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<head><title>dim(Complex) -- Compute the dimension of a complex or co-complex.</title>
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<div><h1>dim(Complex) -- Compute the dimension 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>dim(C)</tt></div>
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<li><span>Function: <a href="../../Macaulay2Doc/html/_dim.html" title="compute the Krull dimension">dim</a></span></li>
<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="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, bigger or equal to -1</span></li>
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<div class="single"><h2>Description</h2>
<div><p>Computes the dimension of a 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 : C=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 : dim C
o4 = 4</pre>
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<tr><td><pre>i5 : bC=boundaryOfPolytope C
o5 = 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
o5 : 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>i6 : dim bC
o6 = 3</pre>
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<tr><td><pre>i7 : dbC=dualize bC
o7 = 0: v v v v v
0 1 2 3 4
o7 : co-complex of dim 0 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {0, 5, 10, 10, 5, 1}, Euler = 1</pre>
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<tr><td><pre>i8 : dim dbC
o8 = 0</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Complex.html" title="The class of all embedded complexes.">Complex</a> -- The class of all embedded complexes.</span></li>
<li><span><a href="___Co__Complex.html" title="The class of all embedded co-complexes.">CoComplex</a> -- The class of all embedded co-complexes.</span></li>
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