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<head><title>localBFunction(RingElement,Ideal) -- local b-function (a.k.a. the local Bernstein-Sato polynomial)</title>
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<div><h1>localBFunction(RingElement,Ideal) -- local b-function (a.k.a. the local Bernstein-Sato 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>b = localBFunction(f,P)</tt></div>
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<li><span>Function: <a href="_local__B__Function_lp__Ring__Element_cm__Ideal_rp.html" title="local b-function (a.k.a. the local Bernstein-Sato polynomial)">localBFunction</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, a polynomial</span></li>
<li><span><tt>P</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, a (prime) ideal</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>b</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, the local b-function <em>b_P(s)</em> in <em>Q[s]</em></span></li>
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<div class="single"><h2>Description</h2>
<div><p>Computes the local b-function of f at P, if P is a prime ideal.</p>
<table class="examples"><tr><td><pre>i1 : R = QQ[x,y]; f = x^2*(x+y+1); P = ideal(x,y);
o3 : Ideal of R</pre>
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<tr><td><pre>i4 : b = localBFunction(f,P)
2 3 1
o4 = s + -s + -
2 2
o4 : QQ[s]</pre>
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<tr><td><pre>i5 : factorBFunction b
1
o5 = (s + 1)(s + -)
2
o5 : Expression of class Product</pre>
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<div class="single"><h2>Caveat</h2>
<div>(feature) If P is not prime, computes the lcm of local b-functions over all primes containing P</div>
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<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="_factor__B__Function_lp__Ring__Element_rp.html" title="factorization of a b-function">factorBFunction</a> -- factorization of 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="_general__B_lp__List_cm__Ring__Element_rp.html" title="global general Bernstein-Sato polynomial">generalB</a> -- global general Bernstein-Sato polynomial</span></li>
<li><span><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> -- compute global b-function and b-operator for a D-module and a polynomial</span></li>
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