Annotation of OpenXM_contrib/pari/src/basemath/base1.c, Revision 1.1
1.1 ! maekawa 1: /**************************************************************/
! 2: /* */
! 3: /* NUMBER FIELDS */
! 4: /* */
! 5: /**************************************************************/
! 6: /* $Id: base1.c,v 1.2 1999/09/23 17:50:55 karim Exp $ */
! 7: #include "pari.h"
! 8: #include "parinf.h"
! 9:
! 10: void
! 11: checkrnf(GEN rnf)
! 12: {
! 13: if (typ(rnf)!=t_VEC) err(idealer1);
! 14: if (lg(rnf)!=12) err(idealer1);
! 15: }
! 16:
! 17: GEN
! 18: checkbnf(GEN bnf)
! 19: {
! 20: if (typ(bnf)!=t_VEC) err(idealer1);
! 21: switch (lg(bnf))
! 22: {
! 23: case 11: return bnf;
! 24: case 10:
! 25: if (typ(bnf[1])==t_POL)
! 26: err(talker,"please apply bnfinit first");
! 27: break;
! 28: case 7:
! 29: return checkbnf((GEN)bnf[1]);
! 30:
! 31: case 3:
! 32: if (typ(bnf[2])==t_POLMOD)
! 33: return checkbnf((GEN)bnf[1]);
! 34: }
! 35: err(idealer1);
! 36: return NULL; /* not reached */
! 37: }
! 38:
! 39: GEN
! 40: checknf(GEN nf)
! 41: {
! 42: if (typ(nf)==t_POL) err(talker,"please apply nfinit first");
! 43: if (typ(nf)!=t_VEC) err(idealer1);
! 44: switch(lg(nf))
! 45: {
! 46: case 10: return nf;
! 47: case 11: return checknf((GEN)nf[7]);
! 48: case 3: if (typ(nf[2]) == t_POLMOD) return checknf((GEN)nf[1]);
! 49: }
! 50: err(idealer1);
! 51: return NULL; /* not reached */
! 52: }
! 53:
! 54: void
! 55: checkbnr(GEN bnr)
! 56: {
! 57: if (typ(bnr)!=t_VEC || lg(bnr)!=7)
! 58: err(talker,"incorrect bigray field");
! 59: (void)checkbnf((GEN)bnr[1]);
! 60: }
! 61:
! 62: void
! 63: checkbnrgen(GEN bnr)
! 64: {
! 65: checkbnr(bnr);
! 66: if (lg(bnr[5])<=3)
! 67: err(talker,"please apply bnrinit(,,1) and not bnrinit(,)");
! 68: }
! 69:
! 70: GEN
! 71: check_units(GEN bnf, char *f)
! 72: {
! 73: GEN nf, x;
! 74: bnf = checkbnf(bnf); nf = checknf(bnf);
! 75: x = (GEN)bnf[8];
! 76: if (lg(x) < 7 || (lg(x[5]) == 1 && lg(nf[6]) > 2))
! 77: err(talker,"missing units in %s", f);
! 78: return (GEN)x[5];
! 79: }
! 80:
! 81: void
! 82: checkid(GEN x, long N)
! 83: {
! 84: if (typ(x)!=t_MAT) err(idealer2);
! 85: if (lg(x) == 1 || lg(x[1]) != N+1)
! 86: err(talker,"incorrect matrix for ideal");
! 87: }
! 88:
! 89: void
! 90: checkbid(GEN bid)
! 91: {
! 92: if (typ(bid)!=t_VEC || lg(bid)!=6 || lg(bid[1])!=3)
! 93: err(talker,"incorrect bigideal");
! 94: }
! 95:
! 96: void
! 97: checkprimeid(GEN id)
! 98: {
! 99: if (typ(id) != t_VEC || lg(id) != 6)
! 100: err(talker,"incorrect prime ideal");
! 101: }
! 102:
! 103: void
! 104: checkprhall(GEN prhall)
! 105: {
! 106: if (typ(prhall) != t_VEC || lg(prhall) != 3 || typ(prhall[1]) != t_MAT)
! 107: err(talker,"incorrect prhall format");
! 108: }
! 109:
! 110: void
! 111: check_pol_int(GEN x)
! 112: {
! 113: long k = lg(x)-1;
! 114: for ( ; k>1; k--)
! 115: if (typ(x[k])!=t_INT) err(talker,"polynomial not in Z[X]");
! 116: }
! 117:
! 118: GEN
! 119: get_primeid(GEN x)
! 120: {
! 121: if (typ(x) != t_VEC) return NULL;
! 122: if (lg(x) == 3) x = (GEN)x[1];
! 123: if (lg(x) != 6 || typ(x[3]) != t_INT) return NULL;
! 124: return x;
! 125: }
! 126:
! 127: GEN
! 128: get_bnf(GEN x, int *t)
! 129: {
! 130: switch(typ(x))
! 131: {
! 132: case t_POL: *t = typ_POL; return NULL;
! 133: case t_QUAD: *t = typ_Q ; return NULL;
! 134: case t_VEC:
! 135: switch(lg(x))
! 136: {
! 137: case 3:
! 138: if (typ(x[2]) != t_POLMOD) break;
! 139: return get_bnf((GEN)x[1],t);
! 140: case 6 : *t = typ_QUA; return NULL;
! 141: case 10: *t = typ_NF; return NULL;
! 142: case 11: *t = typ_BNF; return x;
! 143: case 7 : *t = typ_BNR;
! 144: x = (GEN)x[1]; if (typ(x)!=t_VEC || lg(x)!=11) break;
! 145: return x;
! 146: }
! 147: case t_MAT:
! 148: if (lg(x)==2)
! 149: switch(lg(x[1]))
! 150: {
! 151: case 8: case 11:
! 152: *t = typ_CLA; return NULL;
! 153: }
! 154: }
! 155: *t = typ_NULL; return NULL;
! 156: }
! 157:
! 158: GEN
! 159: get_nf(GEN x, int *t)
! 160: {
! 161: switch(typ(x))
! 162: {
! 163: case t_POL : *t = typ_POL; return NULL;
! 164: case t_QUAD: *t = typ_Q ; return NULL;
! 165: case t_VEC:
! 166: switch(lg(x))
! 167: {
! 168: case 3:
! 169: if (typ(x[2]) != t_POLMOD) break;
! 170: return get_nf((GEN)x[1],t);
! 171: case 10: *t = typ_NF; return x;
! 172: case 11: *t = typ_BNF;
! 173: x = (GEN)x[7]; if (typ(x)!=t_VEC || lg(x)!=10) break;
! 174: return x;
! 175: case 7 : *t = typ_BNR;
! 176: x = (GEN)x[1]; if (typ(x)!=t_VEC || lg(x)!=11) break;
! 177: x = (GEN)x[7]; if (typ(x)!=t_VEC || lg(x)!=10) break;
! 178: return x;
! 179:
! 180: case 14: case 20:
! 181: *t = typ_ELL; return NULL;
! 182: }break;
! 183: case t_MAT:
! 184: if (lg(x)==2)
! 185: switch(lg(x[1]))
! 186: {
! 187: case 8: case 11:
! 188: *t = typ_CLA; return NULL;
! 189: }
! 190: }
! 191: *t = typ_NULL; return NULL;
! 192: }
! 193:
! 194: /*************************************************************************/
! 195: /** **/
! 196: /** GALOIS GROUP **/
! 197: /** **/
! 198: /*************************************************************************/
! 199:
! 200: /* exchange elements i and j in vector x */
! 201: static GEN
! 202: transroot(GEN x, int i, int j)
! 203: {
! 204: long k;
! 205: x = dummycopy(x);
! 206: k=x[i]; x[i]=x[j]; x[j]=k; return x;
! 207: }
! 208:
! 209: #define randshift (BITS_IN_RANDOM - 3)
! 210:
! 211: GEN
! 212: tschirnhaus(GEN x)
! 213: {
! 214: long a, v = varn(x), av = avma;
! 215: GEN u, p1 = cgetg(5,t_POL);
! 216:
! 217: if (typ(x)!=t_POL) err(notpoler,"tschirnhaus");
! 218: if (lgef(x) < 4) err(constpoler,"tschirnhaus");
! 219: if (v) { u=dummycopy(x); setvarn(u,0); x=u; }
! 220: p1[1] = evalsigne(1)|evalvarn(0)|evallgef(5);
! 221: do
! 222: {
! 223: a = mymyrand() >> randshift; if (a==0) a =1; p1[4]=lstoi(a);
! 224: a = mymyrand() >> (randshift-1); if (a>=4) a-=8; p1[3]=lstoi(a);
! 225: a = mymyrand() >> (randshift-1); if (a>=4) a-=8; p1[2]=lstoi(a);
! 226: u = caract2(x,p1,v); a=avma;
! 227: }
! 228: while (lgef(srgcd(u,derivpol(u))) > 3); /* while u not separable */
! 229: if (DEBUGLEVEL>1)
! 230: fprintferr("Tschirnhaus transform. New pol: %Z",u);
! 231: avma=a; return gerepileupto(av,u);
! 232: }
! 233: #undef randshift
! 234:
! 235: int
! 236: gpolcomp(GEN p1, GEN p2)
! 237: {
! 238: int s,j = lgef(p1)-2;
! 239:
! 240: if (lgef(p2)-2 != j)
! 241: err(bugparier,"gpolcomp (different degrees)");
! 242: for (; j>=2; j--)
! 243: {
! 244: s = absi_cmp((GEN)p1[j], (GEN)p2[j]);
! 245: if (s) return s;
! 246: }
! 247: return 0;
! 248: }
! 249:
! 250: /* pol is assumed to be non-zero, primitive and integral */
! 251: static GEN
! 252: primitive_pol_to_monic(GEN pol, GEN *ptlead)
! 253: {
! 254: long n = lgef(pol)-1;
! 255: GEN p1,lead,res;
! 256:
! 257: if (gcmp1((GEN)pol[n])) { if (ptlead) *ptlead = NULL; return pol; }
! 258: res = cgetg(n+1,t_POL); res[1]=pol[1];
! 259: lead = (GEN) pol[n]; p1 = gun;
! 260: res[n] = un; n--;
! 261: if (n>1) res[n] = pol[n];
! 262: for (n--; n>1; n--)
! 263: {
! 264: p1 = mulii(lead,p1);
! 265: res[n] = lmulii(p1,(GEN)pol[n]);
! 266: }
! 267: if (ptlead) *ptlead = lead; return res;
! 268: }
! 269:
! 270: /* compute x1*x2^2 + x2*x3^2 + x3*x4^2 + x4*x1^2 */
! 271: static GEN
! 272: get_F4(GEN x)
! 273: {
! 274: GEN p1=gzero;
! 275: long i;
! 276:
! 277: for (i=1; i<=4; i++)
! 278: p1 = gadd(p1, gmul((GEN)x[i], gsqr((GEN)x[(i&3)+1])));
! 279: return p1;
! 280: }
! 281:
! 282: GEN galoisbig(GEN x, long prec);
! 283: GEN roots_to_pol(GEN a, long v);
! 284:
! 285: GEN
! 286: galois(GEN x, long prec)
! 287: {
! 288: long av=avma,av1,i,j,k,n,f,l,l2,e,e1,pr,ind;
