<?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>resolution(ChainComplex) -- Resolves a ChainComplex.</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_substitute_lp__Chain__Complex_cm__Ring_rp.html">next</a> | <a href="_koszul__Complex.html">previous</a> | <a href="_substitute_lp__Chain__Complex_cm__Ring_rp.html">forward</a> | <a href="_koszul__Complex.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>resolution(ChainComplex) -- Resolves a ChainComplex.</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>resolution C</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="../../Macaulay2Doc/html/_resolution.html" title="projective resolution">resolution</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>C</tt>, <span>a <a href="../../Macaulay2Doc/html/___Chain__Complex.html">chain complex</a></span>, </span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span>ChainComplexMap</span></li> </ul> </div> </li> <li><div class="single"><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="../../Macaulay2Doc/html/_resolution_lp..._cm_sp__Degree__Limit_sp_eq_gt_sp..._rp.html">DegreeLimit => ...</a>, -- compute only up to this degree</span></li> <li><span><a href="../../Macaulay2Doc/html/_resolution_lp..._cm_sp__Hard__Degree__Limit_sp_eq_gt_sp..._rp.html">HardDegreeLimit => ...</a>, </span></li> <li><span><a href="../../Macaulay2Doc/html/_resolution_lp..._cm_sp__Length__Limit_sp_eq_gt_sp..._rp.html">LengthLimit => ...</a>, -- stop when the resolution reaches this length</span></li> <li><span><a href="../../Macaulay2Doc/html/_resolution_lp..._cm_sp__Pair__Limit_sp_eq_gt_sp..._rp.html">PairLimit => ...</a>, -- stop when this number of pairs has been handled</span></li> <li><span><a href="../../Macaulay2Doc/html/_resolution_lp..._cm_sp__Sort__Strategy_sp_eq_gt_sp..._rp.html">SortStrategy => ...</a>, </span></li> <li><span><a href="../../Macaulay2Doc/html/_resolution_lp..._cm_sp__Stop__Before__Computation_sp_eq_gt_sp..._rp.html">StopBeforeComputation => ...</a>, -- whether to stop the computation immediately</span></li> <li><span><a href="../../Macaulay2Doc/html/_resolution_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">Strategy => ...</a>, </span></li> <li><span><a href="../../Macaulay2Doc/html/_resolution_lp..._cm_sp__Syzygy__Limit_sp_eq_gt_sp..._rp.html">SyzygyLimit => ...</a>, -- stop when this number of syzygies are obtained</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>Returns a surjective ChainComplexMap whose source consistsof free R-modules, where R = C.ring.<table class="examples"><tr><td><pre>i1 : R = ZZ/32003[a..d] o1 = R o1 : PolynomialRing</pre> </td></tr> <tr><td><pre>i2 : I = monomialCurveIdeal(R,{1,2,3}) 2 2 o2 = ideal (c - b*d, b*c - a*d, b - a*c) o2 : Ideal of R</pre> </td></tr> <tr><td><pre>i3 : C = koszulComplex(ideal vars R) ** (R^1/I);</pre> </td></tr> <tr><td><pre>i4 : CResMap = res C;</pre> </td></tr> <tr><td><pre>i5 : CRes = source CResMap 1 16 45 59 41 14 2 o5 = R <-- R <-- R <-- R <-- R <-- R <-- R <-- 0 0 1 2 3 4 5 6 7 o5 : ChainComplex</pre> </td></tr> <tr><td><pre>i6 : isQuism CResMap o6 = true</pre> </td></tr> </table> </div> </div> </div> </body> </html>