static GEN
Z2x_rshift(GEN y, long x)
{
GEN z;
long i, l;
if (!x) return pol0_Flx(y[1]);
z = cgetg_copy(y, &l); z[1] = y[1];
for(i=2; i<l; i++) z[i] = y[i]>>x;
return Flx_renormalize(z, l);
}
static GEN
vtilde(GEN K, GEN x, GEN T, GEN deg, GEN ell, long prec)
{
GEN G, E, vG;
long i, l;
if (typ(x) != t_MAT) return vtilde_i(K,x,T,deg,ell,prec);
G = gel(x,1); vG = cgetg_copy(G, &l);
E = gel(x,2);
for (i = 1; i < l; i++) gel(vG, i) = vtilde_i(K, gel(G,i),T,deg,ell,prec);
return RgV_dotproduct(E, vG);
}
static GEN
ellsylow(GEN cyc, GEN ell)
{
long i, l;
GEN d = cgetg_copy(cyc, &l);
for (i = 1; i < l; i++)
{
GEN c = gel(cyc,i), a;
if (!Z_pvalrem(c, ell, &a)) break;
gel(d,i) = diviiexact(c, a);
}
setlg(d, i); return d;
}
/* Given a number field K and a prime p, return
* S = places of K above p [primedec]
* R = corresponding p-adic factors of K.pol (mod p^k), in the same order */
static GEN
padicfact(GEN K, GEN S, long k)
{
GEN R, p = pr_get_p(gel(S,1));
GEN T = gel(factorpadic(nf_get_pol(K), p, k), 1);
long l, i;
S = idealprimedec(K, p);
R = cgetg_copy(S, &l);
for (i = 1; i < l; i++)
{
long j = get_ZpX_index(K, gel(S,i), T);
gel(R,i) = gel(T,j);
gel(T,j) = NULL;
}
return R;
}