[GAP Forum] cyclotomic detection

[marta asaeda]

Hello,

I am wondering about the following: the roots of the polynomial
p:=x^3-8*x^2+17*x-5
are known to be cyclotomic integers because the galois group of p is
Z_3, by Kronecker's thm abelian extension of Q sit in a cyclotomic
field. However I do the following:

gap>  x:=Indeterminate(Rationals, "x");;
gap> p:=x^3-8*x^2+17*x-5;;
gap> e:=AlgebraicExtension(Rationals, p);
<field in characteristic 0>
gap> IsField(e);
true
gap> d:=RootOfDefiningPolynomial(e);
(a)
gap> IsCyclotomic(d);
false
gap> d in Cyclotomics;
false
gap> IsCyc(d);
false
gap> IsIntegralCyclotomic(d);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `IsIntegralCyclotomic' on 1 arguments ca\
lled from

It looks like gap is saying that d is not a cyclotomic, and it doesn't
know if it is a cyclotomic integer.  I wonder what's wrong here.... I
appreciate if you could let me know what's going on...

Best

Marta