### 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^2-4~~*I)(x^2+4*I) 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.