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 | 1 | initial version |
Is this what you are looking for?
Define the number fields and their rings of integers.
sage: K.<a> = NumberField(x^2+5)
sage: L.<i> = K.extension(x^2+1)
sage: OK = K.ring_of_integers()
sage: OL = L.ring_of_integers()
Define the ideals generated by 2 and by a+1.
sage: J = OL.principal_ideal(2)
sage: JJ = OL.principal_ideal(a + 1)
Take the sum.
sage: J + JJ
Fractional ideal (-i + 1)
| | 2 | No.2 Revision |
Is this what you are looking for?
Define the number fields and their rings of integers.
sage: K.<a> = NumberField(x^2+5)
sage: L.<i> = K.extension(x^2+1)
sage: OK = K.ring_of_integers()
sage: OL = L.ring_of_integers()
Define the ideals generated by 2 and by a+1.
sage: J = OL.principal_ideal(2)
sage: JJ = OL.principal_ideal(a + 1)
Take the sum.
sage: H = J + JJ
JJ; H
Fractional ideal (-i + 1)
Prime factors.
sage: H.prime_factors()
[Fractional ideal (-i + 1)]
sage: H.is_prime()
True
