<?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>taylorResolution -- Gives the Taylor resolution of a monomial ideal I.</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div>next | <a href="_taylor.html">previous</a> | forward | <a href="_taylor.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>taylorResolution -- Gives the Taylor resolution of a monomial ideal I.</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>taylorResolution(I)</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>I</tt>, </span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span>ChainComplex</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><tt>LengthLimit => ...</tt> (missing documentation<!-- tag: taylorResolution(..., LengthLimit => ...) -->), </span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : R = ZZ/101[a,b] o1 = R o1 : PolynomialRing</pre> </td></tr> <tr><td><pre>i2 : I = monomialIdeal (ideal vars R)^3 3 2 2 3 o2 = monomialIdeal (a , a b, a*b , b ) o2 : MonomialIdeal of R</pre> </td></tr> <tr><td><pre>i3 : T = taylorResolution(I) 1 4 6 4 1 o3 = R <-- R <-- R <-- R <-- R 0 1 2 3 4 o3 : ChainComplex</pre> </td></tr> <tr><td><pre>i4 : T.dd 1 4 o4 = 0 : R <--------------------- R : 1 | a3 a2b ab2 b3 | 4 6 1 : R <-------------------------------- R : 2 {3} | -b -b2 0 -b3 0 0 | {3} | a 0 -b 0 -b2 0 | {3} | 0 a2 a 0 0 -b | {3} | 0 0 0 a3 a2 a | 6 4 2 : R <----------------------- R : 3 {4} | b b2 0 0 | {5} | -1 0 b 0 | {4} | a 0 0 b | {6} | 0 -1 -1 0 | {5} | 0 a 0 -1 | {4} | 0 0 a2 a | 4 1 3 : R <-------------- R : 4 {5} | -b | {6} | 1 | {6} | -1 | {5} | a | o4 : ChainComplexMap</pre> </td></tr> </table> </div> </div> <div class="waystouse"><h2>Ways to use <tt>taylorResolution</tt> :</h2> <ul><li>taylorResolution(MonomialIdeal)</li> </ul> </div> </div> </body> </html>