def parametric_log_deriv_heu(fa, fd, wa, wd, DE, c1=None):
    # TODO: finish writing this and write tests
    c1 = c1 or Dummy('c1')

    p, a = fa.div(fd)
    q, b = wa.div(wd)

    B = max(0, derivation(DE.t, DE).degree(DE.t) - 1)
    C = max(p.degree(DE.t), q.degree(DE.t))

    if q.degree(DE.t) > B:
        eqs = [p.nth(i) - c1*q.nth(i) for i in range(B + 1, C + 1)]
        s = solve(eqs, c1)
        if not s or not s[c1].is_Rational:
            # deg(q) > B, no solution for c.
            return None

        N, M = s[c1].as_numer_denom()  # N and M are integers
        N, M = Poly(N, DE.t), Poly(M, DE.t)

        nfmwa = N*fa*wd - M*wa*fd
        nfmwd = fd*wd
        Qv = is_log_deriv_k_t_radical_in_field(N*fa*wd - M*wa*fd, fd*wd, DE,
            'auto')
        if Qv is None:
            # (N*f - M*w) is not the logarithmic derivative of a k(t)-radical.
            return None

        Q, e, v = Qv
        if e != 1:
            return None

        if Q.is_zero or v.is_zero:
            return None

        return (Q*N, Q*M, v)

    if p.degree(DE.t) > B:
        return None

    c = lcm(fd.as_poly(DE.t).LC(), wd.as_poly(DE.t).LC())
    l = fd.monic().lcm(wd.monic())*Poly(c, DE.t)
    ln, ls = splitfactor(l, DE)
    z = ls*ln.gcd(ln.diff(DE.t))

    if not z.has(DE.t):
        raise NotImplementedError("parametric_log_deriv_heu() "
            "heuristic failed: z in k.")

    u1, r1 = (fa*l.quo(fd)).div(z)  # (l*f).div(z)
    u2, r2 = (wa*l.quo(wd)).div(z)  # (l*w).div(z)

    eqs = [r1.nth(i) - c1*r2.nth(i) for i in range(z.degree(DE.t))]
    s = solve(eqs, c1)
    if not s or not s[c1].is_Rational:
        # deg(q) <= B, no solution for c.
        return None

    M, N = s[c1].as_numer_denom()

    nfmwa = N.as_poly(DE.t)*fa*wd - M.as_poly(DE.t)*wa*fd
    nfmwd = fd*wd
    Qv = is_log_deriv_k_t_radical_in_field(nfmwa, nfmwd, DE)
    if Qv is None:
        # (N*f - M*w) is not the logarithmic derivative of a k(t)-radical.
        return None

    Q, v = Qv

    if Q.is_zero or v.is_zero:
        return None

    return (Q*N, Q*M, v)
Parametric logarithmic derivative heuristic.
dataset/ETHPy150Open sympy/sympy/sympy/integrals/prde.py/parametric_log_deriv_heu