Annotation of OpenXM_contrib/pari-2.2/src/modules/galois.c, Revision 1.1
1.1 ! noro 1: /* $Id: galois.c,v 1.12 2001/09/27 19:39:39 karim Exp $
! 2:
! 3: Copyright (C) 2000 The PARI group.
! 4:
! 5: This file is part of the PARI/GP package.
! 6:
! 7: PARI/GP is free software; you can redistribute it and/or modify it under the
! 8: terms of the GNU General Public License as published by the Free Software
! 9: Foundation. It is distributed in the hope that it will be useful, but WITHOUT
! 10: ANY WARRANTY WHATSOEVER.
! 11:
! 12: Check the License for details. You should have received a copy of it, along
! 13: with the package; see the file 'COPYING'. If not, write to the Free Software
! 14: Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */
! 15:
! 16: /**************************************************************/
! 17: /* */
! 18: /* Galois group for degree between 8 and 11 (included) */
! 19: /* */
! 20: /**************************************************************/
! 21: #include "pari.h"
! 22:
! 23: #define NMAX 11 /* maximum degree */
! 24:
! 25: typedef char *OBJ;
! 26: typedef OBJ *POBJ;
! 27: typedef OBJ PERM;
! 28: typedef POBJ GROUP;
! 29: typedef POBJ RESOLVANTE;
! 30:
! 31: static long isin_G_H(GEN po, GEN *r, long n1, long n2);
! 32:
! 33: static long N,CAR,PREC,PRMAX,TSCHMAX,coeff[9][10];
! 34: static char SID[] = { 0,1,2,3,4,5,6,7,8,9,10,11 };
! 35: static char* str_base = GPDATADIR;
! 36:
! 37: static long par_N, *par_vec;
! 38:
! 39: static void
! 40: do_par(long k, long n, long m)
! 41: {
! 42: long i;
! 43:
! 44: if (n<=0)
! 45: {
! 46: GEN p1 = new_chunk(par_N+1);
! 47: for (i=1; i<k ; i++) p1[i] = par_vec[i];
! 48: for ( ; i<=par_N; i++) p1[i] = 0;
! 49: return;
! 50: }
! 51: if (n<m) m=n;
! 52: for (i=1; i<=m; i++)
! 53: {
! 54: par_vec[k] = i;
! 55: do_par(k+1, n-i, i);
! 56: }
! 57: }
! 58:
! 59: /* compute the partitions of m. T[0][0] = p(m) */
! 60: static long **
! 61: partitions(long n)
! 62: {
! 63: long av,av1,i, j = 1, l = n+1;
! 64: GEN T;
! 65:
! 66: par_vec = new_chunk(l); par_N = n;
! 67: l = l*sizeof(long);
! 68: av = avma; do_par(1,n,n); av1 = avma;
! 69: T = new_chunk((av-av1)/l + 1);
! 70: for (i=av-l; i>=av1; i-=l) T[j++]=i;
! 71:
! 72: if (DEBUGLEVEL > 7)
! 73: {
! 74: fprintferr("Partitions of %ld: p(%ld) = %ld\n",n,n,j-1);
! 75: for (i=1; i<j; i++)
! 76: {
! 77: fprintferr("i = %ld: ",i);
! 78: for (l=1; l<=n; l++)
! 79: fprintferr("%ld ",((long**)T)[i][l]);
! 80: fprintferr("\n"); flusherr();
! 81: }
! 82: }
! 83: T[0] = lgeti(1); ((long**)T)[0][0] = j-1;
! 84: return (long**)T;
! 85: }
! 86:
! 87: /* affect to the permutation x the N arguments that follow */
! 88: static void
! 89: _aff(char *x,...)
! 90: {
! 91: va_list args; long i;
! 92: va_start(args,x); for (i=1; i<=N; i++) x[i] = va_arg(args,int);
! 93: va_end(args);
! 94: }
! 95:
! 96: /* return an array of length |len| from the arguments (for galoismodulo) */
! 97: static GEN
! 98: _gr(long len,...)
! 99: {
! 100: va_list args;
! 101: long i, l = labs(len);
! 102: GEN x = new_chunk(l+1);
! 103:
! 104: va_start(args,len); x[0] = len;
! 105: for (i=1; i<=l; i++) x[i] = va_arg(args,int);
! 106: va_end(args); return x;
! 107: }
! 108:
! 109: /* create a permutation with the N arguments of the function */
! 110: static PERM
! 111: _cr(char a,...)
