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<h3 class="section">17.7 Rational Approximations</h3>
<a name="XREFrat"></a><dl>
<dt><a name="index-rat"></a>: <em><var>s</var> =</em> <strong>rat</strong> <em>(<var>x</var>, <var>tol</var>)</em></dt>
<dt><a name="index-rat-1"></a>: <em>[<var>n</var>, <var>d</var>] =</em> <strong>rat</strong> <em>(<var>x</var>, <var>tol</var>)</em></dt>
<dd>
<p>Find a rational approximation to <var>x</var> within the tolerance defined by
<var>tol</var> using a continued fraction expansion.
</p>
<p>For example:
</p>
<div class="example">
<pre class="example">rat (pi) = 3 + 1/(7 + 1/16) = 355/113
rat (e) = 3 + 1/(-4 + 1/(2 + 1/(5 + 1/(-2 + 1/(-7)))))
= 1457/536
</pre></div>
<p>When called with two output arguments return the numerator and denominator
separately as two matrices.
</p>
<p><strong>See also:</strong> <a href="#XREFrats">rats</a>.
</p></dd></dl>
<a name="XREFrats"></a><dl>
<dt><a name="index-rats"></a>: <em></em> <strong>rats</strong> <em>(<var>x</var>, <var>len</var>)</em></dt>
<dd><p>Convert <var>x</var> into a rational approximation represented as a string.
</p>
<p>The string can be converted back into a matrix as follows:
</p>
<div class="example">
<pre class="example">r = rats (hilb (4));
x = str2num (r)
</pre></div>
<p>The optional second argument defines the maximum length of the string
representing the elements of <var>x</var>. By default <var>len</var> is 9.
</p>
<p>If the length of the smallest possible rational approximation exceeds
<var>len</var>, an asterisk (*) padded with spaces will be returned instead.
</p>
<p><strong>See also:</strong> <a href="Terminal-Output.html#XREFformat">format</a>, <a href="#XREFrat">rat</a>.
</p></dd></dl>
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