Waldek Hebisch <hebi...@math.uni.wroc.pl> writes: > I am not aware of resonable mathematical definition. Above > I used "natural" in informal way.
Yes, I know, and I'd be surprised if there was a "mathematical" definition. But it would be good to find something that's at least close to a definition. I have to digest the rest of your email later. Martin >> Things that come to mind: >> >> * it seems that we need to have ordering even if no "natural" order is >> available, as in EXPR INT. >> > > Main reason to have order is printing. Linear form means that we > will have some order of terms. In principle we could print things > in more or less random order, but it seems better to consistently > use the same order. > > There are a few places (like choosing between exp(x) and exp(-x)) > where we essentially need to implement axiom of choice. Again, > using unnatural order is resonable in such situation. > >> * Possibly we also want to have two different orders: a fast one, and a >> mathematical one... >> > > AFAICS in most cases even fast order would be slower than > alternatives. For example using hash tables is faster than > binary search. I would rather say that because user sees > reslult sorted in "technical" way we want this order to > stay reasonably close to natural one. > >> * in python, as far as I know, any two things are comparable, and it's >> (if I remember correctly) expressively designed for hashing etc., >> i.e. for exactly the same functionality you have in mind for >> Comparable. >> >> I think I would be nice to reflect this intention very clearly even in >> the name of the category. Brainstorming: OrderedDatastructure. >> > > Well, I do not care much about name. But Comparble was intended > to avoid confusion with OrderedSet -- using Ordered as part > of new name IMHO maximizes confusion. > >> PS: one final personal thing: I strongly prefer >> >> Expression(R: Comparable): Exports >> >> over >> >> Expression(R : Comparable): Exports >> >> > > You mean spacing? I definitely prefer the second form, > the first IMHO lacks visual balance. More generally, I think > that operators in general should be surrounded by spaces, > except for most thightly binding operator like *, ::, @, $. --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to fricas-devel@googlegroups.com To unsubscribe from this group, send email to fricas-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~----------~----~----~----~------~----~------~--~---
