<?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>indices(RingElement) -- indices of variables occurring in a polynomial</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_induced__Map.html">next</a> | <a href="_indices_lp__Hash__Table_rp.html">previous</a> | <a href="_induced__Map.html">forward</a> | <a href="_indices_lp__Hash__Table_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>indices(RingElement) -- indices of variables occurring in a polynomial</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>indices f</tt></div>
</dd></dl>
</div>
</li>
<li><span>Function: <a href="_indices.html" title="indices of a polynomial; also components for a direct sum">indices</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span>, or <span>a <a href="___Matrix.html">matrix</a></span>over a polynomial ring</span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><span>a <a href="___List.html">list</a></span>, of integers, the indices of the variables occurring in the polynomial or matrix</span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div>The first variable in a polynomial ring has index 0, the second has index 1, etc. This function returns a list (in ascending order) of the indices of all of the variables that occur in <tt>f</tt>.<table class="examples"><tr><td><pre>i1 : R = QQ[a..g]
o1 = R
o1 : PolynomialRing</pre>
</td></tr>
<tr><td><pre>i2 : F = a^3+b^2*c+3*f^10*d-1+e-e
10 3 2
o2 = 3d*f + a + b c - 1
o2 : R</pre>
</td></tr>
<tr><td><pre>i3 : indices F
o3 = {0, 1, 2, 3, 5}
o3 : List</pre>
</td></tr>
<tr><td><pre>i4 : index a
o4 = 0</pre>
</td></tr>
<tr><td><pre>i5 : support F
o5 = {a, b, c, d, f}
o5 : List</pre>
</td></tr>
</table>
The same works for matrices.<table class="examples"><tr><td><pre>i6 : M = matrix"a+b,c+e;2a-e,3b-c4"
o6 = | a+b c+e |
| 2a-e -c4+3b |
2 2
o6 : Matrix R <--- R</pre>
</td></tr>
<tr><td><pre>i7 : indices M
o7 = {0, 1, 2, 4}
o7 : List</pre>
</td></tr>
<tr><td><pre>i8 : support M
o8 = {a, b, c, e}
o8 : List</pre>
</td></tr>
</table>
This use of <a href="_indices.html" title="indices of a polynomial; also components for a direct sum">indices</a> has no relationship with the use for specifying parts of a direct sum</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_index.html" title="numeric index of a ring variable">index</a> -- numeric index of a ring variable</span></li>
<li><span><a href="_support.html" title="list of variables occurring in a polynomial or matrix">support</a> -- list of variables occurring in a polynomial or matrix</span></li>
<li><span><a href="_indices.html" title="indices of a polynomial; also components for a direct sum">indices</a> -- indices of a polynomial; also components for a direct sum</span></li>
<li><span><a href="___Ring_sp_us_sp__Z__Z.html" title="get a ring variable by index">Ring _ ZZ</a> -- get a ring variable by index</span></li>
</ul>
</div>
</div>
</body>
</html>
