def as_terms(self):
        """Transform an expression to a list of terms. """
        from sympy.core import Add, Mul, S
        from sympy.core.exprtools import decompose_power

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

        for term in Add.make_args(self):
            coeff, _term = term.as_coeff_Mul()

            coeff = complex(coeff)
            cpart, ncpart = {}, []

            if _term is not S.One:
                for factor in Mul.make_args(_term):
                    if factor.is_number:
                        try:
                            coeff *= complex(factor)
                        except ValueError:
                            pass
                        else:
                            continue

                    if factor.is_commutative:
                        base, exp = decompose_power(factor)

                        cpart[base] = exp
                        gens.add(base)
                    else:
                        ncpart.append(factor)

            coeff = coeff.real, coeff.imag
            ncpart = tuple(ncpart)

            terms.append((term, (coeff, cpart, ncpart)))

        gens = sorted(gens, key=Basic.sorted_key)

        k, indices = len(gens), {}

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

        result = []

        for term, (coeff, cpart, ncpart) in terms:
            monom = [0]*k

            for base, exp in cpart.iteritems():
                monom[indices[base]] = exp

            result.append((term, (coeff, tuple(monom), ncpart)))

        return result, gens

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 KeyError:
                        if not factor.free_symbols.intersection(opt.gens):
                            coeff.append(factor)
                        else:
                            raise PolynomialError("%s contains an element of "
                                                  "the set of generators." % factor)

            monom = tuple(monom)

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

        polys.append(poly)

    return polys, opt.gens

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 = {}

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

            for factor in Mul.make_args(term):
                if factor.is_Number:
                    coeff.append(factor)
                else:
                    try:
                        base, exp = decompose_power(factor)

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

                        monom[indices[base]] = exp
                    except KeyError:
                        if not factor.has(*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

def test_decompose_power():
    assert decompose_power(x) == (x, 1)
    assert decompose_power(x**2) == (x, 2)
    assert decompose_power(x**(2*y)) == (x**y, 2)
    assert decompose_power(x**(2*y/3)) == (x**(y/3), 2)

def _parallel_dict_from_expr_no_gens(exprs, opt):
    """Transform expressions into a multinomial form and figure out generators. """
    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] = 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)