! 112: {
! 113: static char x[NMAX+1];
! 114: va_list args;
! 115: long i;
! 116:
! 117: va_start(args, a); x[0] = N; x[1] = a;
! 118: for (i=2; i<=N; i++) x[i] = va_arg(args,int);
! 119: va_end(args); return x;
! 120: }
! 121:
! 122: static PERM
! 123: permmul(PERM s1, PERM s2)
! 124: {
! 125: long i, n1 = s1[0];
! 126: PERM s3 = gpmalloc(n1+1);
! 127: for (i=1; i<=n1; i++) s3[i]=s1[(int)s2[i]];
! 128: s3[0]=n1; return s3;
! 129: }
! 130:
! 131: static void
! 132: printperm(PERM perm)
! 133: {
! 134: long i, n = perm[0];
! 135: fprintferr("(");
! 136: for (i=1; i<=n; i++) fprintferr(" %d",perm[i]);
! 137: fprintferr(" )\n");
! 138: }
! 139:
! 140: /* ranger dans l'ordre decroissant (quicksort) */
! 141: static void
! 142: ranger(long *t, long n)
! 143: {
! 144: long tpro,l,r,i,j;
! 145:
! 146: l=1+n/2; r=n; tpro=t[1];
! 147: for(;;)
! 148: {
! 149: if (l>1) { l--; tpro=t[l]; }
! 150: else
! 151: {
! 152: tpro=t[r]; t[r]=t[1]; r--;
! 153: if (r==1) { t[1]=tpro; return; }
! 154: }
! 155: i=l;
! 156: for (j=i<<1; j<=r; j<<=1)
! 157: {
! 158: if (j < r && t[j] > t[j+1]) j++;
! 159: if (t[j] >= tpro) break;
! 160: t[i] = t[j]; i=j;
! 161: }
! 162: t[i]=tpro;
! 163: }
! 164: }
! 165:
! 166: /* 0 if t1=t2, -1 if t1<t2, 1 if t1>t2 */
! 167: static long
! 168: compareupletlong(long *t1,long *t2)
! 169: {
! 170: long i;
! 171: for (i=1; i<=N; i++)
! 172: if (t1[i]!=t2[i]) return (t1[i] < t2[i])? -1: 1;
! 173: return 0;
! 174: }
! 175:
! 176: /* return i if typ = TYP[i], 0 otherwise */
! 177: static long
! 178: numerotyp(long **TYP, long *galtyp)
! 179: {
! 180: long i, nb = TYP[0][0];
! 181: for (i=1; i<=nb; i++)
! 182: if (!compareupletlong(galtyp,TYP[i])) return i;
! 183: return 0;
! 184: }
! 185:
! 186: static int
! 187: raye(long *g, long num)
! 188: {
! 189: long i, nb = labs(g[0]);
! 190: for (i=1; i<=nb; i++)
! 191: if (g[i] == num) return 0;
! 192: return 1;
! 193: }
! 194:
! 195: /* we can never determine the group completely in there */
! 196: static long
! 197: rayergroup11(long num, long *gr)
! 198: {
! 199: long r = 0;
! 200:
! 201: if (CAR)
! 202: switch(num)
! 203: {
! 204: case 2: case 5:
! 205: if (gr[3]) { gr[3]=0; r++; }
! 206: case 3: case 6: case 7:
! 207: if (gr[2]) { gr[2]=0; r++; }
! 208: case 4:
! 209: if (gr[1]) { gr[1]=0; r++; }
! 210: }
! 211: else
! 212: switch(num)
! 213: {
! 214: case 2: case 3:
! 215: if (gr[1]) { gr[1]=0; r++; }
! 216: }
! 217: return r;
! 218: }
! 219:
! 220: static long
! 221: rayergroup(long **GR, long num, long *gr)
! 222: {
! 223: long i,nbgr,r;
! 224:
! 225: if (!GR) return rayergroup11(num,gr);
! 226: nbgr = lg(GR); r = 0 ;
! 227: if (CAR)
! 228: {
! 229: for (i=1; i<nbgr; i++)
