@c Copyright (C) 1996-2015 John W. Eaton
@c
@c This file is part of Octave.
@c
@c Octave is free software; you can redistribute it and/or modify it
@c under the terms of the GNU General Public License as published by the
@c Free Software Foundation; either version 3 of the License, or (at
@c your option) any later version.
@c
@c Octave is distributed in the hope that it will be useful, but WITHOUT
@c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
@c FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
@c for more details.
@c
@c You should have received a copy of the GNU General Public License
@c along with Octave; see the file COPYING.  If not, see
@c <http://www.gnu.org/licenses/>.

@node Sets
@chapter Sets

Octave has a number of functions for managing sets of data.  A set is defined
as a collection of unique elements and is typically represented by a vector of
numbers sorted in ascending order.  Any vector or matrix can be converted to a
set by removing duplicates through the use of the @code{unique} function.
However, it isn't necessary to explicitly create a set as all of the functions
which operate on sets will convert their input to a set before proceeding.

@DOCSTRING(unique)

@menu
* Set Operations::
@end menu

@node Set Operations
@section Set Operations

Octave supports several basic set operations.  Octave can compute the union,
intersection, and difference of two sets.  Octave also supports the
@emph{Exclusive Or} set operation.

The functions for set operations all work in the same way by accepting two
input sets and returning a third set.  As an example, assume that @code{a} and
@code{b} contains two sets, then

@example
union (a, b)
@end example

@noindent
computes the union of the two sets.

Finally, determining whether elements belong to a set can be done with the
@code{ismember} function.  Because sets are ordered this operation is very
efficient and is of order O(log2(n)) which is preferable to the @code{find}
function which is of order O(n).

@DOCSTRING(intersect)

@DOCSTRING(union)

@DOCSTRING(setdiff)

@DOCSTRING(setxor)

@DOCSTRING(ismember)

@DOCSTRING(powerset)