I would like to calculate the maximal order of a field for which I already know at which primes we should maximize.

This means that the discriminant does not have to be factored, which is normally the bottleneck of this algorithm.

I did d = [2,3,5,7,11,13,17,19] K.<y> = NumberField([x^2 - di for di in d], maximize_at_primes=[2]) RR = K.maximal_order()

The last command did not finish overnight, but gave the following warning:
"*** Warning: MPQS: number too big to be factored with MPQS,
giving up."
Which seems to indicate that the program is indeed trying to perform a large factorization despite the command "maximize_at_primes=[2]"

Meanwhile, Magma has no problem performing this computation in a few hours: R<x> := PolynomialRing(Integers()); K := NumberField([x^2 - 2,x^2 - 3 , x^2-5,x^2-7,x^2 - 11,x^2 - 13 , x^2 - 17 , x^2 - 19]:Abs); O := MaximalOrder(K: Ramification := [2]);

Am I doing something wrong ?

JF Biasse