# Essays/Insert

< Essays

`/ `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 and product is .

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`+`%/ y`generalized continued fraction; e.g. `+`%/ 3,6,.~*:1+2*i.n`approximates`+`*/ }:,x,.y`computation of `x p. y`by Horner's rule`y {~ /:@/:@,/ ((-i.)#y)#:x`computation of `x A. y`;`(<@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.