Polynome Galois Group when field is not Q

asked 2023-02-21 17:00:32 +0200

André gravatar image

updated 2023-02-23 01:37:05 +0200

dan_fulea gravatar image

Hello, I am very new to Sagemath, and in this forum, so apologies if I'm doing something wrong.

When I compute the galois group with a polynome based on $\Bbb Q$, it works as expected:

R1.< x > = PolynomialRing(QQ)

P=x^4-2

G1=P.galois_group()

I get the correct answer : G1 Transitive group number 3 of degree 4

However if I try to compute the galois group in $\Bbb Q[i]$:

R2.< i > = QQ.extension(x^2+1)

P2 = P.change_ring(R2)

G2=P2.galois_group()

I get an error:

AttributeError: 'PolynomialRing_field_with_category.element_class' object has no attribute 'galois_group'

Is there any mean to compute galois group in fields different from $\Bbb Q$ ?

Thank you.

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Comments

Galois groups are associated rather to extensions of fields. One can use the method galois_group at some number field. Also extensions of such fields have the method. In the moment, the absolute Galois group is returned also for number fields constructed as extensions, however a deprecation error announces that this will change in the future.

For instance:

sage: K.<s> = NumberField(x^2 + 1)
sage: L.<t> = K.extension(x^2 + 2)

sage: L.galois_group()
/usr/lib/python3.10/site-packages/sage/rings/number_field/number_field.py:6252: DeprecationWarning: Use .absolute_field().galois_group() if you want the Galois group of the absolute field
See https://trac.sagemath.org/28782 for details.
  return GaloisGroup_v2(self, algorithm=alg...
dan_fulea gravatar imagedan_fulea ( 2023-02-23 01:46:23 +0200 )edit
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