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<H1><A NAME="SECTION0071500000000000000000">
5.15 <tt class="module">sets</tt> --
         Unordered collections of unique elements</A>
</H1>

<P>
<A NAME="module-sets"></A>

<P>

<span class="versionnote">New in version 2.3.</span>

<P>
The <tt class="module">sets</tt> module provides classes for constructing and manipulating
unordered collections of unique elements.  Common uses include membership
testing, removing duplicates from a sequence, and computing standard math
operations on sets such as intersection, union, difference, and symmetric
difference.

<P>
Like other collections, sets support <code><var>x</var> in <var>set</var></code>,
<code>len(<var>set</var>)</code>, and <code>for <var>x</var> in <var>set</var></code>.  Being an
unordered collection, sets do not record element position or order of
insertion.  Accordingly, sets do not support indexing, slicing, or
other sequence-like behavior.

<P>
Most set applications use the <tt class="class">Set</tt> class which provides every set
method except for <tt class="method">__hash__()</tt>. For advanced applications requiring
a hash method, the <tt class="class">ImmutableSet</tt> class adds a <tt class="method">__hash__()</tt>
method but omits methods which alter the contents of the set. Both
<tt class="class">Set</tt> and <tt class="class">ImmutableSet</tt> derive from <tt class="class">BaseSet</tt>, an
abstract class useful for determining whether something is a set:
<code>isinstance(<var>obj</var>, BaseSet)</code>.

<P>
The set classes are implemented using dictionaries.  Accordingly, the
requirements for set elements are the same as those for dictionary keys;
namely, that the element defines both <tt class="method">__eq__</tt> and <tt class="method">__hash__</tt>.
As a result, sets
cannot contain mutable elements such as lists or dictionaries.
However, they can contain immutable collections such as tuples or
instances of <tt class="class">ImmutableSet</tt>.  For convenience in implementing
sets of sets, inner sets are automatically converted to immutable
form, for example, <code>Set([Set(['dog'])])</code> is transformed to
<code>Set([ImmutableSet(['dog'])])</code>.

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><span class="typelabel">class</span>&nbsp;<tt id='l2h-1380' xml:id='l2h-1380' class="class">Set</tt></b>(</nobr></td>
  <td><var></var><big>[</big><var>iterable</var><big>]</big><var></var>)</td></tr></table></dt>
<dd>
Constructs a new empty <tt class="class">Set</tt> object.  If the optional <var>iterable</var>
parameter is supplied, updates the set with elements obtained from iteration.
All of the elements in <var>iterable</var> should be immutable or be transformable
to an immutable using the protocol described in
section&nbsp;<A href="immutable-transforms.html#immutable-transforms">5.15.3</A>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><span class="typelabel">class</span>&nbsp;<tt id='l2h-1381' xml:id='l2h-1381' class="class">ImmutableSet</tt></b>(</nobr></td>
  <td><var></var><big>[</big><var>iterable</var><big>]</big><var></var>)</td></tr></table></dt>
<dd>
Constructs a new empty <tt class="class">ImmutableSet</tt> object.  If the optional
<var>iterable</var> parameter is supplied, updates the set with elements obtained
from iteration.  All of the elements in <var>iterable</var> should be immutable or
be transformable to an immutable using the protocol described in
section&nbsp;<A href="immutable-transforms.html#immutable-transforms">5.15.3</A>.

<P>
Because <tt class="class">ImmutableSet</tt> objects provide a <tt class="method">__hash__()</tt> method,
they can be used as set elements or as dictionary keys.  <tt class="class">ImmutableSet</tt>
objects do not have methods for adding or removing elements, so all of the
elements must be known when the constructor is called.
</dl>

