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<head><title>isStable -- determines whether the mth Hilbert point of I is GIT stable</title>
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<div><h1>isStable -- determines whether the mth Hilbert point of I is GIT stable</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>isStable(3,I)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, specifies which Hilbert point to test</span></li>
<li><span><span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, the ideal</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div>Bayer and Morrison showed that GIT stability of the mth Hilbert point of I with respect to the maximal torus acting on a polynomial ring by scaling the variables can be tested by whether <i>State</i><sub>m</sub>(I) contains a certain point.<table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre>
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<tr><td><pre>i2 : I = ideal(a*c-b^2,a*d-b*c,b*d-c^2);
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : isStable(3,I)
LP algorithm being used: "cddgmp".
polymake: WARNING: directory /Users/dan/.polymake created for keeping personal user settings
polymake: used package cddlib
Implementation of the double description method of Motzkin et al.
Copyright by Komei Fukuda.
http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html
VERTICES
1 9 6 6 9
1 9 3 12 6
1 7 5 14 4
1 5 8 14 3
1 3 12 12 3
1 6 12 3 9
1 4 14 5 7
1 3 14 8 5
LP algorithm being used: "cddgmp".
polymake: used package cddlib
Implementation of the double description method of Motzkin et al.
Copyright by Komei Fukuda.
http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html
VERTICES
1 9 6 6 9
1 9 3 12 6
1 7 5 14 4
1 5 8 14 3
1 3 12 12 3
1 6 12 3 9
1 4 14 5 7
1 3 14 8 5
o3 = true</pre>
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<tr><td><pre>i4 : I = ideal(a^2,b^2,b*c);
o4 : Ideal of R</pre>
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<tr><td><pre>i5 : isStable(3,I)
LP algorithm being used: "cddgmp".
polymake: used package cddlib
Implementation of the double description method of Motzkin et al.
Copyright by Komei Fukuda.
http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html
VERTICES
1 11 13 6 3
LP algorithm being used: "cddgmp".
polymake: used package cddlib
Implementation of the double description method of Motzkin et al.
Copyright by Komei Fukuda.
http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html
VERTICES
1 33/4 33/4 33/4 33/4
1 11 13 6 3
o5 = false</pre>
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<div class="waystouse"><h2>Ways to use <tt>isStable</tt> :</h2>
<ul><li>isStable(ZZ,Ideal)</li>
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