def __pow__(self, n):
"""
Return the `n^{th}` power of a factorization, which is got by
combining together like factors.
EXAMPLES::
sage: f = factor(-100); f
-1 * 2^2 * 5^2
sage: f^3
-1 * 2^6 * 5^6
sage: f^4
2^8 * 5^8
sage: F = factor(2006); F
2 * 17 * 59
sage: F**2
2^2 * 17^2 * 59^2
sage: R.<x,y> = FreeAlgebra(ZZ, 2)
sage: F = Factorization([(x,3), (y, 2), (x,1)]); F
x^3 * y^2 * x
sage: F**2
x^3 * y^2 * x^4 * y^2 * x
"""
from sage.groups.generic import power
return power(self, n, Factorization([]))
def __pow__(self, n):
"""
Return the `n^{th}` power of a factorization, which is got by
combining together like factors.
EXAMPLES::
sage: f = factor(-100); f
-1 * 2^2 * 5^2
sage: f^3
-1 * 2^6 * 5^6
sage: f^4
2^8 * 5^8
sage: F = factor(2006); F
2 * 17 * 59
sage: F**2
2^2 * 17^2 * 59^2
sage: R.<x,y> = FreeAlgebra(ZZ, 2)
sage: F = Factorization([(x,3), (y, 2), (x,1)]); F
x^3 * y^2 * x
sage: F**2
x^3 * y^2 * x^4 * y^2 * x
"""
from sage.groups.generic import power
return power(self, n, Factorization([]))
def __pow__(self, n):
"""
Return the `n^{th}` power of a factorization, which is got by
combining together like factors.
EXAMPLES::
sage: f = factor(-100); f
-1 * 2^2 * 5^2
sage: f^3
-1 * 2^6 * 5^6
sage: f^4
2^8 * 5^8
sage: K.<a> = NumberField(x^3 - 39*x - 91)
sage: F = K.factor(7); F
(Fractional ideal (7, a)) * (Fractional ideal (7, a + 2)) * (Fractional ideal (7, a - 2))
sage: F^9
(Fractional ideal (7, a))^9 * (Fractional ideal (7, a + 2))^9 * (Fractional ideal (7, a - 2))^9
sage: R.<x,y> = FreeAlgebra(ZZ, 2)
sage: F = Factorization([(x,3), (y, 2), (x,1)]); F
x^3 * y^2 * x
sage: F**2
x^3 * y^2 * x^4 * y^2 * x
"""
if not isinstance(n, Integer):
try:
n = Integer(n)
except TypeError:
raise TypeError("Exponent n (= %s) must be an integer." % n)
if n == 1:
return self
if n == 0:
return Factorization([])
if self.is_commutative():
return Factorization([(p, n * e) for p, e in self],
unit=self.unit()**n,
cr=self.__cr,
sort=False,
simplify=False)
from sage.groups.generic import power
return power(self, n, Factorization([]))
def __pow__(self, n):
"""
Return the `n^{th}` power of a factorization, which is got by
combining together like factors.
EXAMPLES::
sage: f = factor(-100); f
-1 * 2^2 * 5^2
sage: f^3
-1 * 2^6 * 5^6
sage: f^4
2^8 * 5^8
sage: K.<a> = NumberField(x^3 - 39*x - 91)
sage: F = K.factor(7); F
(Fractional ideal (7, a)) * (Fractional ideal (7, a + 2)) * (Fractional ideal (7, a - 2))
sage: F^9
(Fractional ideal (7, a))^9 * (Fractional ideal (7, a + 2))^9 * (Fractional ideal (7, a - 2))^9
sage: R.<x,y> = FreeAlgebra(ZZ, 2)
sage: F = Factorization([(x,3), (y, 2), (x,1)]); F
x^3 * y^2 * x
sage: F**2
x^3 * y^2 * x^4 * y^2 * x
"""
if not isinstance(n, Integer):
try:
n = Integer(n)
except TypeError:
raise TypeError("Exponent n (= %s) must be an integer." % n)
if n == 1:
return self
if n == 0:
return Factorization([])
if self.is_commutative():
return Factorization(
[(p, n * e) for p, e in self], unit=self.unit() ** n, cr=self.__cr, sort=False, simplify=False
)
from sage.groups.generic import power
return power(self, n, Factorization([]))