Q1. = NumberField(x^3- 2);Q1; Q2.= CyclotomicField(3);Q2; Q3.<c> = Q2.extension(x^3 - 2);Q3;
Q3.absolute_polynomial();
G=Q3.galois_group();G; G.number_field();Q 1.is_galois(); Q2.is_galois();
G2=Q2.galois_group('pari');G2; G1.<m>=Q1.galois_group('pari');G1;
Traceback (click to the left of this block for traceback) ... AttributeError: 'GaloisGroup_v1' object has no attribute '_first_ngens'
This code works fine:
sage: Q1.<a> = NumberField(x^3- 2)
sage: Q1
Number Field in a with defining polynomial x^3 - 2
sage: G1=Q1.galois_group('pari')
sage: G1
Galois group PARI group [6, -1, 2, "S3"] of degree 3 of the Number Field in a with defining polynomial x^3 - 2
The other fields do not play a role in your error. Your mistake is to have written
sage: G1.<m>=Q1.galois_group('pari')
since the syntax where you put ".<m>" after the identifier being defined is a short-cut only works when that object has generators which can be accessed in a certain way. You can see how Sage is preparsing the incorrect line like this:
sage: preparse("G1.<m>=Q1.galois_group('pari')")
"G1 = Q1.galois_group('pari', names=('m',)); (m,) = G1._first_ngens(1)"
So the Galois group G1 is being assigned OK, but does not have a function of the name expected by that input syntax. In fact G1 has very few functions.
thank you very much!
when I use the Q1.composite_fields(Q2).galois_group(),the same.
another question:relevance betwween Galois Data and GaloisGroup_v1.
in magma,before I run galois-group, some time result is name "Galois Data"--some strange Acronyms by number and letters. who an how define "Galois Data"?I ask magma,but no reply back.
There are several different ways in which Galois groups are labelled, which can be confusing. The web page http://www.lmfdb.org/GaloisGroup/ might be useful here: try clicking on the word "label" near the bottom of that page.
Asked: 2013-12-19 04:15:22 +0100
Seen: 460 times
Last updated: Dec 22 '13
Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.