! 230: if (gr[i] && GR[i][0] < 0 && raye(GR[i],num)) { gr[i]=0; r++; }
! 231: }
! 232: else
! 233: {
! 234: for (i=1; i<nbgr; i++)
! 235: if (gr[i] && GR[i][0] > 0 && raye(GR[i],num)) { gr[i]=0; r++; }
! 236: }
! 237: return r;
! 238: }
! 239:
! 240: static long
! 241: galmodp(GEN pol, GEN dpol, long **TYP, long *gr, long **GR)
! 242: {
! 243: long p = 0, i,k,l,n,nbremain,dtyp[NMAX+1];
! 244: byteptr d = diffptr;
! 245: GEN p1;
! 246:
! 247: switch(N)
! 248: {
! 249: case 8: nbremain = CAR? 28: 22; break;
! 250: case 9: nbremain = CAR? 18: 16; break;
! 251: case 10: nbremain = CAR? 12: 33; break;
! 252: default: nbremain = CAR? 5: 3; break; /* case 11 */
! 253: }
! 254:
! 255: k = gr[0]; for (i=1; i<k; i++) gr[i]=1;
! 256: for (k=1; k<15; k++, d++)
! 257: {
! 258: p += *d; if (!*d) err(primer1);
! 259: if (smodis(dpol,p)) /* p does not divide dpol */
! 260: {
! 261: p1 = simplefactmod(pol,stoi(p));
! 262: p1 = (GEN)p1[1]; l = lg(p1);
! 263: for (i=1; i<l ; i++) dtyp[i] = itos((GEN)(p1[l-i]));
! 264: for ( ; i<=N; i++) dtyp[i] = 0;
! 265: ranger(dtyp,N); n = numerotyp(TYP,dtyp);
! 266: if (!n) return 1; /* only for N=11 */
! 267: nbremain -= rayergroup(GR,n,gr);
! 268: if (nbremain==1) return 1;
! 269: }
! 270: }
! 271: return 0;
! 272: }
! 273:
! 274: static long
! 275: _aux(GEN z)
! 276: {
! 277: return signe(z)? ((expo(z)+165) >> TWOPOTBITS_IN_LONG) - lg(z)
! 278: : (expo(z)+101) >> TWOPOTBITS_IN_LONG;
! 279: }
! 280:
! 281: static long
! 282: suffprec(GEN z)
! 283: {
! 284: long s,t;
! 285:
! 286: if (typ(z)==t_COMPLEX)
! 287: {
! 288: s=_aux((GEN)z[1]);
! 289: t=_aux((GEN)z[2]); return (t>s)? t: s;
! 290: }
! 291: return _aux(z);
! 292: }
! 293:
! 294: static void
! 295: preci(GEN *r, long p)
! 296: {
! 297: GEN x;
! 298: long d,i;
! 299:
! 300: if (p>PRMAX) err(talker,"too large precision in preci()");
! 301: for (d=0; d<TSCHMAX; d++) for (i=1; i<=N; i++)
! 302: {
! 303: x = (GEN) r[d][i];
! 304: if (typ(x)==t_COMPLEX) { setlg(x[1],p); setlg(x[2],p); } else setlg(x,p);
! 305: }
! 306: }
! 307:
! 308: static long
! 309: getpreci(GEN *r)
! 310: {
! 311: GEN x = (GEN)r[0][1];
! 312: return (typ(x)==t_COMPLEX)? lg(x[1]): lg(x);
! 313: }
! 314:
! 315: static void
! 316: new_pol(GEN *r, long *a, long d)
! 317: {
! 318: long av,i,j;
! 319: GEN x, p1;
! 320: for (i=1; i<=N; i++)
! 321: {
! 322: av =avma; p1 = (GEN)r[0][i]; x = gaddsg(a[0], p1);
! 323: for (j=1; j<=d; j++) x = gaddsg(a[j], gmul(p1,x));
! 324: r[d][i] = (long) gerepileupto(av,x);
! 325: }
! 326: }
! 327:
! 328: static void
! 329: rangeroots(GEN newr, GEN oldr)
! 330: {
! 331: long av = avma,i,j,k,z[NMAX+1],t[NMAX+1];
! 332: GEN diff,diff0;
! 333:
! 334: k = 0; /* gcc -Wall */
