Perhaps also worth considering: cos`(-@sin),:sin`cos
Thanks, -- Raul On Sat, Dec 19, 2020 at 12:25 PM Roger Hui <rogerhui.can...@gmail.com> wrote: > > > However, when it comes to avoiding unnecessary bracket pairs, your > second pair is a candidate as well. > > Ah, but no, the goal is not necessarily to avoid unnecessary parenthesis; > the goal is ... beauty (or "prettity", as you put it). Consider: > > (cos , -@sin) ,: (sin , cos) > (cos , -@sin) ,: sin , cos > > The expressions are equivalent, but which is more beautiful? (I do believe > that your original expression, even with the quibbles on its > parenthesization, is already more beautiful than all the other expressions > in this thread.) > > There are other examples: > > 0. Arguably the very first APL one-liner: > > (x>0)-(x<0) > > found in §1.4 of *A Programming Language > <https://www.jsoftware.com/papers/APL.htm>* [Iverson 1962]. It computes > the *signum* (sign) of x, _1, 0, or 1 according to whether x is <0, =0, or > >0. (Exercise for the reader: which is the *second* APL one-liner ever?) > > 1. What I am guessing is Ken Iverson's favorite APL expression: > > (0,x)+(x,0) > > It computes the next set of binomial coefficients, starting from ,0. See > §11.7 of *APL Since 1978 <https://dl.acm.org/doi/pdf/10.1145/3386319>* [Hui > & Kromberg 2020] for the reasons why I so guess. > > > > On Sat, Dec 19, 2020 at 12:35 AM Ben Gorte <bgo...@gmail.com> wrote: > > > I'm afraid I cannot fully satisfy your curiosity. You are completely right > > concerning prettity, balance, and symmetry. > > Furthermore, my brackets surrounding the entire expression are superfluous > > indeed (like all pairs of brackets surrounding entire expressions?). > > > > However, when it comes to avoiding unnecessary bracket pairs, your second > > pair is a candidate as well. > > At the same time I must admit that omitting it, for the sole purpose of > > avoiding unnecessary brackets, is testing one's luck (but I won). > > > > Greetings from Sydney, > > Ben > > > > On Sat, 19 Dec 2020 at 18:49, Roger Hui <rogerhui.can...@gmail.com> wrote: > > > > > > R =: ((cos , -@sin) ,: sin , cos) > > > > > > I am curious why the definition isn't > > > > > > (cos , -@sin) ,: (sin , cos) > > > > > > It seems prettier (more balanced, more symmetric). > > > > > > > > > > > > On Fri, Dec 18, 2020 at 3:56 AM Ben Gorte <bgo...@gmail.com> wrote: > > > > > > > Perhaps I'm missing the point, but I would say: > > > > > > > > R =: ((cos , -@sin) ,: sin , cos) > > > > > > > > R 1r6p1 > > > > > > > > 0.866025 _0.5 > > > > > > > > 0.5 0.866025 > > > > > > > > > > > > Ben > > > > > > > > > > > ---------------------------------------------------------------------- > > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
