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
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