def _parallel_dict_from_expr_no_gens(exprs, opt):
    if opt.domain is not None:
        def _is_coeff(factor):
            return factor in opt.domain
    elif opt.extension is True:
        def _is_coeff(factor):
            return factor.is_algebraic
    elif opt.greedy is not False:
        def _is_coeff(factor):
            return False
    else:
        def _is_coeff(factor):
            return factor.is_number

    gens, reprs = set([]), []

    for expr in exprs:
        terms = []

        if expr.is_Equality:
            expr = expr.lhs - expr.rhs

        for term in Add.make_args(expr):
            coeff, elements = [], {}

            for factor in Mul.make_args(term):
                if not _not_a_coeff(factor) and (factor.is_Number or _is_coeff(factor)):
                    coeff.append(factor)
                else:
                    if opt.series is False:
                        base, exp = decompose_power(factor)

                        if exp < 0:
                            exp, base = -exp, Pow(base, -S.One)
                    else:
                        base, exp = decompose_power_rat(factor)

                    elements[base] = elements.setdefault(base, 0) + exp
                    gens.add(base)

            terms.append((coeff, elements))

        reprs.append(terms)

    if not gens:
        if len(exprs) == 1:
            arg = exprs[0]
        else:
            arg = (exprs,)

        raise GeneratorsNeeded("specify generators to give %s a meaning" % arg)

    gens = _sort_gens(gens, opt=opt)
    k, indices = len(gens), {}

    for i, g in enumerate(gens):
        indices[g] = i

    polys = []

    for terms in reprs:
        poly = {}

        for coeff, term in terms:
            monom = [0]*k

            for base, exp in term.items():
                monom[indices[base]] = exp

            monom = tuple(monom)

            if monom in poly:
                poly[monom] += Mul(*coeff)
            else:
                poly[monom] = Mul(*coeff)

        polys.append(poly)

    return polys, tuple(gens)
Transform expressions into a multinomial form and figure out generators.
dataset/ETHPy150Open sympy/sympy/sympy/polys/polyutils.py/_parallel_dict_from_expr_no_gens