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<head><title>dim(SimplicialComplex) -- dimension of a simplicial complex</title>
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<div><h1>dim(SimplicialComplex) -- dimension of a simplicial 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 D</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>D</tt>, <span>a <a href="___Simplicial__Complex.html">simplicial 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>, the maximum number of vertices in a face minus one</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : loadPackage "SimplicialComplexes";</pre>
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The following simplicial complex consists of a tetrahedron, with two triangles attached, two more edges and an isolated vertex. Since the largest facet has 4 vertices, this complex has dimension 3.<table class="examples"><tr><td><pre>i2 : R = ZZ[a..h];</pre>
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<tr><td><pre>i3 : D = simplicialComplex{a*b*c*d, a*b*e, c*d*f, f*g, g*a, h}
o3 = | h fg ag cdf abe abcd |
o3 : SimplicialComplex</pre>
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<tr><td><pre>i4 : dim D
o4 = 3</pre>
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The void complex has dimension minus infinity, while the irrelevant complex has dimension -1.<table class="examples"><tr><td><pre>i5 : void = simplicialComplex monomialIdeal 1_R;</pre>
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<tr><td><pre>i6 : dim void
o6 = -infinity
o6 : InfiniteNumber</pre>
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<tr><td><pre>i7 : irrelevant = simplicialComplex {1_R};</pre>
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<tr><td><pre>i8 : dim irrelevant
o8 = -1</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="index.html" title="simplicial complexes">SimplicialComplexes</a> -- simplicial complexes</span></li>
<li><span><a href="_is__Pure.html" title="whether the facets are equidimensional">isPure</a> -- whether the facets are equidimensional</span></li>
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