i1 : loadPackage "Elimination"; |
i2 : A = QQ[u,v,x,y,z]; |
i3 : I = ideal "x-uv,y-uv2,z-u2" 2 2 o3 = ideal (- u*v + x, - u*v + y, - u + z) o3 : Ideal of A |
i4 : eliminate(I,{u,v}) 4 2 o4 = ideal(x - y z) o4 : Ideal of A |
Alternatively, we could take the coimage of the ring homomorphism g corresponding to f.
i5 : g = map(QQ[u,v],QQ[x,y,z],{x => u*v, y => u*v^2, z => u^2}) 2 2 o5 = map(QQ [u, v],QQ [x, y, z],{u*v, u*v , u }) o5 : RingMap QQ [u, v] <--- QQ [x, y, z] |
i6 : coimage g QQ [x, y, z] o6 = ------------ 4 2 x - y z o6 : QuotientRing |