human
Complete the below
@public
def roots(f, *gens, **flags):

    ''''Computes symbolic roots of a univariate polynomial.
    Given a univariate polynomial f with symbolic coefficients (or
    a list of the polynomial\'s coefficients), returns a dictionary
    with its roots and their multiplicities.
    Only roots expressible via radicals will be returned.  To get
    a complete set of roots use RootOf class or numerical methods
    instead. By default cubic and quartic formulas are used in
    the algorithm. To disable them because of unreadable output
    set ``cubics=False`` or ``quartics=False`` respectively. If cubic
    roots are real but are expressed in terms of complex numbers
    (casus irreducibilis [1]) the ``trig`` flag can be set to True to
    have the solutions returned in terms of cosine and inverse cosine
    functions.
    To get roots from a specific domain set the ``filter`` flag with
    one of the following specifiers: Z, Q, R, I, C. By default all
    roots are returned (this is equivalent to setting ``filter=\'C\'``).
    By default a dictionary is returned giving a compact result in
    case of multiple roots.  However to get a list containing all
    those roots set the ``multiple`` flag to True.
the list will
    have identical roots appearing next to each other in the result.
    (For a given Poly, the all_roots method will give the roots in
    sorted numerical order.)
    Examples
    >>> from sympy import Poly, roots
    >>> from sympy.abc import x, y
    >>> roots(x**2 - 1, x)
    {-1: 1, 1: 1}
    >>> p = Poly(x**2-1, x)
    >>> roots(p)
    {-1: 1, 1: 1}
    >>> p = Poly(x**2-y, x, y)
    >>> roots(Poly(p, x))
    {-sqrt(y): 1, sqrt(y): 1}
    >>> roots(x**2 - y, x)
    {-sqrt(y): 1, sqrt(y): 1}
    >>> roots([1, 0, -1])
    {-1: 1, 1: 1}
    References
    1. http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method'
    '''
 Give me a the Python code you requested?
assistant
#Here is the Python code you requested.
    from sympy.polys.polytools import to_rational_coeffs
    flags = dict(flags)
    auto = flags.pop('auto', True)
    cubics = flags.pop('cubics', True)
    trig = flags.pop('trig', False)
    quartics = flags.pop('quartics', True)
    quintics = flags.pop('quintics', False)
    multiple = flags.pop('multiple', False)
    filter = flags.pop('filter', None)
    predicate = flags.pop('predicate', None)
    if isinstance(f, list):
        if gens:
            raise ValueError('redundant    generators    given')
        x = Dummy('x')
        (poly, i) = ({}, (len(f) - 1))
        for coeff in f:
            (poly[i], i) = (sympify(coeff), (i - 1))
        f = Poly(poly, x, field=True)
    else:
        try:
            f = Poly(f, *gens, **flags)
            if ((f.length == 2) and (f.degree() != 1)):
                n = f.degree()
                npow_bases = []
                expr = f.as_expr()
                con = expr.as_independent(*gens)[0]
                for p in Mul.make_args(con):
                    if (p.is_Pow and (not (p.exp % n))):
                        npow_bases.append((p.base ** (p.exp / n)))
                    else:
                        other.append(p)
                    if npow_bases:
                        b = Mul(*npow_bases)
                        B = Dummy()
                        d = roots(Poly(((expr - con) + ((B ** n) * Mul(*others))), *gens, **flags), *gens, **flags)
                        rv = {}
                        for (k, v) in d.items():
                            rv[k.subs(B, b)] = v
                        return rv
        except GeneratorsNeeded:
            if multiple:
                return []
            else:
                return {}
        if f.is_multivariate:
            raise PolynomialError('multivariate    polynomials    are    not    supported')
    def _update_dict(result, root, k):
        if (root in result):
            result[root] += k
        else:
            result[root] = k
    def _try_decompose(f):
        'Find    roots    using  ...