! 335: for (i=1; i<=N; i++) t[i]=1;
! 336: for (i=1; i<=N; i++)
! 337: {
! 338: diff0 = gun;
! 339: for (j=1; j<=N; j++)
! 340: if (t[j])
! 341: {
! 342: diff = gabs(gsub((GEN)oldr[i], (GEN)newr[j]), PREC);
! 343: if (gcmp(diff,diff0) < 0) { diff0=diff; k=j; }
! 344: }
! 345: z[i]=newr[k]; t[k]=0;
! 346: }
! 347: avma=av; for (i=1; i<=N; i++) newr[i]=z[i];
! 348: }
! 349:
! 350: /* clean up roots. If root is real replace it by its real part */
! 351: GEN
! 352: myroots(GEN p, long prec)
! 353: {
! 354: GEN y,x = roots(p,prec);
! 355: long i,lx = lg(x);
! 356: for (i=1; i<lx; i++)
! 357: {
! 358: y = (GEN)x[i];
! 359: if (signe(y[2])) break; /* remaining roots are complex */
! 360: x[i]=y[1]; /* root is real; take real part */
! 361: }
! 362: return x;
! 363: }
! 364:
! 365: /* increase the roots accuracy */
! 366: static void
! 367: moreprec(GEN po, GEN *r, long pr)
! 368: {
! 369: if (DEBUGLEVEL) { fprintferr("$$$$$ New prec = %ld\n",pr); flusherr(); }
! 370: if (pr > PRMAX)
! 371: { /* recompute roots */
! 372: GEN p1;
! 373: long d = PRMAX + 5;
! 374:
! 375: PRMAX = (pr < d)? d: pr;
! 376: p1 = myroots(po,PRMAX); rangeroots(p1,*r); *r=p1;
! 377: for (d=1; d<TSCHMAX; d++) new_pol(r,coeff[d],d);
! 378: }
! 379: preci(r,pr);
! 380: }
! 381:
! 382: #define setcard_obj(x,n) ((x)[0] = (char*)(n))
! 383: #define getcard_obj(x) ((long)((x)[0]))
! 384:
! 385: /* allocate a list of m arrays of length n (index 0 is codeword) */
! 386: static POBJ
! 387: alloc_pobj(long n, long m)
! 388: {
! 389: long i, sz = (m+1)*sizeof(OBJ) + (n+1)*m;
! 390: POBJ g = (POBJ) gpmalloc(sz);
! 391: OBJ gpt = (OBJ) (g + (m+1));
! 392:
! 393: for (i=1; i<=m; i++) { g[i] = gpt; gpt += (n+1); }
! 394: setcard_obj(g, m); return g;
! 395: }
! 396:
! 397: /* swap args ! Return an empty RESOLVANTE */
! 398: #define allocresolv(n,m) alloc_pobj(m, n)
! 399:
! 400: static GROUP
! 401: allocgroup(long n, long card)
! 402: {
! 403: GROUP gr = alloc_pobj(n,card);
! 404: long i;
! 405:
! 406: for (i=1; i<=card; i++) gr[i][0]=(char)n;
! 407: return gr;
! 408: }
! 409:
! 410: static char *
! 411: name(char *pre, long n, long n1, long n2, long no)
! 412: {
! 413: static char chn[128];
! 414: static char *base = NULL;
! 415: char ch[6];
! 416:
! 417: if (!base) {
! 418: base = os_getenv("GP_DATA_DIR");
! 419: if (!base)
! 420: base = str_base;
! 421: }
! 422: sprintf(chn, "%s/%s%ld_%ld_%ld", base, pre, n, n1, n2);
! 423: if (no) { sprintf(ch,"_%ld",no); strcat(chn, ch); }
! 424: return chn;
! 425: }
! 426:
! 427: #ifdef UNIX
! 428: # include <fcntl.h>
! 429: #endif
! 430: #ifndef O_RDONLY
! 431: # define O_RDONLY 0
! 432: #endif
! 433:
! 434: static long
! 435: galopen(char *s)
! 436: {
