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<head><title>groebnerFan -- the fan of all groebner bases of an ideal</title>
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<div><h1>groebnerFan -- the fan of all groebner bases of an ideal</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>P = groebnerFan(I)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, of which to compute the fan</span></li>
<li><span><tt>Symmetries</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, of permutations of the variables leaving the ideal invariant</span></li>
</ul>
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<li><div class="single">Outputs:<ul><li><span><tt>P</tt>, <span>a <a href="../../Macaulay2Doc/html/___Hash__Table.html">hash table</a></span>, containing all the data of the polyhedral fan of <tt>I</tt>.</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="_groebner__Fan.html">Symmetries => ...</a>, -- the fan of all groebner bases of an ideal</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[symbol a..symbol f];</pre>
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<tr><td><pre>i2 : I = pfaffians(4, genericSkewMatrix(R,4))
o2 = ideal(c*d - b*e + a*f)
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : P = groebnerFan(I)
LP algorithm being used: "cddgmp".
LP algorithm being used: "cddgmp".
o3 = PolymakeObject{...11...}
o3 : PolymakeObject</pre>
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<tr><td><pre>i4 : peek P
o4 = PolymakeObject{AMBIENT_DIM => 6 }
CONES => {{}, {0}, {1}, {2}, {0, 1}, {0, 2}, {1, 2}}
DIM => 6
F_VECTOR => {1, 3, 3}
LINEALITY_DIM => 4
LINEALITY_SPACE => | 1 0 0 0 0 -1 |
| 0 1 0 0 -1 0 |
| 0 0 1 0 1 1 |
| 0 0 0 1 1 1 |
MAXIMAL_CONES => {{}, {0}, {1}, {2}, {0, 1}, {0, 2}, {1, 2}}
N_RAYS => 3
ORTH_LINEALITY_SPACE => | 1 0 -1 -1 0 1 |
| 0 1 -1 -1 1 0 |
PURE => 1
RAYS => | -2 1 1 1 1 -2 |
| 1 -2 1 1 -2 1 |
| 1 1 -2 -2 1 1 |</pre>
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<div class="single"><h2>Caveat</h2>
<div><div>Requires loading of the Polymake package to make the PolymakeObject type available.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_gfan.html" title="all initial ideals of an ideal">gfan</a> -- all initial ideals of an ideal</span></li>
<li><span><a href="_initial__Ideal.html" title="initial ideal with respect to a weight vector">initialIdeal</a> -- initial ideal with respect to a weight vector</span></li>
<li><span><a href="_groebner__Cone.html" title="the cone whose interior weight vectors give the given initial ideal">groebnerCone</a> -- the cone whose interior weight vectors give the given initial ideal</span></li>
<li><span><a href="___Symmetries.html" title="permutations leaving an ideal invariant to speed up gfan computations.">Symmetries</a> -- permutations leaving an ideal invariant to speed up gfan computations.</span></li>
</ul>
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<div class="waystouse"><h2>Ways to use <tt>groebnerFan</tt> :</h2>
<ul><li>groebnerFan(Ideal)</li>
</ul>
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