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<head><title>intersect -- compute an intersection</title>
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<div><h1>intersect -- compute an intersection</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>intersect (M,N,...,P) </tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>(M,N,...,P)</tt>, <span>a <a href="___List.html">list</a></span> or <span>a <a href="___Sequence.html">sequence</a></span> of modules or ideals that are submodules of the same module or ideals in the same ring</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Module.html">module</a></span> or <span>an <a href="___Ideal.html">ideal</a></span> that is the intersection of the elements in the list or in the sequence.</span></li>
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<div class="single"><h2>Description</h2>
<div>This function calculates the intersection of submodules of the same free module, or of ideals in the same ring.<p>The following example computes the intersection of a sequence of ideals.</p>
<table class="examples"><tr><td><pre>i1 : R=ZZ/101[a..d];</pre>
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<tr><td><pre>i2 : I=intersect(ideal(a,b),ideal(b,c),ideal(c,d),ideal(d,a))
o2 = ideal (b*d, a*c)
o2 : Ideal of R</pre>
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<p>The following example computes the intersection of a list of modules.</p>
<table class="examples"><tr><td><pre>i3 : R=ZZ[x,y,z];</pre>
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<tr><td><pre>i4 : M=image matrix{{3*x},{3*x}};</pre>
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<tr><td><pre>i5 : N=image matrix{{5*y},{5*y}};</pre>
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<tr><td><pre>i6 : P=image matrix{{7*z},{7*z}};</pre>
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<tr><td><pre>i7 : intersect{M,N,P}
o7 = image | 105xyz |
| 105xyz |
2
o7 : R-module, submodule of R</pre>
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<p>The command <a href="_intersect.html" title="compute an intersection">intersect</a> will only work with proper ideals. To intersect an ideal with a ring, use <a href="_select__In__Subring.html" title="select columns in a subring">selectInSubring</a> along with the elimination ordering, see <a href="___Eliminate.html" title="elimination order">Eliminate</a>.</p>
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<div class="waystouse"><h2>Ways to use <tt>intersect</tt> :</h2>
<ul><li>intersect(List)</li>
<li>intersect(Sequence)</li>
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