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<!DOCTYPE html> <html lang="en"> <head> <title>extractBlocks -- displays components of a map in a labeled complex</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="A-infinity algebra and module structures on free resolutions" href="index.html">AInfinity</a> » <a title="compute a resolution from A-infinity structures" href="_burke__Resolution.html">burkeResolution</a> » <a title="displays components of a map in a labeled complex" href="_extract__Blocks.html">extractBlocks</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 | <a href="_display__Blocks.html">previous</a> | <a href="_golod__Betti.html">forward</a> | <a href="_display__Blocks.html">backward</a> | <a href="_burke__Resolution.html">up</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>extractBlocks -- displays components of a map in a labeled complex</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">M = extractBlocks(f, sour)</code></dd> <dd><code class="language-macaulay2">M = extractBlocks(f, tar, sour)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">sour</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, list of ZZ, the label of a summand of the source of f</span></li> <li><span><span class="tt">sour</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, list of ZZ, the label of a summand of the source of f OR list of lists of ZZ, specifying multiple summands</span></li> <li><span><span class="tt">tar</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, same as sour, but for the target of f</span></li> </ul> </li> <li>Outputs: <ul> <li><span><span class="tt">M</span>, <span>a <a title="the class of all matrices" href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, the submatrix specified by tar and sour</span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>The terms of the <a title="compute a resolution from A-infinity structures" href="_burke__Resolution.html">burkeResolution</a> resolution are direct sums of labeled modules. the function <a title="displays information about the blocks of a map or maps between direct sum modules" href="_picture.html">picture</a> shows the symbols associated to the summands, while the function extractBlocks provides the submatrix associated with the summands specified.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : R = ZZ/101[a,b,c,d]/ideal(a^2, b^2, c^3, d^4) o1 = R o1 : QuotientRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : M = R^1/ideal(a*b,c*d) o2 = cokernel | ab cd | 1 o2 : R-module, quotient of R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : F = burkeResolution(M,5) 1 6 17 42 112 295 o3 = R <-- R <-- R <-- R <-- R <-- R 0 1 2 3 4 5 o3 : Complex</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : picture F.dd_3 +------+---+------+------+ o4 = | |{3}|{3, 0}|{2, 1}| +------+---+------+------+ | {2} | * | 8 | 8 | +------+---+------+------+ |{2, 0}| . | . | * | +------+---+------+------+</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : extractBlocks(F.dd_3, {2,1}) o5 = {3} | 0 a b 0 0 0 -b 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {3} | 0 0 a 0 0 0 -a -b 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {4} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {4} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -c 0 -d3 0 0 0 0 d3 0 | {5} | 0 0 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 | {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 | {5} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 | {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c2 0 0 0 -d -c2 0 | {6} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 | {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 | {6} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 | {2} | 0 ab 0 cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 0 ab 0 cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 ab 0 cd 0 0 0 0 0 0 0 0 | {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab 0 cd 0 0 | 17 24 o5 : Matrix R <-- R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i6 : extractBlocks(F.dd_3,{2,0}, {2,1}) o6 = {2} | 0 ab 0 cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 0 ab 0 cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 ab 0 cd 0 0 0 0 0 0 0 0 | {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab 0 cd 0 0 | 4 24 o6 : Matrix R <-- R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i7 : extractBlocks(F.dd_3,{2,0}, {{3,0},{2,1}}) o7 = {2} | 0 0 0 0 0 0 0 ab 0 cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 ab 0 cd 0 0 0 0 0 0 0 0 0 0 0 0 0 {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab 0 cd 0 0 0 0 0 0 0 {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab 0 cd 0 ------------------------------------------------------------------------ 0 | 0 | 0 | 0 | 4 30 o7 : Matrix R <-- R</code></pre> </td> </tr> </table> </div> <div> <h2>See also</h2> <ul> <li><span><a title="compute a resolution from A-infinity structures" href="_burke__Resolution.html">burkeResolution</a> -- compute a resolution from A-infinity structures</span></li> <li><span><a title="displays information about the blocks of a map or maps between direct sum modules" href="_picture.html">picture</a> -- displays information about the blocks of a map or maps between direct sum modules</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">extractBlocks</span>:</h2> <ul> <li><kbd>extractBlocks(Matrix,List)</kbd></li> <li><kbd>extractBlocks(Matrix,List,List)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="displays components of a map in a labeled complex" href="_extract__Blocks.html">extractBlocks</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function.html">method function</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">AInfinity.m2:1456:0</span>.</p> </div> </div> </div> </body> </html>