human
Complete this python program:
def TR2i(rv, half=False):
assistant
#Here is the Python code you requested.

    """Converts ratios involving sin and cos as follows::
    sin(x)/cos(x) -> tan(x)
    sin(x)/(cos(x) + 1) -> tan(x/2) if half=True
    Examples
    >>> from sympy.simplify.fu import TR2i
    >>> from sympy.abc import x, a
    >>> from sympy import sin, cos
    >>> TR2i(sin(x)/cos(x))
    tan(x)
    Powers of the numerator and denominator are also recognized
    >>> TR2i(sin(x)**2/(cos(x) + 1)**2, half=True)
    tan(x/2)**2
    The transformation does not take place unless assumptions allow
    (i.e. the base must be positive or the exponent must be an integer
    for both numerator and denominator)
    >>> TR2i(sin(x)**a/(cos(x) + 1)**a)
    (cos(x) + 1)**(-a)*sin(x)**a
    """
    def f(rv):
        if (not rv.is_Mul):
            return rv
        (n, d) = rv.as_numer_denom()
        if (n.is_Atom or d.is_Atom):
            return rv
        def ok(k, e):
            return ((e.is_integer or k.is_positive) and ((k.func in (sin, cos)) or (half and k.is_Add and (len(k.args) >= 2) and any((any((((ai.func is cos) or (ai.is_Pow and (ai.base is cos))) for ai in Mul.make_args(a))) for a in k.args)))))
        n = n.as_powers_dict()
        ndone = [(k, n.pop(k)) for k in list(n.keys()) if (not ok(k, n[k]))]
        if (not n):
            return rv
        d = d.as_powers_dict()
        ddone = [(k, d.pop(k)) for k in list(d.keys()) if (not ok(k, d[k]))]
        if (not d):
            return rv
        def factorize(d, ddone):
            newk = []
            for k in d:
                if (k.is_Add and (len(k.args) > 1)):
                    knew = (factor(k) if half else factor_terms(k))
                    if (knew != k):
                        newk.append((k, knew))
            if newk:
                for (i, (k, knew)) in enumerate(newk):
                    del d[k]
                    newk[i] = knew
                newk = Mul(*newk).as_powers_dict()
                for k in newk:
                    v = (d[k] + newk[k])
                    if ok(k, v):
                        d[k] = v
                    else:
                        ddone.append((k, v))
                del newk
        factorize(n, ndone)
        factorize(d, ddone)
        t = []
        for k in n:
            if (k.func is sin):
                a = cos(k.args[0], evaluate=False)
                if ((a in d) and (d[a] == n[k])):
                    t.append((tan(k.args[0]) ** n[k]))
                    n[k] = d[a] = None
                elif half:
                    a1 = (1 + a)
                    if ((a1 in d) and (d[a1] == n[k])):
                        t.append((tan((k.args[0] / 2)) ** n[k]))
                        n[k] = d[a1] = None
            elif (k.func is cos):
                a =...