! 289: GEN x1,p1,p2,p3,p4,p5,p6,w,y,z,ee;
! 290: static int ind5[20]={2,5,3,4, 1,3,4,5, 1,5,2,4, 1,2,3,5, 1,4,2,3};
! 291: static int ind6[60]={3,5,4,6, 2,6,4,5, 2,3,5,6, 2,4,3,6, 2,5,3,4,
! 292: 1,4,5,6, 1,5,3,6, 1,6,3,4, 1,3,4,5, 1,6,2,5,
! 293: 1,2,4,6, 1,5,2,4, 1,3,2,6, 1,2,3,5, 1,4,2,3};
! 294: if (typ(x)!=t_POL) err(notpoler,"galois");
! 295: n=lgef(x)-3; if (n<=0) err(constpoler,"galois");
! 296: if (n>11) err(impl,"galois of degree higher than 11");
! 297: x = gdiv(x,content(x));
! 298: for (i=2; i<=n+2; i++)
! 299: if (typ(x[i])!=t_INT) err(polrationer,"galois");
! 300: if (gisirreducible(x) != gun)
! 301: err(impl,"galois of reducible polynomial");
! 302:
! 303: if (n<4)
! 304: {
! 305: if (n<3)
! 306: {
! 307: avma=av; y=cgetg(4,t_VEC);
! 308: y[1] = (n==1)? un: deux;
! 309: y[2]=lnegi(gun);
! 310: }
! 311: else /* n=3 */
! 312: {
! 313: f=carreparfait(discsr(x));
! 314: avma=av; y=cgetg(4,t_VEC);
! 315: if (f) { y[1]=lstoi(3); y[2]=un; }
! 316: else { y[1]=lstoi(6); y[2]=lnegi(gun); }
! 317: }
! 318: y[3]=un; return y;
! 319: }
! 320: x1 = x = primitive_pol_to_monic(x,NULL); av1=avma;
! 321: if (n>7) return galoisbig(x,prec);
! 322: for(;;)
! 323: {
! 324: switch(n)
! 325: {
! 326: case 4: z = cgetg(7,t_VEC);
! 327: for(;;)
! 328: {
! 329: p1=roots(x,prec);
! 330: z[1] = (long)get_F4(p1);
! 331: z[2] = (long)get_F4(transroot(p1,1,2));
! 332: z[3] = (long)get_F4(transroot(p1,1,3));
! 333: z[4] = (long)get_F4(transroot(p1,1,4));
! 334: z[5] = (long)get_F4(transroot(p1,2,3));
! 335: z[6] = (long)get_F4(transroot(p1,3,4));
! 336: p4 = roots_to_pol(z,0);
! 337: p5=grndtoi(greal(p4),&e);
! 338: e1=gexpo(gimag(p4)); if (e1>e) e=e1;
! 339: if (e <= -10) break;
! 340: prec = (prec<<1)-2;
! 341: }
! 342: p6 = modulargcd(p5, derivpol(p5));
! 343: if (typ(p6)==t_POL && lgef(p6)>3) goto tchi;
! 344: p2 = (GEN)factor(p5)[1];
! 345: switch(lg(p2)-1)
! 346: {
! 347: case 1: f=carreparfait(discsr(x)); avma=av; y=cgetg(4,t_VEC);
! 348: y[3]=un;
! 349: if (f) { y[2]=un; y[1]=lstoi(12); return y; }
! 350: y[2]=lnegi(gun); y[1]=lstoi(24); return y;
! 351:
! 352: case 2: avma=av; y=cgetg(4,t_VEC);
! 353: y[3]=un; y[2]=lnegi(gun); y[1]=lstoi(8); return y;
! 354:
! 355: case 3: avma=av; y=cgetg(4,t_VEC);
! 356: y[1]=lstoi(4); y[3]=un;
! 357: y[2] = (lgef(p2[1])==5)? un: lnegi(gun);
! 358: return y;
! 359:
! 360: default: err(bugparier,"galois (bug1)");
! 361: }
! 362:
! 363: case 5: z = cgetg(7,t_VEC);
! 364: ee = new_chunk(7); w = new_chunk(7);
! 365: for(;;)
! 366: {
! 367: for(;;)
! 368: {
! 369: p1=roots(x,prec);
! 370: for (l=1; l<=6; l++)
! 371: {
! 372: p2=(l==1)?p1: ((l<6)?transroot(p1,1,l): transroot(p1,2,5));
! 373: p3=gzero;
! 374: for (k=0,i=1; i<=5; i++,k+=4)
! 375: {
! 376: p5 = gadd(gmul((GEN)p2[ind5[k]],(GEN)p2[ind5[k+1]]),
! 377: gmul((GEN)p2[ind5[k+2]],(GEN)p2[ind5[k+3]]));
! 378: p3 = gadd(p3, gmul(gsqr((GEN)p2[i]),p5));
! 379: }
! 380: w[l]=lrndtoi(greal(p3),&e);
! 381: e1 = gexpo(gimag(p3)); if (e1>e) e=e1;
! 382: ee[l]=e; z[l] = (long)p3;
! 383: }
! 384: p4 = roots_to_pol(z,0);
! 385: p5=grndtoi(greal(p4),&e);
! 386: e1 = gexpo(gimag(p4)); if (e1>e) e=e1;
! 387: if (e <= -10) break;
! 388: prec = (prec<<1)-2;
! 389: }
! 390: p6 = modulargcd(p5,derivpol(p5));
! 391: if (typ(p6)==t_POL && lgef(p6)>3) goto tchi;
! 392: p3=(GEN)factor(p5)[1];
! 393: f=carreparfait(discsr(x));
! 394: if (lg(p3)-1==1)
! 395: {
! 396: avma=av; y=cgetg(4,t_VEC); y[3]=un;
! 397: if (f) { y[2]=un; y[1]=lstoi(60); return y; }
! 398: else { y[2]=lneg(gun); y[1]=lstoi(120); return y; }
! 399: }
! 400: if (!f)
! 401: {
! 402: avma=av; y=cgetg(4,t_VEC);
! 403: y[3]=un; y[2]=lneg(gun); y[1]=lstoi(20); return y;
! 404: }
! 405: pr = - (bit_accuracy(prec) >> 1);
! 406: for (l=1; l<=6; l++)
! 407: if (ee[l] <= pr && gcmp0(poleval(p5,(GEN)w[l]))) break;
! 408: if (l>6) err(bugparier,"galois (bug4)");
! 409: p2=(l==6)? transroot(p1,2,5):transroot(p1,1,l);
! 410: p3=gzero;
! 411: for (i=1; i<=5; i++)
! 412: {
! 413: j=(i%5)+1;
! 414: p3=gadd(p3,gmul(gmul((GEN)p2[i],(GEN)p2[j]),
! 415: gsub((GEN)p2[j],(GEN)p2[i])));
! 416: }
! 417: p5=gsqr(p3); p4=grndtoi(greal(p5),&e);
! 418: e1 = gexpo(gimag(p5)); if (e1>e) e=e1;
! 419: if (e <= -10)
! 420: {
! 421: if (gcmp0(p4)) goto tchi;
! 422: f=carreparfait(p4); avma=av; y=cgetg(4,t_VEC);
! 423: y[3]=y[2]=un; y[1]=lstoi(f?5:10);
! 424: return y;
! 425: }
! 426: prec=(prec<<1)-2;
! 427: }
! 428:
! 429: case 6: z = cgetg(7, t_VEC);
! 430: for(;;)
! 431: {
! 432: for(;;)
! 433: {
! 434: p1=roots(x,prec);
! 435: for (l=1; l<=6; l++)
! 436: {
! 437: p2=(l==1)?p1:transroot(p1,1,l);
! 438: p3=gzero; k=0;
! 439: for (i=1; i<=5; i++) for (j=i+1; j<=6; j++)
! 440: {
! 441: p5=gadd(gmul((GEN)p2[ind6[k]],(GEN)p2[ind6[k+1]]),
! 442: gmul((GEN)p2[ind6[k+2]],(GEN)p2[ind6[k+3]]));
! 443: p3=gadd(p3,gmul(gsqr(gmul((GEN)p2[i],(GEN)p2[j])),p5)); k+=4;
! 444: }
! 445: z[l] = (long)p3;
! 446: }
! 447: p4=roots_to_pol(z,0);
! 448: p5=grndtoi(greal(p4),&e);
! 449: e1 = gexpo(gimag(p4)); if (e1>e) e=e1;
! 450: if (e <= -10) break;
! 451: prec=(prec<<1)-2;
! 452: }
! 453: p6 = modulargcd(p5,derivpol(p5));
! 454: if (typ(p6)==t_POL && lgef(p6)>3) goto tchi;
! 455: p2=(GEN)factor(p5)[1];
! 456: switch(lg(p2)-1)
! 457: {
! 458: case 1:
! 459: z = cgetg(11,t_VEC); ind=0;
! 460: p3=gadd(gmul(gmul((GEN)p1[1],(GEN)p1[2]),(GEN)p1[3]),
! 461: gmul(gmul((GEN)p1[4],(GEN)p1[5]),(GEN)p1[6]));
! 462: z[++ind] = (long)p3;
! 463: for (i=1; i<=3; i++)
! 464: for (j=4; j<=6; j++)
! 465: {
! 466: p2=transroot(p1,i,j);
! 467: p3=gadd(gmul(gmul((GEN)p2[1],(GEN)p2[2]),(GEN)p2[3]),
! 468: gmul(gmul((GEN)p2[4],(GEN)p2[5]),(GEN)p2[6]));
! 469: z[++ind] = (long)p3;
! 470: }
! 471: p4 = roots_to_pol(z,0);
! 472: p5=grndtoi(greal(p4),&e);
! 473: e1 = gexpo(gimag(p4)); if (e1>e) e=e1;
! 474: if (e <= -10)
! 475: {
! 476: p6 = modulargcd(p5,derivpol(p5));
! 477: if (typ(p6)==t_POL && lgef(p6)>3) goto tchi;
! 478: p2=(GEN)factor(p5)[1];
! 479: f=carreparfait(discsr(x));
! 480: avma=av; y=cgetg(4,t_VEC); y[3]=un;
! 481: if (lg(p2)-1==1)
! 482: {
! 483: if (f) { y[2]=un; y[1]=lstoi(360); }
! 484: else { y[2]=lnegi(gun); y[1]=lstoi(720); }
! 485: }
! 486: else
! 487: {
! 488: if (f) { y[2]=un; y[1]=lstoi(36); }
! 489: else { y[2]=lnegi(gun); y[1]=lstoi(72); }
! 490: }
! 491: return y;
! 492: }
! 493: prec=(prec<<1)-2; break;
! 494:
! 495: case 2: l2=lgef(p2[1])-3; if (l2>3) l2=6-l2;
! 496: switch(l2)
! 497: {
! 498: case 1: f=carreparfait(discsr(x));
! 499: avma=av; y=cgetg(4,t_VEC); y[3]=un;
! 500: if (f) { y[2]=un; y[1]=lstoi(60); }
! 501: else { y[2]=lneg(gun); y[1]=lstoi(120); }
! 502: return y;
! 503: case 2: f=carreparfait(discsr(x));
! 504: if (f)
! 505: {
! 506: avma=av; y=cgetg(4,t_VEC);
! 507: y[3]=y[2]=un; y[1]=lstoi(24);
! 508: }
! 509: else
! 510: {
! 511: p3=(lgef(p2[1])==5) ? (GEN)p2[2]:(GEN)p2[1];
! 512: f=carreparfait(discsr(p3));
! 513: avma=av; y=cgetg(4,t_VEC); y[2]=lneg(gun);
! 514: if (f) { y[1]=lstoi(24); y[3]=deux; }
! 515: else { y[1]=lstoi(48); y[3]=un; }
! 516: }
! 517: return y;
! 518: case 3: f=carreparfait(discsr((GEN)p2[1]))
! 519: || carreparfait(discsr((GEN)p2[2]));
! 520: avma=av; y=cgetg(4,t_VEC);
! 521: y[3]=un; y[2]=lneg(gun); y[1]=lstoi(f? 18: 36);
! 522: return y;
! 523: }
! 524: case 3:
! 525: for (l2=1; l2<=3; l2++)
! 526: if (lgef(p2[l2])>=6) p3=(GEN)p2[l2];
! 527: if (lgef(p3)==6)
! 528: {
! 529: f=carreparfait(discsr(p3)); avma=av; y=cgetg(4,t_VEC);
! 530: y[2]=lneg(gun); y[1]=lstoi(f? 6: 12);
! 531: }
! 532: else
! 533: {
! 534: f=carreparfait(discsr(x)); avma=av; y=cgetg(4,t_VEC);
