--Consider parameterization of --tangent surface of twisted cubic, i.e. --x=t+u --y=t^2-2tu --z=t^3-3t^2u R=QQ[t,u,x,y,z,MonomialOrder=>Lex] I=ideal(x-t-u,y-t^2-2*t*u,z-t^3-3*t^2*u) J=ideal groebnerBasis I --only eq without t or u is J_0 --can get this also with eliminate({t,u},I) --we might want to work in a new ring now S=QQ[(gens(R))_{2..4}] --2nd elim ideal is I2=ideal sub(J_0,S) --or with the second command I2=sub(eliminate({t,u},I),S) degree I2