Question: two different answers just like a bug for operator calculations

Dear,i meet a problem in Physics package.i can't find why i got two different answers.

restart; with(Physics); Setup(mathematicalnotation = true);Setup(op = {C});

Cp := Dagger(C);

alg := %Commutator(Cp, C) = -1;

Setup(alg)

S := sqrt(N-(Dagger(C)+sqrt(N)*conjugate(eta))*(C+sqrt(N)*eta)):

eq1 := collect(expand(op(1, S)), N):

xi = op(1, eq1);

f := map(simplify, map(proc (x) options operator, arrow; x*sqrt(xi) end proc, convert(series(sqrt(subsop(1 = xi, (-conjugate(eta)*eta+1)*N+(-C*conjugate(eta)-Physics:-Dagger(C)*eta)*(N^(1/2))-Physics:-`*`(Physics:-Dagger(C), C))*(1/xi)), xi = infinity, 3), polynom)));

g := `assuming`([map(simplify, convert(series(sqrt(subsop(1 = xi, (-conjugate(eta)*eta+1)*N+(-C*conjugate(eta)-Physics:-Dagger(C)*eta)*(N^(1/2))-Physics:-`*`(Physics:-Dagger(C), C))), xi = infinity, 2), polynom))], [xi > 0]);

map(proc (x) options operator, arrow; simplify(factor(x)) end proc, collect(Simplify(f-g), [eta, Dagger(eta)]))

 the question is, the last one ,it's not zero.i beileve its right from f method,but f method wrong.why got two diferent answers.i guess its bug in g .

Thank you in advance.