> < ^ From:

> < ^ Subject:

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

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