Hi Nathann, On 2014-05-27, Nathann Cohen <nathann.co...@gmail.com> wrote: > I do not understand much about categories, but if we implement > multiplication by a positive integer for semigroups and multiplication by a > negative integer for semigroup with inverse, won't this automatically give > a ZZ-Module structure to any additive abelian group ?
If I am not mistaken, this is already the case. > And more technically, > isn't it the case that every additive abelian parent in Sage will be > detected as a ZZ-Module ? No, and I think the question/suggestion is how to add this feature. Perhaps one could say that the difference between "X has an action by ZZ" and "X is a ZZ-module" is the same as duck-typing versus typecheck. If X happens to have an action by ZZ, then a duck-typist (and a mathematician) would say that it is a ZZ-module. sage: P.<x> = GF(2)[] sage: P.get_action(ZZ, operator.mul) Right scalar multiplication by Integer Ring on Univariate Polynomial Ring in x over Finite Field of size 2 (using NTL) However, Sage's category framework does not use the above duck typing of modules. Instead, it asks whether P's category is a sub-category of the category of ZZ-modules: sage: P.category().is_subcategory(Modules(ZZ)) False This is not the case, and hence "P not in Modules(ZZ)" in spite of the existence of a ZZ-action. Now, the point of the question/suggestion is this: sage: P.category().is_subcategory(CommutativeAdditiveGroups()) True Since CommutativeAdditiveGroups() and Modules(ZZ) are mathematically the same, we should somehow identify these two categories, and then P would be immediately recognised as ZZ-module. Now, the question is how to implement this categorial identity. Modules(R) already uses some black magic (overriding __new__!) in order to achieve "Modules(QQ) is VectorSpaces(QQ)". Similarly, one might think of making "Modules(ZZ)" return "CommutativeAdditiveGroups()". 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/d/optout.
