def _parallel_dict_from_expr_if_gens(exprs, opt):
    """Transform expressions into a multinomial form given generators. """
    k, indices = len(opt.gens), {}

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

    polys = []

    for expr in exprs:
        poly = {}

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

        for term in Add.make_args(expr):
            coeff, monom = [], [0]*k

            for factor in Mul.make_args(term):
                if not _not_a_coeff(factor) and factor.is_Number:
                    coeff.append(factor)
                else:
                    try:
                        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)

                        monom[indices[base]] = exp
                    except __HOLE__:
                        if not factor.free_symbols.intersection(opt.gens):
                            coeff.append(factor)
                        else:
                            raise PolynomialError("%s contains an element of the generators set" % factor)

            monom = tuple(monom)

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

        polys.append(poly)

    return polys, opt.gens
dataset/ETHPy150Open sympy/sympy/sympy/polys/polyutils.py/_parallel_dict_from_expr_if_gens