human
What is a Python code to compute    all    monomials    with    degree    less    than    ``n``    that    are\n                                not    divisible    by    any    element    of    ``leading_monomials`` given the following:
I wrote the below code

    from sympy import solve
    quick = args.pop('quick', True)
    polynomial = args.pop('polynomial', False)
    debug('ratsimpmodprime', expr)
    (num, denom) = cancel(expr).as_numer_denom()
    try:
        (polys, opt) = parallel_poly_from_expr(([num, denom] + G), *gens, **args)
    except PolificationFailed:
        return expr
    domain = opt.domain
    if domain.has_assoc_Field:
        opt.domain = domain.get_field()
    else:
        raise DomainError(("can't    compute    rational    simplification    over    %s" % domain))
    leading_monomials = [g.LM(opt.order) for g in polys[2:]]
    tested = set()
    def staircase(n):
        '\n                                Compute    all    monomials    with    degree    less    than    ``n``    that    are\n                                not    divisible    by    any    element    of    ``leading_monomials``.\n                                '
        if (n == 0):
            return [1]
        S = []
        for mi in combinations_with_replacement(range(len(opt.gens)), n):
            m = ([0] * len(opt.gens))
            for i in mi:
                m[i] += 1
            if all([(monomial_div(m, lmg) is None) for lmg in leading_monomials]):
                S.append(m)
        return ([Monomial(s).as_expr(*opt.gens) for s in S] + staircase((n - 1)))
    def _ratsimpmodprime(a, b, allsol, N=0, D=0):
        '\n                                Computes    a    rational    simplification    of    ``a/b``    which    minimizes\n                                the    sum    of    the    total    degrees    of    the    numerator    and    the    denominator.\n\n                                The    algorithm    proceeds    by    looking    at    ``a    *    d    -    b    *    c``    modulo\n                                the    ideal    generated    by    ``G``    for    some    ``c``    and    ``d``    with    degree\n                                less    than    ``a``    and    ``b``    respectively.\n                                The   ...

What's a good function header?
assistant
#Here is Python code to compute    all    monomials    with    degree    less    than    ``n``    that    are\n                                not    divisible    by    any    element    of    ``leading_monomials``.

def ratsimpmodprime(expr, G, *gens, **args):