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<head><title>dim(Face) -- Compute the dimension of a face.</title>
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<div><h1>dim(Face) -- Compute the dimension of a face.</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(F)</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>F</tt>, <span>a <a href="___Face.html">face</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 face. If F.indices is present (usually the case by construction) this requires no computations.</p>
<p>If F.indices is not present but a polynomial ring R can be associated to F (which is the case if F.ofComplex is present (or given as a second argument) or F is non-empty) then R.grading (which can be installed by <a href="_add__Coker__Grading.html" title="Stores a cokernel grading in a polynomial ring.">addCokerGrading</a>) is used to compute the dimension of the plane spanned by F.</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 : bC=boundaryOfPolytope C
o4 = 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
o4 : 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>i5 : F=bC.fc_2_0
o5 = x x x
0 1 2
o5 : face with 3 vertices</pre>
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<tr><td><pre>i6 : dim(face vert F,R)
o6 = 2</pre>
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<div class="single"><h2>Caveat</h2>
<div><div>If F.indices is not present this returns a dimension as explained above but note that this does not check whether F is a face of the convex hull of the rows of R.grading.</div>
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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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