A range is a dense list of integers, such that the difference between
consecutive elements is a nonzero constant. Ranges can be abbreviated
with the syntactic construct
[ first, second .. last ] or, if the
difference between consecutive elements is 1, as
[ first .. last ].
first > last,
[first,second..last] is the empty list,
which by definition is also a range. If first = last,
[first,second..last] is a singleton list, which is a range too.
last - first must be divisible by the increment
- first, otherwise an error is signalled.
Note that a range is just a special case of a list. So everything that
is possible for lists (see Lists) is also possible for ranges. Thus
you can access elements in such a range (see List Elements), test for
membership (see In), etc. You can even assign to such a range (see
List Assignment). Of course, unless you assign
second-first to the entry
resulting list will no longer be a range.
Most often ranges are used in connection with the
for-loop (see For).
Here the construct
for var in [first..last] do statements od replaces the
for var from first to last do statements od, which is more
usual in other programming languages.
Note that a range is at the same time also a set (see Sets), because it contains no holes or duplicates and is sorted, and also a vector (see Vectors), because it contains no holes and all elements are integers.
gap> r := [10..20]; [ 10 .. 20 ] gap> Length( r ); 11 gap> r; 12 gap> 17 in r; true gap> r := 25;; r; [ 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 25 ] gap> r := [1,3..17]; [ 1, 3 .. 17 ] gap> Length( r ); 9 gap> r; 7 gap> r := [0,-1..-9]; [ 0, -1 .. -9 ] gap> r; -4 gap> r := [ 1, 4 .. 32 ]; Error, Range: <high>-<low> must be divisible by <inc> gap> s := ;; for i in [10..20] do Add( s, i^2 ); od; s; [ 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400 ]
The first section in this chapter describes the function that tests if a list is a range (see IsRange).
The other section tells you more about the internal representation of ranges (see More about Ranges).
IsRange( obj )
true if obj, which may be an object of any type, is
a range and
false otherwise. A range is a list without holes such that
the elements are integers with a constant increment. Will cause an error
if obj is an unassigned variable.
gap> IsRange( [1,2,3] ); true # this list is a range gap> IsRange( [7,5,3,1] ); true # this list is a range gap> IsRange( [1,2,4,5] ); false # this list is a set and a vector, but not a range gap> IsRange( [1,,3,,5,,7] ); false # this list contains holes gap> IsRange( 1 ); false # is not even a list gap> IsRange(  ); true # the empty list is a range by definition gap> IsRange(  ); true # singleton lists are a range by definition too
31.2 More about Ranges
For some lists the kernel knows that they are in fact ranges. Those lists are represented internally in a compact way instead of the ordinary way. This is important since this representation needs only 12 bytes for the entire list while the ordinary representation needs 4 length bytes.
Note that a list that is represented in the ordinary way might still be a range. It is just that GAP3 does not know this. This section tells you under which circumstances a range is represented in the compact way, so you can write your program in such a way that you make best use of this compact representation for ranges.
Lists created by the syntactic construct
[ first, second .. last
] are of course known to be ranges and are represented in the compact
If you call
IsRange for a list represented the ordinary way that is
indeed a range,
IsRange will note this, change the representation from
the ordinary to the compact representation, and then return
If you change a range that is represented in the compact way, by
Append, the range will be converted to the
ordinary representation, even if the change is such that the resulting
list is still a proper range.
Suppose you have built a proper range in such a way that it is
represented in the ordinary way and that you now want to convert it to
the compact representation to save space. Then you should call
with that list as an argument. If it is indeed a proper range,
will convert it to the compact representation. You can think of the call
IsRange as a hint to GAP3 that this list is a proper range.
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