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<a name="Functions-and-Variables-for-pslq"></a>
<div class="header">
<p>
Previous: <a href="maxima_340.html#Introduction-to-pslq" accesskey="p" rel="previous">Introduction to pslq</a>, Up: <a href="maxima_339.html#pslq_002dpkg" accesskey="u" rel="up">pslq-pkg</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Functions-and-Variables-for-pslq-1"></a>
<h3 class="section">81.2 Functions and Variables for pslq</h3>
<a name="guess_005fexact_005fvalue"></a><a name="Item_003a-pslq_002fdeffn_002fguess_005fexact_005fvalue"></a><dl>
<dt><a name="index-guess_005fexact_005fvalue"></a>Function: <strong>guess_exact_value</strong> <em>(<var>x</var>)</em></dt>
<dd>
<p>When <var>x</var> is a floating point number or bigfloat,
<code>guess_exact_value</code> tries to find an exact expression
(in terms of radicals, logarithms, exponentials, and the constant <code>%pi</code>)
which is nearly equal to the given number.
If <code>guess_exact_value</code> cannot find such an expression,
<var>x</var> is returned unchanged.
</p>
<p>When <var>x</var> is rational number or other mapatom
(other than a float or bigfloat),
<var>x</var> is returned unchanged.
</p>
<p>Otherwise, <var>x</var> is a nonatomic expression,
and <code>guess_exact_value</code> is applied to each of the arguments of <var>x</var>.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) load ("pslq.mac");
(%o1) pslq.mac
(%i2) root: float (sin (%pi/12));
(%o2) 0.2588190451025207
(%i3) guess_exact_value (root);
sqrt(2 - sqrt(3))
(%o3) -----------------
2
(%i4) L: makelist (root^i, i, 0, 4);
(%o4) [1.0, 0.2588190451025207, 0.06698729810778066,
0.01733758853025369, 0.004487298107780675]
(%i5) m: pslq_integer_relation(%);
(%o5) [- 1, 0, 16, 0, - 16]
(%i6) makelist (x^i, i, 0, 4) . m;
4 2
(%o6) (- 16 x ) + 16 x - 1
(%i7) solve(%);
sqrt(sqrt(3) + 2) sqrt(sqrt(3) + 2)
(%o7) [x = - -----------------, x = -----------------,
2 2
sqrt(2 - sqrt(3)) sqrt(2 - sqrt(3))
x = - -----------------, x = -----------------]
2 2
</pre></div>
</dd></dl>
<a name="Item_003a-pslq_002fdeffn_002fpslq_005finteger_005frelation"></a><dl>
<dt><a name="index-pslq_005finteger_005frelation"></a>Function: <strong>pslq_integer_relation</strong> <em>(<var>L</var>)</em></dt>
<dd>
<p>Implements the PSLQ algorithm [1] to find integer relations between bigfloat numbers.
</p>
<p>For a given list <var>L</var> of floating point numbers,
<code>pslq_integer_relation</code> returns a list of integers <var>m</var>
such that <code><var>m</var> . <var>L</var> = 0</code>
(with absolute residual error less than <code>pslq_threshold</code>).
</p>
<p>[1] D.H.Bailey: Integer Relation Detection and Lattice Reduction.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) load ("pslq.mac");
(%o1) pslq.mac
(%i2) root: float (sin (%pi/12));
(%o2) 0.2588190451025207
(%i3) L: makelist (root^i, i, 0, 4);
(%o3) [1.0, 0.2588190451025207, 0.06698729810778066,
0.01733758853025369, 0.004487298107780675]
(%i4) m: pslq_integer_relation(%);
(%o4) [- 1, 0, 16, 0, - 16]
(%i5) m . L;
(%o5) - 2.359223927328458E-16
(%i6) float (10^(2 - fpprec));
(%o6) 1.0E-14
(%i7) is (abs (m . L) < 10^(2 - fpprec));
(%o7) true
</pre></div>
</dd></dl>
<a name="Item_003a-pslq_002fdefvr_002fpslq_005fprecision"></a><dl>
<dt><a name="index-pslq_005fprecision"></a>Variable: <strong>pslq_precision</strong></dt>
<dd><p>Default value: <code>10^(fpprec - 2)</code>
</p>
<p>Maximum magnitude of some intermediate results in <code>pslq_integer_relation</code>.
The search fails if one of the intermediate results has elements
larger than <code>pslq_precision</code>.
</p>
</dd></dl>
<a name="Item_003a-pslq_002fdefvr_002fpslq_005fthreshold"></a><dl>
<dt><a name="index-pslq_005fthreshold"></a>Variable: <strong>pslq_threshold</strong></dt>
<dd><p>Default value: <code>10^(2 - fpprec)</code>
</p>
<p>Threshold for absolute residual error of integer relation found by <code>pslq_integer_relation</code>.
</p>
</dd></dl>
<a name="Item_003a-pslq_002fdefvr_002fpslq_005fdepth"></a><dl>
<dt><a name="index-pslq_005fdepth"></a>Variable: <strong>pslq_depth</strong></dt>
<dd><p>Default value: <code>20 * <var>n</var></code>
</p>
<p>Number of iterations of the PSLQ algorithm.
</p>
<p>The default value is 20 times <var>n</var>,
where <var>n</var> is the length of the list of numbers supplied to <code>pslq_integer_relation</code>.
</p>
</dd></dl>
<a name="Item_003a-pslq_002fdefvr_002fpslq_005fstatus"></a><dl>
<dt><a name="index-pslq_005fstatus"></a>Variable: <strong>pslq_status</strong></dt>
<dd>
<p>Indicates success or failure for an integer relation search by <code>pslq_integer_relation</code>.
</p>
<p>When <code>pslq_status</code> is 1, it indicates an integer relation was found,
and the absolute residual error is less than <code>pslq_threshold</code>.
</p>
<p>When <code>pslq_status</code> is 2, it indicates an integer relation was not found
because some intermediate results are larger than <code>pslq_precision</code>.
</p>
<p>When <code>pslq_status</code> is 3, it indicates an integer relation was not found
because the number of iterations <code>pslq_depth</code> was reached.
</p>
</dd></dl>
<hr>
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<p>
Previous: <a href="maxima_340.html#Introduction-to-pslq" accesskey="p" rel="previous">Introduction to pslq</a>, Up: <a href="maxima_339.html#pslq_002dpkg" accesskey="u" rel="up">pslq-pkg</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
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