# 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