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<head><title>sublatticeBasis -- computes a basis for the sublattice generated by integral vectors or the lattice points of a polytope</title>
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<div><h1>sublatticeBasis -- computes a basis for the sublattice generated by integral vectors or the lattice points of a polytope</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> B = sublatticeBasis M </tt><br/><tt>B = sublatticeBasis P</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, over <a href="../../Macaulay2Doc/html/___Z__Z.html" title="the class of all integers">ZZ</a> with each column representing a sublattice generator</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>B</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, A matrix over <a href="../../Macaulay2Doc/html/___Z__Z.html" title="the class of all integers">ZZ</a> containing a sublattice basis</span></li>
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<div class="single"><h2>Description</h2>
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<tt>sublatticeBasis</tt> computes a basis for the sublattice generated by the columns of<tt>M</tt> or
by the lattice points of<tt>P</tt>.<table class="examples"><tr><td><pre>i1 : P = convexHull transpose matrix {{0,0,0},{1,0,0},{0,1,0},{1,1,3}}
o1 = {ambient dimension => 3 }
dimension of lineality space => 0
dimension of polyhedron => 3
number of facets => 4
number of rays => 0
number of vertices => 4
o1 : Polyhedron</pre>
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<tr><td><pre>i2 : sublatticeBasis P
o2 = | 0 1 1 |
| 1 0 1 |
| 0 0 3 |
3 3
o2 : Matrix ZZ <--- ZZ</pre>
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<div class="waystouse"><h2>Ways to use <tt>sublatticeBasis</tt> :</h2>
<ul><li>sublatticeBasis(Matrix)</li>
<li>sublatticeBasis(Polyhedron)</li>
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