macsyma on Tue, 20 Aug 2019 05:29:25 +0200
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Re: the minimal polynomial over the composite field
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- To: "pari-users@pari.math.u-bordeaux.fr" <pari-users@pari.math.u-bordeaux.fr>
- Subject: Re: the minimal polynomial over the composite field
- From: macsyma <macsyma@yahoo.co.jp>
- Date: Tue, 20 Aug 2019 12:29:18 +0900 (JST)
- Delivery-date: Tue, 20 Aug 2019 05:29:25 +0200
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- Reply-to: macsyma <macsyma@yahoo.co.jp>
Thank you, Bill.
> 1) Whenever you can, use nfisincl rather than nffactor.
> 2) Since q is Galois over Q, instead of nfsubfields+nffactor,
> you should use G=galoisinit(q); galoisfixedfield(G,...,2)
I cannot determine which part of my code your advice points to.
Could you explain using the step i = 3
of tst002(nfsubfields(x^35-2,840)), for example.
tst002(gx) =
{
my(P = select(r -> r - 2, factor(poldegree(gx))[, 1]),
p, q, s, t, u, A = gx, gi);
for(i = 1, #P,
q = polcyclo(p = P[i], u = eval(concat("c", p)));
[s, t] = nfsubfields(q)[-2..-2][1];
gi = nffactor(q, subst(liftpol(nffactor(s, gx)[1, 1]), u, t))[1, 1];
A = if(#variables(A) == 1, gi, if(#variables(gi) == 1, A, RgX_gcd_simple(A, gi) )));
liftpol(A/pollead(A))
};
macsyma