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<head><title>linSpace -- computes a basis of the lineality space</title>
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<div><h1>linSpace -- computes a basis of the lineality space</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> LS = linSpace C </tt><br/><tt>LS = linSpace F </tt><br/><tt>LS = linSpace P</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>C</tt>, <span>a <a href="___Cone.html">convex rational cone</a></span></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>
<li><span><tt>P</tt>, <span>a <a href="___Polyhedron.html">convex polyhedron</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>LS</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><p/>
<tt>linSpace</tt> returns a basis of the lineality space of the
input as the columns of the matrix <tt>LS</tt>. The lineality space of a
Fan is the lineality space of any Cone of the Fan, since they all have the
same lineality space.<table class="examples"><tr><td><pre>i1 : M = matrix {{1,1,1},{0,1,0},{-1,1,-1},{-1,-1,-1},{0,-1,0},{1,-1,1}};
6 3
o1 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i2 : v = matrix {{2},{1},{2},{2},{1},{2}};
6 1
o2 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i3 : P = intersection(M,v)
o3 = {ambient dimension => 3 }
dimension of lineality space => 1
dimension of polyhedron => 3
number of facets => 6
number of rays => 0
number of vertices => 6
o3 : Polyhedron</pre>
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<tr><td><pre>i4 : linSpace P
o4 = | 1 |
| 0 |
| -1 |
3 1
o4 : Matrix QQ <--- QQ</pre>
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<tr><td><pre>i5 : C = dualCone intersection M
o5 = {ambient dimension => 3 }
dimension of lineality space => 2
dimension of the cone => 2
number of facets => 0
number of rays => 0
o5 : Cone</pre>
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<tr><td><pre>i6 : linSpace C
o6 = | 0 1 |
| 1 0 |
| 0 1 |
3 2
o6 : Matrix QQ <--- QQ</pre>
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<div class="waystouse"><h2>Ways to use <tt>linSpace</tt> :</h2>
<ul><li>linSpace(Cone)</li>
<li>linSpace(Fan)</li>
<li>linSpace(Polyhedron)</li>
</ul>
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