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<head><title>hilbertBasis -- calculates the Hilbert basis of the cone; invokes "hilbert" from 4ti2</title>
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<div><h1>hilbertBasis -- calculates the Hilbert basis of the cone; invokes "hilbert" from 4ti2</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>hilbertBasis(A) or hilbertBasis(A, InputType => "lattice")</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>A</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, defining the cone <i>{z : Az = 0, z ≥0 }</i></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>, whose rows form the Hilbert basis of the cone <i>{z : Az = 0, z ≥0 }</i> or the cone <i>{z A : z is an integral vector and z A ≥0 }</i> if <tt>InputType => "lattice"</tt> is used</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="_hilbert__Basis.html">InputType => ...</a>, -- calculates the Hilbert basis of the cone; invokes "hilbert" from 4ti2</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : A = matrix "1,1,1,1; 1,2,3,4"
o1 = | 1 1 1 1 |
| 1 2 3 4 |
2 4
o1 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i2 : B = syz A
o2 = | 1 2 |
| -2 -3 |
| 1 0 |
| 0 1 |
4 2
o2 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i3 : hilbertBasis(transpose B)
-------------------------------------------------
4ti2 version 1.3.2, Copyright (C) 2006 4ti2 team.
4ti2 comes with ABSOLUTELY NO WARRANTY.
This is free software, and you are welcome
to redistribute it under certain conditions.
For details, see the file COPYING.
-------------------------------------------------
Final basis has 1 inhomogeneous, 3 homogeneous and 0 free elements.
4ti2 Total Time: 0.00 secs
using temporary file name /tmp/M2-3907-1
o3 = | 3 2 1 0 |
| 0 1 2 3 |
| 1 1 1 1 |
3 4
o3 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i4 : hilbertBasis(A, InputType => "lattice")
-------------------------------------------------
4ti2 version 1.3.2, Copyright (C) 2006 4ti2 team.
4ti2 comes with ABSOLUTELY NO WARRANTY.
This is free software, and you are welcome
to redistribute it under certain conditions.
For details, see the file COPYING.
-------------------------------------------------
Final basis has 1 inhomogeneous, 3 homogeneous and 0 free elements.
4ti2 Total Time: 0.00 secs
using temporary file name /tmp/M2-3907-2
o4 = | 3 2 1 0 |
| 0 1 2 3 |
| 1 1 1 1 |
3 4
o4 : Matrix ZZ <--- ZZ</pre>
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<div class="waystouse"><h2>Ways to use <tt>hilbertBasis</tt> :</h2>
<ul><li>hilbertBasis(Matrix)</li>
</ul>
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