load(grobner);
F:1+f1*t+f2*t^2+f3*t^3;
G:1+g1*t+g2*t^2+g3*t^3+g4*t^4;

Fr:expand((1-r1*t)*(1-r2*t)*(1-r3*t));
ANS1:subst([t=r1*t],G)*subst([t=r2*t],G)*subst([t=r3*t],G);
/* ANS2:expand(ANS1); */
L:[coeff(F-Fr,t^3),coeff(F-Fr,t^2),coeff(F-Fr,t)];
VARS:[r1,r2,r3,f1,f2,f3];
B:poly_grobner(L,VARS);

ANS3:-poly_normal_form(ANS1,B,VARS);
ANS4:collectterms(expand(ANS3));
ANS40:makelist(coeff(ANS4,t^j)*t^j,j,0,20);
Rel:[f1=coeff(Fr,t),f2=coeff(Fr,t^2),f3=coeff(Fr,t^3)];
ANS5:subst(Rel,ANS4);

CHECK1:expand(ANS1-ANS5);