u;.n  (Conjunction)

CUT (_)  The phrase u;. 1 y applies u to each of a set of intervals of items of y  to produce the items of the result. Each interval begins at an occurrence of the delimiter 0{y. For example, if s=. 5 3:

	  <;.1 y=.' worlds on worlds'
+-------+---+-------+
| worlds| on| worlds|
+-------+---+-------+
  $;.1 y	    s$i.9     +/;.1 s$i.9
7		       0 1 2	    9 12 15
3		       3 4 5	    3  5  7
7		       6 7 8
		        0 1 2
		        3 4 5

The phrase u;._1 y differs only in that the delimiters are excluded from the intervals. In u;.2 and u;._2 the delimiter is the last item, and marks the ends of intervals.

The phrase u;.0 y applies u to y after reversing y along each axis, and is equivalent to (0 _1 */$y) u;.0 y.

The monads u;.3 and u;._3 apply u to tessellation by "maximal cubes", that is, they are defined by their dyadic cases using the left argument  ($$y)$<./$y.

CUT (_ _)  The dyads u;.1 and u;._1 and u;.2 and u;._2 differ from the monads in that the intervals are delimited by the ones in  the boolean  argument x. Thus:

   x=. 0 1 0 0 1 [ y=. i. 5 3
   y	         x+/;.1 y     x+/;.2 y
 0  1  2 	 18 21 24      3  5  7
 3  4  5	  12 13 14     27 30 33
 6  7  8
 9 10 11
12 13 14

The phrase x u;.0 y applies u to a rectangle or cuboid of y with one vertex at the point in y indexed by v=.0{x, and with the opposite vertex determined as follows: the dimension is |1{x, but the rectangle extends back from v along any axis for which the index k{v is negative. Finally, the order of the selected elements is reversed along each axis k for which k{1{x is negative. For example:
	  (1 _2,:_2 3)+;.0 i. 4 5 
11 12 13 
6   7  8

The cases u;.3 and u;._3 provide (possibly overlapping) tessellations. The phrase x u;._3 y applies u to each complete rectangle of size |1{x obtained by beginning at all positions obtained as integer multiples of (each element of) the movement vector 0{x. As in u;.0, reversal of each piece occurs along an axis for which the dimension 1{x is negative.

The degenerate case of a list x is equivalent to the left argument 1,:x, and therefore provides a complete tessellation of size x.

The case u;.3 differs from u;._3 only in that any shards of sizes less than |1{x are included. For example:

	  y
abcdef
ghijkl
mnopqr
stuvwx
yzABCD
   (3 2;2 3)<;.3 y
+---+---+--+
|abc|cde|ef|   
|ghi|ijk|kl|
+---+---+--+
|stu|uvw|wx|
|yzA|ABC|CD|
+---+---+--+