ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 19 Jan 2018 22:28:45 -0600Calculation of maximal order fails even when using "maximize_at_primes"http://ask.sagemath.org/question/40677/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 BiasseThu, 18 Jan 2018 08:58:26 -0600http://ask.sagemath.org/question/40677/calculation-of-maximal-order-fails-even-when-using-maximize_at_primes/Comment by dan_fulea for <p>I would like to calculate the maximal order of a field for which I already know at which primes we should maximize. </p>
<p>This means that the discriminant does not have to be factored, which is normally the bottleneck of this algorithm. </p>
<p>I did</p>
<pre><code>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()
</code></pre>
<p>The last command did not finish overnight, but gave the following warning: </p>
<pre><code>"*** Warning: MPQS: number too big to be factored with MPQS,
giving up."
</code></pre>
<p>Which seems to indicate that the program is indeed trying to perform a large factorization despite the command "maximize_at_primes=[2]"</p>
<p>Meanwhile, Magma has no problem performing this computation in a few hours: </p>
<pre><code>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]);
</code></pre>
<p>Am I doing something wrong ? </p>
<p>JF Biasse</p>
http://ask.sagemath.org/question/40677/calculation-of-maximal-order-fails-even-when-using-maximize_at_primes/?comment=40706#post-id-40706It works with
dList = [2, 3, 5, 7, 11, 13, 17, ] # 19 ]
R.<x> = QQ[x]
K.<y> = NumberField( [x^2 - d for d in dList], maximize_at_primes=[2] )
OK = K.maximal_order()
but...
*** Warning: increasing stack size to 32000000.
verbose 1 (6543: free_module.py, multimod echelon) Multimodular echelon algorithm on 128 x 128 matrix
verbose 2 (6543: free_module.py, multimod echelon) height_guess = 2076385617243711727353355782311411899772372408038309933386259999677333955016854228620026448792887828786397991320445399766866678950732790947545067887986660268471278769895143492372467042027529879207196673345345584512908590113904289000422474215540912881...
and there are many other digits (totally 423).
Adding the 19 in the `dList` seems to be too much for the resources here.Fri, 19 Jan 2018 22:28:45 -0600http://ask.sagemath.org/question/40677/calculation-of-maximal-order-fails-even-when-using-maximize_at_primes/?comment=40706#post-id-40706