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<head><title>embeddingComplex -- The embedding complex of a complex or co-complex.</title>
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<div><h1>embeddingComplex -- The embedding complex of a complex or co-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>embeddingComplex(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>an <a href="___Complex.html">embedded complex</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><p>The embedding complex of a complex or co-complex.</p>
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<table class="examples"><tr><td><pre>i1 : R=QQ[x_0..x_4]
o1 = R
o1 : PolynomialRing</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 : C0=simplex(R)
o3 = 4: x x x x x
0 1 2 3 4
o3 : complex of dim 4 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 5, 10, 10, 5, 1}, Euler = 0</pre>
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<tr><td><pre>i4 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0)
o4 = ideal (x x , x x , x x , x x , x x )
0 1 1 2 2 3 3 4 0 4
o4 : Ideal of R</pre>
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<tr><td><pre>i5 : C=idealToComplex(I)
o5 = 1: x x x x x x x x x x
0 2 0 3 1 3 1 4 2 4
o5 : 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>i6 : embeddingComplex C
o6 = 4: x x x x x
0 1 2 3 4
o6 : complex of dim 4 embedded in dim 4 (printing facets)
equidimensional, simplicial</pre>
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<tr><td><pre>i7 : idealToComplex(I,C0)
o7 = 1: x x x x x x x x x x
0 2 0 3 1 3 1 4 2 4
o7 : 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>i8 : complexToIdeal(C)
o8 = ideal (x x , x x , x x , x x , x x )
0 1 1 2 2 3 0 4 3 4
o8 : Ideal of R</pre>
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<tr><td><pre>i9 : cC=idealToCoComplex(I,C0)
o9 = 2: x x x x x x x x x x x x x x x
0 1 3 0 2 3 0 2 4 1 2 4 1 3 4
o9 : co-complex of dim 2 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {0, 0, 0, 5, 5, 1}, Euler = 1</pre>
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<tr><td><pre>i10 : cC==complement C
o10 = true</pre>
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<tr><td><pre>i11 : I==coComplexToIdeal(cC)
o11 = true</pre>
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<tr><td><pre>i12 : dualize cC
o12 = 1: v v v v v v v v v v
0 2 0 3 1 3 1 4 2 4
o12 : 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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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_complex__To__Ideal.html" title="The monomial ideal associated to a complex.">complexToIdeal</a> -- The monomial ideal associated to a complex.</span></li>
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<div class="waystouse"><h2>Ways to use <tt>embeddingComplex</tt> :</h2>
<ul><li>embeddingComplex(Complex)</li>
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