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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 types: numeric or empty, symbol, literal (1 byte or 2 byte characters), and boxed, are so ordered; within them, a lower rank precedes a higher, and arrays to be compared are padded with fills if necessary to have the same shape. Complex arguments are ordered by real part, then by imaginary. Boxed arrays are ordered according to the opened elements.


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