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<head><title>DlocalizeAll -- localization of a D-module (extended version)</title>
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<div><h1>DlocalizeAll -- localization of a D-module (extended version)</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>DlocalizeAll(M,f), DlocalizeAll(I,f)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="../../Macaulay2Doc/html/___Module.html">module</a></span>, over the Weyl algebra <em>D</em></span></li>
<li><span><tt>I</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, which represents the module <em>M = D/I</em></span></li>
<li><span><tt>f</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, a polynomial</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Hash__Table.html">hash table</a></span>, which contains the localized moduleM<sub>f</sub> = M[f<sup>-1</sup>] and some additional information</span></li>
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<li><div class="single"><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="___Dlocalize_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">Strategy => ...</a>, -- strategy for computing a localization of a D-module</span></li>
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<div class="single"><h2>Description</h2>
<div>An extension of <a href="___Dlocalize.html" title="localization of a D-module">Dlocalize</a> that in addition computes the localization map, the b-function, and the power s of the generator f<sup>s</sup>.<table class="examples"><tr><td><pre>i1 : W = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx,y=>Dy}]
o1 = W
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : M = W^1/(ideal(x*Dx+1, Dy))
o2 = cokernel | xDx+1 Dy |
1
o2 : W-module, quotient of W</pre>
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<tr><td><pre>i3 : f = x^2-y^3
3 2
o3 = - y + x
o3 : W</pre>
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<tr><td><pre>i4 : DlocalizeAll(M, f)
o4 = HashTable{GeneratorPower => -2 }
4 5 5 7
IntegrateBfunction => (s)(s + 1)(s + -)(s + -)(s + -)(s + -)
3 3 6 6
LocMap => | y6-2x2y3+x4 |
LocModule => cokernel | 3xDx+2yDy+15 y3Dy-x2Dy+6y2 |
o4 : HashTable</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Dlocalize.html" title="localization of a D-module">Dlocalize</a> -- localization of a D-module</span></li>
<li><span><a href="___Ann__Fs.html" title="the annihilating ideal of f^s">AnnFs</a> -- the annihilating ideal of f^s</span></li>
<li><span><a href="___Dintegration.html" title="integration modules of a D-module">Dintegration</a> -- integration modules of a D-module</span></li>
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<div class="waystouse"><h2>Ways to use <tt>DlocalizeAll</tt> :</h2>
<ul><li>DlocalizeAll(Ideal,RingElement)</li>
<li>DlocalizeAll(Module,RingElement)</li>
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