ker(phi: RINGHOM): IDEAL

/**/  R ::= QQ[x,y,z,w];
/**/  Use S ::= QQ[s,t];
/**/  phi := PolyAlgebraHom(R, S, [s^3, s^2*t, s*t^2, t^3]);
/**/  ker(phi);
ideal(z^2 -y*w,  y*z -x*w,  y^2 -x*z)

/**/  SmodJ := NewQuotientRing(S, "t+s");
/**/  use SmodJ;
/**/  psi := PolyAlgebraHom(R, SmodJ, [s^3, s^2*t, s*t^2, t^3]);
/**/  ker(psi);
ideal(x +w, y -w, z +w)

/**/  RmodI := NewQuotientRing(R, "x+y");
/**/  ker(InducedHom(RmodI, psi));
ideal((z +w),  (y -w))