/* 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)));
}
void
pariplot(GEN a, GEN b, GEN code, GEN ysmlu,GEN ybigu, long prec)
{
const char BLANK = ' ', YY = '|', XX_UPPER = '\'', XX_LOWER = '.';
long jz, j, i, sig;
pari_sp av = avma;
int jnew, jpre = 0; /* for lint */
GEN x, dx;
double diff, dyj, ysml, ybig, y[ISCR+1];
screen scr;
char buf[80], z;
sig=gcmp(b,a); if (!sig) return;
if (sig<0) { x=a; a=b; b=x; }
x = gtofp(a, prec); push_lex(x, code);
dx = divru(gtofp(gsub(b,a),prec), ISCR-1);
for (j=1; j<=JSCR; j++) scr[1][j]=scr[ISCR][j]=YY;
for (i=2; i<ISCR; i++)
{
scr[i][1] = XX_LOWER;
scr[i][JSCR]= XX_UPPER;
for (j=2; j<JSCR; j++) scr[i][j] = BLANK;
}
ysml = ybig = 0.; /* -Wall */
for (i=1; i<=ISCR; i++)
{
pari_sp av2 = avma;
y[i] = gtodouble( READ_EXPR(code,x) );
avma = av2;
if (i == 1)
ysml = ybig = y[1];
else
{
if (y[i] < ysml) ysml = y[i];
if (y[i] > ybig) ybig = y[i];
}
x = addrr(x,dx);
}
avma = av;
if (ysmlu) ysml = gtodouble(ysmlu);
if (ybigu) ybig = gtodouble(ybigu);
diff = ybig - ysml;
if (!diff) { ybig += 1; diff= 1.; }
dyj = ((JSCR-1)*3+2) / diff;
/* work around bug in gcc-4.8 (32bit): plot(x=-5,5,sin(x)))) */
jz = 3 - (long)(ysml*dyj + 0.5); /* 3 - DTOL(ysml*dyj) */
z = PICTZERO(jz); jz /= 3;
for (i=1; i<=ISCR; i++)
{
if (0<=jz && jz<=JSCR) scr[i][jz]=z;
j = 3 + DTOL((y[i]-ysml)*dyj);
jnew = j/3;
if (i > 1) fill_gap(scr, i, jnew, jpre);
if (0<=jnew && jnew<=JSCR) scr[i][jnew] = PICT(j);
jpre = jnew;
}
pari_putc('\n');
pari_printf("%s ", dsprintf9(ybig, buf));
for (i=1; i<=ISCR; i++) pari_putc(scr[i][JSCR]);
pari_putc('\n');
for (j=(JSCR-1); j>=2; j--)
{
pari_puts(" ");
for (i=1; i<=ISCR; i++) pari_putc(scr[i][j]);
pari_putc('\n');
}
pari_printf("%s ", dsprintf9(ysml, buf));
for (i=1; i<=ISCR; i++) pari_putc(scr[i][1]);
pari_putc('\n');
{
char line[10 + 32 + 32 + ISCR - 9];
sprintf(line, "%10s%-9.7g%*.7g\n"," ",todbl(a),ISCR-9,todbl(b));
pari_printf(line);
}
pop_lex(1);
}
