(f, *gens, **args)
Compute the factorization of expression, ``f``, into irreducibles. (To
    factor an integer into primes, use ``factorint``.)

    There two modes implemented: symbolic and formal. If ``f`` is not an
    instance of :class:`Poly` and generators are not specified, then the
    former mode is used. Otherwise, the formal mode is used.

    In symbolic mode, :func:`factor` will traverse the expression tree and
    factor its components without any prior expansion, unless an instance
    of :class:`Add` is encountered (in this case formal factorization is
    used). This way :func:`factor` can handle large or symbolic exponents.

    By default, the factorization is computed over the rationals. To factor
    over other domain, e.g. an algebraic or finite field, use appropriate
    options: ``extension``, ``modulus`` or ``domain``.

    Examples
    ========

    >>> from sympy import factor, sqrt
    >>> from sympy.abc import x, y

    >>> factor(2*x**5 + 2*x**4*y + 4*x**3 + 4*x**2*y + 2*x + 2*y)
    2*(x + y)*(x**2 + 1)**2

    >>> factor(x**2 + 1)
    x**2 + 1
    >>> factor(x**2 + 1, modulus=2)
    (x + 1)**2
    >>> factor(x**2 + 1, gaussian=True)
    (x - I)*(x + I)

    >>> factor(x**2 - 2, extension=sqrt(2))
    (x - sqrt(2))*(x + sqrt(2))

    >>> factor((x**2 - 1)/(x**2 + 4*x + 4))
    (x - 1)*(x + 1)/(x + 2)**2
    >>> factor((x**2 + 4*x + 4)**10000000*(x**2 + 1))
    (x + 2)**20000000*(x**2 + 1)

    By default, factor deals with an expression as a whole:

    >>> eq = 2**(x**2 + 2*x + 1)
    >>> factor(eq)
    2**(x**2 + 2*x + 1)

    If the ``deep`` flag is True then subexpressions will
    be factored:

    >>> factor(eq, deep=True)
    2**((x + 1)**2)

    See Also
    ========
    sympy.ntheory.factor_.factorint
Compute the factorization of expression, ``f``, into irreducibles. (To
    factor an integer into primes, use ``factorint``.)
Compute the factorization of expression f into irreducibles . ( To factor an integer into primes use factorint . )
def factor(f, *gens, **args):
    """
    Compute the factorization of expression, ``f``, into irreducibles. (To
    factor an integer into primes, use ``factorint``.)

    There two modes implemented: symbolic and formal. If ``f`` is not an
    instance of :class:`Poly` and generators are not specified, then the
    former mode is used. Otherwise, the formal mode is used.

    In symbolic mode, :func:`factor` will traverse the expression tree and
    factor its components without any prior expansion, unless an instance
    of :class:`Add` is encountered (in this case formal factorization is
    used). This way :func:`factor` can handle large or symbolic exponents.

    By default, the factorization is computed over the rationals. To factor
    over other domain, e.g. an algebraic or finite field, use appropriate
    options: ``extension``, ``modulus`` or ``domain``.

    Examples
    ========

    >>> from sympy import factor, sqrt
    >>> from sympy.abc import x, y

    >>> factor(2*x**5 + 2*x**4*y + 4*x**3 + 4*x**2*y + 2*x + 2*y)
    2*(x + y)*(x**2 + 1)**2

    >>> factor(x**2 + 1)
    x**2 + 1
    >>> factor(x**2 + 1, modulus=2)
    (x + 1)**2
    >>> factor(x**2 + 1, gaussian=True)
    (x - I)*(x + I)

    >>> factor(x**2 - 2, extension=sqrt(2))
    (x - sqrt(2))*(x + sqrt(2))

    >>> factor((x**2 - 1)/(x**2 + 4*x + 4))
    (x - 1)*(x + 1)/(x + 2)**2
    >>> factor((x**2 + 4*x + 4)**10000000*(x**2 + 1))
    (x + 2)**20000000*(x**2 + 1)

    By default, factor deals with an expression as a whole:

    >>> eq = 2**(x**2 + 2*x + 1)
    >>> factor(eq)
    2**(x**2 + 2*x + 1)

    If the ``deep`` flag is True then subexpressions will
    be factored:

    >>> factor(eq, deep=True)
    2**((x + 1)**2)

    See Also
    ========
    sympy.ntheory.factor_.factorint

    """
    f = sympify(f)
    if args.pop('deep', False):
        partials = {}
        muladd = f.atoms(Mul, Add)
        for p in muladd:
            fac = factor(p, *gens, **args)
            if (fac.is_Mul or fac.is_Pow) and fac != p:
                partials[p] = fac
        return f.xreplace(partials)

    try:
        return _generic_factor(f, gens, args, method='factor')
    except PolynomialError as msg:
        if not f.is_commutative:
            from sympy.core.exprtools import factor_nc
            return factor_nc(f)
        else:
            raise PolynomialError(msg)
def factor ( f , * gens , * * args ) : f = sympify ( f ) if args . pop ( 'deep' , False ) : partials = { } muladd = f . atoms ( Mul , Add ) for p in muladd : fac = factor ( p , * gens , * * args ) if ( fac . is_Mul or fac . is_Pow ) and fac != p : partials [ p ] = fac return f . xreplace ( partials ) try : return _generic_factor ( f , gens , args , method = 'factor' ) except PolynomialError as msg : if not f . is_commutative : from sympy . core . exprtools import factor_nc return factor_nc ( f ) else : raise PolynomialError ( msg )