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authorMarshall Lochbaum <mwlochbaum@gmail.com>2021-02-11 15:19:25 -0500
committerMarshall Lochbaum <mwlochbaum@gmail.com>2021-02-11 15:31:24 -0500
commitf4d45e6721784c23419045b0ec496d8460efc871 (patch)
tree3e1eeddabbd352c6f4fb2be88db5badfd6a081e2 /spec
parentae8d0791777e9ff3e43569089ddd446b666ac626 (diff)
Dyadic scan inverse
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@@ -142,7 +142,6 @@ Inverses of other modifiers and derived functions or modifiers obtained from the
| `Β¨` | `{!0<≑𝕩⋄𝕨𝔽⁼¨𝕩}` |
| `⌜` | `{!0<≑𝕩⋄ π”½βΌβŒœπ•©;}` | Monadic case only
| `˘` | `{!0<=π•©β‹„π•¨π”½βΌΛ˜π•©}` |
-| `` ` `` | `{!0<=𝕩⋄(⊏∾¯1βŠΈβ†“π”½βΌΒ¨1βŠΈβ†“)⍟(1<β‰ )𝕩}` |
| `F∘G` | `{𝕨G⁼F⁼𝕩}` |
| `F G` | |
| `Β·F G` | |
@@ -157,6 +156,10 @@ Inverses of other modifiers and derived functions or modifiers obtained from the
| `k𝔽𝔾` | `𝔾⁼{𝕨𝔽𝔾𝕩}(kπ”½βΌβŠ’)` | Constant `k`
| `𝔽𝔾K` | `𝔽⁼kπ”ΎΛœβΌβŠ’` | Constant `k`
+| Mod | Inverse
+|---------|---------
+| `` ` `` | `{!0<=𝕩 β‹„ 𝕨 (Β»π”½βΌΒ¨βŠ’){(βŠβˆΎβŠπ”½1βŠΈβ†“)⍟(1<β‰ )βŠ˜π”½} 𝕩}`
+
## Under
The Under 2-modifier `⌾` conceptually applies its left operand under the action of its right operand. Setting `zβ†π•¨π”½βŒΎπ”Ύπ•©`, it satisfies `(𝕨𝔽○𝔾𝕩) ≑ 𝔾z`. We might say that `𝔾` transforms values to a new domain, and `βŒΎπ”Ύ` lifts actions `𝔽` performed in this domain to the original domain of values. For example, addition in the logarithmic domain corresponds to multiplication in the linear domain: `+⌾(⋆⁼)` is `Γ—` (but less precise if computed in floating point).