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<!DOCTYPE html> <html lang="en"> <head> <title>chooseGoodMinors -- returns an ideal generated by interesting minors in a matrix</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="faster linear algebra, especially for computation of minors" href="index.html">FastMinors</a> :: <a title="returns an ideal generated by interesting minors in a matrix" href="_choose__Good__Minors.html">chooseGoodMinors</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> <a href="_choose__Random__Submatrix.html">next</a> | <a href="index.html">previous</a> | <a href="_choose__Random__Submatrix.html">forward</a> | <a href="index.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>chooseGoodMinors -- returns an ideal generated by interesting minors in a matrix</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">chooseGoodMinors(count, minorSize, M)</code></dd> <dd><code class="language-macaulay2">chooseGoodMinors(count, minorSize, M, I)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">count</span>, <span>an <a title="the class of all integers" href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, </span></li> <li><span><span class="tt">minorSize</span>, <span>an <a title="the class of all integers" href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, </span></li> <li><span><span class="tt">M</span>, <span>a <a title="the class of all matrices" href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, </span></li> <li><span><span class="tt">I</span>, <span>an <a title="the class of all ideals" href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, </span></li> </ul> </li> <li><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>: <ul> <li><span><span class="tt">PeriodicCheckFunction</span><span class="tt"> => </span><span>a <a title="the class of all functions" href="../../Macaulay2Doc/html/___Function.html">function</a></span>, <span>default value null</span>, a function whose argument is the ideal of minors computed so far and which outputs whether the chooseGoodMinors should continue</span></li> <li><span><a title="options to pass to functions in the package RandomPoints" href="___Point__Options.html">PointOptions</a><span class="tt"> => </span><span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, <span>default value {Strategy => Default, Homogeneous => false, Replacement => Binomial, ExtendField => true, PointCheckAttempts => 0, DecompositionStrategy => Decompose, NumThreadsToUse => 1, DimensionFunction => dim, Verbose => false}</span>, options to be passed to the RandomPoints package</span></li> <li><span><a title="DetStrategy is a strategy for allowing the user to choose how determinants (or rank), is computed" href="___Det__Strategy.html">DetStrategy</a><span class="tt"> => </span><span class="tt">...</span>, <span>default value Cofactor</span>, <span>DetStrategy is a strategy for allowing the user to choose how determinants (or rank), is computed</span></span></li> <li><span><a title="strategies for choosing submatrices" href="___Strategy__Default.html">Strategy</a><span class="tt"> => </span><span class="tt">...</span>, <span>default value new OptionTable from {Points => 0, Random => 16, GRevLexLargest => 0, LexSmallestTerm => 16, LexLargest => 0, LexSmallest => 16, GRevLexSmallestTerm => 16, RandomNonzero => 16, GRevLexSmallest => 16}</span>, <span>strategies for choosing submatrices</span></span></li> <li><span><span class="tt">Verbose</span><span class="tt"> => </span><span class="tt">...</span>, <span>default value false</span></span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>an <a title="the class of all ideals" href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, </span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>This returns an ideal generated by approximately <span class="tt">count</span> minors of size <span class="tt">minorSize</span> of the matrix M.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : R = QQ[x, y, z];</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : M = matrix{{x,y,0}, {y,z,0}, {0,0,0}} o2 = | x y 0 | | y z 0 | | 0 0 0 | 3 3 o2 : Matrix R <-- R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : chooseGoodMinors(1, 2, M, Strategy=>StrategyDefaultNonRandom) 2 o3 = ideal(- y + x*z) o3 : Ideal of R</code></pre> </td> </tr> </table> <div> <p>The ideal <span class="tt">I</span> is used in the <span class="tt">Points</span> portion of the <span class="tt">Strategy</span>. Only points where that ideal vanishes will be considered.</p> </div> <div> <p>The option <span class="tt">PeriodicCheckFunction</span> can be set to a function which will periodically evaluate the partially computed ideal of minors via the given function (which should return a boolean value). If that function returns <span class="tt">true</span> then <span class="tt">chooseGoodMinors</span> will terminate. For instance, one can set it to periodically check whether the dimension of the ideal is at most zero via <span class="tt">PeriodicCheckFunction => (J -> dim J <= 0)</span>.</p> </div> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">chooseGoodMinors</span>:</h2> <ul> <li><kbd>chooseGoodMinors(ZZ,ZZ,Matrix)</kbd></li> <li><kbd>chooseGoodMinors(ZZ,ZZ,Matrix,Ideal)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="returns an ideal generated by interesting minors in a matrix" href="_choose__Good__Minors.html">chooseGoodMinors</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function__With__Options.html">method function with options</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">FastMinors.m2:1625:0</span>.</p> </div> </div> </div> </body> </html>
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