<?xml version=
"1.0" encoding=
"UTF-8"?>
<!
DOCTYPE html PUBLIC
"-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<
html xmlns=
"http://www.w3.org/1999/xhtml" xml:lang=
"en">
<
head>
<
script type=
"text/javascript"
src=
"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</
script>
<
title>GAP (FLOAT) - Chapter
4: Implemented packages</
title>
<
meta http-equiv=
"content-type" content=
"text/html; charset=UTF-8" />
<
meta name=
"generator" content=
"GAPDoc2HTML" />
<
link rel=
"stylesheet" type=
"text/css" href=
"manual.css" />
<
script src=
"manual.js" type=
"text/javascript"></
script>
<
script type=
"text/javascript">overwriteStyle();</
script>
</
head>
<
body class=
"chap4" onload=
"jscontent()">
<
div class=
"chlinktop"><
span class=
"chlink1">Goto Chapter: </
span><
a href=
"chap0_mj.html">Top<
/a> <a href="chap1_mj.html">1</a> <a href="chap2_mj.html">2</a> <a href="chap3_mj.html">3</a> <a href="chap4_mj.html">4</a> <a href="chapBib_mj.html">Bib</a> <a href="chapInd_mj.html">Ind</a> </div>
<div class="chlinkprevnexttop"> <a href="chap0_mj.html">[Top of Book]</a> <a href="chap0_mj.html#contents">[Contents]</a> <a href="chap3_mj.html">[Previous Chapter]</a> <a href="chapBib_mj.html">[Next Chapter]</a> </div>
<p id="mathjaxlink" class="pcenter"><a href="chap4.html">[MathJax off]</a></p>
<p><a id="X82DC33E982C4D157" name="X82DC33E982C4D157"></a></p>
<div class="ChapSects"><a href="chap4_mj.html#X82DC33E982C4D157">4 <span class="Heading">Implemented packages</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X79E38C3781F79E35">4.1 <span class="Heading">MPFR</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4_mj.html#X82B38FFE86A5A0B5">4.1-1 IsMPFRFloat</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.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_mj.html#X842290DB8034BF90">4.2-1 IsMPFIFloat</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.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_mj.html#X7D7AD4C67FF04E38">4.3-1 IsMPCFloat</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.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_mj.html#X794C3A0F7925BDA1">4.4-1 IsCXSCReal</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.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_mj.html#X832DFC257C5C4D32">4.5-1 FPLLLReducedBasis</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4_mj.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">&#an style='color: green'>8227; 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">&#an style='color: green'>8227; 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">&#an style='color: green'>8227; 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">&#an style='color: green'>8227; 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">&#an style='color: green'>8227; 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">&#an style='color: green'>8227; 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">&#an style='color: green'>8227; 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">&#an style='color: green'>8227; 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">&#an style='color: green'>8227; 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">&#an style='color: green'>8227; 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">&#an style='color: green'>8227; 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">&#an style='color: green'>8227; 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">&#an style='color: green'>8227; 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">&#an style='color: green'>8227; 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">&#an style='color: green'>8227; 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">&#an style='color: green'>8227; 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>
<div class="chlinkprevnextbot"> <a href="chap0_mj.html">[Top of Book]</a> <a href="chap0_mj.html#contents">[Contents]</a> <a href="chap3_mj.html">[Previous Chapter]</a> <a href="chapBib_mj.html">[Next Chapter]</a> </div>
<div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a> <a href="chap1_mj.html">1</a> <a href="chap2_mj.html">2</a> <a href="chap3_mj.html">3</a> <a href="chap4_mj.html">4</a> <a href="chapBib_mj.html">Bib</a> <a href="chapInd_mj.html">Ind</a> </div>
<hr />
<p class="foot">generated by <a href="http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p>
</body>
</html>
¤ Dauer der Verarbeitung: 0.4 Sekunden
¤
*© Formatika GbR, Deutschland
