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<title>5.13.1 Set Objects </title>
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<H2><A NAME="SECTION0071310000000000000000"><!--x--></A><A NAME="set-objects"><!--z--></A>
<BR>
5.13.1 Set Objects
</H2>
<P>
Instances of <tt class="class">Set</tt> and <tt class="class">ImmutableSet</tt> both provide
the following operations:
<P>
<table border align="center" style="border-collapse: collapse">
<thead>
<tr class="tableheader">
<th align="center"><b>Operation</b> </th>
<th align="center"><b>Equivalent</b> </th>
<th align="left"><b>Result</b> </th>
</tr>
</thead>
<tbody valign="baseline">
<tr><td align="center" valign="baseline"><code>len(<var>s</var>)</code></td>
<td align="center"> </td>
<td align="left">cardinality of set <var>s</var></td><P>
<tr><td align="center" valign="baseline"><code><var>x</var> in <var>s</var></code></td>
<td align="center"> </td>
<td align="left">test <var>x</var> for membership in <var>s</var></td>
<tr><td align="center" valign="baseline"><code><var>x</var> not in <var>s</var></code></td>
<td align="center"> </td>
<td align="left">test <var>x</var> for non-membership in <var>s</var></td>
<tr><td align="center" valign="baseline"><code><var>s</var>.issubset(<var>t</var>)</code></td>
<td align="center"><code><var>s</var> <= <var>t</var></code></td>
<td align="left">test whether every element in <var>s</var> is in <var>t</var></td>
<tr><td align="center" valign="baseline"><code><var>s</var>.issuperset(<var>t</var>)</code></td>
<td align="center"><code><var>s</var> >= <var>t</var></code></td>
<td align="left">test whether every element in <var>t</var> is in <var>s</var></td><P>
<tr><td align="center" valign="baseline"><code><var>s</var>.union(<var>t</var>)</code></td>
<td align="center"><var>s</var> | <var>t</var></td>
<td align="left">new set with elements from both <var>s</var> and <var>t</var></td>
<tr><td align="center" valign="baseline"><code><var>s</var>.intersection(<var>t</var>)</code></td>
<td align="center"><var>s</var> & <var>t</var></td>
<td align="left">new set with elements common to <var>s</var> and <var>t</var></td>
<tr><td align="center" valign="baseline"><code><var>s</var>.difference(<var>t</var>)</code></td>
<td align="center"><var>s</var> - <var>t</var></td>
<td align="left">new set with elements in <var>s</var> but not in <var>t</var></td>
<tr><td align="center" valign="baseline"><code><var>s</var>.symmetric_difference(<var>t</var>)</code></td>
<td align="center"><var>s</var> ^ <var>t</var></td>
<td align="left">new set with elements in either <var>s</var> or <var>t</var> but not both</td>
<tr><td align="center" valign="baseline"><code><var>s</var>.copy()</code></td>
<td align="center"> </td>
<td align="left">new set with a shallow copy of <var>s</var></td></tbody>
</table>
<P>
Note, the non-operator versions of <tt class="method">union()</tt>,
<tt class="method">intersection()</tt>, <tt class="method">difference()</tt>, and
<tt class="method">symmetric_difference()</tt> will accept any iterable as an argument.
In contrast, their operator based counterparts require their arguments to
be sets. This precludes error-prone constructions like
<code>Set('abc') & 'cbs'</code> in favor of the more readable
<code>Set('abc').intersection('cbs')</code>.
<span class="versionnote">Changed in version 2.3.1:
Formerly all arguments were required to be sets.</span>
<P>
In addition, both <tt class="class">Set</tt> and <tt class="class">ImmutableSet</tt>
support set to set comparisons. Two sets are equal if and only if
every element of each set is contained in the other (each is a subset
of the other).
A set is less than another set if and only if the first set is a proper
subset of the second set (is a subset, but is not equal).
A set is greater than another set if and only if the first set is a proper
superset of the second set (is a superset, but is not equal).
