Top and leaves of an expression : sommet feuille op

### 2.15.3 Top and leaves of an expression : `sommet feuille op`

An operator is an infixed function : for exemple ’+’ is an operator and ’sin’ is a function.
An expression can be represented by a tree. The top of the tree is either an operator, or a function and the leaves of the tree are the arguments of the operator or of the function (see also 2.37.11).
The instruction `sommet` (resp `feuille` (or `op`)) returns the top (resp. the list of the leaves) of an expression.
Input :

`sommet(sin(x+2))`

Output :

`’sin’`

Input :

`sommet(x+2*y)`

Output :

`’+’`

Input :

`feuille(sin(x+2))`

Or :

`op(sin(x+2))`

Output :

`x+2`

Input :

`feuille(x+2*y)`

Or :

`op(x+2*y)`

Output :

`(x,2*y)`

Remark
Suppose that a function is defined by a program, for example let us define the `pgcd` function :

`pgcd(a,b):={local r; while (b!=0) {r:=irem(a,b);a:=b;b:=r;} return a;}`

Then input :

`sommet(pgcd)`

Output :

`’program’`

Then input :

`feuille(pgcd)[0]`

Output :

`(a,b)`

Then input :

`feuille(pgcd)[1]`

Output :

`(0,0) or (15,25) if the last input was pgcd(15,25)`

Then input :

`feuille(pgcd)[2]`

Output :

`The body of the program : {local r;....return(a);}`