// Digit reversal
GEN
rev(GEN n, long B)
{
pari_sp av = avma;
if (typ(n) != t_INT)
pari_err_TYPE("rev", n);
GEN m = modis(n, B);
n = divis(n, B);
pari_sp btop = avma, st_lim = stack_lim(btop, 1);
while (signe(n)) {
m = addis(mulis(m, B), smodis(n, B));
n = divis(n, B);
if (low_stack(st_lim, stack_lim(btop, 1)))
gerepileall(btop, 2, &m, &n);
}
m = gerepilecopy(av, m);
return m;
}
/* return a bound for T_2(P), P | polbase
* max |b_i|^2 <= 3^{3/2 + d} / (4 \pi d) [P]_2,
* where [P]_2 is Bombieri's 2-norm
* Sum over conjugates
*/
static GEN
nf_Beauzamy_bound(GEN nf, GEN polbase)
{
GEN lt,C,run,s, G = gmael(nf,5,2), POL, bin;
long i,prec,precnf, d = degpol(polbase), n = degpol(nf[1]);
precnf = gprecision(G);
prec = MEDDEFAULTPREC;
bin = vecbinome(d);
POL = polbase + 2;
/* compute [POL]_2 */
for (;;)
{
run= real_1(prec);
s = real_0(prec);
for (i=0; i<=d; i++)
{
GEN p1 = gnorml2(arch_for_T2(G, gmul(run, gel(POL,i)))); /* T2(POL[i]) */
if (!signe(p1)) continue;
if (lg(p1) == 3) break;
/* s += T2(POL[i]) / binomial(d,i) */
s = addrr(s, gdiv(p1, gel(bin,i+1)));
}
if (i > d) break;
prec = (prec<<1)-2;
if (prec > precnf)
{
nffp_t F; remake_GM(nf, &F, prec); G = F.G;
if (DEBUGLEVEL>1) pari_warn(warnprec, "nf_factor_bound", prec);
}
}
lt = leading_term(polbase);
s = gmul(s, mulis(sqri(lt), n));
C = powrshalf(stor(3,DEFAULTPREC), 3 + 2*d); /* 3^{3/2 + d} */
return gdiv(gmul(C, s), gmulsg(d, mppi(DEFAULTPREC)));
}
