2018-01-18 23:45:35 -0500 received badge ● Good Question (source) 2018-01-18 13:44:36 -0500 received badge ● Editor (source) 2018-01-18 09:46:39 -0500 received badge ● Nice Question (source) 2018-01-18 09:06:58 -0500 received badge ● Student (source) 2018-01-18 09:05:08 -0500 asked a question Calculation of maximal order fails even when using "maximize_at_primes" 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. = NumberField([x^2 - di for di in d], maximize_at_primes=) 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=" Meanwhile, Magma has no problem performing this computation in a few hours: R := 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 := );  Am I doing something wrong ? JF Biasse