load("grobner");


deg_a:2;

vars_al:makelist(concat (x_,i),i,deg_a);
/*
varsa:makelist(concat (a,i),i,deg_a);
varsb:makelist(concat (b,i),i,deg_a);
*/
varsa:[a,b];
varsb:[p,q];

f:product((1-vars_al[k]*T),k,1,length(vars_al));
f0:1+sum(varsa[k]*T^k,k,1,deg_a);
 g:1+sum(varsb[k]*T^k,k,1,length(varsb));
fg:product(subst(vars_al[k]*T,T,g),k,1,length(vars_al));

i_def:expand(f-f0);
deg_r:hipow(i_def,T);
rel:makelist(coeff(i_def,T,k),k,deg_r);
vall: append(vars_al,varsa,varsb);

B:poly_buchberger(rel,vall);
/* fgr:divide(fg,T^(deg_a+1))[2]; */
fgr:expand(fg);
RES0:poly_normal_form(fgr,B,vall);
RES1:collectterms(RES0,T);
RES2:collectterms(RES1/subst(0,T,RES1));