m/ (Adverb) INSERT (_) If m is a gerund, then m/y inserts successive verbs from m between items of y. Thus, +`*/i.6 is 0+1*2+3*4+5. The gerund m may extend cyclically. ________________________________ u/ (Adverb) INSERT (_) u/y applies the dyad u between the items of y. Thus: i.3 2 +/i.3 2 */2 3 4 0 1 6 9 24 2 3 4 5 If y has no items (that is, 0=#y), the result of u/y is the identity element of the verb u. An identity element of a function u is a value e such that either x u e is x, or e u x is x for every x in the domain (or perhaps some significant sub-domain such as boolean) of u. This definition of insertion over an argument having zero items extends partitioning identities of the form (+/y)–:(+/k{.y)+ +/k}.y to the cases k=. 0 and k=. #y. The identity function of a verb u is a function ifu such that (ifu y)–:(u/y) if 0=#y. The identity functions are: $&0&}.&$ < > + – +. ~: | $&1&}.&$ = <: >: * % *. %: ^ ! $&_&}.&$ <. $&__&}.&$ >. i.&(0&,)&(2&}.)&$ , i.&(1&{.)&}.&$ @. { =&i.&(1&{.)&}.&$ %. +/ . * ifu&# u/ $&(v^:_1 ifu$0)&}.&$ u&.v FUNCTION TABLE (_ _) If x and y are numeric lists, then x */ y is their multiplication table. For example: 1 2 3 */ 4 5 6 7 4 5 6 7 8 10 12 14 12 15 18 21 In general, each cell of x is applied to the entire y. Thus x u/ y is x u"(lu,_) y.