Re: the minimal polynomial over the composite field

[macsyma <macsyma@yahoo.co.jp>]

> You can force-update the branch bill-nfsplitting.
> There is a new function galoissplittinginit, which is like
> galoisinit(nfsplitting(...)) but using nfsplitting(,,2).
> (it is not complete yet, only G[1..6] is filled, but it is sufficient
> for galoisfixedfield).
> 
> Here your last example (20s instead of 33min)
> 
> G=galoissplittinginit(x^17-2);
> \\  ***  last result computed in 19,276 ms.
> cj=galoisconjclasses(G);
> [subf,inc,fact]=galoisfixedfield(G,cj[8],2);
> \\  ***  last result computed in 168 ms.
> z17=nfisisom(subf,polcyclo(17,y))[1];
> \\  ***  last result computed in 36 ms.
> liftpol(subst(fact,y,Mod(z17,polcyclo(17,y))))
> %6 =
> [x^17+(-51272*y^15-12104*y^14-11016*y^13-60996*y^12-7616*y^11-12342*y^10-37128*y^9+12376*y^8-12410*y^7-17136*y^6+36244*y^5-13736*y^4-12648*y^3+26520*y^2-24752*y-12376),...
> 
> If it is still not fast enough for you, you need to compute the action of Galois
> group of the polynomial on the p-adic roots (using an improved polgalois), and
> use a suitable implementation of galoisfixedfield to compute the
> cyclic subfields and the related factorization.
> 
> Cheers,
> Bill.
>

Thank you for the new function.
I've tried it with some examples,
unfortunately, it doesn't seem to speed up my code at the moment
so I look forward to future progress.

macsyma