! 437: long fd = os_open(s,O_RDONLY);
! 438: if (fd == -1)
! 439: err(talker,"galois files not available in this version, sorry");
! 440: if (DEBUGLEVEL > 3) msgtimer("opening %s",s);
! 441: return fd;
! 442: }
! 443:
! 444: static char
! 445: bin(char c)
! 446: {
! 447: if (c>='0' && c<='9') c=c-'0';
! 448: else if (c>='A' && c<='Z') c=c-'A'+10;
! 449: else if (c>='a' && c<='z') c=c-'a'+36;
! 450: else err(talker,"incorrect value in bin()");
! 451: return c;
! 452: }
! 453:
! 454: #define BUFFS 512
! 455: /* fill in g[i][j] (i<=n, j<=m) with (buffered) data from fd */
! 456: static void
! 457: read_obj(POBJ g, long fd, long n, long m)
! 458: {
! 459: char ch[BUFFS];
! 460: long i,j, k = BUFFS;
! 461:
! 462: i = j = 1;
! 463: for(;;)
! 464: {
! 465: if (k==BUFFS) { os_read(fd,ch,BUFFS); k=0; }
! 466: g[i][j++] = bin(ch[k++]);
! 467: if (j>m) { j=1; i++; if (i>n) break; }
! 468: }
! 469: os_close(fd); if (DEBUGLEVEL > 3) msgtimer("read_object");
! 470: }
! 471: #undef BUFFS
! 472:
! 473: /* the first 8 bytes contain size data (possibly padded with \0) */
! 474: static GROUP
! 475: lirecoset(long n1, long n2, long n)
! 476: {
! 477: GROUP gr, grptr;
! 478: char c, ch[8];
! 479: long no,m,cardgr,fd;
! 480:
! 481: if (n<11 || n1<8)
! 482: {
! 483: fd = galopen(name("COS", n, n1, n2, 0));
! 484: os_read(fd,&c,1); m=bin(c); os_read(fd,&c,1);
! 485: os_read(fd,ch,6); cardgr=atol(ch); gr=allocgroup(m,cardgr);
! 486: read_obj(gr, fd,cardgr,m); return gr;
! 487: }
! 488: m = 11; cardgr = 45360;
! 489: gr = grptr = allocgroup(n, 8 * cardgr);
! 490: for (no=1; no<=8; no++)
! 491: {
! 492: fd = galopen(name("COS", n, n1, n2, no)); os_read(fd,ch,8);
! 493: read_obj(grptr, fd,cardgr,m); grptr += cardgr;
! 494: }
! 495: return gr;
! 496: }
! 497:
! 498: static RESOLVANTE
! 499: lireresolv(long n1, long n2, long n, long *nv, long *nm)
! 500: {
! 501: RESOLVANTE b;
! 502: char ch[5];
! 503: long fd;
! 504:
! 505: fd = galopen(name("RES", n, n1, n2, 0));
! 506: os_read(fd,ch,5); *nm=atol(ch);
! 507: os_read(fd,ch,3); *nv=atol(ch);
! 508: b = allocresolv(*nm,*nv);
! 509: read_obj(b, fd,*nm,*nv); return b;
! 510: }
! 511:
! 512: static GEN
! 513: monomial(GEN r, PERM bb, long nbv)
! 514: {
! 515: long i; GEN p1 = (GEN)r[(int)bb[1]];
! 516:
! 517: for (i=2; i<=nbv; i++) p1 = gmul(p1, (GEN)r[(int)bb[i]]);
! 518: return p1;
! 519: }
! 520:
! 521: static GEN
! 522: gpolynomial(GEN r, RESOLVANTE aa, long nbm, long nbv)
! 523: {
! 524: long i; GEN p1 = monomial(r,aa[1],nbv);
! 525:
! 526: for (i=2; i<=nbm; i++) p1 = gadd(p1, monomial(r,aa[i],nbv));
! 527: return p1;
! 528: }
! 529:
! 530: static void
! 531: zaux1(GEN *z, GEN *r)
! 532: {
! 533: GEN p2,p1;
! 534: p2=gsub(r[1],gadd(r[2],r[5]));
