On Fri, Aug 08, 2014 at 03:50:42PM -0400, Igor Schein wrote:
> Package: pari
> Version: git
>
> ? {P=
> x^128 - 1120*x^120 + 893536*x^112 - 592023168*x^104 + 933565471680*x^96 - 27
> 9147419588096*x^88 + 97872513449015808*x^80 - 17306583154941093888*x^72 + 10
> 28710836666577348096*x^64 - 15092876667291282579456*x^56 + 85376864819323865
> 7048576*x^48 + 13620414760387994411106304*x^40 + 47258011128063825927979008*
> x^32 - 918389645734030486929408*x^24 + 10975455361012103249920*x^16 - 759042
> 706029150208*x^8 + 14048223625216
> ;}
> ? polisirreducible(P)
> 0
> ? type(galoisinit(P))
> "t_VEC"
>
> galoisinit() fails to detect a reducible polynomial and produces a false
> positive, which can be dangerous.
> To alleviate the risk, the user must *always* check reducibility first, but
> then why not task galoisinit() with doing that to begin with?

The user might already know that the polynomial is irreducible ?
I am quite sure you already reported a similar item.

In this instance as in the previous one, the result returned by galoisinit is
valid, which you can check by doing:

? S=galoispermtopol(G,G.gen);
? [subst(P,x,Mod(s,P))|s<-S]
%17 = [0,0,0,0]

So galoisinit actually find a subgroup of the automorphism group of the étale
algebra \Q[X]/(P).

Cheers,
Bill.