<P>
The subset and equality comparisons do not generalize to a complete
ordering function. For example, any two disjoint sets are not equal and
are not subsets of each other, so <i>all</i> of the following return
<code>False</code>: <code><var>a</var><<var>b</var></code>, <code><var>a</var>==<var>b</var></code>, or
<code><var>a</var>><var>b</var></code>.
Accordingly, sets do not implement the <tt class="method">__cmp__</tt> method.
<P>
Since sets only define partial ordering (subset relationships), the output
of the <tt class="method">list.sort()</tt> method is undefined for lists of sets.
<P>
The following table lists operations available in <tt class="class">ImmutableSet</tt>
but not found in <tt class="class">Set</tt>:
<P>
<table border align="center" style="border-collapse: collapse">
<thead>
<tr class="tableheader">
<th align="center"><b>Operation</b> </th>
<th align="left"><b>Result</b> </th>
</tr>
</thead>
<tbody valign="baseline">
<tr><td align="center" valign="baseline"><code>hash(<var>s</var>)</code></td>
<td align="left">returns a hash value for <var>s</var></td></tbody>
</table>
<P>
The following table lists operations available in <tt class="class">Set</tt>
but not found in <tt class="class">ImmutableSet</tt>:
<P>
<table border align="center" style="border-collapse: collapse">
<thead>
<tr class="tableheader">
<th align="center"><b>Operation</b> </th>
<th align="center"><b>Equivalent</b> </th>
<th align="left"><b>Result</b> </th>
</tr>
</thead>
<tbody valign="baseline">
<tr><td align="center" valign="baseline"><code><var>s</var>.union_update(<var>t</var>)</code></td>
<td align="center"><var>s</var> |= <var>t</var></td>
<td align="left">return set <var>s</var> with elements added from <var>t</var></td>
<tr><td align="center" valign="baseline"><code><var>s</var>.intersection_update(<var>t</var>)</code></td>
<td align="center"><var>s</var> &= <var>t</var></td>
<td align="left">return set <var>s</var> keeping only elements also found in <var>t</var></td>
<tr><td align="center" valign="baseline"><code><var>s</var>.difference_update(<var>t</var>)</code></td>
<td align="center"><var>s</var> -= <var>t</var></td>
<td align="left">return set <var>s</var> after removing elements found in <var>t</var></td>
<tr><td align="center" valign="baseline"><code><var>s</var>.symmetric_difference_update(<var>t</var>)</code></td>
<td align="center"><var>s</var> ^= <var>t</var></td>
<td align="left">return set <var>s</var> with elements from <var>s</var> or <var>t</var>
but not both</td><P>
<tr><td align="center" valign="baseline"><code><var>s</var>.add(<var>x</var>)</code></td>
<td align="center"> </td>
<td align="left">add element <var>x</var> to set <var>s</var></td>
<tr><td align="center" valign="baseline"><code><var>s</var>.remove(<var>x</var>)</code></td>
<td align="center"> </td>
<td align="left">remove <var>x</var> from set <var>s</var>; raises KeyError if not present</td>
<tr><td align="center" valign="baseline"><code><var>s</var>.discard(<var>x</var>)</code></td>
<td align="center"> </td>
<td align="left">removes <var>x</var> from set <var>s</var> if present</td>
<tr><td align="center" valign="baseline"><code><var>s</var>.pop()</code></td>
<td align="center"> </td>
<td align="left">remove and return an arbitrary element from <var>s</var>; raises
KeyError if empty</td>
<tr><td align="center" valign="baseline"><code><var>s</var>.clear()</code></td>
<td align="center"> </td>
<td align="left">remove all elements from set <var>s</var></td></tbody>
</table>
<P>
Note, the non-operator versions of <tt class="method">union_update()</tt>,
<tt class="method">intersection_update()</tt>, <tt class="method">difference_update()</tt>, and
<tt class="method">symmetric_difference_update()</tt> will accept any iterable as
an argument.
<span class="versionnote">Changed in version 2.3.1:
Formerly all arguments were required to be sets.</span>
<P>
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<span class="release-info">Release 2.3.4, documentation updated on May 20, 2004.</span>
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