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In APL the old-style subscripting works like this:

A is 2 3 4 5 reshape iota 120  (makes a 2x3x4x5 array of the integers to 120)

A[;1 3;;2 4]

returns a 2x2x4x3 array with with Ai2j(1,3,or5) missing.

Derive does substantially the same thing with proper use of parentheses. The above would be written

(A sub sub [1,3]) sub sub sub sub [2,4]

However Derive's subscripting has an inconsistency -

APL

A[2;1 3;1 3;2 4 5]

 62  64  65
 72  74  75
          
102 104 105
112 114 115

Derive

A sub 2 sub sub [1,3] sub sub sub [1,3] sub sub sub sub [2,4]

results in nonsense, but

A sub 2 sub [1,3] sub sub [1,3] sub sub sub [2,4]

yields the correct result:

⎡⎡ 62  64  65 ⎤  ,⎡ 102  104  105 ⎤⎤
⎣⎣ 72  74  75 ⎦  ,⎣ 112  114  115 ⎦⎦

Why?

Apparenly Derive treats the first two subscripts as if they always apply to matrices - an array of dimension N is really an array of vectors of dimension N-1.

Another example:

APL

A[;2;1 3;2 4 5]

22 24 25
32 34 35
       
82 84 85
92 94 95

Derive

A sub sub 2 sub sub [1,3] sub sub sub [2,4,5]

⎡⎡ 22  24  25 ⎤   ⎡ 82  84  85 ⎤⎤
⎣⎣ 32  34  35 ⎦ , ⎣ 92  94  95 ⎦⎦

But notice

APL

A[;;1 3;2 4 5]

  2   4   5
 12  14  15
          
 22  24  25
 32  34  35
          
 42  44  45
 52  54  55
          
          
 62  64  65
 72  74  75
          
 82  84  85
 92  94  95
          
102 104 105
112 114 115
    
Derive

A sub sub sub [1,3] sub sub sub sub [2,4,5]

⎡ ⎡  2   4   5   ⎤  ⎡ 22  24  25 ⎤   ⎡ 42    44    45 ⎤  ⎤
⎢ ⎣ 12  14  15 ⎦  ⎣ 32  34  35 ⎦   ⎣ 52    54    55 ⎦  ⎥
⎢                                                                         ⎥
⎢ ⎡ 62  64  65 ⎤  ⎡ 82  84  85 ⎤  ⎡ 102  104  105 ⎤ ⎥
⎣ ⎣ 72  74  75 ⎦  ⎣ 92  94  95 ⎦  ⎣ 112  114  115 ⎦ ⎦

This is annoying but internally consistent.

-drl