Dear GAP-Forum,

> >David Burggraf asked:
[snip]
> Using the software KANT 2.0 (Kalculations in Algebraic Number Theory), which
> is very similar to GAP, type the commands:
>
> Galois(x^12-12*x+1);
> Galois(11*x^12-12/11*x^11+1);
>
> KANT 2.0 can determine galois groups of polynmials up to degree 15. Can this
> be done in GAP3 in a relatively easy way?
>
> David.

In GAP3 you need to do the following:

x:=Indeterminate( Rationals );
x.name:="x";
Galois(x^12-12*x+1);
Galois(11*x^12-12/11*x^11+1);

In general, GAP3 is much slower then KANT in finding Galois groups ( unless
the group is S_n or A_n, where it's fast for both). PARI, on the other hand,
is faster than KANT ( save for odd degree-11 groups ). However, PARI cannot
go beyond degree-11. This comes from my personal experience of
comparing all three packages. While, it's somewhat of a off-topic, I
thought people might find this overview useful.

Is there a chance of speeding up Galois() for GAP4?

Igor