# Function Field DIVision, compute a/b in Q(x)[y]/(f)
FFDIV:=proc(f,x,y,a,b)
	local d,q,i;
	if nargs=4 then
		d:=normal(a);
		RETURN(FFDIV(f,x,y,numer(d),denom(d)))
	fi;
	d:=degree(f,y);
	q:=convert([seq(qc[i]*y^i,i=0..d-1)],`+`);
	evala(Normal(subs(solve(evala({coeffs(collect(rem(collect(q*b-a,y),
	f,y),y,numer),y)}),{seq(qc[i],i=0..d-1)}),q)))
end:

# So what happens is I write q*b-a = 0 where q is a polynomial in y with
# undetermined coefficients. Then compute linear equations for these
# coefficients, solve them, and the quotient q=a/b is determined.
# It's amazing that this silly method is faster than the method in Maple 5.3.