•index — Fresh indices
•index n gives ⍳n along an axis with a fresh name. stem •index n starts the name with the text stem. The name is _, the stem, · and a random part of 64 bits written as 13 digits, as in _b·k3f9q2m7x1c0p. Two calls give different names, except with a chance of about one in 10¹⁹. •index maps over an array of numbers, with the same stem for each.
A name that starts with _ is hidden. Plain display leaves hidden axis names out. Any key or name that starts with _ and contains · displays up to its last ·, then …. Box mode and ⍴ show a fresh name as _b·…. To keep a long key or name of your own short on screen, start it with _ and put a · before the part to leave out: ["_note·long description":3] displays as ["_note·…":3]. •literal⁻¹ writes every name in full. A hidden name meets a visible one as if that axis had no name, and the result keeps the visible name:
i←•index 3 ⋄ v←⍳["v":3]
i ⍝ 0 1 2
⍴i ⍝ ["_·…":3]ₓ
⍴i+v ⍝ ["v":3]ₓIndices with different names build a grid, in arithmetic and in selection. An index used twice pairs with itself. Here x.[i]-x.[j] holds the difference between every pair of items of x, and m.[i i] is the diagonal of m:
x←10 20 40 ⋄ [i j]←•index 3 3
⌈/,|x.[i]-x.[j] ⍝ 30
m←[1 2 3⋄4 5 6⋄7 8 9]
+/m.[i i] ⍝ 15Indices name the axes of a formula, as einsum’s letters do. In this product, k pairs by name and +/⍠k sums along it. b and o build the result’s grid. ⍉⁻¹ reorders its axes by name:
xu←[2 3]⍴⍳6ₓ ⋄ wu←[3 4]⍴⍳12ₓ
[b o k]←•index 2 4 3
y←+/⍠k xu.[b k]×wu.[k o]
∧/,y=xu+.×wu ⍝ $t
∧/,([o b]⍉⁻¹ y)=⍉xu+.×wu ⍝ $tNames from •index can’t collide with the names on a caller’s data. ⍳["i":n] gives a name that the caller chooses.
Errors: DOMAIN for a stem that isn’t text.