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<H2><A NAME="s11">11.</A> <A HREF="slshfun.html#toc11">Set Functions</A></H2>

These functions manipulate arrays and lists as sets.

<H2><A NAME="complement"></A> <A NAME="ss11.1">11.1</A> <A HREF="slshfun.html#toc11.1">complement</A>
</H2>

<DL>
<DT> Synopsis <DD>
Extract the elements of a set that are not contained in other sets.
<DT> Usage <DD>
<CODE>indices = complement (a, b, ..., c)</CODE>
<DT> Description <DD>
This function computes the elements of the first argument (<CODE>a</CODE>)
that are not contained in the sets given by the other arguments
(<CODE>b,...,c</CODE>) and returns them in the form of indices into the
first argument.
<DT> Example <DD>

<BLOCKQUOTE><CODE>
<PRE>
 a = {"foo", PI, 7};
 b = [1,2,3,PI];
 indices = complement (a, b);
</PRE>
</CODE></BLOCKQUOTE>

Upon return, <CODE>indices</CODE> will have the value <CODE>[0, 2]</CODE> since
<CODE>a[0]</CODE> and <CODE>a[2]</CODE> are not contained in <CODE>b</CODE>.
<DT> Notes <DD>
A set may either be an Array_Type or a List_Type object.
For a homogeneous collection of objects, it is better to
use an Array_Type. i.e., <CODE>[1,2,3]</CODE> instead of <CODE>{1,2,3}</CODE>.
<DT> See Also <DD>
<CODE>intersection, ismember, union, unique</CODE>
</DL>

<H2><A NAME="intersection"></A> <A NAME="ss11.2">11.2</A> <A HREF="slshfun.html#toc11.2">intersection</A>
</H2>

<DL>
<DT> Synopsis <DD>
Extract the common elements of two or more sets
<DT> Usage <DD>
<CODE>indices = complement (a, b, ..., c)</CODE>
<DT> Description <DD>
This function computes the common elements of two or more sets and
returns them in the form of indices into the first argument.
<DT> Example <DD>

<BLOCKQUOTE><CODE>
<PRE>
 a = {"foo", 7, PI};
 b = {PI, "bar", "foo"};
 indices = intersection (a, b);
</PRE>
</CODE></BLOCKQUOTE>

Upon return, <CODE>indices</CODE> will have the value <CODE>[0, 2]</CODE> since
<CODE>a[0]</CODE> and <CODE>a[2]</CODE> are the common elements of the sets.
<DT> Notes <DD>
A set may either be an Array_Type or a List_Type object.
For a homogeneous collection of objects, it is better to
use an Array_Type. i.e., <CODE>[1,2,3]</CODE> instead of <CODE>{1,2,3}</CODE>.
<DT> See Also <DD>
<CODE>complement, ismember, union, unique</CODE>
</DL>

<H2><A NAME="ismember"></A> <A NAME="ss11.3">11.3</A> <A HREF="slshfun.html#toc11.3">ismember</A>
</H2>

<DL>
<DT> Synopsis <DD>
test to see if the elements of one set are members of another
<DT> Usage <DD>
<CODE>val = ismember (a, b)</CODE>
<DT> Description <DD>
This function may be used to see which of the elements of the set
<CODE>a</CODE> are members of the set <CODE>b</CODE>. It returns a boolean
array indicating whether or not the corresponding element of
<CODE>a</CODE> is a member of <CODE>b</CODE>.
<DT> Notes <DD>
A set may either be an Array_Type or a List_Type object.
For a homogeneous collection of objects, it is better to
use an Array_Type. i.e., <CODE>[1,2,3]</CODE> instead of <CODE>{1,2,3}</CODE>.
<DT> See Also <DD>
<CODE>complement, intersection, union, unique</CODE>
</DL>

<H2><A NAME="union"></A> <A NAME="ss11.4">11.4</A> <A HREF="slshfun.html#toc11.4">union</A>
</H2>

<DL>
<DT> Synopsis <DD>
Form a set of the unique elements of one ore more subsets
<DT> Usage <DD>
<CODE>abc = union (a, b,..., c)</CODE>
<DT> Description <DD>
This function interprets each of its arguments as a set, then merges
them together and returns only the unique elements. The returned
value may either be an <CODE>Array_Type</CODE> or a <CODE>List_Type</CODE>
object.
<DT> Notes <DD>
A set may either be an Array_Type or a List_Type object.
For a homogeneous collection of objects, it is better to
use an Array_Type. i.e., <CODE>[1,2,3]</CODE> instead of <CODE>{1,2,3}</CODE>.
<DT> See Also <DD>
<CODE>complement, intersection, ismember, unique</CODE>
</DL>

<H2><A NAME="unique"></A> <A NAME="ss11.5">11.5</A> <A HREF="slshfun.html#toc11.5">unique</A>
</H2>

<DL>
<DT> Synopsis <DD>
Get the indices of the unique elements of a set
<DT> Usage <DD>
<CODE>indices = unique (A)</CODE>
<DT> Description <DD>
This function returns an array of the indices of the unique elements
of a set.
<DT> Notes <DD>
A set may either be an Array_Type or a List_Type object.
For a homogeneous collection of objects, it is better to
use an Array_Type. i.e., <CODE>[1,2,3]</CODE> instead of <CODE>{1,2,3}</CODE>.
<DT> See Also <DD>
<CODE>complement, intersection, ismember, union</CODE>
</DL>

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