<?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>pointsMat -- produces the matrix of values of the standard monomials on a set of points</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div>next | <a href="_points__By__Intersection.html">previous</a> | forward | <a href="_points__By__Intersection.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>pointsMat -- produces the matrix of values of the standard monomials on a set of points</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>(A,stds) = pointsMat(M,R)</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, in which each column consists of the coordinates of a point</span></li>
<li><span><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html">polynomial ring</a></span>, coordinate ring of the affine space containing the points</span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><tt>A</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, standard monomials evaluated on points</span></li>
<li><span><tt>stds</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, whose entries are the standard monomials</span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div>This function uses the Buchberger-Moeller algorithm to compute a the matrix <tt>A</tt> in which the columns are indexed by standard monomials, the rows are indexed by points, and the entries are given by evaluation. The ordering of the standard monomials is recorded in the matrix <tt>stds</tt> which has a single column. Here is a simple example.<table class="examples"><tr><td><pre>i1 : M = random(ZZ^3, ZZ^5)
o1 = | 9 8 5 5 6 |
| 0 7 7 0 2 |
| 3 1 7 4 4 |
3 5
o1 : Matrix ZZ <--- ZZ</pre>
</td></tr>
<tr><td><pre>i2 : R = QQ[x,y,z]
o2 = R
o2 : PolynomialRing</pre>
</td></tr>
<tr><td><pre>i3 : (A,stds) = pointsMat(M,R)
o3 = (| 1 3 0 9 9 |, {0} | 1 |)
| 1 1 7 8 1 | {-1} | z |
| 1 7 7 5 49 | {-1} | y |
| 1 4 0 5 16 | {-1} | x |
| 1 4 2 6 16 | {-2} | z2 |
o3 : Sequence</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>Caveat</h2>
<div>Program does not check that the points are distinct.</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_points.html" title="produces the ideal and initial ideal from the coordinates of a finite set of points">points</a> -- produces the ideal and initial ideal from the coordinates of a finite set of points</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>pointsMat</tt> :</h2>
<ul><li>pointsMat(Matrix,Ring)</li>
</ul>
</div>
</div>
</body>
</html>
