number fields and irreducible polynomials
Hello gentle people. Let's see an example.
f=x^2+4
g=x^4+16
F=NumberField(f,'a')
The extension field of F
by g
cannot obtained by F.extension(g(s),'s')
although we input s=var('s')
before.
Because g
is reducible in F
. ( g=(x^2-4I)(x^2+4I) )
Can I check irreducibility of a polynomial in a number field?
Is there any method which makes a number field by given polynomial?
Thanks in advance.