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Macaulay2Doc > basic commutative algebra > M2SingularBook > Singular Book 1.8.11

Singular Book 1.8.11 -- intersection of ideals

Intersecting ideals using the Macaulay2 intersect function.
i1 : A = QQ[x,y,z];
i2 : I1 = ideal(x,y);

o2 : Ideal of A
i3 : I2 = ideal(y^2,z);

o3 : Ideal of A
i4 : intersect(I1,I2)

                       2
o4 = ideal (y*z, x*z, y )

o4 : Ideal of A
Now we use the method described in the Singular book in section 1.8.7.
i5 : B = QQ[t,x,y,z];
i6 : I1 = substitute(I1,B);

o6 : Ideal of B
i7 : I2 = substitute(I2,B);

o7 : Ideal of B
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
i9 : eliminate(J,t)

                       2
o9 = ideal (y*z, x*z, y )

o9 : Ideal of B