! 535: p2=gmul(p2,gsub(r[2],r[5]));
! 536: p1=gmul(p2,r[1]);
! 537: p2=gsub(r[3],gadd(r[2],r[4]));
! 538: p2=gmul(p2,gsub(r[4],r[2]));
! 539: p1=gadd(p1,gmul(p2,r[3]));
! 540: p2=gmul(r[5],gsub(r[4],r[5]));
! 541: z[1]=gadd(p1,gmul(p2,r[4]));
! 542:
! 543: p2=gsub(r[1],gadd(r[3],r[4]));
! 544: p2=gmul(p2,gsub(r[3],r[4]));
! 545: p1=gmul(p2,r[1]);
! 546: p2=gsub(r[5],gadd(r[3],r[2]));
! 547: p2=gmul(p2,gsub(r[2],r[3]));
! 548: p1=gadd(p1,gmul(p2,r[5]));
! 549: p2=gmul(r[4],gsub(r[2],r[4]));
! 550: z[2]=gadd(p1,gmul(p2,r[2]));
! 551: }
! 552:
! 553: static void
! 554: zaux(GEN *z, GEN *r)
! 555: {
! 556: zaux1(z, r); zaux1(z+2, r+5);
! 557: }
! 558:
! 559: static GEN
! 560: gpoly(GEN rr, long n1, long n2)
! 561: {
! 562: GEN p1,p2,z[6], *r = (GEN*)rr; /* syntaxic kludge */
! 563: long i,j;
! 564:
! 565: if (N==8)
! 566: {
! 567: if (n1==47 && n2==46)
! 568: {
! 569: p1=gsub(r[3],r[4]);
! 570: for (i=1; i<3; i++) for (j=i+1; j<5; j++) p1 = gmul(p1,gsub(r[i],r[j]));
! 571: for (i=5; i<8; i++) for (j=i+1; j<9; j++) p1 = gmul(p1,gsub(r[i],r[j]));
! 572: p2=r[1];
! 573: for (i=2; i<5; i++) p2=gadd(p2,r[i]);
! 574: for (i=5; i<9; i++) p2=gsub(p2,r[i]);
! 575: }
! 576: else /* n1==44 && n2==40 */
! 577: {
! 578: for (i=1; i<5; i++) z[i] = gadd(r[2*i-1],r[2*i]);
! 579: p1 = gsub(r[1],r[2]);
! 580: for (i=2; i<5; i++) p1 = gmul(p1,gsub(r[2*i-1],r[2*i]));
! 581: p2=gsub(z[3],z[4]);
! 582: for (i=1; i<3; i++) for (j=i+1; j<5; j++) p2 = gmul(p2,gsub(z[i],z[j]));
! 583: }
! 584: return gmul(p1,p2);
! 585: }
! 586:
! 587: if (N==9)
! 588: {
! 589: if (n1==31 && n2==29)
! 590: {
! 591: p1=gsub(r[2],r[3]);
! 592: for (j=2; j<4; j++) p1 = gmul(p1,gsub(r[1],r[j]));
! 593: for (i=4; i<6; i++) for (j=i+1; j<7; j++) p1 = gmul(p1,gsub(r[i],r[j]));
! 594: p2 = gsub(r[8],r[9]);
! 595: for (j=8; j<10; j++) p2 = gmul(p2,gsub(r[7],r[j]));
! 596: }
! 597: else /* ((n1==34 && n2==31) || (n1=33 && n2==30)) */
! 598: {
! 599: p1=r[1]; for (i=2; i<4; i++) p1=gadd(p1,r[i]);
! 600: p2=r[4]; for (i=5; i<7; i++) p2=gadd(p2,r[i]);
! 601: p1=gmul(p1,p2);
! 602: p2=r[7]; for (i=8; i<10; i++) p2=gadd(p2,r[i]);
! 603: }
! 604: return gmul(p1,p2);
! 605: }
! 606:
! 607: if (N==10)
! 608: {
! 609: if ((n1==45 && n2==43) || (n1==44 && n2==42))
! 610: {
! 611: p1=r[1]; for (i=2; i<6; i++) p1=gadd(p1,r[i]);
! 612: p2=r[6]; for (i=7; i<11; i++) p2=gadd(p2,r[i]);
! 613: return gmul(p1,p2);
! 614: }
! 615: else if ((n1==45 && n2==39) || (n1==44 && n2==37))
! 616: {
! 617: p1 = gadd(r[1],r[2]);
! 618: for (i=2; i<6; i++) p1 = gmul(p1,gadd(r[2*i-1],r[2*i]));
! 619: return p1;
! 620: }
! 621: else if ((n1==43 && n2==41) || (n1==33 && n2==27))
! 622: {
! 623: p1=gsub(r[4],r[5]);
