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

7.2. USING MAGMA 47
> OK := MaximalOrder(K);
> I := 7*OK;
> J := (OK!a)*OK;
> M := I/J;
> M;
Fractional Principal Ideal of OK
Generator:
-7/5*OK.1 + 14/5*OK.2
> Factorization(M);
[
,
]
In the next chapter, we will learn about discriminants and an algorithm for
“factoring primes”, that is writing an ideal pOK as a product of prime ideals of OK.