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<head><title>cones -- computes all cones of a fan of a certain dimension</title>
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<div><h1>cones -- computes all cones of a fan of a certain dimension</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> L = cones(d,F)</tt></div>
</dd></dl>
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</li>
<li><div class="single">Inputs:<ul><li><span><tt>d</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, between 0 and the dimension of the fan</span></li>
<li><span><tt>F</tt>, <span>an object of class <a href="___Fan.html" title="the class of all fans">Fan</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span></span></li>
</ul>
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</li>
</ul>
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<div class="single"><h2>Description</h2>
<div><p/>
<tt>cones</tt> computes the <a href="../../Macaulay2Doc/html/___List.html" title="the class of all lists -- {...}">List</a> of all Cones in <tt>F</tt> of dimension <tt>d</tt>.<table class="examples"><tr><td><pre>i1 : F = normalFan hypercube 3
o1 = {ambient dimension => 3 }
number of generating cones => 8
number of rays => 6
top dimension of the cones => 3
o1 : Fan</pre>
</td></tr>
<tr><td><pre>i2 : L = cones(2,F)
o2 = {{ambient dimension => 3 }, {ambient dimension => 3
dimension of lineality space => 0 dimension of lineality space =>
dimension of the cone => 2 dimension of the cone => 2
number of facets => 2 number of facets => 2
number of rays => 2 number of rays => 2
------------------------------------------------------------------------
}, {ambient dimension => 3 }, {ambient dimension => 3
0 dimension of lineality space => 0 dimension of lineality space
dimension of the cone => 2 dimension of the cone => 2
number of facets => 2 number of facets => 2
number of rays => 2 number of rays => 2
------------------------------------------------------------------------
}, {ambient dimension => 3 },
=> 0 dimension of lineality space => 0
dimension of the cone => 2
number of facets => 2
number of rays => 2
------------------------------------------------------------------------
{ambient dimension => 3 }, {ambient dimension => 3
dimension of lineality space => 0 dimension of lineality space =>
dimension of the cone => 2 dimension of the cone => 2
number of facets => 2 number of facets => 2
number of rays => 2 number of rays => 2
------------------------------------------------------------------------
}, {ambient dimension => 3 }, {ambient dimension => 3
0 dimension of lineality space => 0 dimension of lineality space
dimension of the cone => 2 dimension of the cone => 2
number of facets => 2 number of facets => 2
number of rays => 2 number of rays => 2
------------------------------------------------------------------------
}, {ambient dimension => 3 },
=> 0 dimension of lineality space => 0
dimension of the cone => 2
number of facets => 2
number of rays => 2
------------------------------------------------------------------------
{ambient dimension => 3 }, {ambient dimension => 3
dimension of lineality space => 0 dimension of lineality space =>
dimension of the cone => 2 dimension of the cone => 2
number of facets => 2 number of facets => 2
number of rays => 2 number of rays => 2
------------------------------------------------------------------------
}}
0
o2 : List</pre>
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<p/>
To actually see the cones of the fan we can look at their
rays, for example:<table class="examples"><tr><td><pre>i3 : apply(L,rays)
o3 = {| 0 0 |, | -1 0 |, | -1 0 |, | 0 0 |, | -1 0 |, | 0 0 |, | 1 0 |,
| -1 0 | | 0 0 | | 0 -1 | | -1 0 | | 0 0 | | 1 0 | | 0 0 |
| 0 -1 | | 0 -1 | | 0 0 | | 0 1 | | 0 1 | | 0 1 | | 0 1 |
------------------------------------------------------------------------
| 1 0 |, | 1 0 |, | 1 0 |, | 0 0 |, | -1 0 |}
| 0 1 | | 0 -1 | | 0 0 | | 1 0 | | 0 1 |
| 0 0 | | 0 0 | | 0 -1 | | 0 -1 | | 0 0 |
o3 : List</pre>
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<div class="waystouse"><h2>Ways to use <tt>cones</tt> :</h2>
<ul><li>cones(ZZ,Fan)</li>
</ul>
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