(x, s, p, f)
return linear_congruence(alpha, beta, p)
Used in gf_csolve to generate solutions of f(x) cong 0 mod(p**(s + 1))
    from the solutions of f(x) cong 0 mod(p**s).

    Examples
    ========

    >>> from sympy.polys.galoistools import _raise_mod_power
    >>> from sympy.polys.galoistools import csolve_prime

    These is the solutions of f(x) = x**2 + x + 7 cong 0 mod(3)

    >>> f = [1, 1, 7]
    >>> csolve_prime(f, 3)
    [1]
    >>> [ i for i in range(3) if not (i**2 + i + 7) % 3]
    [1]

    The solutions of f(x) cong 0 mod(9) are constructed from the
    values returned from _raise_mod_power:

    >>> x, s, p = 1, 1, 3
    >>> V = _raise_mod_power(x, s, p, f)
    >>> [x + v * p**s for v in V]
    [1, 4, 7]

    And these are confirmed with the following:

    >>> [ i for i in range(3**2) if not (i**2 + i + 7) % 3**2]
    [1, 4, 7]
Used in gf_csolve to generate solutions of f(x) cong 0 mod(p**(s + 1))
    from the solutions of f(x) cong 0 mod(p**s).
Used in gf_csolve to generate solutions of f ( x ) cong 0 mod ( p ** ( s + 1 )) from the solutions of f ( x ) cong 0 mod ( p ** s ) .
def _raise_mod_power(x, s, p, f):
    """
    Used in gf_csolve to generate solutions of f(x) cong 0 mod(p**(s + 1))
    from the solutions of f(x) cong 0 mod(p**s).

    Examples
    ========

    >>> from sympy.polys.galoistools import _raise_mod_power
    >>> from sympy.polys.galoistools import csolve_prime

    These is the solutions of f(x) = x**2 + x + 7 cong 0 mod(3)

    >>> f = [1, 1, 7]
    >>> csolve_prime(f, 3)
    [1]
    >>> [ i for i in range(3) if not (i**2 + i + 7) % 3]
    [1]

    The solutions of f(x) cong 0 mod(9) are constructed from the
    values returned from _raise_mod_power:

    >>> x, s, p = 1, 1, 3
    >>> V = _raise_mod_power(x, s, p, f)
    >>> [x + v * p**s for v in V]
    [1, 4, 7]

    And these are confirmed with the following:

    >>> [ i for i in range(3**2) if not (i**2 + i + 7) % 3**2]
    [1, 4, 7]

    """
    from sympy.polys.domains import ZZ
    f_f = gf_diff(f, p, ZZ)
    alpha = gf_value(f_f, x)
    beta = - gf_value(f, x) // p**s
    return linear_congruence(alpha, beta, p)
def _raise_mod_power ( x , s , p , f ) : from sympy . polys . domains import ZZ f_f = gf_diff ( f , p , ZZ ) alpha = gf_value ( f_f , x ) beta = - gf_value ( f , x ) // p ** s return linear_congruence ( alpha , beta , p )