! 535: if (f) { y[2]=un; y[1]=lstoi(12); }
! 536: else { y[2]=lneg(gun); y[1]=lstoi(24); }
! 537: }
! 538: y[3]=un; return y;
! 539: case 4: avma=av; y=cgetg(4,t_VEC);
! 540: y[1]=lstoi(6); y[2]=lneg(gun); y[3]=deux; return y;
! 541: default: err(bugparier,"galois (bug3)");
! 542: }
! 543: }
! 544:
! 545: case 7: z = cgetg(36,t_VEC);
! 546: for(;;)
! 547: {
! 548: ind = 0; p1=roots(x,prec); p4=gun;
! 549: for (i=1; i<=5; i++)
! 550: for (j=i+1; j<=6; j++)
! 551: {
! 552: p6 = gadd((GEN)p1[i],(GEN)p1[j]);
! 553: for (k=j+1; k<=7; k++)
! 554: z[++ind] = (long) gadd(p6,(GEN)p1[k]);
! 555: }
! 556: p4 = roots_to_pol(z,0);
! 557: p5 = grndtoi(greal(p4),&e);
! 558: e1 = gexpo(gimag(p4)); if (e1>e) e=e1;
! 559: if (e <= -10) break;
! 560: prec = (prec<<1)-2;
! 561: }
! 562: p6 = modulargcd(p5,derivpol(p5));
! 563: if (typ(p6)==t_POL && lgef(p6)>3) goto tchi;
! 564: p2=(GEN)factor(p5)[1];
! 565: switch(lg(p2)-1)
! 566: {
! 567: case 1: f=carreparfait(discsr(x)); avma=av; y=cgetg(4,t_VEC); y[3]=un;
! 568: if (f) { y[2]=un; y[1]=lstoi(2520); }
! 569: else { y[2]=lneg(gun); y[1]=lstoi(5040); }
! 570: return y;
! 571: case 2: f=lgef(p2[1])-3; avma=av; y=cgetg(4,t_VEC); y[3]=un;
! 572: if (f==7 || f==28) { y[2]=un; y[1]=lstoi(168); }
! 573: else { y[2]=lneg(gun); y[1]=lstoi(42); }
! 574: return y;
! 575: case 3: avma=av; y=cgetg(4,t_VEC);
! 576: y[3]=y[2]=un; y[1]=lstoi(21); return y;
! 577: case 4: avma=av; y=cgetg(4,t_VEC);
! 578: y[3]=un; y[2]=lneg(gun); y[1]=lstoi(14); return y;
! 579: case 5: avma=av; y=cgetg(4,t_VEC);
! 580: y[3]=y[2]=un; y[1]=lstoi(7); return y;
! 581: default: err(talker,"galois (bug2)");
! 582: }
! 583: }
! 584: tchi: avma=av1; x=tschirnhaus(x1);
! 585: }
! 586: }
! 587:
! 588: GEN
! 589: galoisapply(GEN nf, GEN aut, GEN x)
! 590: {
! 591: long av=avma,tetpil,lx,j,N;
! 592: GEN p,p1,y,pol;
! 593:
! 594: nf=checknf(nf); pol=(GEN)nf[1];
! 595: if (typ(aut)==t_POL) aut = gmodulcp(aut,pol);
! 596: else
! 597: {
! 598: if (typ(aut)!=t_POLMOD || !gegal((GEN)aut[1],pol))
! 599: err(talker,"incorrect galois automorphism in galoisapply");
! 600: }
! 601: switch(typ(x))
! 602: {
! 603: case t_INT: case t_INTMOD: case t_FRAC: case t_FRACN: case t_PADIC:
! 604: avma=av; return gcopy(x);
! 605:
! 606: case t_POLMOD: x = (GEN) x[2]; /* fall through */
! 607: case t_POL:
! 608: p1 = gsubst(x,varn(pol),aut);
! 609: if (typ(p1)!=t_POLMOD || !gegal((GEN)p1[1],pol)) p1 = gmodulcp(p1,pol);
! 610: return gerepileupto(av,p1);
! 611:
! 612: case t_VEC:
! 613: if (lg(x)==3)
! 614: {
! 615: y=cgetg(3,t_VEC);
! 616: y[1]=(long)galoisapply(nf,aut,(GEN)x[1]);
! 617: y[2]=lcopy((GEN)x[2]); return gerepileupto(av, y);
! 618: }
! 619: if (lg(x)!=6) err(typeer,"galoisapply");
! 620: y=cgetg(6,t_VEC); y[1]=x[1]; y[3]=x[3]; y[4]=x[4];
! 621: p = (GEN)x[1];
! 622: p1=centermod(galoisapply(nf,aut,(GEN)x[2]), p);
! 623: if (is_pm1(x[3]))
! 624: if (ggval(subres(gmul((GEN)nf[7],p1),pol), p) > itos((GEN)x[4]))
! 625: p1[1] = (signe(p1[1]) > 0)? lsub((GEN)p1[1], p)
! 626: : ladd((GEN)p1[1], p);
! 627: y[2]=(long)p1;
! 628: y[5]=(long)centermod(galoisapply(nf,aut,(GEN)x[5]), p);
! 629: tetpil=avma; return gerepile(av,tetpil,gcopy(y));
! 630:
! 631: case t_COL:
! 632: N=lgef(pol)-3;
! 633: if (lg(x)!=N+1) err(typeer,"galoisapply");
! 634: p1=galoisapply(nf,aut,gmul((GEN)nf[7],x)); tetpil=avma;
! 635: return gerepile(av,tetpil,algtobasis(nf,p1));
! 636:
! 637: case t_MAT:
! 638: lx=lg(x); if (lx==1) return cgetg(1,t_MAT);
! 639: N=lgef(pol)-3;
! 640: if (lg(x[1])!=N+1) err(typeer,"galoisapply");
! 641: p1=cgetg(lx,t_MAT);
! 642: for (j=1; j<lx; j++) p1[j]=(long)galoisapply(nf,aut,(GEN)x[j]);
! 643: if (lx==N+1) p1 = idealhermite(nf,p1);
! 644: return gerepileupto(av,p1);
! 645: }
! 646: err(typeer,"galoisapply");
! 647: return NULL; /* not reached */
! 648: }
! 649:
! 650: GEN pol_to_monic(GEN pol, GEN *lead);
! 651: int cmp_pol(GEN x, GEN y);
! 652:
! 653: static GEN
! 654: get_nfpol(GEN x, GEN *nf)
! 655: {
! 656: if (typ(x) == t_POL) { *nf = NULL; return x; }
! 657: *nf = checknf(x); return (GEN)(*nf)[1];
! 658: }
! 659:
! 660: /* if fliso test for isomorphism, for inclusion otherwise. */
! 661: static GEN
! 662: nfiso0(GEN a, GEN b, long fliso)
! 663: {
! 664: long av=avma,tetpil,n,m,i,vb,lx;
! 665: GEN nfa,nfb,p1,y,la,lb;
! 666:
! 667: a = get_nfpol(a, &nfa);
! 668: b = get_nfpol(b, &nfb);
! 669: if (fliso && nfa && !nfb) { p1=a; a=b; b=p1; p1=nfa; nfa=nfb; nfb=p1; }
! 670: m=lgef(a)-3;
! 671: n=lgef(b)-3; if (m<=0 || n<=0) err(constpoler,"nfiso or nfincl");
! 672: if (fliso)
! 673: { if (n!=m) return gzero; }
! 674: else
! 675: { if (n%m) return gzero; }
! 676:
! 677: if (nfb) lb = NULL; else b = pol_to_monic(b,&lb);
! 678: if (nfa) la = NULL; else a = pol_to_monic(a,&la);
! 679: if (nfa && nfb)
! 680: {
! 681: if (fliso)
! 682: {
! 683: if (!gegal((GEN)nfa[2],(GEN)nfb[2])
! 684: || !gegal((GEN)nfa[3],(GEN)nfb[3])) return gzero;
! 685: }
! 686: else
! 687: if (!divise((GEN)nfb[3], gpowgs((GEN)nfa[3],n/m))) return gzero;
! 688: }
! 689: else
! 690: {
! 691: GEN da = nfa? (GEN)nfa[3]: discsr(a);
! 692: GEN db = nfb? (GEN)nfb[3]: discsr(b);
! 693: if (fliso)
! 694: {
! 695: p1=gdiv(da,db);
! 696: if (typ(p1)==t_FRAC) p1=mulii((GEN)p1[1],(GEN)p1[2]);
! 697: if (!carreparfait(p1)) { avma=av; return gzero; }
! 698: }
! 699: else
! 700: {
! 701: long q=n/m;
! 702: GEN fa=factor(da), ex=(GEN)fa[2];
! 703: fa=(GEN)fa[1]; lx=lg(fa);
! 704: for (i=1; i<lx; i++)
! 705: if (mod2((GEN)ex[i]) && !divise(db,gpowgs((GEN)fa[i],q)))
! 706: { avma=av; return gzero; }
! 707: }
! 708: }
! 709: a = dummycopy(a); setvarn(a,0);
! 710: b = dummycopy(b); vb=varn(b);
! 711: if (nfb)
! 712: {
! 713: if (vb == 0) nfb = gsubst(nfb, 0, polx[MAXVARN]);
! 714: y = lift_intern(nfroots(nfb,a));
! 715: }
! 716: else
! 717: {
! 718: if (vb == 0) setvarn(b, fetch_var());
! 719: y = (GEN)polfnf(a,b)[1]; lx = lg(y);
! 720: for (i=1; i<lx; i++)
! 721: {
! 722: if (lgef(y[i]) != 4) { setlg(y,i); break; }
! 723: y[i] = (long)gneg_i(lift_intern(gmael(y,i,2)));
! 724: }
! 725: y = gen_sort(y, 0, cmp_pol);
! 726: settyp(y, t_VEC);
! 727: if (vb == 0) delete_var();
! 728: }
! 729: lx = lg(y); if (lx==1) { avma=av; return gzero; }
! 730: for (i=1; i<lx; i++)
! 731: {
! 732: p1 = (GEN)y[i]; setvarn(p1, vb);
! 733: if (lb) p1 = poleval(p1, gmul(polx[vb],lb));
! 734: y[i] = la? ldiv(p1,la): (long)p1;
! 735: }
! 736: tetpil=avma; return gerepile(av,tetpil,gcopy(y));
! 737: }
! 738:
! 739: GEN
! 740: nfisisom(GEN a, GEN b)
! 741: {
! 742: return nfiso0(a,b,1);
! 743: }
! 744:
! 745: GEN
! 746: nfisincl(GEN a, GEN b)
! 747: {
! 748: return nfiso0(a,b,0);
! 749: }
! 750:
! 751: /*************************************************************************/
! 752: /** **/
! 753: /** INITALG **/
! 754: /** **/
! 755: /*************************************************************************/
! 756: GEN LLL_nfbasis(GEN *x, GEN polr, GEN base, long prec);
! 757: GEN eleval(GEN f,GEN h,GEN a);
! 758: int canon_pol(GEN z);
! 759: GEN mat_to_vecpol(GEN x, long v);
! 760: GEN vecpol_to_mat(GEN v, long n);
! 761:
! 762: /* For internal use. compute trace(x mod pol), sym=polsym(pol,deg(pol)-1) */
! 763: GEN
! 764: quicktrace(GEN x, GEN sym)
! 765: {
! 766: GEN p1 = gzero;
! 767: long i;
! 768:
! 769: if (signe(x))
! 770: {
! 771: sym--;
! 772: for (i=lgef(x)-1; i>1; i--)
! 773: p1 = gadd(p1, gmul((GEN)x[i],(GEN)sym[i]));
! 774: }
! 775: return p1;
! 776: }
! 777:
! 778: /* Seek a new, simpler, polynomial pol defining the same number field as
! 779: * x (assumed to be monic at this point).
