The most confusing thing about this operator, in all its guises, is that it is not a syntactic construction, and so the resulting sequences do not splice themselves into enclosing lists, as in each of the following examples.
i1 : {10..10}
o1 = {1 : (10)}
o1 : List
|
i2 : {10..8}
o2 = {()}
o2 : List
|
i3 : {3..5,8..10}
o3 = {(3, 4, 5), (8, 9, 10)}
o3 : List
|
Use splice to fix that.
i4 : splice {3..5,8..10}
o4 = {3, 4, 5, 8, 9, 10}
o4 : List
|
If a type of list, instead of a sequence, is desired, use toList or the operator new.
i5 : 0..5 o5 = (0, 1, 2, 3, 4, 5) o5 : Sequence |
i6 : toList (0..5)
o6 = {0, 1, 2, 3, 4, 5}
o6 : List
|
i7 : new Array from 0..5 o7 = [0, 1, 2, 3, 4, 5] o7 : Array |
i8 : new Sum from 0..5 o8 = 0 + 1 + 2 + 3 + 4 + 5 o8 : Expression of class Sum |
The operator can be used with sequences or lists, whose elements are of various types, to produce rectangular intervals.
i9 : (0,0)..(1,3) o9 = ((0, 0), (0, 1), (0, 2), (0, 3), (1, 0), (1, 1), (1, 2), (1, 3)) o9 : Sequence |
i10 : p_(0,a) .. p_(1,c)
o10 = (p , p , p , p , p , p )
0,a 0,b 0,c 1,a 1,b 1,c
o10 : Sequence
|
i11 : p_(1,1) .. q_(2,2)
o11 = (p , p , p , p , q , q , q , q )
1,1 1,2 2,1 2,2 1,1 1,2 2,1 2,2
o11 : Sequence
|
Use ..< instead to get a sequence that stops short of the endpoint.
This operator may be used as a binary operator in an expression like x..y. The user may install binary methods for handling such expressions with code such as
X .. Y := (x,y) -> ...
where X is the class of x and Y is the class of y.