Some new GP features
galoissplittinginit
galoissplittinginit(P) is a faster alternative to
galoisinit(nfsplitting(P)) that assumes P irreducible.
but does not require the group to be weakly supersolvable.
? P = x^5+20*x+16;
? polgalois(P)
%36 = [60,1,1,"A5"]
? G = galoissplittinginit(P);
? G.pol == nfsplitting(P)
%38 = 1
? galoisidentify(G)
%39 = [60,5]
? galoisfixedfield(G,[G.group[2],G.group[6]],1)
%40 = x^6-1600*x^4+1536000*x^2+32768000*x+163840000