! 780: * *ptx receives pol
! 781: * *ptdx receives disc(pol)
! 782: * *ptrev expresses the new root in terms of the old one.
! 783: * base updated in place.
! 784: * prec = 0 <==> field is totally real
! 785: */
! 786: static void
! 787: nfinit_reduce(long flag, GEN *px, GEN *pdx, GEN *prev, GEN *pbase, long prec)
! 788: {
! 789: GEN chbas,a,phimax,dxn,s,sn,p1,p2,p3,polmax,rev,polr;
! 790: GEN x = *px, dx = *pdx, base = *pbase;
! 791: long i,j,nmax,numb,flc,v=varn(x), n=lg(base)-1;
! 792:
! 793: if (n == 1)
! 794: {
! 795: *px = gsub(polx[v],gun); *pdx = gun;
! 796: *prev = polymodrecip(gmodulcp(gun, x)); return;
! 797: }
! 798: polr = prec? roots(x, prec): NULL;
! 799: if (polr)
! 800: for (s=gzero,i=1; i<=n; i++) s = gadd(s,gnorm((GEN)polr[i]));
! 801: else
! 802: s = subii(sqri((GEN)x[n+1]), shifti((GEN)x[n],1));
! 803:
! 804: chbas = LLL_nfbasis(&x,polr,base,prec);
! 805: if (DEBUGLEVEL) msgtimer("LLL basis");
! 806:
! 807: phimax=polx[v]; polmax=dummycopy(x);
! 808: nmax=(flag & nf_PARTIAL)?min(n,3):n;
! 809:
! 810: for (numb=0,i=2; i<=nmax || (!numb && i<=n); i++)
! 811: { /* cf pols_for_polred */
! 812: if (DEBUGLEVEL>2) { fprintferr("i = %ld\n",i); flusherr(); }
! 813: p1 = a = gmul(base,(GEN)chbas[i]); p3=content(p1);
! 814: if (gcmp1(p3)) p3 = NULL; else p1 = gdiv(p1,p3);
! 815: p1 = caract2(x,p1,v);
! 816: if (p3)
! 817: for (p2=gun, j=lgef(p1)-2; j>=2; j--)
! 818: {
! 819: p2 = gmul(p2,p3); p1[j] = lmul((GEN)p1[j], p2);
! 820: }
! 821: p2 = modulargcd(derivpol(p1),p1);
! 822: if (lgef(p2) > 3) continue;
! 823:
! 824: if (DEBUGLEVEL>3) outerr(p1);
! 825: dxn=discsr(p1); flc=absi_cmp(dxn,dx); numb++;
! 826: if (flc>0) continue;
! 827:
! 828: if (polr)
! 829: for (sn=gzero,j=1; j<=n; j++)
! 830: sn = gadd(sn,gnorm(poleval(a,(GEN)polr[j])));
! 831: else
! 832: sn = subii(sqri((GEN)p1[n+1]), shifti((GEN)p1[n],1));
! 833: if (flc>=0)
! 834: {
! 835: flc=gcmp(sn,s);
! 836: if (flc>0 || (!flc && gpolcomp(p1,polmax) >= 0)) continue;
! 837: }
! 838: dx=dxn; s=sn; polmax=p1; phimax=a;
! 839: }
! 840: if (!numb)
! 841: {
! 842: if (gisirreducible(x)!=gun) err(redpoler,"nfinit_reduce");
! 843: err(talker,"you have found a counter-example to a conjecture, "
! 844: "please send us\nthe polynomial as soon as possible");
! 845: }
! 846: if (phimax == polx[v]) /* no improvement */
! 847: rev = gmodulcp(phimax,x);
! 848: else
! 849: {
! 850: if (canon_pol(polmax) < 0) phimax = gneg_i(phimax);
! 851: if (DEBUGLEVEL>1) fprintferr("polmax = %Z\n",polmax);
! 852: p2 = gmodulcp(phimax,x); rev = polymodrecip(p2);
! 853: a = base; base = cgetg(n+1,t_VEC);
! 854: p1 = (GEN)rev[2];
! 855: for (i=1; i<=n; i++)
! 856: base[i] = (long)eleval(polmax, (GEN)a[i], p1);
! 857: p1 = vecpol_to_mat(base,n); p2=denom(p1); p1=gmul(p2,p1);
! 858: p1 = gdiv(hnfmod(p1,detint(p1)), p2);
! 859: base = mat_to_vecpol(p1,v);
! 860: }
! 861: *px=polmax; *pdx=dx; *prev=rev; *pbase = base;
! 862: }
! 863:
! 864: /* pol belonging to Z[x], return a monic polynomial generating the same field
! 865: * as pol (x-> ax+b)) set lead = NULL if pol was monic (after dividing
! 866: * by the content), and to to leading coeff otherwise.
! 867: * No garbage collecting done.
! 868: */
! 869: GEN
! 870: pol_to_monic(GEN pol, GEN *lead)
! 871: {
! 872: long n = lgef(pol)-1;
! 873: GEN p1;
! 874:
! 875: if (n==1 || gcmp1((GEN)pol[n])) { *lead = NULL; return pol; }
! 876:
! 877: p1=content(pol); if (!gcmp1(p1)) pol = gdiv(pol,p1);
! 878: return primitive_pol_to_monic(pol,lead);
! 879: }
! 880:
! 881: GEN
! 882: make_TI(GEN nf, GEN TI, GEN con)
! 883: {
! 884: GEN z, p1 = hnfmod(TI,detint(TI)), d = dethnf(p1);
! 885: long n = lg(TI)-1;
! 886:
! 887: d = mulii(d, gpowgs(con, n));
! 888: p1 = ideal_two_elt(nf, p1); p1 = gmul(p1,con);
! 889: z = cgetg(4,t_VEC);
! 890: z[1]=p1[1]; z[2]=p1[2]; z[3]=(long)d; return z;
! 891: }
! 892:
! 893: /* basis = integer basis. roo = real part of the roots */
! 894: GEN
! 895: make_M(long n,long ru,GEN basis,GEN roo)
! 896: {
! 897: GEN p1,res = cgetg(n+1,t_MAT);
! 898: long i,j;
! 899:
! 900: for (j=1; j<=n; j++)
! 901: {
! 902: p1=cgetg(ru+1,t_COL); res[j]=(long)p1;
! 903: for (i=1; i<=ru; i++)
! 904: p1[i]=(long)poleval((GEN)basis[j],(GEN)roo[i]);
! 905: }
! 906: if (DEBUGLEVEL>4) msgtimer("matrix M");
! 907: return res;
! 908: }
! 909:
! 910: GEN
! 911: make_MC(long n,long r1,long ru,GEN M)
! 912: {
! 913: GEN p1,p2,res=cgetg(ru+1,t_MAT);
! 914: long i,j,av,tetpil;
! 915:
! 916: for (j=1; j<=ru; j++)
! 917: {
! 918: p1=cgetg(n+1,t_COL); res[j]=(long)p1;
! 919: for (i=1; i<=n; i++)
! 920: {
! 921: av=avma; p2=gconj(gcoeff(M,j,i)); tetpil=avma;
! 922: p1[i] = (j<=r1)? (long)p2: lpile(av,tetpil,gmul2n(p2,1));
! 923: }
! 924: }
! 925: if (DEBUGLEVEL>4) msgtimer("matrix MC");
! 926: return res;
! 927: }
! 928:
! 929: GEN
! 930: get_roots(GEN x,long r1,long ru,long prec)
! 931: {
! 932: GEN roo = (typ(x)==t_VEC)? dummycopy(x): roots(x,prec);
! 933: long i;
! 934:
! 935: for (i=1; i<=r1; i++) roo[i]=lreal((GEN)roo[i]);
! 936: for ( ; i<=ru; i++) roo[i]=roo[(i<<1)-r1];
! 937: roo[0]=evaltyp(t_VEC)|evallg(ru+1); return roo;
! 938: }
! 939:
! 940: GEN
! 941: get_mul_table(GEN x,GEN bas,GEN *ptT)
! 942: {
! 943: long i,j,k, n = lgef(x)-3;
! 944: GEN T,sym,mul=cgetg(n*n+1,t_MAT);
! 945:
! 946: for (j=1; j<=n*n; j++) mul[j]=lgetg(n+1,t_COL);
! 947: if (ptT)
! 948: {
! 949: sym = polsym(x,n-1); T=cgetg(n+1,t_MAT); *ptT = T;
! 950: for (j=1; j<=n; j++) T[j]=lgetg(n+1,t_COL);
! 951: }
! 952: for (i=1; i<=n; i++)
! 953: for (j=i; j<=n; j++)
! 954: {
! 955: GEN t = gres(gmul((GEN)bas[j],(GEN)bas[i]), x);
! 956: GEN a = (GEN)mul[j+(i-1)*n];
! 957: GEN b = (GEN)mul[i+(j-1)*n];
! 958: long l = lgef(t)-1;
! 959: for (k=1; k<l ; k++) a[k] = b[k] = t[k+1];
! 960: for ( ; k<=n; k++) a[k] = b[k] = zero;
! 961: if (ptT) coeff(T,i,j) = coeff(T,j,i) = (long)quicktrace(t,sym);
! 962: }
! 963: return mul;
! 964: }
! 965:
! 966: /* Initialize the number field defined by the polynomial x (in variable v)
! 967: * flag & nf_REGULAR
! 968: * regular behaviour (no different).
