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<h3 class="section">17.7 Rational Approximations</h3>
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<p><a name="doc_002drat"></a>
<div class="defun">
— Function File: <var>s</var> = <b>rat</b> (<var>x, tol</var>)<var><a name="index-rat-1937"></a></var><br>
— Function File: [<var>n</var>, <var>d</var>] = <b>rat</b> (<var>x, tol</var>)<var><a name="index-rat-1938"></a></var><br>
<blockquote>
<p>Find a rational approximation to <var>x</var> within the tolerance defined
by <var>tol</var> using a continued fraction expansion. For 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>
<p>Called with two arguments returns the numerator and denominator separately
as two matrices.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002drats.html#doc_002drats">rats</a>.
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<p><a name="doc_002drats"></a>
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— Built-in Function: <b>rats</b> (<var>x, len</var>)<var><a name="index-rats-1939"></a></var><br>
<blockquote><p>Convert <var>x</var> into a rational approximation represented as a string.
You can convert the string back into a matrix as follows:
<pre class="example"> r = rats(hilb(4));
x = str2num(r)
</pre>
<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.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dformat.html#doc_002dformat">format</a>, <a href="doc_002drat.html#doc_002drat">rat</a>.
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