SubalgebraHom(R: RING, L: LIST): RINGHOM

/**/ use QQ[s,t];
/**/ L := [s^3, s^2*t, s*t^2, t^3];

/**/ ReprRing ::= QQ[x,y,z,w];
/**/ phi := SubalgebraHom(ReprRing, L);
/**/ phi;
RingHom(RingWithID(256, "QQ[x,y,z,w]") --> RingWithID(257, "QQ[s,t]")
  sending (x |--> s^3) & (y |--> s^2*t) & (z |--> s*t^2) & (w |--> t^3))

/**/ ker(phi);  --> implicitization
ideal(z^2 -y*w,  y*z -x*w,  y^2 -x*z)

/**/ SubalgRepr := preimage0(phi, s^6*t^6);  SubalgRepr;
x^2*w^2
/**/ phi(SubalgRepr);
s^6*t^6