<?xml version="1.0" encoding="utf-8" ?> <!-- for emacs: -*- coding: utf-8 -*- --> <!-- Apache may like this line in the file .htaccess: AddCharset utf-8 .html --> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" > <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head><title>Matrix _ Array -- component of map corresponding to summand of source</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="___Matrix_sp_us_sp__List.html">next</a> | <a href="___Matrix_sp^_sp__Z__Z.html">previous</a> | <a href="___Matrix_sp_us_sp__List.html">forward</a> | <a href="___Matrix_sp^_sp__Z__Z.html">backward</a> | up | <a href="index.html">top</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> | <a href="http://www.math.uiuc.edu/Macaulay2/">Macaulay2 web site</a></div> </td> </tr> </table> <hr/> <div><h1>Matrix _ Array -- component of map corresponding to summand of source</h1> <div class="single"><h2>Synopsis</h2> <ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>F_[i,j,...,k]</tt></div> </dd></dl> </div> </li> <li><span>Operator: <a href="__us.html" title="a binary operator, used for subscripting and access to elements">_</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>F</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, or <span>a <a href="___Chain__Complex__Map.html">chain complex map</a></span> or <span>a <a href="___Graded__Module__Map.html">graded module map</a></span></span></li> <li><span><tt>[i,j,...,k]</tt>, an array of indices</span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, <span>a <a href="___Chain__Complex__Map.html">chain complex map</a></span>, or <span>a <a href="___Graded__Module__Map.html">graded module map</a></span></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>The source of the module or chain complex <tt>F</tt> should be a direct sum, and the result is the component of this map corresponding to the sum of the components numbered or named <tt>i, j, ..., k</tt>. Free modules are regarded as direct sums of modules. In otherwords, this routine returns the map given by certain blocks of columns.<table class="examples"><tr><td><pre>i1 : R = ZZ[a..d];</pre> </td></tr> <tr><td><pre>i2 : F = (vars R) ++ ((vars R) ++ matrix{{a-1,b-3}}) o2 = | a b c d 0 0 0 0 0 0 | | 0 0 0 0 a b c d 0 0 | | 0 0 0 0 0 0 0 0 a-1 b-3 | 3 10 o2 : Matrix R <--- R</pre> </td></tr> <tr><td><pre>i3 : F_[1] o3 = | 0 0 0 0 0 0 | | a b c d 0 0 | | 0 0 0 0 a-1 b-3 | 3 6 o3 : Matrix R <--- R</pre> </td></tr> <tr><td><pre>i4 : F_[1]^[1] o4 = | a b c d 0 0 | | 0 0 0 0 a-1 b-3 | 2 6 o4 : Matrix R <--- R</pre> </td></tr> </table> <p>If the components have been given names (see <a href="_direct__Sum.html" title="direct sum of modules or maps">directSum</a>), use those instead.</p> <table class="examples"><tr><td><pre>i5 : N = (a=>vars R) ++ (b=>vars R) o5 = | a b c d 0 0 0 0 | | 0 0 0 0 a b c d | 2 8 o5 : Matrix R <--- R</pre> </td></tr> <tr><td><pre>i6 : N_[a] o6 = | a b c d | | 0 0 0 0 | 2 4 o6 : Matrix R <--- R</pre> </td></tr> <tr><td><pre>i7 : N = directSum(x1 => matrix{{a,b-1}}, x2 => matrix{{a-3,b-17,c-35}}, x3 => vars R) o7 = | a b-1 0 0 0 0 0 0 0 | | 0 0 a-3 b-17 c-35 0 0 0 0 | | 0 0 0 0 0 a b c d | 3 9 o7 : Matrix R <--- R</pre> </td></tr> <tr><td><pre>i8 : N_[x1,x3] o8 = | a b-1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 a b c d | 3 6 o8 : Matrix R <--- R</pre> </td></tr> </table> <p>This works the same way for maps between chain complexes.</p> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="___Matrix_sp^_sp__Array.html" title="component of map corresponding to summand of target">Matrix ^ Array</a> -- component of map corresponding to summand of target</span></li> <li><span><a href="___Module_sp_us_sp__Array.html" title="inclusion from summand">Module _ Array</a> -- inclusion from summand</span></li> <li><span><a href="_direct__Sum.html" title="direct sum of modules or maps">directSum</a> -- direct sum of modules or maps</span></li> </ul> </div> </div> </body> </html>