%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %A range.tex GAP documentation Martin Schoenert %% %A @(#)$Id: range.tex,v 3.8 1994/06/09 09:29:42 vfelsch Rel $ %% %Y Copyright 1990-1992, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany %% %% This file describes those functions that mainly deal with ranges. %% %H $Log: range.tex,v $ %H Revision 3.8 1994/06/09 09:29:42 vfelsch %H updated output of examples %H %H Revision 3.7 1993/02/19 10:48:42 gap %H adjustments in line length and spelling %H %H Revision 3.6 1993/02/12 11:39:35 felsch %H new example fixed %H %H Revision 3.5 1993/02/10 18:56:42 martin %H changed the description for extended ranges %H %H Revision 3.4 1993/02/05 08:07:20 felsch %H examples fixed %H %H Revision 3.3 1991/12/27 16:07:04 martin %H revised everything for GAP 3.1 manual %H %H Revision 3.2 1991/07/26 09:01:07 martin %H changed |\GAP\ | to |{\GAP}| %H %H Revision 3.1 1991/07/25 16:16:59 martin %H fixed some minor typos %H %H Revision 3.0 1991/04/11 11:32:53 martin %H Initial revision under RCS %H %% \Chapter{Ranges} 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 '[ , .. ]' or, if the difference between consecutive elements is 1, as '[ .. ]'. If ' > ', '[,..]' is the empty list, which by definition is also a range. If = , '[,..]' is a singleton list, which is a range too. Note that ' - ' must be divisible by the increment ' - ', 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 ' + -' to the entry '[Length()+1]', the 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 in [..] do od' replaces the \\ 'for from to do 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[3]; 12 gap> 17 in r; true gap> r[12] := 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[4]; 7 gap> r := [0,-1..-9]; [ 0, -1 .. -9 ] gap> r[5]; -4 gap> r := [ 1, 4 .. 32 ]; Error, Range: - must be divisible by 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"). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{IsRange}\index{test!for a range} 'IsRange( )' 'IsRange' returns 'true' if , 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 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( [1] ); true # singleton lists are a range by definition too | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Section{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 {\GAP} 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 '[ , .. ]' are of course known to be ranges and are represented in the compact way. 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 'true'; If you change a range that is represented in the compact way, by assignment, 'Add' or '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 'IsRange' with that list as an argument. If it is indeed a proper range, 'IsRange' will convert it to the compact representation. You can think of the call to 'IsRange' as a hint to {\GAP} that this list is a proper range. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %E Emacs . . . . . . . . . . . . . . . . . . . . . local Emacs variables %% %% Local Variables: %% mode: outline %% outline-regexp: "\\\\Chapter\\|\\\\Section" %% fill-column: 73 %% eval: (hide-body) %% End: %%