Intro 27. Obverse and Under

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27. Obverse and Under
The result of`f^:_1` is called the obverse of the function`f` ;`` if`f=: g :. h`,`` this obverse is`h`,`` and it is otherwise an inverse of`f` .`` Inverses are provided for over 25 primitives (including the case of the square root illustrated in Section 11), as well as many bonded dyads such as`-&3` and`10&^.` and`2&o.` .`` Moreover,`u@v^:_1` is given by`(v^:_1)@(u^:_1)` .`` For example:

       fFc=: (32&+)@(*&1.8)
       ]b=:fFc _40 0 100
    _40 32 212

       cFf=: fFc^:_1
       cFf b
    _40 0 100

The result of the phrase`f &. g` is the verb`(g^:_1)@(f & g)` .`` The function`g` can be viewed as preparation (which is done before and undone after) for the application of the "main" function`f` .`` For example:

       b=: 0 0 1 0 1 0 1 1 0 0 0
       sup=: </\                   Suppress ones after the first
       sup b
    0 0 1 0 0 0 0 0 0 0 0

       |. sup |. b                 Suppress ones before the last
    0 0 0 0 0 0 0 1 0 0 0

       sup&.|. b
    0 0 0 0 0 0 0 1 0 0 0

       3 +&.^. 4                   Multiply by applying the exponential
    12                             to the sum of logarithms

       (^.3)+(^.4)
    2.48491

       ^ (^.3)+(^.4)
    12

       ]c=: 1 2 3;4 5;6 7 8
    +-----+---+-----+
    |1 2 3|4 5|6 7 8|
    +-----+---+-----+

       |.&.> c                     Open, reverse, and then box
    +-----+---+-----+
    |3 2 1|5 4|8 7 6|
    +-----+---+-----+

Exercises

27.1 | Use the following as exercises in reading and writing. Try using arguments such as`a=: 2 3 5 7` and`b=: 1 2 3 4` and`c=: <@i."0 i. 3 4` :
    f=: +&.^                       Multiplication by addition of natural logs
    g=: +&.(10&^.)                 Multiplication using base-10 logs
    h=: *&.^                       Addition from multiplication
    i=: |.&.>                      Reverse each box
    j=: +/&.>                      Sum each box
    k=: +/&>                       Sum each box and leave open

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