..
-- range operatorl..r
defines a ``range'' with the left bound
l
and the right bound r
.
l .. r _range(l, r)
l, r |
- | arbitrary MuPAD objects |
an expression of type "_range"
.
l
, r
int
, array
, op
, or the sequence operator $
. Usually, l..r
represents a real interval (e.g., int(f(x), x = l..r)
), or the sequence of
integers from l
to r
._range(l, r)
is equivalent to l..r
.Dom::Interval
._range
is a function of the system kernel.A range can be defined with the ..
operator
as well as with a call to the function _range
:
>> _range(1, 42), 1..42
1..42, 1..42
In the following call, the range represents an interval:
>> int(x, x = l..r)
2 2 r l -- - -- 2 2
Ranges can be used for accessing the operands of expressions or to define the dimension of an array:
>> op(f(a, b, c, d, e), 2..4)
b, c, d
>> array(1..3, [a1, a2,a3])
+- -+ | a1, a2, a3 | +- -+
Ranges can also be used for creating expression sequences:
>> i^3 $ i = 1..5
1, 8, 27, 64, 125
The range operator ..
is a technical device
that does not check its parameters with respect to their semantics. It
just creates a range which is interpreted in the context in which it is
used later. Any bounds are accepted:
>> float(PI) .. -sqrt(2)/3
1/2 2 3.141592654..- ---- 3