[GAP Forum] Understanding factorisation of polynomials using ALNUTH

[Dr. Kashyap Rajeevsarathy]

Dear Forum,

I am trying to understand the factorisation of polynomials in ALNUTH.
Consider the following example:






*gap> pol :=
UnivariatePolynomial(Rationals,[6,0,-5,0,1]);x_1^4-5*x_1^2+6gap> L :=
SplittingField(pol);<algebraic extension over the Rationals of degree
4>gap> FactorsPolynomialAlgExt(L,pol); [ x_1+(-1/20*a^3+9/10*a),
x_1+(-1/40*a^3+19/20*a), x_1+(1/40*a^3-19/20*a), x_1+(1/20*a^3-9/10*a) ]*

How should we interpret the symbol 'a' here? In other words, is there is a
way to realise the constant terms in these these symbolic expressions
(involving a) in the factors as (plus or minus) Sqrt{2} and Sqrt{3}.

Maybe it is too much to ask, but in general, can GAP display these real
roots as a list of radicals (for example Sqrt{2}, Sqrt{3} etc.), as it does
while displaying characters.
Sincerely,
Kashyap

-- 
Kashyap Rajeevsarathy
Assistant Professor,
Indian Institute of Science Education and Research (IISER) Bhopal,
Indore By-pass Road,
Bhauri, Bhopal - 462066,
Madhya Pradesh, India.
Phone: +91-755-669-2364
Website: https://home.iiserb.ac.in/~kashyap