I'd like to factor an ideal in a number field into prime ideals, exactly as in this example from the Sage documentation:
sage: K.<a> = NumberField(x^4 + 23); K Number Field in a with defining polynomial x^4 + 23 sage: I = K.ideal(19); I Fractional ideal (19) sage: F = I.factor(); F (Fractional ideal (19, 1/2*a^2 + a - 17/2)) * (Fractional ideal (19, 1/2*a^2 - a - 17/2))
What is the easiest way to achieve this in Mathematica?
It doesn't seem there is any built-in functionality for this. Is there are package available that I'm not seeing? Or should I just call PARI, via mathlink or a shell?