software to compute the degree of the splitting field of a polynomial over $\mathbb{Q}$

Question

I want to do some experiments regarding the degree of the splitting field $\mathbb{Q}$ of a certain class of polynomials in $\mathbb{Q}[T]$. Is there some software that is able to compute the (degree of the) splitting field of a given such polynomial? Are there for example macaulay2 packages or is it implemented in mathematica, maple etc.?

Answer 1

SageMath can do this. It's free. One can even try it out online.

An example from their documentation:

sage: R.<x> = PolynomialRing(QQ)  
sage: K.<a> = (x^3 + 2).splitting_field(); K  
Number Field in a with defining polynomial x^6 + 3*x^5 + 6*x^4 + 11*x^3 + 12*x^2 - 3*x + 1