<?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>globalB(Ideal,RingElement) -- compute global b-function and b-operator for a D-module and a polynomial</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_global__B__Function_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">next</a> | <a href="_gkz_lp..._cm_sp__Vars_sp_eq_gt_sp..._rp.html">previous</a> | <a href="_global__B__Function_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">forward</a> | <a href="_gkz_lp..._cm_sp__Vars_sp_eq_gt_sp..._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>globalB(Ideal,RingElement) -- compute global b-function and b-operator for a D-module and 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>H = globalB(I,f)</tt></div>
</dd></dl>
</div>
</li>
<li><span>Function: <a href="_global__B_lp__Ideal_cm__Ring__Element_rp.html" title="compute global b-function and b-operator for a D-module and a polynomial">globalB</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, a holonomic ideal</span></li>
<li><span><tt>f</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, a polynomial in a Weyl algebra (should not contain differential variables)</span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><tt>H</tt>, <span>a <a href="../../Macaulay2Doc/html/___Hash__Table.html">hash table</a></span>, containing the keys <tt>Bpolynomial</tt> and <tt>Boperator</tt></span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div>The algorithm used here is a modification of the original algorithm of Oaku for computing Bernstein-Sato polynomials<table class="examples"><tr><td><pre>i1 : R = QQ[x, dx, WeylAlgebra => {x=>dx}]
o1 = R
o1 : PolynomialRing</pre>
</td></tr>
<tr><td><pre>i2 : f = x^7
7
o2 = x
o2 : R</pre>
</td></tr>
<tr><td><pre>i3 : b = globalB(ideal dx, f)
7
o3 = HashTable{Boperator => dx }
7 6 5 4 3 2
Bpolynomial => 823543s + 3294172s + 5411854s + 4705960s + 2321767s + 643468s + 91476s + 5040
o3 : HashTable</pre>
</td></tr>
<tr><td><pre>i4 : factorBFunction b.Bpolynomial
1 2 3 4 5 6
o4 = (s + 1)(s + -)(s + -)(s + -)(s + -)(s + -)(s + -)
7 7 7 7 7 7
o4 : Expression of class Product</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_b__Function.html" title="b-function">bFunction</a> -- b-function</span></li>
<li><span><a href="_global__B__Function_lp__Ring__Element_rp.html" title="global b-function (else known as the Bernstein-Sato polynomial)">globalBFunction</a> -- global b-function (else known as the Bernstein-Sato polynomial)</span></li>
<li><span><a href="_factor__B__Function_lp__Ring__Element_rp.html" title="factorization of a b-function">factorBFunction</a> -- factorization of a b-function</span></li>
</ul>
</div>
</div>
</body>
</html>
