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Grade Up /:  _ _ _ Sort Up

/: grades any argument, yielding a permutation vector; (/:y){y sorts y in ascending order. For example:
   n=: 3 1 4 2 1 3 3
   ]g=: /: n
1 4 3 0 5 6 2

   g { n
1 1 2 3 3 3 4
  x/:y is (/:y){x ; i.e., x is sorted to an order specified by y . In particular, y/:y (or /:~y) sorts y . For example:
   y=: 'popfly'
   y /: 3 1 4 1 5 9
ofpply
    
   y /: y
floppy

Elements of /:y that select equal elements of y are in ascending order. If y is a table, /:y grades the base value of the rows, using a base larger than twice the magnitude of any of the elements. Higher ranks are treated as ,.y , (as if its items were each ravelled).

If y is literal, /:y grades according to the collating sequence determined by the alphabet a.; another collating sequence cs can be imposed by grading cs i. y . For example:
   ]n=: 3 1 4 1 6,2 7 1 8 3,:6 1 8 0 3
3 1 4 1 6
2 7 1 8 3
6 1 8 0 3

   /: n
1 0 2

   Aa=: ' ',. a. {~ 65 97 +/ i. 26
   x=: words=: >;: 'When eras die'
   j=: <./Aa i."1 _ x
   x ; (x/:x) ; (x/:j) ; Aa
+----+----+----+---------------------------+
|When|When|die | ABCDEFGHIJKLMNOPQRSTUVWXYZ|
|eras|die |eras| abcdefghijklmnopqrstuvwxyz|
|die |eras|When|                           |
+----+----+----+---------------------------+
The three types: numeric or empty, literal, and boxed, are so ordered; within them, a lower rank precedes a higher, and a smaller shape precedes a larger. Complex arguments are ordered by real part, then by imaginary. Boxed arrays are ordered according to the opened elements.



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