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<head><title>RingMap RingElement -- apply a ring map</title>
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<div><h1>RingMap RingElement -- apply 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>f X</tt></div>
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<li><span>Operator: <a href="___S__P__A__C__E.html" title="blank operator; often used for function application, making polynomial rings">SPACE</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Ring__Map.html">ring map</a></span>, a ring map from <tt>R</tt> to <tt>S</tt>.</span></li>
<li><span><tt>X</tt>, <span>a <a href="___Ring__Element.html">ring element</a></span>, <span>an <a href="___Ideal.html">ideal</a></span>, <span>a <a href="___Matrix.html">matrix</a></span>, <span>a <a href="___Vector.html">vector</a></span>, <span>a <a href="___Module.html">module</a></span>, or <span>a <a href="___Chain__Complex.html">chain complex</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Ring__Element.html">ring element</a></span>, the image of X under the ring map f. The result has the same type as X, except that its ring will be S.</span></li>
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<div class="single"><h2>Description</h2>
<div>If <tt>X</tt> is a module then it must be either free or a submodule of a free module. If <tt>X</tt> is a chain complex, then every module of <tt>X</tt> must be free or a submodule of a free module.<table class="examples"><tr><td><pre>i1 : R = QQ[x,y];</pre>
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<tr><td><pre>i2 : S = QQ[t];</pre>
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<tr><td><pre>i3 : f = map(S,R,{t^2,t^3})
2 3
o3 = map(S,R,{t , t })
o3 : RingMap S <--- R</pre>
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<tr><td><pre>i4 : f (x+y^2)
6 2
o4 = t + t
o4 : S</pre>
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<tr><td><pre>i5 : f image vars R
o5 = image | t2 t3 |
1
o5 : S-module, submodule of S</pre>
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<tr><td><pre>i6 : f ideal (x^2,y^2)
4 6
o6 = ideal (t , t )
o6 : Ideal of S</pre>
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<tr><td><pre>i7 : f resolution coker vars R
1 2 1
o7 = S <-- S <-- S <-- 0
0 1 2 3
o7 : ChainComplex</pre>
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<div class="single"><h2>Caveat</h2>
<div>If the rings <tt>R</tt> and <tt>S</tt> have different degree monoids, then the degrees of the image might need to be changed, since Macaulay2 sometimes doesn't have enough information to determine the image degrees of elements of a free module.</div>
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