/* [L:K] = ell^k; return 1 if L/K is locally cyclotomic at ell, 0 otherwise */
long
rnfislocalcyclo(GEN rnf)
{
pari_sp av = avma;
GEN K, L, S, SK, TK, SLs, SL2, TL, ell;
ulong ll;
long i, j, k, lk, lSK;
checkrnf(rnf);
lk = rnf_get_degree(rnf);
if (lk == 1) return 1;
k = uisprimepower(lk, &ll);
if (!k) pari_err_IMPL("rnfislocalcyclo for non-l-extensions");
ell = utoi(ll);
K = rnf_get_nf(rnf);
L = rnf_build_nfabs(rnf, nf_get_prec(K));
S = rnfidealprimedec(rnf, ell);
SK = gel(S,1);
SLs = gel(S,2);
SL2 = shallowconcat1(SLs);
TK = padicfact(K, SK, 100); lSK = lg(SK);
TL = padicfact(L, SL2, 100);
for (i = 1; i < lSK; i++)
{
long eK = etilde(K, gel(SK,i), gel(TK,i));
GEN SL = gel(SLs,i);
long lSL = lg(SL);
for (j = 1; j < lSL; j++)
{
long iS = gen_search(SL2, gel(SL,j), 0, (void*)&cmp_prime_over_p,
&cmp_nodata);
long eL = etilde(L, gel(SL,j), gel(TL,iS));
if (dvdui(eL/eK, ell)) { avma = av; return 0; }
}
};
avma = av; return 1;
}
GEN
concat1(GEN x)
{
pari_sp av = avma;
return gerepilecopy(av, shallowconcat1(x));
}
