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<head><title>Singular Book 1.3.3 -- properties of ring maps</title>
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<div><h1>Singular Book 1.3.3 -- properties of ring maps</h1>
<div><table class="examples"><tr><td><pre>i1 : S = QQ[a,b,c];</pre>
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<tr><td><pre>i2 : R = QQ[x,y,z];</pre>
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<tr><td><pre>i3 : phi = map(R,S,{x,y,x^2-y^3})
3 2
o3 = map(R,S,{x, y, - y + x })
o3 : RingMap R <--- S</pre>
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<tr><td><pre>i4 : isInjective phi
o4 = false</pre>
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<tr><td><pre>i5 : ker phi
3 2
o5 = ideal(b - a + c)
o5 : Ideal of S</pre>
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Packaged code for computing preimage is missing, but it's easy to do, as follows.<table class="examples"><tr><td><pre>i6 : psi = map(R,S,{x,x+y,z-x^2+y^3})
3 2
o6 = map(R,S,{x, x + y, y - x + z})
o6 : RingMap R <--- S</pre>
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<tr><td><pre>i7 : isInjective psi
o7 = true</pre>
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<tr><td><pre>i8 : ker psi
o8 = ideal ()
o8 : Ideal of S</pre>
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