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<head><title>factorBFunction(RingElement) -- factorization of a b-function</title>
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<div><h1>factorBFunction(RingElement) -- factorization of a b-function</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>bFunction b</tt></div>
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<li><span>Function: <a href="_factor__B__Function_lp__Ring__Element_rp.html" title="factorization of a b-function">factorBFunction</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>b</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, a polynomial obtained via one of the b-function routines</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Product.html">product expression</a></span>, the factorization of <tt>b</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><b>Fact. </b>The roots of any b-function are rational.<table class="examples"><tr><td><pre>i1 : R = QQ[x, dx, WeylAlgebra => {x=>dx}]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : f = x^10
10
o2 = x
o2 : R</pre>
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<tr><td><pre>i3 : b = globalBFunction f
10 11 9 66 8 363 7 157773 6 180411 5 341693 4 16819 3
o3 = s + --s + --s + ---s + ------s + ------s + ------s + -----s +
2 5 20 10000 20000 100000 20000
------------------------------------------------------------------------
1594197 2 66429 567
--------s + -------s + -------
12500000 6250000 1562500
o3 : QQ[s]</pre>
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<tr><td><pre>i4 : factorBFunction b
1 1 2 3 4 1 3 7 9
o4 = (s + 1)(s + -)(s + -)(s + -)(s + -)(s + -)(s + --)(s + --)(s + --)(s + --)
2 5 5 5 5 10 10 10 10
o4 : Expression of class Product</pre>
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<div class="single"><h2>Caveat</h2>
<div>f should be an output of one of the b-function routines</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="_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>
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