ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 02 Oct 2016 00:26:00 -0500number fields and irreducible polynomialshttps://ask.sagemath.org/question/35028/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.SeminSun, 02 Oct 2016 00:26:00 -0500https://ask.sagemath.org/question/35028/