Essays/Insert

/ is an adverb and u/y applies the dyad u between the items of y . For example, +/y computes the sum. This differs from conventional mathematical notation in making explicit that there is an adverb and that no special symbol is required for u/ for each function u . For example, in conventional notation sum is $\sum$ and product is $\prod$.

The more general m/y inserts successive verbs from the gerund m between items of y , extending m cyclically as required.

Some examples of insert:

+/ y	sum
*/ y	product; (!n) = */1+i.n
-/ y	alternating sum; e.g. -/ z (^%!@]) 1+2*i.n approximates sin z
>./ y	maximum
<./ y	minimum
(+%)/ y	continued fraction; e.g. (+%)/n$1 approximates $\phi$
+`%/ y	generalized continued fraction; e.g. +`%/ 3,6,.~*:1+2*i.n approximates $\pi$
+`*/ }:,x,.y	computation of x p. y by Horner's rule
y {~ /:@/:@,/ ((-i.)#y)#:x	computation of x A. y ; see Permutation Index
(<@i.@>:@I.~ C. ,)/ y	an O(n^2^) sort of vector y
*./ #&> C. p	the size of the subgroup generated by permutation p
*./ b	Are all of b true?
+./ b	Is any of b true?
~:/ b	1 iff the number of 1s is odd
=/ b	1 iff the number of 0s is even
</ b	1 iff b is all 0s followed by a 1

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Contributed by Roger Hui.