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<head><title>dim(Module) -- compute the Krull dimension</title>
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<div><h1>dim(Module) -- compute the Krull dimension</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 M</tt></div>
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<li><span>Function: <a href="_dim.html" title="compute the Krull dimension">dim</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="___Module.html">module</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>an <a href="___Z__Z.html">integer</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div>Computes the Krull dimension of the module <tt>M</tt><table class="examples"><tr><td><pre>i1 : R = ZZ/31991[a,b,c,d]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : I = monomialCurveIdeal(R,{1,2,3})
2 2
o2 = ideal (c - b*d, b*c - a*d, b - a*c)
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : M = Ext^1(I,R)
o3 = cokernel {-3} | c b a |
{-3} | d c b |
2
o3 : R-module, quotient of R</pre>
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<tr><td><pre>i4 : dim M
o4 = 2</pre>
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<tr><td><pre>i5 : N = Ext^0(I,R)
o5 = image {-2} | c2-bd |
{-2} | bc-ad |
{-2} | b2-ac |
3
o5 : R-module, submodule of R</pre>
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<tr><td><pre>i6 : dim N
o6 = 4</pre>
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Note that the dimension of the zero module is <tt>-1</tt>.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_dim_lp__Ring_rp.html" title="compute the Krull dimension">dim(Ring)</a> -- compute the Krull dimension</span></li>
<li><span><a href="_dim_lp__Ideal_rp.html" title="compute the Krull dimension">dim(Ideal)</a> -- compute the Krull dimension</span></li>
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