! 624: for (i=1; i<4; i++) for (j=i+1; j<6; j++) p1=gmul(p1,gsub(r[i],r[j]));
! 625: p2=gsub(r[9],r[10]);
! 626: for (i=6; i<9; i++) for (j=i+1; j<11; j++) p2=gmul(p2,gsub(r[i],r[j]));
! 627: return gmul(p1,p2);
! 628: }
! 629: else if ((n1==43 && n2==33) || (n1==42 && n2==28) || (n1==41 && n2==27)
! 630: || (n1==40 && n2==21))
! 631: {
! 632: p2=gadd(r[2],r[5]);
! 633: p2=gsub(p2,gadd(r[3],r[4]));
! 634: p1=gmul(p2,r[1]);
! 635: p2=gsub(r[3],gadd(r[4],r[5]));
! 636: p1=gadd(p1,gmul(p2,r[2]));
! 637: p2=gsub(r[4],r[5]);
! 638: p1=gadd(p1,gmul(p2,r[3]));
! 639: z[1]=gadd(p1,gmul(r[4],r[5]));
! 640:
! 641: p2=gadd(r[7],r[10]);
! 642: p2=gsub(p2,gadd(r[8],r[9]));
! 643: p1=gmul(p2,r[6]);
! 644: p2=gsub(r[8],gadd(r[9],r[10]));
! 645: p1=gadd(p1,gmul(p2,r[7]));
! 646: p2=gsub(r[9],r[10]);
! 647: p1=gadd(p1,gmul(p2,r[8]));
! 648: z[2]=gadd(p1,gmul(r[9],r[10]));
! 649: return gadd(gsqr(z[1]), gsqr(z[2]));
! 650: }
! 651: else if (n1==41 && n2==40)
! 652: {
! 653: p1=gsub(r[4],r[5]);
! 654: for (i=1; i<4; i++) for (j=i+1; j<6; j++) p1 = gmul(p1,gsub(r[i],r[j]));
! 655: p2=gsub(r[9],r[10]);
! 656: for (i=6; i<9; i++) for (j=i+1; j<11; j++) p2 = gmul(p2,gsub(r[i],r[j]));
! 657: return gadd(p1,p2);
! 658: }
! 659: else if ((n1==41 && n2==22) || (n1==40 && n2==11) || (n1==17 && n2==5)
! 660: || (n1==10 && n2==4) || (n1==9 && n2==3) || (n1==6 && n2==1))
! 661: {
! 662: p1=gadd(r[1],r[6]);
! 663: for (i=2; i<6; i++) p1=gmul(p1,gadd(r[i],r[i+5]));
! 664: return p1;
! 665: }
! 666: else if ((n1==39 && n2==38) || (n1==29 && n2==25))
! 667: {
! 668: for (i=1; i<6; i++) z[i]=gadd(r[2*i-1],r[2*i]);
! 669: p1=gsub(r[1],r[2]);
! 670: for (i=2; i<6; i++) p1=gmul(p1,gsub(r[2*i-1],r[2*i]));
! 671: p2=gsub(z[4],z[5]);
! 672: for (i=1; i<4; i++) for (j=i+1; j<6; j++) p2=gmul(p2,gsub(z[i],z[j]));
! 673: return gmul(p1,p2);
! 674: }
! 675: else if ((n1==39 && n2==36) || (n1==37 && n2==34) || (n1==29 && n2==23)
! 676: || (n1==24 && n2==15))
! 677: {
! 678: for (i=1; i<6; i++) z[i]=gadd(r[2*i-1],r[2*i]);
! 679: p1=gsub(z[4],z[5]); p2=gmul(gsub(z[3],z[4]),gsub(z[3],z[5]));
! 680: for (i=1; i<3; i++) for (j=i+1; j<6; j++) p2=gmul(p2,gsub(z[i],z[j]));
! 681: return gmul(p1,p2);
! 682: }
! 683: else if ((n1==39 && n2==29) || (n1==38 && n2==25) || (n1==37 && n2==24)
! 684: || (n1==36 && n2==23) || (n1==34 && n2==15))
! 685: {
! 686: for (i=1; i<6; i++) z[i]=gadd(r[2*i-1],r[2*i]);
! 687: p2=gadd(z[2],z[5]); p2=gsub(p2,gadd(z[3],z[4]));
! 688: p1=gmul(p2,z[1]);
! 689: p2=gsub(z[3],gadd(z[4],z[5]));
! 690: p1=gadd(p1,gmul(p2,z[2]));
! 691: p2=gsub(z[4],z[5]);
! 692: p1=gadd(p1,gmul(p2,z[3]));
! 693: p1=gadd(p1,gmul(z[4],z[5])); return gsqr(p1);
! 694: }
