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<head><title>mPosHullFaces -- Faces of a positive hull.</title>
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<div><h1>mPosHullFaces -- Faces of a positive hull.</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>mPosHullFaces(L)</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>
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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>
</ul>
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</li>
<li><div class="single"><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_to__File.html">toFile => ...</a>, -- Store result in a file.</span></li>
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<div class="single"><h2>Description</h2>
<div><p>Returns a list of</p>
<p>- a <a href="../../Macaulay2Doc/html/___Matrix.html" title="the class of all matrices">Matrix</a> A with the rays of the positive hull of L in its rows</p>
<p>- a list of lists with the faces of the convex hull sorted by increasing dimension.</p>
<p></p>
<p>The rays of the faces are represented by the indices of the rows of A.</p>
<p>This uses the Convex functions posHull and faces.</p>
<p>The positive hull of L is required to be strictly convex.</p>
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<table class="examples"><tr><td><pre>i1 : L= {{0,1,1,0,0},{0,1,0,1,0},{0,1,0,0,0},{1,0,0,0,1},{1,0,-1,-1,-1},{1,0,0,0,0}};</pre>
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<tr><td><pre>i2 : L=apply(L,vector)
o2 = {| 0 |, | 0 |, | 0 |, | 1 |, | 1 |, | 1 |}
| 1 | | 1 | | 1 | | 0 | | 0 | | 0 |
| 1 | | 0 | | 0 | | 0 | | -1 | | 0 |
| 0 | | 1 | | 0 | | 0 | | -1 | | 0 |
| 0 | | 0 | | 0 | | 1 | | -1 | | 0 |
o2 : List</pre>
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<tr><td><pre>i3 : P=mPosHullFaces(L)
o3 = {| 0 1 1 0 0 |, {{{}}, {{1}, {2}, {3}, {4}, {5}, {6}}, {{1, 3}, {2,
| 0 1 0 1 0 |
| 0 1 0 0 0 |
| 1 0 0 0 1 |
| 1 0 -1 -1 -1 |
| 1 0 0 0 0 |
------------------------------------------------------------------------
3}, {3, 4}, {3, 5}, {4, 5}, {5, 6}, {1, 2}, {1, 4}, {1, 5}, {1, 6}, {2,
------------------------------------------------------------------------
4}, {2, 5}, {2, 6}, {4, 6}}, {{1, 3, 5}, {2, 3, 5}, {3, 4, 5}, {4, 5,
------------------------------------------------------------------------
6}, {2, 4, 5}, {1, 4, 5}, {1, 2, 5}, {1, 2, 3}, {2, 3, 4}, {1, 3, 4},
------------------------------------------------------------------------
{1, 5, 6}, {2, 5, 6}, {1, 2, 4}, {1, 2, 6}, {1, 4, 6}, {2, 4, 6}}, {{2,
------------------------------------------------------------------------
3, 4, 5}, {1, 3, 4, 5}, {1, 2, 3, 5}, {1, 2, 3, 4}, {2, 4, 5, 6}, {1, 4,
------------------------------------------------------------------------
5, 6}, {1, 2, 5, 6}, {1, 2, 4, 6}}, {{1, 2, 3, 4, 5, 6}}}}
o3 : List</pre>
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<div class="waystouse"><h2>Ways to use <tt>mPosHullFaces</tt> :</h2>
<ul><li>mPosHullFaces(List)</li>
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