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<head><title>localCohom(List,Ideal) -- local cohomology of a polynomial ring</title>
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<div><h1>localCohom(List,Ideal) -- local cohomology of a polynomial ring</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>localCohom(l,I)</tt></div>
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<li><span>Function: <a href="_local__Cohom.html" title="local cohomology">localCohom</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>l</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span></span></li>
<li><span><tt>I</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span></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>, the local cohomology of <tt>I</tt> in the degrees specified by <em>l</em></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="_local__Cohom_lp..._cm_sp__Loc__Strategy_sp_eq_gt_sp..._rp.html">LocStrategy => ...</a>, -- specify localization strategy for local cohomology</span></li>
<li><span><a href="_local__Cohom_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">Strategy => ...</a>, -- specify strategy for local cohomology</span></li>
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<div class="single"><h2>Description</h2>
<div>See <a href="_local__Cohom_lp__Ideal_rp.html" title="local cohomology of a polynomial ring">localCohom(Ideal)</a> for the full description.<table class="examples"><tr><td><pre>i1 : W = QQ[X, dX, Y, dY, Z, dZ, WeylAlgebra=>{X=>dX, Y=>dY, Z=>dZ}]
o1 = W
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : I = ideal (X*(Y-Z), X*Y*Z)
o2 = ideal (X*Y - X*Z, X*Y*Z)
o2 : Ideal of W</pre>
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<tr><td><pre>i3 : h = localCohom({1,2}, I)
o3 = HashTable{1 => subquotient (| -dY-dZ -Y+Z 0 0 0 -dXdY-dXdZ dXY-dXZ XdX+1 0 0 |, | XY-XZ dY+dZ XdX+YdZ-ZdZ -YdZ+ZdZ+1 0 0 0 |)}
| -ZdZ-1 -YZ -YdY-ZdZ-2 -XdX-1 -3dXZdZ-3dX -dXZdZ-dX dXYZ XdXZ+Z dXYdY+dXZdZ+2dX XdXdY+dY | | XYZ 0 0 0 YdY-ZdZ XdX-ZdZ ZdZ+1 |
2 => cokernel | -XYZ XY-XZ 3XdX-2YdY-2ZdZ YdY+ZdZ+3 Y2dY-2YdYZ-2YZdZ+Z2dZ |
o3 : HashTable</pre>
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<tr><td><pre>i4 : pruneLocalCohom h
o4 = HashTable{1 => | dZ dY X | }
2 => | Y-Z Z2 dYZ+ZdZ+2 XdX+2 |
o4 : HashTable</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_prune__Local__Cohom_lp__Hash__Table_rp.html" title="prunes local cohomology modules">pruneLocalCohom</a> -- prunes local cohomology modules</span></li>
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