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| author | Marshall Lochbaum <mwlochbaum@gmail.com> | 2022-07-08 22:06:05 -0400 |
|---|---|---|
| committer | Marshall Lochbaum <mwlochbaum@gmail.com> | 2022-07-08 22:06:05 -0400 |
| commit | 7fa325f583a59a1999cd8ce093a49f8048a3e05c (patch) | |
| tree | 5157b1cbd4af6318eb77b3fcf5d80420d0cba46d /docs/doc/rank.html | |
| parent | 9ce4441a2fec2f6bd301f9cf5ad801c9534d34eb (diff) | |
Simplify and update Couple/Merge docs
Diffstat (limited to 'docs/doc/rank.html')
| -rw-r--r-- | docs/doc/rank.html | 2 |
1 files changed, 1 insertions, 1 deletions
diff --git a/docs/doc/rank.html b/docs/doc/rank.html index 8cf63ad2..631693cf 100644 --- a/docs/doc/rank.html +++ b/docs/doc/rank.html @@ -219,7 +219,7 @@ <span class='Function'>≢</span> <span class='Function'>⊑</span> <span class='Function'><</span><span class='Modifier2'>⎉</span><span class='Number'>2</span> <span class='Function'>↕</span><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>0</span> ⟨ 1 0 ⟩ </pre> -<p>We can build a frame array using <code><span class='Function'><</span><span class='Modifier2'>⎉</span><span class='Number'>2</span></code>, as shown above. In the general case, the frame remains conceptual: the actual array <code><span class='Function'><</span><span class='Modifier2'>⎉</span><span class='Number'>2</span> <span class='Value'>x</span></code> is never created, and the result might also not have the shape <code><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>2</span></code>. But the result shape does always have <code><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>2</span></code> as a prefix. Rank maps over these axes, leaving them intact. And it can be defined in terms of the cell-splitting function <code><span class='Function'><</span><span class='Modifier2'>⎉</span><span class='Value'>k</span></code>, and its inverse <a href="couple.html#merge-and-array-theory">Merge</a> (<code><span class='Function'>></span></code>).</p> +<p>We can build a frame array using <code><span class='Function'><</span><span class='Modifier2'>⎉</span><span class='Number'>2</span></code>, as shown above. In the general case, the frame remains conceptual: the actual array <code><span class='Function'><</span><span class='Modifier2'>⎉</span><span class='Number'>2</span> <span class='Value'>x</span></code> is never created, and the result might also not have the shape <code><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>2</span></code>. But the result shape does always have <code><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>2</span></code> as a prefix. Rank maps over these axes, leaving them intact. And it can be defined in terms of the cell-splitting function <code><span class='Function'><</span><span class='Modifier2'>⎉</span><span class='Value'>k</span></code>, and its inverse <a href="couple.html">Merge</a> (<code><span class='Function'>></span></code>).</p> <pre><span class='Function'>F</span><span class='Modifier2'>⎉</span><span class='Value'>k</span> <span class='Value'>x</span> <span class='Gets'>←→</span> <span class='Function'>>F</span><span class='Modifier'>¨</span><span class='Function'><</span><span class='Modifier2'>⎉</span><span class='Value'>k</span> <span class='Value'>x</span> </pre> <p>That is, <code><span class='Function'>F</span><span class='Modifier2'>⎉</span><span class='Value'>k</span></code> splits its argument into <code><span class='Value'>k</span></code>-cells, applies <code><span class='Function'>F</span></code> to each of these (in index order, of course), then merges the results into a single array.</p> |