8.2.3 Top and leaves of an expression
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 function (see also
Section 6.1.10).
The sommet command
finds the top of an expression.
-
sommet takes
expr, an expression.
- sommet(expr) returns the top of
expr.
Examples
The op or
feuille
command finds the list of the leaves of an expression.
-
op takes
expr, an expression.
- op(expr) returns the leaves of
expr.
Examples
or:
or:
If the top of an expression expr is an infixed operator, the
left hand side will be expr[1] and the right hand side
will be expr[2]. The left and
right commands are alternative commands
to find the sides (see Section 5.2.4, Section 6.5.1,
Section 6.6.2, Section 6.3.6, Section 9.3.4 and
Section 9.3.5 for other uses of left and right.)
-
left and right take one argument:
expr, an expression whose top is an infixed operator.
- left(expr) returns the left side of
the operator.
- right(expr) returns the right side of
the operator.
Examples
Remark.
If a function is defined by a program (see Section 25.1.2) then
the top will be the function ’program’ and the leaves will be
a sequence consisting of the arguments of the defined function,
followed by a sequence of 0s (one for each argument) followed
by the body of the function. For example, define the pgcd
function:
| pgcd(a,b):={
local r;
while (b!=0) {
r:=irem(a,b);
a:=b; b:=r;
}
return a;
} |
Then:
or:
or:
or:
| { local r;
while(b<>0) {
r:=irem(a,b);
a:=b;
b:=r;
}
return a;
} |