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<head><title>trivialDeformations -- Compute the trivial deformations.</title>
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<div><h1>trivialDeformations -- Compute the trivial deformations.</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>trivialDeformations(C)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>C</tt>, <span>an <a href="___Complex.html">embedded complex</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, of <a href="___First__Order__Deformation.html" title="The class of all first order deformations of monomial ideals.">FirstOrderDeformation</a></span></li>
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<div class="single"><h2>Description</h2>
<div><p>Compute the deformations induced by root automorphisms of the embedding space (i.e., excluding those coming from the torus).</p>
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<table class="examples"><tr><td><pre>i1 : R=QQ[x_0..x_4];</pre>
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<tr><td><pre>i2 : addCokerGrading(R)
o2 = | -1 -1 -1 -1 |
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 1 0 |
| 0 0 0 1 |
5 4
o2 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i3 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0)
o3 = ideal (x x , x x , x x , x x , x x )
0 1 1 2 2 3 3 4 0 4
o3 : Ideal of R</pre>
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<tr><td><pre>i4 : C=idealToComplex I
o4 = 1: x x x x x x x x x x
0 2 0 3 1 3 1 4 2 4
o4 : complex of dim 1 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 5, 5, 0, 0, 0}, Euler = -1</pre>
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<tr><td><pre>i5 : T=trivialDeformations C
x x x x x x x x x x x x x x x x x x
1 2 3 4 0 2 3 4 0 1 3 4 0 1 2 4 0 1
o5 = {--, --, --, --, --, --, --, --, --, --, --, --, --, --, --, --, --, --,
x x x x x x x x x x x x x x x x x x
0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4
------------------------------------------------------------------------
x x
2 3
--, --}
x x
4 4
o5 : List</pre>
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<tr><td><pre>i6 : tally apply(T,isTrivial)
o6 = Tally{true => 20}
o6 : Tally</pre>
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<div class="waystouse"><h2>Ways to use <tt>trivialDeformations</tt> :</h2>
<ul><li>trivialDeformations(Complex)</li>
<li>trivialDeformations(Ideal,Matrix)</li>
<li>trivialDeformations(Matrix)</li>
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