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<head><title>removeLowestDimension -- remove components of lowest dimension</title>
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<div><h1>removeLowestDimension -- remove components of lowest 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>removeLowestDimension M</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, an <a href="___Ideal.html" title="the class of all ideals">Ideal</a> or a <a href="___Module.html" title="the class of all modules">Module</a></span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>N</tt>, an <a href="___Ideal.html" title="the class of all ideals">Ideal</a>, respectively a <a href="___Module.html" title="the class of all modules">Module</a>.</span></li>
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<div class="single"><h2>Description</h2>
<div>This function yields the intersection of the primary components of <tt>M</tt>, except those of lowest dimension (and thus returns the ambient free module of <tt>M</tt> (or unit ideal), if <tt>M</tt> is pure dimensional).<p/>
For a very brief description of the method used, see <a href="_top__Components.html" title="compute top dimensional component">topComponents</a>.<p/>
As an example we remove the lowest dimensional component of an ideal I<table class="examples"><tr><td><pre>i1 : R=ZZ/32003[a..d];</pre>
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<tr><td><pre>i2 : I=intersect(ideal(a*b+a^2,b^2),ideal(a^2,b^2,c^2),ideal(b^3,c^3,d^3))
3 2 3 2 3 2 3 3 2 3 3 3 2 2 3 2 3
o2 = ideal (b , b d , b c , a c + a*b*c , a b*d , a d , a c d + a*b*c d )
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : removeLowestDimension I
2 2
o3 = ideal (b , a + a*b)
o3 : Ideal of R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_top__Components.html" title="compute top dimensional component">topComponents</a> -- compute top dimensional component</span></li>
<li><span><a href="_saturate.html" title="saturation of ideal or submodule">saturate</a> -- saturation of ideal or submodule</span></li>
<li><span><a href="_quotient.html" title="quotient or division">quotient</a> -- quotient or division</span></li>
<li><span><a href="_radical.html" title="the radical of an ideal">radical</a> -- the radical of an ideal</span></li>
<li><span><a href="_minimal__Primes.html" title="minimal associated primes of an ideal">minimalPrimes</a> -- minimal associated primes of an ideal</span></li>
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<div class="waystouse"><h2>Ways to use <tt>removeLowestDimension</tt> :</h2>
<ul><li>removeLowestDimension(Ideal)</li>
<li>removeLowestDimension(Module)</li>
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