anti-pattern, so I am seeking ways to >> avoid it. >> >> On Saturday, July 18, 2020 at 11:57:21 PM UTC+2, Christian Nassau wrote: >> > I don't think it's a good idea to have different zeroes in an algebraic >> structure that is also categorized as an abelian group, unless you take the >> point that a "graded abelian group" should not be an "abelian group". >> >> Yes, as I outlined, they should definitely be living in a category where >> the objects are sequences of k-vectorspaces with the structure maps that >> make them k-algebras. But the data that goes into defining an algebra this >> way is no different from usual. >> >> >> - Sverre >> > -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/fa3bdb5e-3052-4fb2-b23c-66932e804569n%40googlegroups.com.
