Polynome Galois Group when field is not Q
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.
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: