Intersecting ideals using the Macaulay2
intersect function.
i1 : A = QQ[x,y,z];
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i2 : I1 = ideal(x,y);
o2 : Ideal of A
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i3 : I2 = ideal(y^2,z);
o3 : Ideal of A
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i4 : intersect(I1,I2)
2
o4 = ideal (y*z, x*z, y )
o4 : Ideal of A
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Now we use the method described in the Singular book in section 1.8.7.
i5 : B = QQ[t,x,y,z];
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i6 : I1 = substitute(I1,B);
o6 : Ideal of B
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i7 : I2 = substitute(I2,B);
o7 : Ideal of B
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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
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i9 : eliminate(J,t)
2
o9 = ideal (y*z, x*z, y )
o9 : Ideal of B
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