Apply a function of one variable to the elements of a list : map apply of

### 2.37.32 Apply a function of one variable to the elements of a list : `map apply of`

`map` or `apply` or `of` applies a function to a list of elements.
`of` is the prefixed function equivalent to the parenthesis : `Xcas` translates `f(x)` internally to `of(f,x)`. It is more natural to call `map` or `apply` than `of`. Be carefull with the order of arguments (that is required for compatibility reasons).
Note that `apply` returns a list (`[]`) even if the second argument is not a list.
Input :

`apply(x->x```^```2,[3,5,1])`

or

`of(x->x```^```2,[3,5,1])`

or

`map([3,5,1],x->x```^```2)`

or first define the function h(x)=x2, input :

`h(x):=x```^```2`

then

`apply(h,[3,5,1])`

or

`of(h,[3,5,1])`

or

`map([3,5,1],h)`

Output :

`[9,25,1]`

Next example, define the function g(x)=[x,x2,x3], input :

`g:=(x)->[x,x```^```2,x```^```3]`

then

`apply(g,[3,5,1])`

or

`of(g,[3,5,1])`

or

`map([3,5,1],g)`

Output :

`[[3,9,27],[5,25,125],[1,1,1]]`

Warning!!! first purge `x` if `x` is not symbolic.
Note that if `l1,l2,l3` are lists `sizes([l1,l2,l3])` is equivalent to `map(size,[l1,l2,l3]`.