Buchberger's Algorithm (1965) computes a Gröbner basis for an ideal
I = ⟨f₁, …, fₛ⟩ ⊆ k[x₁, …, xₙ]. It systematically reduces S-polynomials and adds
non-zero remainders to the generating set until all S-polynomial pairs reduce to zero.
S-Polynomial
S(f, g) =
lcm(LM(f), LM(g))
LT(f)
· f −
lcm(LM(f), LM(g))
LT(g)
· g
where LT = leading term · LM = leading monomial · lcm = least common multiple of monomials
Input