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<head><title>convHull -- The convex hull complex.</title>
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<div><h1>convHull -- The convex hull complex.</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>convHull(L)</tt><br/><tt>convHull(fn)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, of <a href="../../Macaulay2Doc/html/___Vector.html" title="the class of all elements of free modules that are handled by the engine">Vector</a>s</span></li>
<li><span><tt>fn</tt>, <span>a <a href="../../Macaulay2Doc/html/___String.html">string</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>C</tt>, <span>an <a href="___Complex.html">embedded complex</a></span></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="_file.html">file => ...</a>, -- Store result of a computation in a file.</span></li>
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<div class="single"><h2>Description</h2>
<div><p>Returns the convex hull of lattice vectors lying all in the same space. The output has C.isPolytope==true.</p>
<p>If applied to the string fn the result of a previous computation stored via the option <a href="_file.html" title="Store result of a computation in a file.">file</a> is read from the file fn.</p>
<p>The 0-point has to lie in the convex hull.</p>
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<table class="examples"><tr><td><pre>i1 : L={vector {1,0,0},vector {-1,0,0},vector {0,1,0},vector {0,-1,0},vector {0,0,1},vector {0,0,-1}}
o1 = {| 1 |, | -1 |, | 0 |, | 0 |, | 0 |, | 0 |}
| 0 | | 0 | | 1 | | -1 | | 0 | | 0 |
| 0 | | 0 | | 0 | | 0 | | 1 | | -1 |
o1 : List</pre>
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<tr><td><pre>i2 : P=convHull(L)
o2 = 3: y y y y y y
0 1 2 3 4 5
o2 : complex of dim 3 embedded in dim 3 (printing facets)
equidimensional, non-simplicial, F-vector {1, 6, 12, 8, 1}, Euler = 0</pre>
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<tr><td><pre>i3 : dP=boundaryOfPolytope P
o3 = 2: y y y y y y y y y y y y y y y y y y y y y y y y
0 2 4 1 2 4 0 3 4 1 3 4 0 2 5 1 2 5 0 3 5 1 3 5
o3 : complex of dim 2 embedded in dim 3 (printing facets)
equidimensional, simplicial, F-vector {1, 6, 12, 8, 0}, Euler = 1</pre>
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<div class="single"><h2>Caveat</h2>
<div><p>This uses the package Polyhedra.m2 to compute the facets. Too slow compared to Maple/convex.</p>
<div>If the package <i>ConvexInterface</i> is loaded, then this command calls Maple/Convex. See the corresponding option explained at <a href="index.html" title="Deformations of Stanley-Reisner rings and related computations.">SRdeformations</a>.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Complex.html" title="The class of all embedded complexes.">Complex</a> -- The class of all embedded complexes.</span></li>
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<div class="waystouse"><h2>Ways to use <tt>convHull</tt> :</h2>
<ul><li>convHull(List)</li>
<li>convHull(String)</li>
</ul>
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