! 969: * flag & nf_DIFFERENT
! 970: * compute the different.
! 971: * flag & nf_SMALL
! 972: * compute only nf[1] (pol), nf[2] (signature), nf[5][3] (T2) and
! 973: * nf[7] (integer basis), the other components are filled with gzero.
! 974: * flag & nf_REDUCE
! 975: * try a polred first.
! 976: * flag & nf_PARTIAL
! 977: * do a partial polred, not a polredabs
! 978: * flag & nf_ORIG
! 979: * do a polred and return [nfinit(x),Mod(a,red)], where
! 980: * Mod(a,red)=Mod(v,x) (i.e return the base change).
! 981: */
! 982:
! 983: /* here x can be a polynomial, an nf or a bnf */
! 984: GEN
! 985: initalgall0(GEN x, long flag, long prec)
! 986: {
! 987: GEN lead = NULL,nf,ro,bas,mul,mat,M,MC,T,p1,rev,dK,dx,index,fa,res;
! 988: long av=avma,n,i,r1,r2,ru,PRECREG;
! 989:
! 990: if (DEBUGLEVEL) timer2();
! 991: if (typ(x)==t_POL)
! 992: {
! 993: n=lgef(x)-3; if (n<=0) err(constpoler,"initalgall0");
! 994: check_pol_int(x);
! 995: if (gisirreducible(x) == gzero) err(redpoler,"nfinit");
! 996: if (!gcmp1((GEN)x[n+2]))
! 997: {
! 998: x = pol_to_monic(x,&lead);
! 999: if (!(flag & nf_SMALL))
! 1000: {
! 1001: if (!(flag & nf_REDUCE))
! 1002: err(warner,"non-monic polynomial. Result of the form [nf,c].");
! 1003: flag = flag | nf_REDUCE | nf_ORIG;
! 1004: }
! 1005: }
! 1006: bas=allbase4(x,0,&dK,&fa);
! 1007: if (DEBUGLEVEL) msgtimer("round4");
! 1008: dx = discsr(x); r1 = sturm(x);
! 1009: }
! 1010: else
! 1011: {
! 1012: i = lg(x);
! 1013: if (typ(x) == t_VEC && i<=4 && i>=3 && typ(x[1])==t_POL)
! 1014: { /* polynomial + integer basis */
! 1015: bas=(GEN)x[2]; x=(GEN)x[1]; n=lgef(x)-3;
! 1016: if (gisirreducible(x) == gzero) err(redpoler,"nfinit");
! 1017: dx=discsr(x);
! 1018: if (typ(bas) == t_MAT) { mat = bas; bas = mat_to_vecpol(mat,varn(x)); }
! 1019: else mat = vecpol_to_mat(bas,n);
! 1020: dK = gmul(dx, gsqr(det2(mat)));
! 1021: r1 = sturm(x);
! 1022: }
! 1023: else
! 1024: {
! 1025: nf=checknf(x);
! 1026: bas=(GEN)nf[7]; x=(GEN)nf[1]; n=lgef(x)-3;
! 1027: dK=(GEN)nf[3]; dx=mulii(dK, sqri((GEN)nf[4]));
! 1028: r1 = itos(gmael(nf,2,1));
! 1029: }
! 1030: bas[1]=lpolun[varn(x)]; /* it may be gun => SEGV later */
! 1031: if (flag & nf_DIFFERENT) fa = factor(absi(dK));
! 1032: }
! 1033: r2=(n-r1)>>1; ru=r1+r2;
! 1034: PRECREG = prec + (expi(dK)>>(TWOPOTBITS_IN_LONG+1))
! 1035: + (long)((sqrt((double)n)+3) / sizeof(long) * 4);
! 1036: if (flag & nf_REDUCE)
! 1037: {
! 1038: nfinit_reduce(flag, &x, &dx, &rev, &bas, r1==n? 0: prec);
! 1039: if (DEBUGLEVEL) msgtimer("polred");
! 1040: }
! 1041: if (!carrecomplet(divii(dx,dK),&index))
! 1042: err(bugparier,"nfinit (incorrect discriminant)");
! 1043:
! 1044: if (!(flag & nf_SMALL))
! 1045: {
! 1046: mul = get_mul_table(x,bas, &T);
! 1047: if (DEBUGLEVEL) msgtimer("mult. table");
! 1048: p1=vecpol_to_mat(bas,n);
! 1049: }
! 1050:
! 1051: ro=get_roots(x,r1,ru,PRECREG);
! 1052: if (DEBUGLEVEL) msgtimer("roots");
! 1053:
! 1054: if (flag & nf_ORIG)
! 1055: {
! 1056: if (!(flag & nf_REDUCE)) err(talker,"bad flag in initalgall0");
! 1057: res = cgetg(3,t_VEC);
! 1058: }
! 1059: nf=cgetg(10,t_VEC);
! 1060: nf[1]=lcopy(x);
! 1061: nf[2]=lgetg(3,t_VEC);
! 1062: mael(nf,2,1)=lstoi(r1);
! 1063: mael(nf,2,2)=lstoi(r2);
! 1064: nf[3]=lcopy(dK);
! 1065: nf[4]=lcopy(index); mat = cgetg(8,t_VEC);
! 1066: nf[5]=(long)mat;
! 1067: nf[6]=lcopy(ro);
! 1068: nf[7]=lcopy(bas);
! 1069: if (flag & nf_SMALL) nf[8]=nf[9]=zero;
! 1070: else
! 1071: {
! 1072: nf[8]=linvmat(p1);
! 1073: nf[9]=lmul((GEN)nf[8],mul);
! 1074: }
! 1075:
! 1076: M = make_M(n,ru,bas,ro);
! 1077: MC = make_MC(n,r1,ru,M);
! 1078: mat[1]=(long)M;
! 1079: mat[5]=zero; /* dummy for the different */
! 1080: mat[3]=(long)mulmat_real(MC,M);
! 1081: if (flag & nf_SMALL)
! 1082: mat[2]=mat[4]=mat[6]=mat[7]=zero;
! 1083: else
! 1084: {
! 1085: long av2, av3;
! 1086: GEN a2;
! 1087:
! 1088: mat[2]=(long)MC;
! 1089: mat[4]=lcopy(T);
! 1090:
! 1091: av2=avma; p1=ginv(T); av3=avma;
! 1092: mat[6] = lpile(av2,av3, gmul(p1,dK));
! 1093:
! 1094: av2=avma; p1=content((GEN)mat[6]); a2=gdiv((GEN)mat[6],p1);
! 1095: a2 = make_TI(nf,a2,p1); av3=avma;
! 1096: /* Ideal basis for discriminant * (inverse of different) */
! 1097: mat[7] = lpile(av2,av3,gcopy(a2));
! 1098: }
! 1099: if (DEBUGLEVEL>=2) msgtimer("matrices");
! 1100:
! 1101: if (flag & nf_DIFFERENT)
! 1102: {
! 1103: mat[5]=(long)differente(nf,fa);
! 1104: if (DEBUGLEVEL) msgtimer("different");
! 1105: }
! 1106: if (!(flag & nf_ORIG)) res = nf;
! 1107: else
! 1108: {
! 1109: res[1]=(long)nf;
! 1110: res[2]=lead? ldiv(rev,lead): lcopy(rev);
! 1111: }
! 1112: return gerepileupto(av,res);
! 1113: }
! 1114:
! 1115: GEN
! 1116: initalgred(GEN x, long prec)
! 1117: {
! 1118: return initalgall0(x,nf_REDUCE|nf_DIFFERENT,prec);
! 1119: }
! 1120:
! 1121: GEN
! 1122: initalgred2(GEN x, long prec)
! 1123: {
! 1124: return initalgall0(x,nf_REDUCE|nf_DIFFERENT|nf_ORIG,prec);
! 1125: }
! 1126:
! 1127: GEN
! 1128: nfinit0(GEN x, long flag,long prec)
! 1129: {
! 1130: switch(flag)
! 1131: {
! 1132: case 0: return initalgall0(x,nf_DIFFERENT,prec);
! 1133: case 1: return initalgall0(x,nf_REGULAR,prec);
! 1134: case 2: return initalgall0(x,nf_REDUCE|nf_DIFFERENT,prec);
! 1135: case 3: return initalgall0(x,nf_REDUCE|nf_ORIG|nf_DIFFERENT,prec);
! 1136: case 4: return initalgall0(x,nf_REDUCE|nf_PARTIAL|nf_DIFFERENT,prec);
! 1137: case 5: return initalgall0(x,nf_REDUCE|nf_ORIG|nf_PARTIAL|nf_DIFFERENT,prec);
! 1138: case 6: return initalgall0(x,nf_SMALL,prec);
! 1139: default: err(flagerr,"nfinit");
! 1140: }
! 1141: return NULL; /* not reached */
! 1142: }
! 1143:
! 1144: GEN
! 1145: initalg(GEN x, long prec)
! 1146: {
! 1147: return initalgall0(x,nf_DIFFERENT,prec);
! 1148: }
! 1149:
! 1150: GEN
! 1151: nfnewprec(GEN nf, long prec)
! 1152: {
! 1153: long av=avma,i,r1,r2,ru,n,nf_small,tetpil;
! 1154: GEN y,pol,ro,bas,MC,mat,M;
! 1155:
! 1156: if (typ(nf) != t_VEC) err(talker,"incorrect nf in nfnewprec");
! 1157: if (lg(nf) == 11) return bnfnewprec(nf,prec);
! 1158: if (prec <= 0)
! 1159: {
! 1160: ro = (GEN)nf[6];
! 1161: prec = (typ(ro)==t_VEC)?precision((GEN)ro[1]): DEFAULTPREC;
! 1162: return (GEN)prec;
! 1163: }
! 1164:
! 1165: y=cgetg(10,t_VEC);
! 1166: for (i=1; i<=4; i++) y[i]=nf[i];
! 1167: for (i=6; i<=9; i++) y[i]=nf[i];
! 1168: nf_small = gcmp0((GEN)nf[8]);
! 1169: pol=(GEN)nf[1]; n=degree(pol);
! 1170: r1=itos(gmael(nf,2,1)); r2=itos(gmael(nf,2,2)); ru=r1+r2;
! 1171: mat=cgetg(8,t_VEC); y[5]=(long)mat;
! 1172: bas=(GEN)nf[7]; ro=get_roots(pol,r1,ru,prec);
