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<head><title>preimage -- preimage of an ideal under a ring map</title>
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<div><h1>preimage -- preimage of an ideal under a ring map</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>preimage(f,I)</tt></div>
</dd></dl>
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<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, an ideal in the target ring of <tt>f</tt></span></li>
<li><span><tt>f</tt></span></li>
</ul>
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<li><div class="single">Outputs:<ul><li><span>the preimage of <tt>I</tt> under the map <tt>f</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : S = QQ[t,u]
o2 = S
o2 : PolynomialRing</pre>
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<tr><td><pre>i3 : f = map(R,S,{x*y,y*z})
o3 = map(R,S,{x*y, y*z})
o3 : RingMap R <--- S</pre>
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<tr><td><pre>i4 : preimage_f ideal(x^2,y^2)
2 2
o4 = ideal (u , t*u, t )
o4 : Ideal of S</pre>
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<div class="waystouse"><h2>Ways to use <tt>preimage</tt> :</h2>
<ul><li>preimage(RingMap,Ideal)</li>
</ul>
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