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authorMarshall Lochbaum <mwlochbaum@gmail.com>2020-09-20 13:50:30 -0400
committerMarshall Lochbaum <mwlochbaum@gmail.com>2020-09-20 13:50:30 -0400
commitf910f64594053011efd57a97100ad19ee1e39fb4 (patch)
tree33550f94bf4c2ea035e73d6e37395de299e4ab11 /doc/transpose.md
parentbfc6eb1fcc5408ecf415224d47494a4005330da8 (diff)
Use "unit" or "rank-0" instead of "scalar"
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diff --git a/doc/transpose.md b/doc/transpose.md
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@@ -74,8 +74,8 @@ Finally, it's worth noting that, as monadic Transpose moves the first axis to th
Here we define the two valences of Transpose more precisely.
-Monadic transpose is identical to `(=-1˙)⊸⍉`, except that for scalar arguments (including atoms) it returns the array unchanged rather than giving an error.
+Monadic transpose is identical to `(=-1˙)⊸⍉`, except that if the argument is a unit it is returned unchanged rather than giving an error.
-An atom right argument to dyadic Transpose is always enclosed to get a scalar array before doing anything else.
+An atom right argument to dyadic Transpose is always enclosed to get an array before doing anything else.
In dyadic Transpose, the left argument is a number or numeric array of rank 1 or less, and `𝕨≤○≠≢𝕩`. Define the result rank `r←(=𝕩)-+´¬∊𝕨` to be the argument rank minus the number of duplicate entries in the left argument. We require `∧´𝕨<r`. Bring `𝕨` to full length by appending the missing indices: `𝕨∾↩𝕨(¬∘∊˜/⊢)↕r`. Now the result shape is defined to be `⌊´¨𝕨⊔≢𝕩`. Element `i⊑z` of the result `z` is element `(𝕨⊏i)⊑𝕩` of the argument.