! 1173: M = make_M(n,ru,bas,ro);
! 1174: MC = make_MC(n,r1,ru,M);
! 1175: if (nf_small) mat[2]=mat[4]=mat[5]=mat[6]=mat[7]=zero;
! 1176: else
! 1177: {
! 1178: GEN matrices=(GEN)nf[5];
! 1179: y[6]=(long)ro;
! 1180: mat[2]=(long)MC;
! 1181: for (i=4; i<=7; i++) mat[i]=matrices[i];
! 1182: }
! 1183: mat[1]=(long)M;
! 1184: mat[3]=lreal(gmul(MC,M));
! 1185: tetpil=avma; return gerepile(av,tetpil,gcopy(y));
! 1186: }
! 1187:
! 1188: static long
! 1189: nf_pm1(GEN y)
! 1190: {
! 1191: long i,l;
! 1192:
! 1193: if (!is_pm1(y[1])) return 0;
! 1194: l = lg(y);
! 1195: for (i=2; i<l; i++)
! 1196: if (signe(y[i])) return 0;
! 1197: return signe(y[1]);
! 1198:
! 1199: }
! 1200:
! 1201: static GEN
! 1202: is_primitive_root(GEN nf, GEN fa, GEN x, long w)
! 1203: {
! 1204: GEN y, exp = stoi(2), pp = (GEN)fa[1];
! 1205: long i,p, l = lg(pp);
! 1206:
! 1207: for (i=1; i<l; i++)
! 1208: {
! 1209: p = itos((GEN)pp[i]);
! 1210: exp[2] = w / p; y = element_pow(nf,x,exp);
! 1211: if (nf_pm1(y) > 0) /* y = 1 */
! 1212: {
! 1213: if (p!=2 || !gcmp1(gcoeff(fa,i,2))) return NULL;
! 1214: x = gneg_i(x);
! 1215: }
! 1216: }
! 1217: return x;
! 1218: }
! 1219:
! 1220: GEN
! 1221: rootsof1(GEN nf)
! 1222: {
! 1223: long av,tetpil,N,k,i,ws,prec;
! 1224: GEN algun,p1,y,R1,d,list,w;
! 1225:
! 1226: y=cgetg(3,t_VEC); av=avma; nf=checknf(nf);
! 1227: R1=gmael(nf,2,1); algun=gmael(nf,8,1);
! 1228: if (signe(R1))
! 1229: {
! 1230: y[1]=deux;
! 1231: y[2]=lneg(algun); return y;
! 1232: }
! 1233: N=lgef(nf[1])-3; prec=gprecision((GEN)nf[6]);
! 1234: #ifdef LONG_IS_32BIT
! 1235: if (prec < 10) prec = 10;
! 1236: #else
! 1237: if (prec < 6) prec = 6;
! 1238: #endif
! 1239: for (i=1; ; i++)
! 1240: {
! 1241: p1 = fincke_pohst(gmael(nf,5,3),stoi(N),stoi(1000),1,prec,NULL);
! 1242: if (p1) break;
! 1243: if (i == MAXITERPOL) err(accurer,"rootsof1");
! 1244: prec=(prec<<1)-2;
! 1245: if (DEBUGLEVEL) err(warnprec,"rootsof1",prec);
! 1246: nf=nfnewprec(nf,prec);
! 1247: }
! 1248: if (itos(ground((GEN)p1[2])) != N) err(bugparier,"rootsof1 (bug1)");
! 1249: w=(GEN)p1[1]; ws = itos(w);
! 1250: if (ws == 2)
! 1251: {
! 1252: y[1]=deux; avma=av;
! 1253: y[2]=lneg(algun); return y;
! 1254: }
! 1255:
! 1256: d = decomp(w); list = (GEN)p1[3]; k = lg(list);
! 1257: for (i=1; i<k; i++)
! 1258: {
! 1259: p1 = (GEN)list[i];
! 1260: p1 = is_primitive_root(nf,d,p1,ws);
! 1261: if (p1)
! 1262: {
! 1263: tetpil=avma;
! 1264: y[2]=lpile(av,tetpil,gcopy(p1));
! 1265: y[1]=lstoi(ws); return y;
! 1266: }
! 1267: }
! 1268: err(bugparier,"rootsof1");
! 1269: return NULL; /* not reached */
! 1270: }
! 1271:
! 1272: /*******************************************************************/
! 1273: /* */
! 1274: /* DEDEKIND ZETA FUNCTION */
! 1275: /* */
! 1276: /*******************************************************************/
! 1277:
! 1278: ulong smulss(ulong x, ulong y, ulong *rem);
! 1279:
! 1280: static GEN
! 1281: dirzetak0(GEN nf, long N0)
! 1282: {
! 1283: GEN vect,p1,pol,disc,c,c2;
! 1284: long av=avma,i,j,k,lx;
! 1285: ulong limk,q,p,rem;
! 1286: byteptr d=diffptr;
! 1287: long court[] = {evaltyp(t_INT)|m_evallg(3), evalsigne(1)|evallgefint(3),0};
! 1288:
! 1289: pol=(GEN)nf[1]; disc=(GEN)nf[4];
! 1290: c = (GEN) gpmalloc((N0+1)*sizeof(long));
! 1291: c2 = (GEN) gpmalloc((N0+1)*sizeof(long));
! 1292: c2[0]=c[0]=evaltyp(t_VEC) | evallg(N0+1);
! 1293: c2[1]=c[1]=1; for (i=2; i<=N0; i++) c[i]=0;
! 1294: court[2] = 0;
! 1295:
! 1296: while (court[2]<=N0)
! 1297: {
! 1298: court[2] += *d++; if (! *d) err(primer1);
! 1299: if (smodis(disc,court[2])) /* court does not divide index */
! 1300: { vect = (GEN) simplefactmod(pol,court)[1]; lx=lg(vect); }
! 1301: else
! 1302: {
! 1303: p1=primedec(nf,court); lx=lg(p1); vect=cgetg(lx,t_COL);
! 1304: for (i=1; i<lx; i++) vect[i]=mael(p1,i,4);
! 1305: }
! 1306: for (j=1; j<lx; j++)
! 1307: {
! 1308: p1=powgi(court, (GEN)vect[j]); /* p1 = court^f */
! 1309: if (cmpis(p1,N0) <= 0)
! 1310: {
! 1311: q=p=p1[2]; limk=N0/q;
! 1312: for (k=2; k<=N0; k++) c2[k]=c[k];
! 1313: while (q<=N0)
! 1314: {
! 1315: for (k=1; k<=limk; k++) c2[k*q] += c[k];
! 1316: q = smulss(q,p,&rem);
! 1317: if (rem) break;
! 1318: limk /= p;
! 1319: }
! 1320: p1=c; c=c2; c2=p1;
! 1321: }
! 1322: }
! 1323: avma=av;
! 1324: if (DEBUGLEVEL>6) fprintferr(" %ld",court[2]);
! 1325: }
! 1326: if (DEBUGLEVEL>6) { fprintferr("\n"); flusherr(); }
! 1327: free(c2); return c;
! 1328: }
! 1329:
! 1330: GEN
! 1331: dirzetak(GEN nf, GEN b)
! 1332: {
! 1333: GEN z,c;
! 1334: long i;
! 1335:
! 1336: if (typ(b)!=t_INT) err(talker,"not an integer type in dirzetak");
! 1337: if (signe(b)<=0) return cgetg(1,t_VEC);
! 1338: nf = checknf(nf);
! 1339: if (is_bigint(b)) err(talker,"too many terms in dirzetak");
! 1340: c = dirzetak0(nf,itos(b));
! 1341: i = lg(c); z=cgetg(i,t_VEC);
! 1342: for (i-- ; i; i--) z[i]=lstoi(c[i]);
! 1343: free(c); return z;
! 1344: }
! 1345:
! 1346: GEN
! 1347: initzeta(GEN pol, long prec)
! 1348: {
! 1349: GEN nfz,nf,alpha,beta,mu,gr1,gr2,gru,p1,p2,cst,A0,c0,c1,c2,eps,coef;
! 1350: GEN limx,bnf,resi,zet,C,coeflog,racpi,aij,tabj,colzero, *tabcstn, *tabcstni;
! 1351: GEN c_even,ck_even,c_odd,ck_odd,serie_even,serie_odd,serie_exp,Pi;
! 1352: long N0,imin,imax,r1,r2,ru,R,N,i,j,k,n, av,av2,tetpil;
! 1353: long court[] = {evaltyp(t_INT)|m_evallg(3), evalsigne(1)|evallgefint(3),0};
! 1354: stackzone *zone, *zone0, *zone1;
! 1355:
! 1356: /*************** Calcul du residu et des constantes ***************/
! 1357: eps=gmul2n(gun,-bit_accuracy(prec)-6); p1=dbltor(0.5);
! 1358: nfz=cgetg(10,t_VEC);
! 1359: bnf=buchinit(pol,p1,p1,prec+1); prec=(prec<<1)-1;
! 1360: Pi = mppi(prec); racpi=gsqrt(Pi,prec);
! 1361:
! 1362: /* Nb de classes et regulateur */
! 1363: nf=(GEN)bnf[7]; N=lgef(nf[1])-3;
! 1364: gr1=gmael(nf,2,1); gr2=gmael(nf,2,2);
! 1365: r1=itos(gr1); r2=itos(gr2); ru=r1+r2; R=ru+2;
! 1366: av=avma; p1=(GEN)bnf[8]; p2 = gmul(gmul2n(gmael(p1,1,1),r1), (GEN)p1[2]);
! 1367: tetpil = avma; resi=gerepile(av,tetpil,gdiv(p2, gmael(p1,4,1)));
! 1368:
! 1369: /* Calcul de N0 */
! 1370: cst = cgetr(prec); av = avma;
! 1371: mu = gadd(gmul2n(gr1,-1),gr2);
! 1372: alpha = gmul2n(stoi(ru+1),-1);
! 1373: beta = gpui(gdeux,gmul2n(gr1,-1),DEFAULTPREC);
! 1374: A0 = gmul2n(gpowgs(mu,R),r1);
! 1375: A0 = gmul(A0,gpowgs(gmul2n(Pi,1),1-ru));
! 1376: A0 = gsqrt(A0,DEFAULTPREC);
! 1377:
! 1378: c1 = gmul(mu,gpui(beta,ginv(mu),DEFAULTPREC));
! 1379: c0 = gdiv(gmul(A0,gpowgs(gmul2n(Pi,1),ru-1)),mu);
