Thanks again for the explanations. I realize that there were many things about Julia/Nemo which I had misunderstood. Let me explain a little, so I can (i) embarrass myself a little more, and (ii) perhaps give an indication of common mistakes, for anyone who would write a tutorial about Julia/Nemo :-)
Mistake (1): taking it for OOP. When hearing about the way Julia worked, I jumped when I saw it wasn't OO, and then naturally was looking for ways to emulate OOP with Julia (rather than make the effort of a paradigm shift). And with multi-dispatch, i thought OK, if I want to write code that applies to objects of type A, B and C at once, just declare them A <: X, B <: X and C <: X and define f(x :: X). However this gave me the wrong intuition " A <: X is the same as A inherits from X". At this point, the fact that abstract types could be instantiated was seen as a limitation compared to OOP. And somehow, it is. Except at the same time, the type system does many new things. Apples and oranges, really. Mistake (2): taking types for sets. This little discussion about names reveals another mistake of mine: thinking of types as sets. I thought ZZ <: QQ for example. That's not even consistent with the previous mistake. In Sage say, i'm guessing QQ is of type Field or something, which inherits from a type Ring or something -- but not the other way around! So mistake (1) should have led me to believe QQ <: ZZ. Oh well. Mistake (3): thinking about Sage too much. To my discharge, ZZ in Sage is an object, like 1/2, not a type or anything. This has unconsciously contributed to my confusion greatly. Also the fact that there is a coercion from ZZ to QQ, and somewhere I must have taken A <: B to mean "there is a coercion from A to B". Pierre > -- 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/d/optout.
