human
I wrote the below code

    P = []
    S = []
    Sugars = []
    def Ssugar(i, j):
        'Compute    the    sugar    of    the    S-poly    corresponding    to    (i,    j).'
        LMi = sdm_LM(S[i])
        LMj = sdm_LM(S[j])
        return (max((Sugars[i] - sdm_monomial_deg(LMi)), (Sugars[j] - sdm_monomial_deg(LMj))) + sdm_monomial_deg(sdm_monomial_lcm(LMi, LMj)))
    ourkey = (lambda p: (p[2], O(p[3]), p[1]))
    def update(f, sugar, P):
        'Add    f    with    sugar    ``sugar``    to    S,    update    P.'
        if (not f):
            return P
        k = len(S)
        S.append(f)
        Sugars.append(sugar)
        LMf = sdm_LM(f)
        def removethis(pair):
            (i, j, s, t) = pair
            if (LMf[0] != t[0]):
                return False
            tik = sdm_monomial_lcm(LMf, sdm_LM(S[i]))
            tjk = sdm_monomial_lcm(LMf, sdm_LM(S[j]))
            return ((tik != t) and (tjk != t) and sdm_monomial_divides(tik, t) and sdm_monomial_divides(tjk, t))
        P = [p for p in P if (not removethis(p))]
        N = [(i, k, Ssugar(i, k), sdm_monomial_lcm(LMf, sdm_LM(S[i]))) for i in range(k) if (LMf[0] == sdm_LM(S[i])[0])]
        N.sort(key=ourkey)
        remove = set()
        for (i, p) in enumerate(N):
            for j in range((i + 1), len(N)):
                if sdm_monomial_divides(p[3], N[j][3]):
                    remove.add(j)
        P.extend(reversed([p for (i, p) in enumerate(N) if (not (i in remove))]))
        P.sort(key=ourkey, reverse=True)
        return P
    try:
        numgens = (len(next((x[0] for x in G if x))[0]) - 1)
    except StopIteration:
        if extended:
            return ([], [])
        return []
    coefficients = []
    for (i, f) in enumerate(G):
        P = update(f, sdm_deg(f), P)
        if (extended and f):
            coefficients.append(sdm_from_dict({((i,) + ((0,) * numgens)): K(1)}, O))
    while P:
        (i, j, s, t) = P.pop()
        (f, sf, g, sg) = (S[i], Sugars[i], S[j], Sugars[j])
        if extended:
            (sp, coeff) = sdm_spoly(f,...

What's a good function header?

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Write me a Python code to compute    the    sugar    of    the    S-poly    corresponding    to    (i,    j)?
assistant
#Here is Python code to compute    the    sugar    of    the    S-poly    corresponding    to    (i,    j).

def sdm_groebner(G, NF, O, K, extended=False):