<?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>ideal(Matrix) -- make an ideal</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_ideal_lp__Module_rp.html">next</a> | <a href="_ideal_lp__List_rp.html">previous</a> | <a href="_ideal_lp__Module_rp.html">forward</a> | <a href="_ideal_lp__List_rp.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>ideal(Matrix) -- make an ideal</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>ideal M</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_ideal.html" title="make an ideal">ideal</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, whose <a href="_entries.html" title="lists the entries of a matrix">entries</a> are <a href="___Ring__Element.html">ring elements</a></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>an <a href="___Ideal.html">ideal</a></span>, which is generated by all the entries in <tt>M</tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><table class="examples"><tr><td><pre>i1 : R = ZZ/7[w,x,y,z];</pre> </td></tr> <tr><td><pre>i2 : f = vars R o2 = | w x y z | 1 4 o2 : Matrix R <--- R</pre> </td></tr> <tr><td><pre>i3 : ideal f o3 = ideal (w, x, y, z) o3 : Ideal of R</pre> </td></tr> <tr><td><pre>i4 : g = matrix{{x^2-w*y, x*y-w*z, x*z-y^2},{y^2-x*z,x^2*y-z^2,x^3-y*z}} o4 = | x2-wy xy-wz -y2+xz | | y2-xz x2y-z2 x3-yz | 2 3 o4 : Matrix R <--- R</pre> </td></tr> <tr><td><pre>i5 : ideal g 2 2 2 2 2 3 o5 = ideal (x - w*y, y - x*z, x*y - w*z, x y - z , - y + x*z, x - y*z) o5 : Ideal of R</pre> </td></tr> </table> <p/> The functions <a href="_minors_lp__Z__Z_cm__Matrix_rp.html" title="ideal generated by minors">minors</a>, <a href="_pfaffians.html" title="ideal generated by Pfaffians">pfaffians</a> and <a href="_fitting__Ideal.html">fitting ideal</a> are typically more useful methods of creating an <a href="___Ideal.html">ideal</a> from a matrix.</div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_entries.html" title="lists the entries of a matrix">entries</a> -- lists the entries of a matrix</span></li> <li><span><a href="_flatten.html" title="flatten a list by unnesting lists">flatten</a> -- flatten a list by unnesting lists</span></li> </ul> </div> </div> </body> </html>