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│ Sage Version 6.0, Release Date: 2013-12-17                         │
│ Type "notebook()" for the browser-based notebook interface.        │
│ Type "help()" for help.                                            │
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sage: 
sage: K=CyclotomicField(23, 'z')
sage: z=K.gen()
sage: K.factor(2)
(Fractional ideal (2, z^11 + z^9 + z^7 + z^6 + z^5 + z + 1)) * (Fractional ideal (2, z^11 + z^10 + z^6 + z^5 + z^4 + z^2 + 1))
sage: I=K.factor(2)[0][0]
sage: I
Fractional ideal (2, z^11 + z^9 + z^7 + z^6 + z^5 + z + 1)
sage: 1/I
Fractional ideal (1, 1/2*z^11 + 1/2*z^10 + 1/2*z^6 + 1/2*z^5 + 1/2*z^4 + 1/2*z^2 + 1/2)
sage: K.fractional_ideal([2, z^11 + z^9 + z^7 + z^6 + z^5 + z + 1])
Fractional ideal (2, z^11 + z^9 + z^7 + z^6 + z^5 + z + 1)
sage: list(K.factor(2))
[(Fractional ideal (2, z^11 + z^9 + z^7 + z^6 + z^5 + z + 1), 1),
 (Fractional ideal (2, z^11 + z^10 + z^6 + z^5 + z^4 + z^2 + 1), 1)]
sage: K.factor?
sage: