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<head><title>Singular Book 1.8.18 -- kernel of a ring map</title>
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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_basic_spcommutative_spalgebra.html" title="">basic commutative algebra</a> > <a href="___M2__Singular__Book.html" title="Macaulay2 examples for the Singular book">M2SingularBook</a> > <a href="___Singular_sp__Book_sp1.8.18.html" title="kernel of a ring map">Singular Book 1.8.18</a></div>
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<div><h1>Singular Book 1.8.18 -- kernel of a ring map</h1>
<div>First, we use Macaulay2's <a href="_kernel_lp__Ring__Map_rp.html" title="kernel of a ringmap">kernel(RingMap)</a> function.<table class="examples"><tr><td><pre>i1 : A = QQ[x,y,z];</pre>
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<tr><td><pre>i2 : B = QQ[a,b];</pre>
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<tr><td><pre>i3 : phi = map(B,A,{a^2,a*b,b^2})
2 2
o3 = map(B,A,{a , a*b, b })
o3 : RingMap B <--- A</pre>
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<tr><td><pre>i4 : kernel phi
2
o4 = ideal(y - x*z)
o4 : Ideal of A</pre>
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Now use the elimination of variables method.<table class="examples"><tr><td><pre>i5 : C = QQ[x,y,z,a,b]
o5 = C
o5 : PolynomialRing</pre>
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<tr><td><pre>i6 : H = ideal(x-a^2, y-a*b, z-b^2);
o6 : Ideal of C</pre>
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<tr><td><pre>i7 : eliminate(H, {a,b})
2
o7 = ideal(y - x*z)
o7 : Ideal of C</pre>
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