/* 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); }