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diff --git a/doc/indices.md b/doc/indices.md index 62122175..30a0157a 100644 --- a/doc/indices.md +++ b/doc/indices.md @@ -34,7 +34,7 @@ Unlike `/` and `⊔`, `↕` and `⊑` do use list element indices. For `↕` thi One of the successes of the [leading axis model](https://aplwiki.com/wiki/Leading_axis_theory) is to introduce a kind of index for multidimensional arrays that is easier to work with than list indices. The model introduces [cells](https://aplwiki.com/wiki/Cell), where a cell index is a list of any length up to the containing array's rank. General cell indices are discussed in the next section; first we introduce a special case, indices into major cells or ¯1-cells. These cells naturally form a list, so the index of a major cell is a single number. Such an index can also be considered to select along the first axis, since an index along any axis is a single number. -[Ordering](order.md) functions `⍋⍒` and [search](search.md)/[self-comparison](selfcmp.md) functions `⊐⊒` that depend on cell ordering only really make sense with major cell indices: while other indices have an ordering, it's not very natural. Note that `⊐` only uses the ordering in an incidental way, because it's defined to return the *first* index where a cell in `𝕩` is found. A mathematician would be more interested in a "pre-image" function that returns the set of all indices where a particular value appears. However, programming usefulness and consistency with the other search functions makes searching for the first index a reasonable choice. +[Ordering](order.md) functions `⍋⍒` and [search](search.md)/[self-search](selfcmp.md) functions `⊐⊒` that depend on cell ordering only really make sense with major cell indices: while other indices have an ordering, it's not very natural. Note that `⊐` only uses the ordering in an incidental way, because it's defined to return the *first* index where a cell in `𝕩` is found. A mathematician would be more interested in a "pre-image" function that returns the set of all indices where a particular value appears. However, programming usefulness and consistency with the other search functions makes searching for the first index a reasonable choice. Only one other function—but an important one!—deals with cells rather than elements: [Select](select.md) (`⊏`). Select [allows](leading.md#multiple-axes) either a simple first-axis case where `𝕨` has depth 1 or less (a depth-0 argument is automatically enclosed), and a multi-axis case where it is a list of depth-1 elements. In each case the depth-1 arrays index along a single axis. |