! 1380: c0 = gmul(c0,gpui(c1,gneg_i(alpha),DEFAULTPREC));
! 1381: c2 = gdiv(alpha,mu);
! 1382:
! 1383: p1 = glog(gdiv(c0,eps),DEFAULTPREC);
! 1384: limx = gdiv(gsub(glog(p1,DEFAULTPREC),glog(c1,DEFAULTPREC)),
! 1385: gadd(c2,gdiv(p1,mu)));
! 1386: limx = gmul(gpui(gdiv(c1,p1),mu,DEFAULTPREC),
! 1387: gadd(gun,gmul(alpha,limx)));
! 1388: p1 = gsqrt(absi((GEN)nf[3]),prec);
! 1389: p2 = gmul2n(gpowgs(racpi,N),r2);
! 1390: gaffect(gdiv(p1,p2), cst);
! 1391:
! 1392: av = avma; p1 = gfloor(gdiv(cst,limx)); N0 = p1[2];
! 1393: if (is_bigint(p1) || N0 > 10000000)
! 1394: err(talker,"discriminant too large for initzeta, sorry");
! 1395: if (DEBUGLEVEL>=2)
! 1396: { fprintferr("\ninitzeta:\nN0 = %ld\n",N0); flusherr(); timer2(); }
! 1397:
! 1398: /* Calcul de imax */
! 1399:
! 1400: imin=1; imax=1400;
! 1401: p1 = gmul(gpowgs(gmul2n(racpi,1),r2),gpowgs(stoi(5),r1));
! 1402: p1 = gdiv(p1,gmul(gmul(gsqrt(limx,DEFAULTPREC),gmul2n(eps,4)),
! 1403: gpowgs(racpi,3)));
! 1404: while (imax-imin >= 4)
! 1405: {
! 1406: long itest = (imax+imin)>>1;
! 1407: p2 = gmul(gpowgs(mpfactr(itest,DEFAULTPREC),r2),gpowgs(limx,itest));
! 1408: p2 = gmul(p2,gpowgs(mpfactr(itest/2,DEFAULTPREC),r1));
! 1409: if (gcmp(p2,p1) >= 0) imax=itest; else imin=itest;
! 1410: }
! 1411: imax -= (imax & 1); avma = av;
! 1412: if (DEBUGLEVEL>=2) { fprintferr("imax = %ld\n",imax); flusherr(); }
! 1413: /* Tableau des i/cst (i=1 a N0) */
! 1414:
! 1415: i = prec*N0;
! 1416: zone = switch_stack(NULL,i + 2*(N0+1) + 6*prec);
! 1417: zone1 = switch_stack(NULL,2*i);
! 1418: zone0 = switch_stack(NULL,2*i);
! 1419: switch_stack(zone,1);
! 1420: tabcstn = (GEN*) cgetg(N0+1,t_VEC);
! 1421: tabcstni = (GEN*) cgetg(N0+1,t_VEC);
! 1422: p1 = ginv(cst);
! 1423: for (i=1; i<=N0; i++) { tabcstni[i] = gun; tabcstn[i] = mulsr(i,p1); }
! 1424: switch_stack(zone,0);
! 1425:
! 1426: /********** Calcul des coefficients a(i,j) independants de s **********/
! 1427:
! 1428: zet=cgetg(R,t_VEC); zet[1] = lmpeuler(prec);
! 1429: for (i=2; i<R; i++) zet[i] = (long)gzeta(stoi(i),prec);
! 1430:
! 1431: aij=cgetg(imax+1,t_VEC);
! 1432: for (i=1; i<=imax; i++) aij[i] = lgetg(R,t_VEC);
! 1433:
! 1434: c_even = realun(prec);
! 1435: c_even = gmul2n(c_even,r1);
! 1436: c_odd = gmul(c_even,gpowgs(racpi,r1));
! 1437: if (ru&1) c_odd=gneg_i(c_odd);
! 1438: ck_even=cgetg(R,t_VEC); ck_odd=cgetg(r2+2,t_VEC);
! 1439: for (k=1; k<R; k++)
! 1440: {
! 1441: ck_even[k]=lmul((GEN)zet[k],gadd(gr2,gmul2n(gr1,-k)));
! 1442: if (k&1) ck_even[k]=lneg((GEN)ck_even[k]);
! 1443: }
! 1444: gru=stoi(ru);
! 1445: for (k=1; k<=r2+1; k++)
! 1446: {
! 1447: ck_odd[k]=lmul((GEN)zet[k], gsub(gru, gmul2n(gr1,-k)));
! 1448: if (k&1) ck_odd[k]=lneg((GEN)ck_odd[k]);
! 1449: ck_odd[k]=ladd(gru,(GEN)ck_odd[k]);
! 1450: }
! 1451: ck_odd[1]=lsub((GEN)ck_odd[1],gmul(gr1,glog(gdeux,prec)));
! 1452: serie_even =cgetg(ru+3,t_SER); serie_odd=cgetg(r2+3,t_SER);
! 1453: serie_even[1] = serie_odd[1] = evalsigne(1)+evalvalp(1);
! 1454: i=0;
! 1455:
! 1456: while (i<imax/2)
! 1457: {
! 1458: for (k=1; k<R; k++)
! 1459: serie_even[k+1]=ldivgs((GEN)ck_even[k],k);
! 1460: serie_exp=gmul(c_even,gexp(serie_even,0));
! 1461: p1=(GEN)aij[2*i+1];
! 1462: for (j=1; j<R; j++) p1[j]=serie_exp[ru+3-j];
! 1463:
! 1464: for (k=1; k<=r2+1; k++)
! 1465: serie_odd[k+1]=ldivgs((GEN)ck_odd[k],k);
! 1466: serie_exp=gmul(c_odd,gexp(serie_odd,0));
! 1467: p1=(GEN)aij[2*i+2];
! 1468: for (j=1; j<=r2+1; j++) p1[j]=serie_exp[r2+3-j];
! 1469: for ( ; j<R; j++) p1[j]=zero;
! 1470: i++;
! 1471:
! 1472: c_even = gdiv(c_even,gmul(gpowgs(stoi(i),ru),gpowgs(stoi(2*i-1),r2)));
! 1473: c_odd = gdiv(c_odd, gmul(gpowgs(stoi(i),r2),gpowgs(stoi(2*i+1),ru)));
! 1474: c_even = gmul2n(c_even,-r2);
! 1475: c_odd = gmul2n(c_odd,r1-r2);
! 1476: if (r1&1) { c_even=gneg_i(c_even); c_odd=gneg_i(c_odd); }
! 1477: p1 = gr2; p2 = gru;
! 1478: for (k=1; k<R; k++)
! 1479: {
! 1480: p1=gdivgs(p1,2*i-1); p2=gdivgs(p2,2*i);
! 1481: ck_even[k] = ladd((GEN)ck_even[k], gadd(p1,p2));
! 1482: }
! 1483: p1 = gru; p2 = gr2;
! 1484: for (k=1; k<=r2+1; k++)
! 1485: {
! 1486: p1=gdivgs(p1,2*i+1); p2=gdivgs(p2,2*i);
! 1487: ck_odd[k] = ladd((GEN)ck_odd[k], gadd(p1,p2));
! 1488: }
! 1489: }
! 1490: tetpil=avma; aij=gerepile(av,tetpil,gcopy(aij));
! 1491: if (DEBUGLEVEL>=2) msgtimer("a(i,j)");
! 1492: p1=cgetg(5,t_VEC);
! 1493: p1[1]=lstoi(r1); p1[2]=lstoi(r2); p1[3]=lstoi(imax); p1[4]=(long)bnf;
! 1494: nfz[1]=(long)p1;
! 1495: nfz[2]=(long)resi;
! 1496: nfz[5]=(long)cst;
! 1497: nfz[6]=llog(cst,prec);
! 1498: nfz[7]=(long)aij;
! 1499:
! 1500: /************* Calcul du nombre d'ideaux de norme donnee *************/
! 1501: coef = dirzetak0(nf,N0); tabj = cgetg(N0+1,t_MAT);
! 1502: if (DEBUGLEVEL>=2) msgtimer("coef");
! 1503: colzero=cgetg(ru+2,t_COL); for (j=1; j<=ru+1; j++) colzero[j]=zero;
! 1504: for (i=1; i<=N0; i++)
! 1505: if (coef[i])
! 1506: {
! 1507: GEN t = cgetg(ru+2,t_COL);
! 1508: p1 = glog((GEN)tabcstn[i],prec); setsigne(p1, -signe(p1));
! 1509: t[1] = lstoi(coef[i]); t[2] = lmul((GEN)t[1],p1);
! 1510: for (j=2; j<=ru; j++)
! 1511: {
! 1512: long av2 = avma; p2 = gmul((GEN)t[j],p1);
! 1513: t[j+1] = (long)gerepileuptoleaf(av2, divrs(p2,j));
! 1514: }
! 1515: /* tabj[n,j]=coef(n)*ln(c/n)^(j-1)/(j-1)! */
! 1516: tabj[i] = (long)t;
! 1517: }
! 1518: else tabj[i]=(long)colzero;
! 1519: if (DEBUGLEVEL>=2) msgtimer("a(n)");
! 1520:
! 1521: coeflog=cgetg(N0+1,t_VEC); coeflog[1]=zero;
! 1522: for (i=2; i<=N0; i++)
! 1523: if (coef[i])
! 1524: {
! 1525: court[2]=i; p1=glog(court,prec);
! 1526: setsigne(p1,-1); coeflog[i]=(long)p1;
! 1527: }
! 1528: else coeflog[i] = zero;
! 1529: if (DEBUGLEVEL>=2) msgtimer("log(n)");
! 1530:
! 1531: nfz[3]=(long)tabj;
! 1532: p1 = cgetg(N0+1,t_VECSMALL);
! 1533: for (i=1; i<=N0; i++) p1[i] = coef[i];
! 1534: nfz[8]=(long)p1;
! 1535: nfz[9]=(long)coeflog;
! 1536:
! 1537: /******************** Calcul des coefficients Cik ********************/
! 1538:
! 1539: C = cgetg(ru+1,t_MAT);
! 1540: for (k=1; k<=ru; k++) C[k] = lgetg(imax+1,t_COL);
! 1541: av2 = avma;
! 1542: for (i=1; i<=imax; i++)
! 1543: {
! 1544: stackzone *z;
! 1545: for (k=1; k<=ru; k++)
! 1546: {
! 1547: p1 = NULL;
! 1548: for (n=1; n<=N0; n++)
! 1549: if (coef[n])
! 1550: for (j=1; j<=ru-k+1; j++)
! 1551: {
! 1552: p2 = gmul(tabcstni[n],
! 1553: gmul(gmael(aij,i,j+k), gmael(tabj,n,j)));
! 1554: p1 = p1? gadd(p1,p2): p2;
! 1555: }
! 1556: coeff(C,i,k) = p1? (long)gerepileupto(av2,p1): zero;
! 1557: av2 = avma;
! 1558: }
! 1559: /* use a parallel stack */
