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<head><title>populateCechComplexCC(Ideal,List) -- Cech complex skeleton for the computation of the characteristic cycles of local cohomology modules</title>
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<div><h1>populateCechComplexCC(Ideal,List) -- Cech complex skeleton for the computation of the characteristic cycles of local cohomology modules</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>populateCechComplexCC(I,cc)</tt></div>
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<li><span>Function: <a href="_populate__Cech__Complex__C__C_lp__Ideal_cm__List_rp.html" title="Cech complex skeleton for the computation of the characteristic cycles of local cohomology modules">populateCechComplexCC</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>, at which the local cohomology modules H<sup>i</sup><sub>I</sub>(M) are computed.</span></li>
<li><span><tt>cc</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, the characteristic cycle of a regular holonomic module M</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Mutable__Hash__Table.html">mutable hash table</a></span>, with entries corresponding to the direct summands of the chains in the Cech complex</span></li>
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<div class="single"><h2>Description</h2>
<div>For the ideal I=(f<sub>1</sub>,...,f<sub>k</sub>) the routine computes the characteristic cycles of the localized modules M<sub>f<sub>i<sub>1</sub></sub>,...,f<sub>i<sub>k</sub></sub></sub> and places them in the corresponding places in the Cech complex.<table class="examples"><tr><td><pre>i1 : W = QQ[x_1..x_6, a_1..a_6];</pre>
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<tr><td><pre>i2 : I = minors(2, matrix{{x_1, x_2, x_3}, {x_4, 0, 0}});
o2 : Ideal of W</pre>
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<tr><td><pre>i3 : cc = {ideal W => 1};</pre>
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<div class="single"><h2>Caveat</h2>
<div>The module has to be a regular holonomic complex-analytic module; while the holomicity can be checked by <a href="_is__Holonomic.html" title="determines whether a D-module (or ideal in Weyl algebra) is holonomic">isHolonomic</a> there is no algorithm to check the regularity.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___B__M__M.html" title="the characteristic cycle of the localized $D$-module">BMM</a> -- the characteristic cycle of the localized $D$-module</span></li>
<li><span><a href="_prune__Cech__Complex__C__C_lp__Mutable__Hash__Table_rp.html" title="reduction of the Cech complex that produces characteristic cycles of local cohomology modules">pruneCechComplexCC</a> -- reduction of the Cech complex that produces characteristic cycles of local cohomology modules</span></li>
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