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<head><title>paramBpoly(RingElement,String) -- compute the list of all possible Bernstein-Sato polynomials for a polynomial with parametric coefficients</title>
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<div><h1>paramBpoly(RingElement,String) -- compute the list of all possible Bernstein-Sato polynomials for a polynomial with parametric coefficients</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>paramBpoly(f,filename)</tt></div>
</dd></dl>
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</li>
<li><span>Function: <a href="_param__Bpoly_lp__Ring__Element_cm__String_rp.html" title="compute the list of all possible Bernstein-Sato polynomials for a polynomial with parametric coefficients">paramBpoly</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 in Weyl algebra <em>A_n(Q)</em></span></li>
<li><span><tt>filename</tt>, <span>a <a href="../../Macaulay2Doc/html/___String.html">string</a></span>, the base name for the output files</span></li>
</ul>
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</li>
<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, all possible Bernstein-Sato polynomials</span></li>
</ul>
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</li>
<li><div class="single"><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_param__Bpoly_lp..._cm_sp__Ground__Field_sp_eq_gt_sp..._rp.html">GroundField => ...</a>, -- characteristic for modular computation</span></li>
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</li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : A = (QQ [a,b,c]) [x, y, Dx, Dy, WeylAlgebra => {x=>Dx, y=>Dy}]
o1 = A
o1 : PolynomialRing</pre>
</td></tr>
<tr><td><pre>i2 : paramBpoly(a*x^2 + b*x*y + c*y^2, "quadratic")
2 1
o2 = {(S + 1) , (S + 1)(S + -)}
2
o2 : List</pre>
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<div class="single"><h2>Caveat</h2>
<div>A finite field should be used in place of <em>Q</em> in order to speed up computations. This routine works only on relatively small examples.</div>
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<div class="single"><h2>See also</h2>
<ul><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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