Hi Marc, On 2013-08-14, Marc Mezzarobba <m...@mezzarobba.net> wrote: > Simon King wrote: >> I think quite often one is in a situation that one has two different >> sets (rings, groups, ...) S1, S2, such that there is only one action > of >> S1 on S2 from the left, and thus if one has s1 from S1 and s2 from S2, >> then s1*s2 is not ambiguous. > > I guess it depends what exactly you mean by "only one action of S1 on > S2":
I wrote: "quite often one is in a situation that...". Of course, sometimes there are two or more different actions to be considered at the same time. But I would expect that far more often one has just one action. >think of S1 = K[x][d/dx] and S2 = K[x]. Differential operators act > on polynomials (e.g., d/dx(x) = 1), but there is also an embedding of > K[x] into K[x][d/dx] under which d/dx*x = x*d/dx+1. Do you see what you just did? You use "call notation" for one action, i.e., d/dx(x), but use multiplicative notation for the other action, i.w., d/dx*x. You can do exactly the same with Sage/Python. I guess if you call a differential operator, then it means to apply the operator. And if you define a (multiplicative) action, then "*" will use this action. > The internal > multiplication of K[x][d/dx] applied in this context is not a left > action of K[x][d/dx] _on K[x]_, but I would definitely expect (d/dx)*x > to coerce x to K[x][d/dx] and multiply there. No, I'd rather expect to coerce x into a *non-commutative* version of the polynomial ring K[x][d/dx]. This ring, by the way, is implemented in Sage. And actually I would expect that the parent of d/dx *is* this ring. So, instead of using register_action, it would be enough to tell this non-commutative ring that there is a coercion from K[x]. 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.
