Hi, 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...".
Sorry, apparently I misinterpreted your "thus...". >>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. Yes, except that the second one is not an action of S1 on S2 from the left, but an action of S2 on S1 from the right, isn't it? That's all I wanted to point out: when trying to decide whether there is a single action that makes sense, one has to be careful to take into account actions from both sides and/or actions on larger sets to which the elements coerce. Apologies if I'm stating the obvious :-) >> 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]. Yes, what I denoted K[x][d/dx] was the ring of differential operators with polynomial coefficients. Or do you have something else in mind? Best wishes, -- Marc -- 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.
