# Revision history [back]

### 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?

### 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) 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?