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<head><title>mHomology -- Compute the homology.</title>
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<div><h1>mHomology -- Compute the homology.</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>mHomology(C)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>C</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, of lists with the faces of a complex, sorted by dimension, each face represented by a list of vertices.</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><p>Returns a list of <a href="___Finitely__Generated__Abelian__Group.html" title="Class of finitely generated abelian groups.">FinitelyGeneratedAbelianGroup</a>s with the homology with closed support of C with integer coefficients.</p>
<p>C does not have to be simplicial.</p>
<p>This uses the Convex functions convHull, simplicialsubdiv, pcomplex and homology.</p>
<p>Remark: One should also implement the relative version from Convex.</p>
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<table class="examples"><tr><td><pre>i1 : C={{{}}, {{{-1, -1, -1, -1}}, {{1, 0, 0, 0}}, {{0, 1, 0, 0}}, {{0, 0, 1,0}}, {{0, 0, 0, 1}}}, {{{-1, -1, -1, -1}, {0, 1, 0, 0}}, {{-1, -1, -1,-1}, {0, 0, 1, 0}}, {{1, 0, 0, 0}, {0, 0, 1, 0}}, {{1, 0, 0, 0}, {0, 0, 0,1}}, {{0, 1, 0, 0}, {0, 0, 0, 1}}}, {}, {}, {}};</pre>
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<tr><td><pre>i2 : mHomology(C)
o2 = {ZZ, ZZ, 0, 0, 0}
o2 : List</pre>
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<p></p>
<p>RP2:</p>
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<table class="examples"><tr><td><pre>i3 : C= {{{}}, {{{-1, -1, -1, -1, -1}}, {{1, 0, 0, 0, 0}}, {{0, 1, 0, 0, 0}}, {{0, 0, 1, 0, 0}}, {{0, 0, 0, 1, 0}}, {{0, 0, 0, 0, 1}}}, {{{-1, -1, -1, -1,-1}, {1, 0, 0, 0, 0}}, {{-1, -1, -1, -1, -1}, {0, 1, 0, 0, 0}}, {{1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}}, {{-1, -1, -1, -1, -1}, {0, 0, 1, 0, 0}}, {{1, 0, 0, 0, 0}, {0, 0, 1, 0, 0}}, {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}}, {{-1, -1, -1, -1, -1}, {0, 0, 0, 1, 0}}, {{1, 0, 0, 0, 0}, {0, 0, 0, 1, 0}}, {{0, 1, 0, 0, 0}, {0, 0, 0, 1, 0}}, {{0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}}, {{-1, -1, -1, -1, -1}, {0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0}, {0, 0, 0, 0, 1}}, {{0, 1, 0, 0, 0}, {0, 0, 0, 0, 1}}, {{0, 0, 1, 0, 0}, {0, 0, 0, 0, 1}}, {{0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}}}, {{{-1, -1, -1, -1, -1}, {1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}}, {{1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}}, {{-1, -1, -1, -1, -1}, {1, 0, 0, 0, 0}, {0, 0, 0, 1, 0}}, {{-1, -1, -1, -1, -1}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}}, {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}}, {{-1, -1, -1, -1, -1}, {0, 1, 0, 0, 0}, {0, 0, 0, 0, 1}}, {{-1, -1, -1, -1, -1}, {0, 0, 1, 0, 0}, {0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}}, {{0, 1, 0, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}}}, {}, {}, {}};</pre>
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<tr><td><pre>i4 : mHomology(C)
o4 = {ZZ, ZZ/2, 0, 0, 0, 0}
o4 : List</pre>
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<div class="waystouse"><h2>Ways to use <tt>mHomology</tt> :</h2>
<ul><li>mHomology(List)</li>
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