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<!DOCTYPE html> <html lang="en"> <head> <title>LLLBases : Table of Contents</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="lattice reduction (Lenstra-Lenstra-Lovasz bases)" href="index.html">LLLBases</a> :: <a href="toc.html">Table of Contents</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> next | previous | forward | backward | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <h1>LLLBases : Table of Contents</h1> <ul> <li><span><a title="lattice reduction (Lenstra-Lenstra-Lovasz bases)" href="index.html">LLLBases</a> -- lattice reduction (Lenstra-Lenstra-Lovasz bases)</span> <ul> <li><span><a title="compute an LLL basis" href="___L__L__L.html">LLL</a> -- compute an LLL basis</span></li> <li><span><span class="tt">kernelLLL</span> (missing documentation)<!--tag: kernelLLL--> </span></li> <li><span><a title="compute the gcd of integers, and small multipliers" href="_gcd__L__L__L.html">gcdLLL</a> -- compute the gcd of integers, and small multipliers</span></li> <li><span><span class="tt">hermite</span> (missing documentation)<!--tag: hermite--> </span></li> <li><span><span class="tt">gramm</span> (missing documentation)<!--tag: gramm--> </span></li> <li><span><a title="is a basis an LLL basis?" href="_is__L__L__L.html">isLLL</a> -- is a basis an LLL basis?</span></li> </ul> </li> <li><span><a title="compute BKZ reduced basis instead of an LLL reduced basis" href="___B__K__Z.html">BKZ</a> -- compute BKZ reduced basis instead of an LLL reduced basis</span></li> <li><span><a title="use the original Macaulay2 LLL algorithm" href="___Cohen__Engine.html">CohenEngine</a> -- use the original Macaulay2 LLL algorithm</span></li> <li><span><a title="use the Macaulay2 language LLL algorithm" href="___Cohen__Top__Level.html">CohenTopLevel</a> -- use the Macaulay2 language LLL algorithm</span></li> <li><span><span class="tt">fpLLL</span> (missing documentation)<!--tag: fpLLL--> </span></li> <li><span><a title="use Givens rotations instead of Gram-Schmidt during LLL" href="___Givens.html">Givens</a> -- use Givens rotations instead of Gram-Schmidt during LLL</span></li> <li><span><span class="tt">Hermite</span> (missing documentation)<!--tag: Hermite--> </span></li> <li><span><a title="also find change of basis matrix" href="___L__L__L_lp..._cm__Change__Matrix_eq_gt..._rp.html">LLL(...,ChangeMatrix=>...)</a> -- also find change of basis matrix</span></li> <li><span><a title="choose among different algorithms" href="___L__L__L_lp..._cm__Strategy_eq_gt..._rp.html">LLL(...,Strategy=>...)</a> -- choose among different algorithms</span></li> <li><span><a title="use the all-integer LLL strategy from NTL library" href="___N__T__L.html">NTL</a> -- use the all-integer LLL strategy from NTL library</span></li> <li><span><a title="use double precision real numbers" href="___Real__F__P.html">RealFP</a> -- use double precision real numbers</span></li> <li><span><a title="use quadruple precision real numbers" href="___Real__Q__P.html">RealQP</a> -- use quadruple precision real numbers</span></li> <li><span><a title="use a combination of double precision and quad precision real numbers" href="___Real__Q__P1.html">RealQP1</a> -- use a combination of double precision and quad precision real numbers</span></li> <li><span><a title="use arbitrary precision real numbers" href="___Real__R__R.html">RealRR</a> -- use arbitrary precision real numbers</span></li> <li><span><a title="use extended exponent real numbers" href="___Real__X__D.html">RealXD</a> -- use extended exponent real numbers</span></li> <li><span><a title="the LLL threshold, in interval (1/4,1]" href="___Threshold.html">Threshold</a> -- the LLL threshold, in interval (1/4,1]</span></li> </ul> </body> </html>