# Expand

 `\` `⍀`

Expand (`\`, `⍀`) is a dyadic function or monadic operator that copies each element of the right argument a given number of times and inserts prototype elements, ordering the copies along a specified axis. Typically `\` is called Expand while `⍀` is called "Expand First" or an equivalent.

Expand is usually associated with Replicate (`/`), and the two functions are related to Mesh and Mask. It shares a glyph with Scan even though Expand is naturally a function and Scan must be an operator. This incongruity is sometimes resolved by making Expand an operator itself, and sometimes by function-operator overloading allowing both syntactic elements to coexist.

## Examples

If the right argument is a vector, the number of positive values in the left argument must match the length of the right argument. Each positive value produces copies of the corresponding item on the right argument; a zero or negative value produces one or more prototype elements.

```      1 0 3 ¯2 2\'abc'
a bbb  cc```

For Boolean left argument, Expand is the right inverse of Replicate, as Expand inserts prototype elements at the exact places which Replicate will remove:

```      1 0 0 1 0 1\'abc'
a  b c
1 0 0 1 0 1/'a  b c'
abc```

### High-rank arrays

Expand works along a particular axis, which can be specified in languages with function axis and otherwise is the first axis for `⍀`, and the last axis for `\`.

```      ⎕←A←3 4⍴⎕A
ABCD
EFGH
IJKL
1 0 3 2 ¯2 1\A
A BBBCC  D
E FFFGG  H
I JJJKK  L
3 1 ¯1 2⍀A
ABCD
ABCD
ABCD
EFGH

IJKL
IJKL```

Some implementations allow the right argument to have length 1 along the expansion axis even if other axes have lengths not equal to 1.

```      1 ¯2 3 \ ⍪'abc'
a  aaa
b  bbb
c  ccc```