Essays/Insert

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/ 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



Contributed by Roger Hui.