! 1560: z = i&1? zone1: zone0;
! 1561: switch_stack(z, 1);
! 1562: for (n=1; n<=N0; n++)
! 1563: if (coef[n]) tabcstni[n] = mpmul(tabcstni[n],tabcstn[n]);
! 1564: /* come back */
! 1565: switch_stack(z, 0);
! 1566: }
! 1567: nfz[4] = (long) C;
! 1568: if (DEBUGLEVEL>=2) msgtimer("Cik");
! 1569: gunclone(aij);
! 1570: free((void*)zone); free((void*)zone1); free((void*)zone0);
! 1571: free((void*)coef); return nfz;
! 1572: }
! 1573:
! 1574: GEN
! 1575: gzetakall(GEN nfz, GEN s, long flag, long prec2)
! 1576: {
! 1577: GEN resi,C,cst,cstlog,coeflog,cs,coef;
! 1578: GEN lambd,gammas,gammaunmoins,gammas2,gammaunmoins2,var1,var2;
! 1579: GEN p1,unmoins,gexpro,gar,val,valm,valk,valkm;
! 1580: long ts = typ(s), r1,r2,ru,imax,i,j,k,N0,sl,prec,bigprec, av = avma;
! 1581:
! 1582: if (typ(nfz)!=t_VEC || lg(nfz)!=10 || typ(nfz[1]) != t_VEC)
! 1583: err(talker,"not a zeta number field in zetakall");
! 1584: if (! is_intreal_t(ts) && ts != t_COMPLEX && ! is_frac_t(ts))
! 1585: err(typeer,"gzetakall");
! 1586: resi=(GEN)nfz[2]; C=(GEN)nfz[4]; cst=(GEN)nfz[5];
! 1587: cstlog=(GEN)nfz[6]; coef=(GEN)nfz[8]; coeflog=(GEN)nfz[9];
! 1588: r1 =itos(gmael(nfz,1,1));
! 1589: r2 =itos(gmael(nfz,1,2));
! 1590: imax=itos(gmael(nfz,1,3));
! 1591: N0=lg(coef)-1; ru=r1+r2;
! 1592: /* from initzeta. Certainly excessive, at least if LONG_IS_64BIT */
! 1593: bigprec = min(precision(cst), (prec2<<1) - 1);
! 1594: prec = prec2+1;
! 1595:
! 1596: if (ts==t_COMPLEX && gcmp0(gimag(s))) { s=greal(s); ts = typ(s); }
! 1597: if (ts==t_REAL && !signe(gfrac(s))) { s=mptrunc(s); ts = t_INT; }
! 1598: if (ts==t_INT)
! 1599: {
! 1600: sl=itos(s);
! 1601: if (sl==1) err(talker,"s = 1 is a pole (gzetakall)");
! 1602: if (sl==0)
! 1603: {
! 1604: if (flag) err(talker,"s = 0 is a pole (gzetakall)");
! 1605: if (ru == 1)
! 1606: {
! 1607: if (r1) return gneg(ghalf);
! 1608: return gneg(resi);
! 1609: }
! 1610: return gzero;
! 1611: }
! 1612: if (sl<0 && (r2 || !odd(sl)))
! 1613: {
! 1614: if (!flag) return gzero;
! 1615: s = subsi(1,s); sl = 1-sl;
! 1616: }
! 1617: unmoins=subsi(1,s);
! 1618: lambd = gdiv(resi, mulis(s,sl-1));
! 1619: gammas2=ggamma(gmul2n(s,-1),prec);
! 1620: gar=gpowgs(gammas2,r1);
! 1621: cs=gexp(gmul(cstlog,s),prec);
! 1622: val=s; valm=unmoins;
! 1623: if (sl<0) /* r2 = 0 && odd(sl) */
! 1624: {
! 1625: gammaunmoins2=ggamma(gmul2n(unmoins,-1),prec);
! 1626: var1=var2=gun;
! 1627: for (i=2; i<=N0; i++)
! 1628: if (coef[i])
! 1629: {
! 1630: gexpro=gexp(gmul((GEN)coeflog[i],s),bigprec);
! 1631: var1 = gadd(var1,gmulsg(coef[i],gexpro));
! 1632: var2 = gadd(var2,gdivsg(coef[i],gmulsg(i,gexpro)));
! 1633: }
! 1634: lambd=gadd(lambd,gmul(gmul(var1,cs),gar));
! 1635: lambd=gadd(lambd,gmul(gmul(var2,gdiv(cst,cs)),
! 1636: gpowgs(gammaunmoins2,r1)));
! 1637: for (i=1; i<=imax; i+=2)
! 1638: {
! 1639: valk = val;
! 1640: valkm = valm;
! 1641: for (k=1; k<=ru; k++)
! 1642: {
! 1643: p1 = gcoeff(C,i,k);
! 1644: lambd = gsub(lambd,gdiv(p1,valk )); valk = mulii(val,valk);
! 1645: lambd = gsub(lambd,gdiv(p1,valkm)); valkm = mulii(valm,valkm);
! 1646: }
! 1647: val = addis(val, 2);
! 1648: valm = addis(valm,2);
! 1649: }
! 1650: }
! 1651: else
! 1652: {
! 1653: GEN tabj=(GEN)nfz[3], aij=(GEN)nfz[7];
! 1654:
! 1655: gar = gmul(gar,gpowgs(ggamma(s,prec),r2));
! 1656: var1=var2=gzero;
! 1657: for (i=1; i<=N0; i++)
! 1658: if (coef[i])
! 1659: {
! 1660: gexpro=gexp(gmul((GEN)coeflog[i],s),bigprec);
! 1661: var1 = gadd(var1,gmulsg(coef[i],gexpro));
! 1662: if (sl <= imax)
! 1663: {
! 1664: p1=gzero;
! 1665: for (j=1; j<=ru+1; j++)
! 1666: p1 = gadd(p1, gmul(gmael(aij,sl,j), gmael(tabj,i,j)));
! 1667: var2=gadd(var2,gdiv(p1,gmulsg(i,gexpro)));
! 1668: }
! 1669: }
! 1670: lambd=gadd(lambd,gmul(gmul(var1,cs),gar));
! 1671: lambd=gadd(lambd,gmul(var2,gdiv(cst,cs)));
! 1672: for (i=1; i<=imax; i++)
! 1673: {
! 1674: valk = val;
! 1675: valkm = valm;
! 1676: if (i == sl)
! 1677: for (k=1; k<=ru; k++)
! 1678: {
! 1679: p1 = gcoeff(C,i,k);
! 1680: lambd = gsub(lambd,gdiv(p1,valk)); valk = mulii(val,valk);
! 1681: }
! 1682: else
! 1683: for (k=1; k<=ru; k++)
! 1684: {
! 1685: p1 = gcoeff(C,i,k);
! 1686: lambd = gsub(lambd,gdiv(p1,valk )); valk = mulii(val,valk);
! 1687: lambd = gsub(lambd,gdiv(p1,valkm)); valkm = mulii(valm,valkm);
! 1688: }
! 1689: val = addis(val,1);
! 1690: valm = addis(valm,1);
! 1691: }
! 1692: }
! 1693: }
! 1694: else
! 1695: {
! 1696: GEN Pi = mppi(prec);
! 1697: if (is_frac_t(ts))
! 1698: s = gmul(s, realun(bigprec));
! 1699: else
! 1700: s = gprec_w(s, bigprec);
! 1701:
! 1702: unmoins = gsub(gun,s);
! 1703: lambd = gdiv(resi,gmul(s,gsub(s,gun)));
! 1704: gammas = ggamma(s,prec);
! 1705: gammas2= ggamma(gmul2n(s,-1),prec);
! 1706: gar = gmul(gpowgs(gammas,r2),gpowgs(gammas2,r1));
! 1707: cs = gexp(gmul(cstlog,s),prec);
! 1708: var1 = gmul(Pi,s);
! 1709: gammaunmoins = gdiv(Pi,gmul(gsin(var1,prec),gammas));
! 1710: gammaunmoins2= gdiv(gmul(gmul(gsqrt(Pi,prec),gpui(gdeux,gsub(s,gun),prec)),
! 1711: gammas2),
! 1712: gmul(gcos(gmul2n(var1,-1),prec),gammas));
! 1713: var1 = var2 = gun;
! 1714: for (i=2; i<=N0; i++)
! 1715: if (coef[i])
! 1716: {
! 1717: gexpro = gexp(gmul((GEN)coeflog[i],s),bigprec);
! 1718: var1 = gadd(var1,gmulsg(coef[i], gexpro));
! 1719: var2 = gadd(var2,gdivsg(coef[i], gmulsg(i,gexpro)));
! 1720: }
! 1721: lambd = gadd(lambd,gmul(gmul(var1,cs),gar));
! 1722: lambd = gadd(lambd,gmul(gmul(gmul(var2,gdiv(cst,cs)),
! 1723: gpowgs(gammaunmoins,r2)),
! 1724: gpowgs(gammaunmoins2,r1)));
! 1725: val = s;
! 1726: valm = unmoins;
! 1727: for (i=1; i<=imax; i++)
! 1728: {
! 1729: valk = val;
! 1730: valkm = valm;
! 1731: for (k=1; k<=ru; k++)
! 1732: {
! 1733: p1 = gcoeff(C,i,k);
! 1734: lambd = gsub(lambd,gdiv(p1,valk )); valk = gmul(val, valk);
! 1735: lambd = gsub(lambd,gdiv(p1,valkm)); valkm = gmul(valm,valkm);
! 1736: }
! 1737: if (r2)
! 1738: {
! 1739: val = gadd(val, gun);
! 1740: valm = gadd(valm,gun);
! 1741: }
! 1742: else
! 1743: {
! 1744: val = gadd(val, gdeux);
! 1745: valm = gadd(valm,gdeux); i++;
! 1746: }
! 1747: }
! 1748: }
! 1749: if (!flag) lambd = gdiv(lambd,gmul(gar,cs)); /* zetak */
! 1750: return gerepileupto(av, gprec_w(lambd, prec2));
! 1751: }
! 1752:
! 1753: GEN
! 1754: gzetak(GEN nfz, GEN s, long prec)
! 1755: {
! 1756: return gzetakall(nfz,s,0,prec);
! 1757: }
! 1758:
! 1759: GEN
! 1760: glambdak(GEN nfz, GEN s, long prec)
! 1761: {
! 1762: return gzetakall(nfz,s,1,prec);
! 1763: }
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