<P>

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<LI><A href="set-objects.html">5.15.1 Set Objects</a>
<LI><A href="set-example.html">5.15.2 Example</a>
<LI><A href="immutable-transforms.html">5.15.3 Protocol for automatic conversion to immutable</a>
<LI><A href="comparison-to-builtin-set.html">5.15.4 Comparison to the built-in <tt class="class">set</tt> types</a>
</ul>
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	54
	55	<H1><A NAME="SECTION0071500000000000000000">
	56	5.15 <tt class="module">sets</tt> --
	57	Unordered collections of unique elements</A>
	58	</H1>
	59
	60	<P>
	61	<A NAME="module-sets"></A>
	62
	63	<P>
	64
65	<span class="versionnote">New in version 2.3.</span>
66
67	<P>
68	The <tt class="module">sets</tt> module provides classes for constructing and manipulating
69	unordered collections of unique elements. Common uses include membership
70	testing, removing duplicates from a sequence, and computing standard math
71	operations on sets such as intersection, union, difference, and symmetric
72	difference.
73
74	<P>
75	Like other collections, sets support <code><var>x</var> in <var>set</var></code>,
76	<code>len(<var>set</var>)</code>, and <code>for <var>x</var> in <var>set</var></code>. Being an
77	unordered collection, sets do not record element position or order of
78	insertion. Accordingly, sets do not support indexing, slicing, or
79	other sequence-like behavior.
80
81	<P>
82	Most set applications use the <tt class="class">Set</tt> class which provides every set
83	method except for <tt class="method">__hash__()</tt>. For advanced applications requiring
84	a hash method, the <tt class="class">ImmutableSet</tt> class adds a <tt class="method">__hash__()</tt>
85	method but omits methods which alter the contents of the set. Both
86	<tt class="class">Set</tt> and <tt class="class">ImmutableSet</tt> derive from <tt class="class">BaseSet</tt>, an
87	abstract class useful for determining whether something is a set:
88	<code>isinstance(<var>obj</var>, BaseSet)</code>.
89
90	<P>
91	The set classes are implemented using dictionaries. Accordingly, the
92	requirements for set elements are the same as those for dictionary keys;
93	namely, that the element defines both <tt class="method">__eq__</tt> and <tt class="method">__hash__</tt>.
94	As a result, sets
95	cannot contain mutable elements such as lists or dictionaries.
96	However, they can contain immutable collections such as tuples or
97	instances of <tt class="class">ImmutableSet</tt>. For convenience in implementing
98	sets of sets, inner sets are automatically converted to immutable
99	form, for example, <code>Set([Set(['dog'])])</code> is transformed to
100	<code>Set([ImmutableSet(['dog'])])</code>.
101
102	<P>
103	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
104	<td><nobr><b><span class="typelabel">class</span> <tt id='l2h-1380' xml:id='l2h-1380' class="class">Set</tt></b>(</nobr></td>
105	<td><var></var><big>[</big><var>iterable</var><big>]</big><var></var>)</td></tr></table></dt>
106	<dd>
107	Constructs a new empty <tt class="class">Set</tt> object. If the optional <var>iterable</var>
108	parameter is supplied, updates the set with elements obtained from iteration.
109	All of the elements in <var>iterable</var> should be immutable or be transformable
110	to an immutable using the protocol described in
111	section <A href="immutable-transforms.html#immutable-transforms">5.15.3</A>.
112	</dl>
113
114	<P>
115	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
116	<td><nobr><b><span class="typelabel">class</span> <tt id='l2h-1381' xml:id='l2h-1381' class="class">ImmutableSet</tt></b>(</nobr></td>
117	<td><var></var><big>[</big><var>iterable</var><big>]</big><var></var>)</td></tr></table></dt>
118	<dd>
119	Constructs a new empty <tt class="class">ImmutableSet</tt> object. If the optional
120	<var>iterable</var> parameter is supplied, updates the set with elements obtained
121	from iteration. All of the elements in <var>iterable</var> should be immutable or
122	be transformable to an immutable using the protocol described in
123	section <A href="immutable-transforms.html#immutable-transforms">5.15.3</A>.
124
125	<P>
126	Because <tt class="class">ImmutableSet</tt> objects provide a <tt class="method">__hash__()</tt> method,
127	they can be used as set elements or as dictionary keys. <tt class="class">ImmutableSet</tt>
128	objects do not have methods for adding or removing elements, so all of the
129	elements must be known when the constructor is called.
130	</dl>
131
132	<P>
133
134	<p><br /></p><hr class='online-navigation' />
135	<div class='online-navigation'>
136	<!--Table of Child-Links-->
137	<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></a>
138
139	<UL CLASS="ChildLinks">
140	<LI><A href="set-objects.html">5.15.1 Set Objects</a>
141	<LI><A href="set-example.html">5.15.2 Example</a>
142	<LI><A href="immutable-transforms.html">5.15.3 Protocol for automatic conversion to immutable</a>
143	<LI><A href="comparison-to-builtin-set.html">5.15.4 Comparison to the built-in <tt class="class">set</tt> types</a>
144	</ul>
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