We can calculate Groebner Basis as follows: I want to know the corresponding algorithm. Is it F5?
sage : P.<x ,y="" >="PolynomialRing" (gf(11)="" ,="" order="’lex" ’)<="" p="">
sage : f1 = (x -1)^2 + (y -2)^2 - 3^2
sage : f2 = ( x +1)^2 + (y -1)^2 - 2^2
sage : I = Ideal ( f1 , f2 )
sage : I. groebner_basis ()