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<HTML>
<HEAD>
<TITLE>Vector variables</TITLE>
</HEAD>
<BODY BGCOLOR="#FFFFFF" TEXT="#000000">
<P><A NAME="variablevector"></A>
<font size="+2" color="green">Vector variables</font></P>
<P>
A vector is a one dimension array of double precision real numbers. A
vector can be thought of as a list of numbers. There is no maximum length
for vectors.</P>
<P>
A literal vector can be a list of numbers, such as,
<code>[3;4.2;.456;-8]</code>, or a range of numbers, such as,
<code>[3:21:2]</code>, or an expression that results in a list of
numbers, such as <code>3*[2:5]^2</code>.</p>
<p>
Elements of a list are separated
by semicolons, <CODE>;</CODE>, while the colon, <CODE>:</CODE>, is used as
the range element separator.</P>
<P>
The following table shows the possible ways that
variables can be considered to be equivalent to vectors, that is, can be
used wherever vectors are expected.</P>
<p>
Let <code>a</code> be a scalar and let <code>x</code> be a vector.
Suppose that <code>M</code> is a matrix and <code>V</code> is a vector.</p>
<p>
<center><table cellpadding="2" cols="4">
<tr>
<td><code>V</code></td><td>=</td><td><code>V[i]</code></td><td>for <code>i = 1, ..., LEN(V)</code></td>
</tr><tr>
<td><code>V[x]</code></td><td>=</td><td><code>V[i]</code></td>
<td>for <code>i = x[1], x[2], ..., x[#]</code></td>
</tr><tr>
<td><code>M[x,b]</code></td><td>=</td><td><code>M[i,a]</code></td>
<td>for <code>i = x[1], x[2], ..., x[#]</code></td>
</tr><tr>
<td><code>M[a,x]</code></td><td>=</td><td><code>M[a,j]</code></td>
<td>for <code>j = x[1], x[2], ..., x[#]</code></td>
</table></center></P>
<P>
All vectors have an order property. Vectors are either in ascending order,
descending order, or un-ordered. The type is displayed in the
<a href="../Commands/Show.htm"><CODE>SHOW</CODE></a>
command, where <code>+O</code> means ascending
order, <code>-O</code> means descending order, and no symbol means
un-ordered. For now, being ordered only has an affect on the vector
<a href="../Operators/union.htm">union</a>, <code>/|</code>, and the vector
<a href="../Operators/intersection.htm">intersection</a>, <code>/&</code>, operators.
These operations are much faster if the vector operands are ordered. The
<a href="../Functions/where.htm"><CODE>WHERE</CODE></a>
function produces an ascending order vector, as does the
<a href="../Commands/Sort.htm"><CODE>SORT/UP</CODE></a> command. The
<CODE>SORT/DOWN</CODE> command produces a descending order vector.</P>
<P>
<a href="VariablesS02.htm"><img src="../shadow_left.gif">
<font size=+1 color="olive">Scalar variables</font></a><br>
<a href="VariablesS04.htm"><img src="../shadow_right.gif">
<font size=+1 color="olive">Matrix variables</font></a>
</P>
</body>
</html>
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