human
What is a Python code to compute a Groebner basis with respect to lexicographic ordering given the following:
Complete the below
def groebner_lcm(f, g):

    ''''Computes LCM of two polynomials using Groebner bases.
    The LCM is computed as the unique generater of the intersection
    of the two ideals generated by `f` and `g`. The approach is to
    compute a Groebner basis with respect to lexicographic ordering
    of `t*f` and `(1 - t)*g`, where `t` is an unrelated variable and
    then filtering out the solution that doesn\'t contain `t`.
    References
    1. [Cox97]_'
    '''
assistant
#Here is Python code to compute a Groebner basis with respect to lexicographic ordering
.
    if (f.ring != g.ring):
        raise ValueError('Values    should    be    equal')
    ring = f.ring
    domain = ring.domain
    if ((not f) or (not g)):
        return ring.zero
    if ((len(f) <= 1) and (len(g) <= 1)):
        monom = monomial_lcm(f.LM, g.LM)
        coeff = domain.lcm(f.LC, g.LC)
        return ring.term_new(monom, coeff)
    (fc, f) = f.primitive()
    (gc, g) = g.primitive()
    lcm = domain.lcm(fc, gc)
    f_terms = [(((1,) + monom), coeff) for (monom, coeff) in f.terms()]
    g_terms = ([(((0,) + monom), coeff) for (monom, coeff) in g.terms()] + [(((1,) + monom), (- coeff)) for (monom, coeff) in g.terms()])
    t = Dummy('t')
    t_ring = ring.clone(symbols=((t,) + ring.symbols), order=lex)
    F = t_ring.from_terms(f_terms)
    G = t_ring.from_terms(g_terms)
    basis = groebner([F, G], t_ring)
    def is_independent(h, j):
        return all(((not monom[j]) for monom in h.monoms()))
    H = [h for h in basis if is_independent(h, 0)]
    h_terms = [(monom[1:], (coeff * lcm)) for (monom, coeff) in H[0].terms()]
    h = ring.from_terms(h_terms)
    return h