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<head><title>deRhamAll(RingElement) -- deRham complex for the complement of a hypersurface</title>
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<div><h1>deRhamAll(RingElement) -- deRham complex for the complement of a hypersurface</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>deRhamAll f</tt></div>
</dd></dl>
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<li><span>Function: <a href="_de__Rham__All_lp__Ring__Element_rp.html" title="deRham complex for the complement of a hypersurface">deRhamAll</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></span></li>
</ul>
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</li>
<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Hash__Table.html">hash table</a></span>, containing explicit cohomology classes in the deRham complex for the complement of the hypersurface <em>{f = 0}</em> and supplementary 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="_de__Rham__All_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">Strategy => ...</a>, </span></li>
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<div class="single"><h2>Description</h2>
<div>The routine deRhamAll can be used to compute cup product structures as in the paper 'The cup product structure for complements of affine varieties' by Walther(2000).<p/>
For a more basic functionality see <a href="_de__Rham.html" title="deRham cohomology groups for the complement of a hypersurface">deRham</a>.<table class="examples"><tr><td><pre>i1 : R = QQ[x,y]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : f = x^2-y^3
3 2
o2 = - y + x
o2 : R</pre>
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<tr><td><pre>i3 : deRhamAll f
2 1
o3 = HashTable{BFunction => (s - 1)(s - -)(s - -) }
3 3
1
CohomologyGroups => HashTable{0 => QQ }
1
1 => QQ
2 => 0
LocalizeMap => | -x_2^3+x_1^2 |
1 2 1
OmegaRes => (QQ[x , x , D , D ]) <-- (QQ[x , x , D , D ]) <-- (QQ[x , x , D , D ]) <-- 0
1 2 1 2 1 2 1 2 1 2 1 2
3
0 1 2
PreCycles => HashTable{0 => | 0 |}
| 1 |
1 => | 0 |
| 1 |
| 0 |
2 => 0
TransferCycles => HashTable{0 => | 3x_2^3-3x_1^2 |}
1 => | 2x_1 |
| 3x_2^2 |
2 => 0
1 3 2
VResolution => (QQ[x , x , D , D ]) <-- (QQ[x , x , D , D ]) <-- (QQ[x , x , D , D ]) <-- 0
1 2 1 2 1 2 1 2 1 2 1 2
3
0 1 2
o3 : HashTable</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_de__Rham.html" title="deRham cohomology groups for the complement of a hypersurface">deRham</a> -- deRham cohomology groups for the complement of a hypersurface</span></li>
<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="___Dintegration.html" title="integration modules of a D-module">Dintegration</a> -- integration modules of a D-module</span></li>
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