Simplify and explain multidimensional Windows definition

2 files changed, 2 insertions, 2 deletions

diff --git a/doc/windows.md b/doc/windows.md
index baae3efc..f4ef0fe9 100644
--- a/doc/windows.md
+++ b/doc/windows.md
@@ -106,4 +106,4 @@ The slices are naturally arranged along multiple dimensions according to their s
 
 If `𝕨` has length `0`, then `𝕩` is not sliced along any dimensions. The only slice that results—the entire argument—is then arranged along an additional zero dimensions. In the end, the result is `𝕩`, unchanged.
 
-Here's a more formal definition: `𝕩` is an array. `𝕨` is a number, or numeric list or unit, with `𝕨≤○≠≢𝕩`. The result `z` has shape `𝕨∾¬⟜𝕨⌾((≠𝕨)⊸↑)≢𝕩`, and element `i⊑z` is `i⊑z` ←→ `𝕩⊑˜+´¨(𝕨∾○(↕∘≠)≢𝕩)⊔i`.
+Here's a more formal definition: `𝕩` is an array. `𝕨` is a number, or numeric list or unit, with length `l←≠𝕨` so that `l≤=𝕩`. The result `z` has shape `𝕨 ∾ ¬⟜𝕨⌾(l⊸↑)≢𝕩`, and element `i⊑z` is `j⊑𝕩`, with `j←+´¨(l∾○↕=𝕩)⊔i`. That is, the index list `i` starts with two length-`l` sequences that are added together to produce the first `l` values in `j`. We might also say that each of the first `l` values in `j` is split into two values in `i`.
diff --git a/docs/doc/windows.html b/docs/doc/windows.html
index d48db69b..08450842 100644
--- a/docs/doc/windows.html
+++ b/docs/doc/windows.html
@@ -148,4 +148,4 @@
 </pre>
 <p>The slices are naturally arranged along multiple dimensions according to their starting index. Once again the equivalence <code><span class='Value'>i</span><span class='Function'>⊏</span><span class='Value'>l</span><span class='Function'>↕</span><span class='Value'>x</span></code> ←→ <code><span class='Value'>l</span><span class='Function'>↑</span><span class='Value'>i</span><span class='Function'>↓</span><span class='Value'>x</span></code> holds, provided <code><span class='Value'>i</span></code> and <code><span class='Value'>l</span></code> have the same length.</p>
 <p>If <code><span class='Value'>𝕨</span></code> has length <code><span class='Number'>0</span></code>, then <code><span class='Value'>𝕩</span></code> is not sliced along any dimensions. The only slice that results—the entire argument—is then arranged along an additional zero dimensions. In the end, the result is <code><span class='Value'>𝕩</span></code>, unchanged.</p>
-<p>Here's a more formal definition: <code><span class='Value'>𝕩</span></code> is an array. <code><span class='Value'>𝕨</span></code> is a number, or numeric list or unit, with <code><span class='Value'>𝕨</span><span class='Function'>≤</span><span class='Modifier2'>○</span><span class='Function'>≠≢</span><span class='Value'>𝕩</span></code>. The result <code><span class='Value'>z</span></code> has shape <code><span class='Value'>𝕨</span><span class='Function'>∾¬</span><span class='Modifier2'>⟜</span><span class='Value'>𝕨</span><span class='Modifier2'>⌾</span><span class='Paren'>((</span><span class='Function'>≠</span><span class='Value'>𝕨</span><span class='Paren'>)</span><span class='Modifier2'>⊸</span><span class='Function'>↑</span><span class='Paren'>)</span><span class='Function'>≢</span><span class='Value'>𝕩</span></code>, and element <code><span class='Value'>i</span><span class='Function'>⊑</span><span class='Value'>z</span></code> is <code><span class='Value'>i</span><span class='Function'>⊑</span><span class='Value'>z</span></code> ←→ <code><span class='Value'>𝕩</span><span class='Function'>⊑</span><span class='Modifier'>˜</span><span class='Function'>+</span><span class='Modifier'>´¨</span><span class='Paren'>(</span><span class='Value'>𝕨</span><span class='Function'>∾</span><span class='Modifier2'>○</span><span class='Paren'>(</span><span class='Function'>↕</span><span class='Modifier2'>∘</span><span class='Function'>≠</span><span class='Paren'>)</span><span class='Function'>≢</span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Function'>⊔</span><span class='Value'>i</span></code>.</p>
+<p>Here's a more formal definition: <code><span class='Value'>𝕩</span></code> is an array. <code><span class='Value'>𝕨</span></code> is a number, or numeric list or unit, with length <code><span class='Value'>l</span><span class='Gets'>←</span><span class='Function'>≠</span><span class='Value'>𝕨</span></code> so that <code><span class='Value'>l</span><span class='Function'>≤=</span><span class='Value'>𝕩</span></code>. The result <code><span class='Value'>z</span></code> has shape <code><span class='Value'>𝕨</span> <span class='Function'>∾</span> <span class='Function'>¬</span><span class='Modifier2'>⟜</span><span class='Value'>𝕨</span><span class='Modifier2'>⌾</span><span class='Paren'>(</span><span class='Value'>l</span><span class='Modifier2'>⊸</span><span class='Function'>↑</span><span class='Paren'>)</span><span class='Function'>≢</span><span class='Value'>𝕩</span></code>, and element <code><span class='Value'>i</span><span class='Function'>⊑</span><span class='Value'>z</span></code> is <code><span class='Value'>j</span><span class='Function'>⊑</span><span class='Value'>𝕩</span></code>, with <code><span class='Value'>j</span><span class='Gets'>←</span><span class='Function'>+</span><span class='Modifier'>´¨</span><span class='Paren'>(</span><span class='Value'>l</span><span class='Function'>∾</span><span class='Modifier2'>○</span><span class='Function'>↕=</span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Function'>⊔</span><span class='Value'>i</span></code>. That is, the index list <code><span class='Value'>i</span></code> starts with two length-<code><span class='Value'>l</span></code> sequences that are added together to produce the first <code><span class='Value'>l</span></code> values in <code><span class='Value'>j</span></code>. We might also say that each of the first <code><span class='Value'>l</span></code> values in <code><span class='Value'>j</span></code> is split into two values in <code><span class='Value'>i</span></code>.</p>