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<head><title>closedStar -- The closed star of a face of a complex.</title>
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<div><h1>closedStar -- The closed star of a face of a complex.</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>closedStar(F)</tt></div>
</dd></dl>
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</li>
<li><div class="single">Inputs:<ul><li><span><tt>F</tt>, <span>a <a href="___Face.html">face</a></span></span></li>
<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>an <a href="___Complex.html">embedded complex</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><div>The closed star of the face F of the complex C.</div>
<table class="examples"><tr><td><pre>i1 : R=QQ[x_0..x_4]
o1 = R
o1 : PolynomialRing</pre>
</td></tr>
<tr><td><pre>i2 : C=boundaryOfPolytope simplex(R)
o2 = 3: x x x x x x x x x x x x x x x x x x x x
0 1 2 3 0 1 2 4 0 1 3 4 0 2 3 4 1 2 3 4
o2 : complex of dim 3 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 5, 10, 10, 5, 0}, Euler = -1</pre>
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<tr><td><pre>i3 : F=C.fc_0_0
o3 = x
0
o3 : face with 1 vertex</pre>
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<tr><td><pre>i4 : link(F,C)
o4 = 2: x x x x x x x x x x x x
1 2 3 1 2 4 1 3 4 2 3 4
o4 : complex of dim 2 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 4, 6, 4, 0, 0}, Euler = 1</pre>
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<tr><td><pre>i5 : closedStar(F,C)
o5 = 3: x x x x x x x x x x x x x x x x
0 1 2 3 0 1 2 4 0 1 3 4 0 2 3 4
o5 : complex of dim 3 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 5, 10, 10, 4, 0}, Euler = 0</pre>
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<tr><td><pre>i6 : F=C.fc_1_0
o6 = x x
0 1
o6 : face with 2 vertices</pre>
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<tr><td><pre>i7 : link(F,C)
o7 = 1: x x x x x x
2 3 2 4 3 4
o7 : complex of dim 1 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 3, 3, 0, 0, 0}, Euler = -1</pre>
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<tr><td><pre>i8 : closedStar(F,C)
o8 = 3: x x x x x x x x x x x x
0 1 2 3 0 1 2 4 0 1 3 4
o8 : complex of dim 3 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 5, 10, 9, 3, 0}, Euler = 0</pre>
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<table class="examples"><tr><td><pre>i9 : R=QQ[x_0..x_4]
o9 = R
o9 : PolynomialRing</pre>
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<tr><td><pre>i10 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0)
o10 = ideal (x x , x x , x x , x x , x x )
0 1 1 2 2 3 3 4 0 4
o10 : Ideal of R</pre>
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<tr><td><pre>i11 : C=idealToComplex I
o11 = 1: x x x x x x x x x x
0 2 0 3 1 3 1 4 2 4
o11 : 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>i12 : F=C.fc_0_0
o12 = x
0
o12 : face with 1 vertex</pre>
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<tr><td><pre>i13 : link(F,C)
o13 = 0: x x
2 3
o13 : complex of dim 0 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 2, 0, 0, 0, 0}, Euler = 1</pre>
</td></tr>
<tr><td><pre>i14 : closedStar(F,C)
o14 = 1: x x x x
0 2 0 3
o14 : complex of dim 1 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 3, 2, 0, 0, 0}, Euler = 0</pre>
</td></tr>
<tr><td><pre>i15 : F=C.fc_1_0
o15 = x x
0 2
o15 : face with 2 vertices</pre>
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<tr><td><pre>i16 : link(F,C)
o16 = -1: {}
o16 : complex of dim -1 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 0, 0, 0, 0, 0}, Euler = -1</pre>
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<tr><td><pre>i17 : closedStar(F,C)
o17 = 1: x x
0 2
o17 : complex of dim 1 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 2, 1, 0, 0, 0}, Euler = 0</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_link.html" title="The link of a face of a complex.">link</a> -- The link of a face of a complex.</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>closedStar</tt> :</h2>
<ul><li>closedStar(Face,Complex)</li>
</ul>
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