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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 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 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 Q ?

Thank you.

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 Q, it works as expected:

R1.< x > = PolynomialRing(QQ)
PolynomialRing(QQ)
 P=x^4-2
 
P=x^4-2
 
G1=P.galois_group()G1=P.galois_group()

R2.< i > = QQ.extension(x^2+1)
QQ.extension(x^2+1)
  
P2 = P.change_ring(R2)P.change_ring(R2)
  
G2=P2.galois_group()G2=P2.galois_group()

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 Q, $\Bbb Q$, 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 $Q$ $\Bbb Q$ ?

Thank you.