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<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a>  <a href="chap1.html">1</a>  <a href="chap2.html">2</a>  <a href="chap3.html">3</a>  <a href="chap4.html">4</a>  <a href="chapBib.html">Bib</a>  <a href="chapInd.html">Ind</a>  </div>

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<p><a id="X82DC33E982C4D157" name="X82DC33E982C4D157"></a></p>
<div class="ChapSects"><a href="chap4.html#X82DC33E982C4D157">4 <span class="Heading">Implemented packages</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X79E38C3781F79E35">4.1 <span class="Heading">MPFR</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X82B38FFE86A5A0B5">4.1-1 IsMPFRFloat</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X8145D0A97986133C">4.2 <span class="Heading">MPFI</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X842290DB8034BF90">4.2-1 IsMPFIFloat</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X82C3C26F7C11A26F">4.3 <span class="Heading">MPC</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7D7AD4C67FF04E38">4.3-1 IsMPCFloat</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X82DF12317C250153">4.4 <span class="Heading">CXSC</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X794C3A0F7925BDA1">4.4-1 IsCXSCReal</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7CD9EDF079B439BC">4.5 <span class="Heading">FPLLL</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X832DFC257C5C4D32">4.5-1 FPLLLReducedBasis</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7C759DED84B77805">4.5-2 FPLLLShortestVector</a></span>
</div></div>
</div>

<h3>4 <span class="Heading">Implemented packages</span></h3>

<p><a id="X79E38C3781F79E35" name="X79E38C3781F79E35"></a></p>

<h4>4.1 <span class="Heading">MPFR</span></h4>

<p><a id="X82B38FFE86A5A0B5" name="X82B38FFE86A5A0B5"></a></p>

<h5>4.1-1 IsMPFRFloat</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsMPFRFloat</code></td><td class="tdright">( filter )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TYPE_MPFR</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p>The category of floating-point numbers.</p>

<p>Note that they are treated as commutative and scalar, but are not necessarily associative.</p>

<p><a id="X8145D0A97986133C" name="X8145D0A97986133C"></a></p>

<h4>4.2 <span class="Heading">MPFI</span></h4>

<p><a id="X842290DB8034BF90" name="X842290DB8034BF90"></a></p>

<h5>4.2-1 IsMPFIFloat</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsMPFIFloat</code></td><td class="tdright">( filter )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TYPE_MPFI</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p>The category of intervals of floating-point numbers.</p>

<p>Note that they are treated as commutative and scalar, but are not necessarily associative.</p>

<p><a id="X82C3C26F7C11A26F" name="X82C3C26F7C11A26F"></a></p>

<h4>4.3 <span class="Heading">MPC</span></h4>

<p><a id="X7D7AD4C67FF04E38" name="X7D7AD4C67FF04E38"></a></p>

<h5>4.3-1 IsMPCFloat</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsMPCFloat</code></td><td class="tdright">( filter )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TYPE_MPC</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p>The category of intervals of floating-point numbers.</p>

<p>Note that they are treated as commutative and scalar, but are not necessarily associative.</p>

<p><a id="X82DF12317C250153" name="X82DF12317C250153"></a></p>

<h4>4.4 <span class="Heading">CXSC</span></h4>

<p><a id="X794C3A0F7925BDA1" name="X794C3A0F7925BDA1"></a></p>

<h5>4.4-1 IsCXSCReal</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsCXSCReal</code></td><td class="tdright">( filter )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsCXSCComplex</code></td><td class="tdright">( filter )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsCXSCInterval</code></td><td class="tdright">( filter )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsCXSCBox</code></td><td class="tdright">( filter )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TYPE_CXSC_RP</code></td><td class="tdright">( global variable )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TYPE_CXSC_CP</code></td><td class="tdright">( global variable )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TYPE_CXSC_RI</code></td><td class="tdright">( global variable )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TYPE_CXSC_CI</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p>The category of floating-point numbers.</p>

<p>Note that they are treated as commutative and scalar, but are not necessarily associative.</p>

<p><a id="X7CD9EDF079B439BC" name="X7CD9EDF079B439BC"></a></p>

<h4>4.5 <span class="Heading">FPLLL</span></h4>

<p><a id="X832DFC257C5C4D32" name="X832DFC257C5C4D32"></a></p>

<h5>4.5-1 FPLLLReducedBasis</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FPLLLReducedBasis</code>( <var class="Arg">m</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: A matrix spanning the same lattice as <var class="Arg">m</var>.</p>

<p>This function implements the LLL (Lenstra-Lenstra-Lovász) lattice reduction algorithm via the external library <strong class="pkg">fplll</strong>.</p>

<p>The result is guaranteed to be optimal up to 1%.</p>

<p><a id="X7C759DED84B77805" name="X7C759DED84B77805"></a></p>

<h5>4.5-2 FPLLLShortestVector</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FPLLLShortestVector</code>( <var class="Arg">m</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: A short vector in the lattice spanned by <var class="Arg">m</var>.</p>

<p>This function implements the LLL (Lenstra-Lenstra-Lovász) lattice reduction algorithm via the external library <strong class="pkg">fplll</strong>, and then computes a short vector in this lattice.</p>

<p>The result is guaranteed to be optimal up to 1%.</p>


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