On Tue, Jun 16, 2020 at 6:03 PM Nils Bruin <nbr...@sfu.ca> wrote: > > On Tuesday, June 16, 2020 at 4:40:45 AM UTC-7, kcrisman wrote: >> >> >> For several more points of view (some articulated by people on the current >> thread), see also the (long) discussion that the ticket you mention led to >> on this forum, seven years ago: >> https://groups.google.com/forum/#!topic/sage-devel/tAAb42Edh9o > > > That's quite a thread. One thing I'd like to highlight from there that didn't > seem to get so much traction is a point Marco Streng made about possible > notations for right actions: > > If G is a group acting on the right on a ring R, and a,b in R and s in G then > denoting right-action by right-multiplication has a problem: > > (a*b)*s would suggest it's equal to a*(b*s), which it is generally not. > Exponential notation (a*b)^s does not suffer from this problem. That > disqualifies right-multiplication as a general notation for right-actions to > me.
It becomes more evident if one has to compose not necessarily invertible linear maps. E.g. if one wants to represent linear maps A:F^n -> F^m by matrices, so that A(v), for v in F^n, be given by the matrix/vector multiplication Av, then A should be mxn matrix. Then, if B:F^m->F^k (and so B is kxm) the composition B(A(v)) is matrix product BAv. And one needs to explain why to form the composition F^n-A->F^m-B->F^k one has to do BA:F^n->F_k. So in order to retain the convenience of A(v) being Av, one has to accept that the order of composition is swapped. Or write A(v) as vA, then A is nxm, and B(A(v)) is vAB. Dima > > > -- > 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 view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/fadeb1c0-73ea-427f-9337-5b627bf7b224o%40googlegroups.com. -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAAWYfq0LtoUHqO1gXL%3DBKk5R%3D99wvORAJZhFj9LmqSCnA9n6wA%40mail.gmail.com.
