[GAP Forum] real value approximation

[Alexander Hulpke]

Dear GAP Forum,

On Jul 17, 2008, at 1:18 PM, Paraskevas Alvanos wrote:

>
> x := Indeterminate(Rationals);
> g := x ^2 - 2;
> F := FieldByPolynomial(g);
>
> a := PrimitiveElement(F);
>
> Is it a way to determine which conjugate a.

No -- in fact in this construction it is no particular conjugate, but  
both embeddings are valid.
Algebraically it does not matter which conjugate you pick, that is the  
beauty of Galois theory.

> Can I have an approximate real value of a;
I don't think GAP has a general routine for numerical root  
approximation, though there are of course known algorithms in  
numerical analysis which do so.
>
> Of course a can simple ask
>
> a>0;

Careful: This ordering is an arbitrary ordering (because 0 and a are  
in different domains)
and does not imply any particular embedding. In fact it could be  
possible that both a and -a are both larger than 0.

Best,

     Alexander Hulpke