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16. Partitions (Adverbs)

Used monadically, the results of the adverbs \ and \. and /. provide prefix, suffix, and oblique partitions. They are commonly applied to arithmetic functions such as summation (+/), product over (*/), and continued fractions ((+%)/); we will also illustrate them for box (<), which shows their structure more clearly:
   a=: 2 3 5 7 11 [ t=: 1 2 1 */ 1 3 3 1
  
   ,.&.>((+/\a) ; (+/\.a) ; ((+%)/\a) ; (+//.t);t)
+--+--+-------+--+-------+
| 2|28|      2| 1|1 3 3 1|
| 5|26|2.33333| 5|2 6 6 2|
|10|23| 2.3125|10|1 3 3 1|
|17|18|2.31304|10|       |
|28|11|2.31304| 5|       |
|  |  |       | 1|       |
+--+--+-------+--+-------+
  
   <\a
+-+---+-----+-------+----------+
|2|2 3|2 3 5|2 3 5 7|2 3 5 7 11|
+-+---+-----+-------+----------+

   <\.a
+----------+--------+------+----+--+
|2 3 5 7 11|3 5 7 11|5 7 11|7 11|11|
+----------+--------+------+----+--+

   </.t
+-+---+-----+-----+---+-+
|1|3 2|3 6 1|1 6 3|2 3|1|
+-+---+-----+-----+---+-+
Used dyadically, they provide infix, outfix, and key classification. For example:
   3 <\ a
+-----+-----+------+
|2 3 5|3 5 7|5 7 11|
+-----+-----+------+
 
   _3 <\ a
+-----+----+
|2 3 5|7 11|
+-----+----+

   2<\.a
+------+------+------+-----+
|5 7 11|2 7 11|2 3 11|2 3 5|
+------+------+------+-----+

   1 2 3 1 3 *//. a
14 3 55
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