On Wed, Apr 01, 2015 at 07:44:55AM +0530, Dr. Kashyap Rajeevsarathy wrote: > Dear Forum, > *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?

a denotes any roots of L. You can do a:=RootOfDefiningPolynomial(L); to define a in GAP. > 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}. Just square them: pol := UnivariatePolynomial(Rationals,[6,0,-5,0,1]); L := SplittingField(pol); FactorsPolynomialAlgExt(L,pol); a:=RootOfDefiningPolynomial(L); you get gap> (-1/40*a^3+19/20*a)^2; !3 gap> (-1/20*a^3+9/10*a)^2; !2 > 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. I would suggest you define L explicitely as Q(sqrt(2),sqrt(3)), instead of using SplittingField. Cheers, Bill. _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum