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question about GaloisGroup_v1?

asked 2013-12-18 21:15:22 -0500

cjsh gravatar image
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answered 2013-12-19 23:00:04 -0500

lftabera gravatar image

And the question is?

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answered 2013-12-21 06:56:32 -0500

John Cremona gravatar image

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.

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answered 2013-12-22 16:32:01 -0500

cjsh gravatar image

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.

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Comments

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.

John Cremona gravatar imageJohn Cremona ( 2014-01-04 08:15:45 -0500 )edit

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Asked: 2013-12-18 21:15:22 -0500

Seen: 75 times

Last updated: Dec 22 '13