> 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
