The shape

]report=: i. 2 4 3 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 ($ ; # ; #@$) report Shape, Number of items, Rank +-----+-+-+ |2 4 3|2|3| +-----+-+-+The last

The rank conjunction

,report 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 ,"2 report 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 <@i. s=: 2 5 +---------+ |0 1 2 3 4| |5 6 7 8 9| +---------+ <@i."0 s +---+---------+ |0 1|0 1 2 3 4| +---+---------+Both the left and right ranks of a dyad may be specified. Thus:

10 11 12 (,"0 1 ; ,"1 1 ; ,"1) 0 1 2 +--------+--------------+--------------+ |10 0 1 2|10 11 12 0 1 2|10 11 12 0 1 2| |11 0 1 2| | | |12 0 1 2| | | +--------+--------------+--------------+The

(# b. 0) ; (+/\ b. 0) ; (+/\ % #) b. 0 +-----+-----+-----+ |_ 1 _|_ 0 _|_ _ _| +-----+-----+-----+

**Exercises**

20.1 | Observe the results of the following uses of
the monads produced by the rank conjunction, and comment on them: a=: i. 3 4 5 <"0 a <"1 a <"2 a <"3 a < a <"_1 a <"_2 a mean=: +/ % # mean a mean"1 a mean"2 aAnswer: <"k applies < to each cell
of rank k , with <"(#$a) a
being equivalent to <a . Moreover,
a negative value of k specifies a complementary
rank that is effectively |k less than the rank of
the argument a . |

20.2 | Use the results of the following experiments to state
the relation between the conjunctions @ (Atop)
and @: (At), and compare your conclusions
with the dictionary definition: (g=: <"2) a=: i. 3 4 5 |. @: g a |. @ g a |: @: (<"1) a |: @ (<"1) aAnswer: The rank of the function |. @: g is itself
infinite and |. therefore applies to the entire list
result of g a , consequently reversing it.
On the other hand, the function f @ g inherits
the rank of g , and |. therefore
applies individually to the atoms produced by g ,
producing no effect. |

20.3 | Use the results of the following experiments to comment
on the use of the rank conjunction in dyads: b=: 'ABC' c=: 3 5 $ 'abcdefghijklmno' c b,c b ,"0 1 c b ,"1 1 c b ,"1 c |

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