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<div><h1>Singular Book 1.8.11 -- intersection of ideals</h1>
<div>Intersecting ideals using the Macaulay2 <a href="_intersect.html" title="compute an intersection">intersect</a> function.<table class="examples"><tr><td><pre>i1 : A = QQ[x,y,z];</pre>
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<tr><td><pre>i2 : I1 = ideal(x,y);
o2 : Ideal of A</pre>
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<tr><td><pre>i3 : I2 = ideal(y^2,z);
o3 : Ideal of A</pre>
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<tr><td><pre>i4 : intersect(I1,I2)
2
o4 = ideal (y*z, x*z, y )
o4 : Ideal of A</pre>
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Now we use the method described in the Singular book in section 1.8.7.<table class="examples"><tr><td><pre>i5 : B = QQ[t,x,y,z];</pre>
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<tr><td><pre>i6 : I1 = substitute(I1,B);
o6 : Ideal of B</pre>
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<tr><td><pre>i7 : I2 = substitute(I2,B);
o7 : Ideal of B</pre>
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<tr><td><pre>i8 : J = t*I1 + (1-t)*I2
2 2
o8 = ideal (t*x, t*y, - t*y + y , - t*z + z)
o8 : Ideal of B</pre>
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<tr><td><pre>i9 : loadPackage "Elimination";</pre>
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<tr><td><pre>i10 : eliminate(J,t)
2
o10 = ideal (y*z, x*z, y )
o10 : Ideal of B</pre>
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