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Prefix | m\ u\ _ 0 _ | Infix

`u\y` has`#y` items resulting from applying`u` to each of the prefixes`k{.y` ,`` for`k` from`1` to`#y` .
`m\y` applies successive verbs from the gerund`m` to the prefixes of`y` ,`` extending`m` cyclically as required.

If`x>:0` ,`` the items of`x u\ y` result from applying`u` to each infix of length`x` .`` If`x<0` ,`u` is applied to non-overlapping infixes of length`|x` ,`` including any final shard.
`x m\ y` applies successive verbs from the gerund`m` to the infixes of`y` ,`` extending`m` cyclically as required.

       +/\a=: 1 2 4 8 16                     NB. Subtotals, or partial sums
    1 3 7 15 31

       */\a                                  NB. Partial products
    1 2 8 64 1024

       <\a
    +-+---+-----+-------+----------+
    |1|1 2|1 2 4|1 2 4 8|1 2 4 8 16|
    +-+---+-----+-------+----------+

       <\i.3 4
    +-------+-------+---------+
    |0 1 2 3|0 1 2 3|0 1  2  3|
    |       |4 5 6 7|4 5  6  7|
    |       |       |8 9 10 11|
    +-------+-------+---------+

       (+/\^:_1 +/\ a) ,: */\^:_1 a
    1 2 4 8 16
    1 2 2 2  2

The following examples illustrate the use of the dyad infix:

       (2: -/\ ])  a                         NB. Backward differences
    _1 _2 _4 _8
       (2: -~/\ ]) a                         NB. Forward  differences
    1 2 4 8

       3  <\ 'abcdefgh'
    +---+---+---+---+---+---+
    |abc|bcd|cde|def|efg|fgh|
    +---+---+---+---+---+---+
       _3 <\ 'abcdefgh'
    +---+---+--+
    |abc|def|gh|
    +---+---+--+

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