(ex, pw, x, dom, mp=None)
return res.as_expr()
Returns ``minpoly(ex**pw, x)``

    Parameters
    ==========

    ex : algebraic element
    pw : rational number
    x : indeterminate of the polynomial
    dom: ground domain
    mp : minimal polynomial of ``p``

    Examples
    ========

    >>> from sympy import sqrt, QQ, Rational
    >>> from sympy.polys.numberfields import _minpoly_pow, minpoly
    >>> from sympy.abc import x, y
    >>> p = sqrt(1 + sqrt(2))
    >>> _minpoly_pow(p, 2, x, QQ)
    x**2 - 2*x - 1
    >>> minpoly(p**2, x)
    x**2 - 2*x - 1
    >>> _minpoly_pow(y, Rational(1, 3), x, QQ.frac_field(y))
    x**3 - y
    >>> minpoly(y**Rational(1, 3), x)
    x**3 - y
Returns ``minpoly(ex**pw, x)``
Returns minpoly ( ex ** pw x )
def _minpoly_pow(ex, pw, x, dom, mp=None):
    """
    Returns ``minpoly(ex**pw, x)``

    Parameters
    ==========

    ex : algebraic element
    pw : rational number
    x : indeterminate of the polynomial
    dom: ground domain
    mp : minimal polynomial of ``p``

    Examples
    ========

    >>> from sympy import sqrt, QQ, Rational
    >>> from sympy.polys.numberfields import _minpoly_pow, minpoly
    >>> from sympy.abc import x, y
    >>> p = sqrt(1 + sqrt(2))
    >>> _minpoly_pow(p, 2, x, QQ)
    x**2 - 2*x - 1
    >>> minpoly(p**2, x)
    x**2 - 2*x - 1
    >>> _minpoly_pow(y, Rational(1, 3), x, QQ.frac_field(y))
    x**3 - y
    >>> minpoly(y**Rational(1, 3), x)
    x**3 - y

    """
    pw = sympify(pw)
    if not mp:
        mp = _minpoly_compose(ex, x, dom)
    if not pw.is_rational:
        raise NotAlgebraic("%s doesn't seem to be an algebraic element" % ex)
    if pw < 0:
        if mp == x:
            raise ZeroDivisionError('%s is zero' % ex)
        mp = _invertx(mp, x)
        if pw == -1:
            return mp
        pw = -pw
        ex = 1/ex

    y = Dummy(str(x))
    mp = mp.subs({x: y})
    n, d = pw.as_numer_denom()
    res = Poly(resultant(mp, x**d - y**n, gens=[y]), x, domain=dom)
    _, factors = res.factor_list()
    res = _choose_factor(factors, x, ex**pw, dom)
    return res.as_expr()
def _minpoly_pow ( ex , pw , x , dom , mp = None ) : pw = sympify ( pw ) if not mp : mp = _minpoly_compose ( ex , x , dom ) if not pw . is_rational : raise NotAlgebraic ( "%s doesn't seem to be an algebraic element" % ex ) if pw < 0 : if mp == x : raise ZeroDivisionError ( '%s is zero' % ex ) mp = _invertx ( mp , x ) if pw == - 1 : return mp pw = - pw ex = 1 / ex y = Dummy ( str ( x ) ) mp = mp . subs ( { x : y } ) n , d = pw . as_numer_denom ( ) res = Poly ( resultant ( mp , x ** d - y ** n , gens = [ y ] ) , x , domain = dom ) _ , factors = res . factor_list ( ) res = _choose_factor ( factors , x , ex ** pw , dom ) return res . as_expr ( )