# Revision history [back]

### 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.<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

### 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] [2,3,5,7,11,13,17,19]101 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

### 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]101 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()

010


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

### 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 did

101101
 

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()

010


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

### 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

101


d = [2,3,5,7,11,13,17,19] [2,3,5,7,11,13,17,19]

K.<y> = NumberField([x^2 - di for di in d], maximize_at_primes=[2]) maximize_at_primes=[2])

RR = K.maximal_order()

010


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

### 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

101


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()

010


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:

101


R<x> := PolynomialRing(Integers()); 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); 19]:Abs);

O := MaximalOrder(K: Ramification := [2]);

010


Am I doing something wrong ?

JF Biasse

### 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

101


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()

010


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:

101


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]);

010


Am I doing something wrong ?

JF Biasse

### 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

101
d = [2,3,5,7,11,13,17,19]


d = [2,3,5,7,11,13,17,19]

K.<y> = NumberField([x^2 - di for di in d], maximize_at_primes=[2])

maximize_at_primes=[2]) RR = K.maximal_order()

010


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:

101


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]);

010


Am I doing something wrong ?

JF Biasse

### 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.<y> = NumberField([x^2 - di for di in d], maximize_at_primes=[2])
RR = K.maximal_order()

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:

101


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]);

010


Am I doing something wrong ?

JF Biasse

### 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.<y> = NumberField([x^2 - di for di in d], maximize_at_primes=[2])
RR = K.maximal_order()

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:

101


R<x> := PolynomialRing(Integers());

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);

19]:Abs); O := MaximalOrder(K: Ramification := [2]);

010
[2]);


Am I doing something wrong ?

JF Biasse