A Brief Introduction to Classical and Adelic Algebraic ... - William Stein

46 CHAPTER 7. COMPUTING
[-7, 14]
> J*I;
Principal Ideal of OK
Generator:
[-7, 14]
> I+J;
Principal Ideal of OK
Generator:
[1, 0]
>
> Factorization(I);
[
]
> Factorization(3*OK);
[
]
> Factorization(5*OK);
[
]
> Factorization(11*OK);
[
,
]
We can even work with fractional ideals in Magma.
> K := NumberField(x^2-5);