[GAP Forum] how to build complex field using GAP?

[Alexander Konovalov]

Dear GAP Forum,

On 23 Dec 2007, at 06:29, 董井成 wrote:

> Dear forum:
> how to build complex field using GAP?

GAP supports cyclotomic fields, which are extensions of Rationals
with complex roots of unity. Type

	?Cyclotomics

or

	?CyclotomicField

in the GAP prompt for their description.

In particular, GaussianRationals (see ?GaussianRationals )
constructs the field Q(i), where i^4=1.
In GAP the element i will be represented as E(4).

For example,

gap> R:=GaussianRationals;
GaussianRationals
gap> E(4) in R;
true
gap> E(4)^2;
-1
gap> a:=2+3*E(4);
2+3*E(4)
gap> a in R;
true
gap> a^-1;
2/13-3/13*E(4)
gap> b:=-1+5*E(4);
-1+5*E(4)
gap> a*b;
-17+7*E(4)

Hope this helps,
Alexander Konovalov