def _dmp_rr_trivial_gcd(f, g, u, K):
    """Handle trivial cases in GCD algorithm over a ring. """
    zero_f = dmp_zero_p(f, u)
    zero_g = dmp_zero_p(g, u)
    if_contain_one = dmp_one_p(f, u, K) or dmp_one_p(g, u, K)

    if zero_f or zero_g:
        return tuple(dmp_zeros(3, u, K))
    elif zero_f:
        if K.is_nonnegative(dmp_ground_LC(g, u, K)):
            return g, dmp_zero(u), dmp_one(u, K)
        else:
            return dmp_neg(g, u, K), dmp_zero(u), dmp_ground(-K.one, u)
    elif zero_g:
        if K.is_nonnegative(dmp_ground_LC(f, u, K)):
            return f, dmp_one(u, K), dmp_zero(u)
        else:
            return dmp_neg(f, u, K), dmp_ground(-K.one, u), dmp_zero(u)
    elif if_contain_one:
        return dmp_one(u, K), f, g
    elif query('USE_SIMPLIFY_GCD'):
        return _dmp_simplify_gcd(f, g, u, K)
    else:
        return None
dataset/ETHPy150Open sympy/sympy/sympy/polys/euclidtools.py/_dmp_rr_trivial_gcd/operator `and` -> `or`