From f910f64594053011efd57a97100ad19ee1e39fb4 Mon Sep 17 00:00:00 2001 From: Marshall Lochbaum Date: Sun, 20 Sep 2020 13:50:30 -0400 Subject: Use "unit" or "rank-0" instead of "scalar" --- docs/doc/windows.html | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'docs/doc/windows.html') diff --git a/docs/doc/windows.html b/docs/doc/windows.html index e4613f1a..0f85eab7 100644 --- a/docs/doc/windows.html +++ b/docs/doc/windows.html @@ -50,7 +50,7 @@

The slices are naturally arranged along multiple dimensions according to their starting index. Once again the equivalence i⊏l↕x ←→ l↑i↓x holds, provided i and l have the same length.

If the left argument has length 0, then the argument 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 the same as the argument.

More formally

-

𝕩 is an array. 𝕨 is a number or numeric list or scalar with 𝕨≤○≠≢𝕩. The result z has shape 𝕨∾¬⟜𝕨⌾((≠𝕨)⊸↑)≢𝕩, and element i⊑z is 𝕩⊑˜(≠𝕨)(↑+⌾((≠𝕨)⊸↑)↓)i.

+

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 𝕩⊑˜(≠𝕨)(↑+⌾((≠𝕨)⊸↑)↓)i.

Using Group we could also write i⊑z ←→ 𝕩⊑˜(𝕨∾○(↕∘≠)≢𝕩) +´¨∘⊔ i.

Symmetry

Let's look at an earlier example, along with its transpose.

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