! 695: else if ((n1==39 && n2==22) || (n1==38 && n2==12) || (n1==36 && n2==11)
! 696: || (n1==29 && n2== 5) || (n1==25 && n2== 4) || (n1==23 && n2== 3)
! 697: || (n1==16 && n2== 2) || (n1==14 && n2== 1))
! 698: {
! 699: p1=r[1]; for (i=2; i<6; i++) p1=gadd(p1,r[2*i-1]);
! 700: p2=r[2]; for (i=2; i<6; i++) p2=gadd(p2,r[2*i]);
! 701: return gmul(p1,p2);
! 702: }
! 703: else if (n1==28 && n2==18)
! 704: {
! 705: zaux(z, r);
! 706: p1=gmul(z[1],gsub(z[3],z[4]));
! 707: p2=gmul(z[2],gadd(z[3],z[4])); return gadd(p1,p2);
! 708: }
! 709: else if (n1==27 && n2==20)
! 710: {
! 711: zaux(z, r); p1=gmul(z[1],z[3]); p2=gmul(z[2],z[4]);
! 712: p1 = gsub(p1,p2); p2=r[1];
! 713: for (i=2; i<6 ; i++) p2=gadd(p2,r[i]);
! 714: for ( ; i<11; i++) p2=gsub(p2,r[i]);
! 715: return gmul(p1,p2);
! 716: }
! 717: else if (n1==27 && n2==19)
! 718: {
! 719: zaux(z, r); p1=gmul(z[1],z[3]); p2=gmul(z[2],z[4]);
! 720: return gsub(p1,p2);
! 721: }
! 722: else if ((n1==27 && n2==17) || (n1==21 && n2==9))
! 723: {
! 724: zaux(z, r); p1=gmul(z[1],z[3]); p2=gmul(z[2],z[4]);
! 725: return gadd(p1,p2);
! 726: }
! 727: else if (n1==23 && n2==16)
! 728: {
! 729: for (i=1; i<6; i++) z[i]=gadd(r[2*i-1],r[2*i]);
! 730: p1=gsub(z[1],gadd(z[2],z[5])); p1=gmul(p1,gsub(z[2],z[5]));
! 731: p2=gmul(p1,z[1]); p1=gsub(z[3],gadd(z[2],z[4]));
! 732: p1=gmul( p1,gsub(z[4],z[2])); p2=gadd(p2,gmul(p1,z[3]));
! 733: p1=gmul(z[5],gsub(z[4],z[5])); p2=gadd(p2,gmul(p1,z[4]));
! 734: p1=gsub(r[1],r[2]);
! 735: for (i=2; i<6; i++) p1=gmul(p1,gsub(r[2*i-1],r[2*i]));
! 736: return gmul(p1,p2);
! 737: }
! 738: else if (n1==22 && n2==12)
! 739: {
! 740: for (i=1; i<6; i++) z[i]=gadd(r[i],r[i+5]);
! 741: p1=gsub(r[1],r[6]);
! 742: for (i=2; i<6; i++) p1=gmul(p1,gsub(r[i],r[i+5]));
! 743: p2=gsub(z[4],z[5]);
! 744: for (i=1; i<4; i++) for (j=i+1; j<6; j++) p2=gmul(p2,gsub(z[i],z[j]));
! 745: return gmul(p1,p2);
! 746: }
! 747: else if ((n1==22 && n2==11) || (n1==5 && n2==3))
! 748: {
! 749: for (i=1; i<6; i++) z[i]=gadd(r[i],r[i+5]);
! 750: p1=gsub(z[4],z[5]); p2=gmul(gsub(z[3],z[4]),gsub(z[3],z[5]));
! 751: for (i=1; i<3; i++) for (j=i+1; j<6; j++) p2=gmul(p2,gsub(z[i],z[j]));
! 752: return gmul(p1,p2);
! 753: }
! 754: else if ((n1==22 && n2==5) || (n1==12 && n2==4) || (n1==11 && n2==3))
! 755: {
! 756: for (i=1; i<6; i++) z[i]=gadd(r[i],r[i+5]);
! 757: p2=gadd(z[2],z[5]); p2=gsub(p2,gadd(z[3],z[4])); p1=gmul(p2,z[1]);
! 758: p2=gsub(z[3],gadd(z[4],z[5])); p1=gadd(p1,gmul(p2,z[2]));
! 759: p2=gsub(z[4],z[5]);
! 760: p1=gadd(p1,gmul(p2,z[3])); p1=gadd(p1,gmul(z[4],z[5]));
! 761: return gsqr(p1);
! 762: }
! 763: else if (n1==21 && n2==10)
! 764: {
! 765: zaux(z, r); p1=gmul(z[1],z[4]); p2=gmul(z[2],z[3]);
! 766: return gsub(p1,p2);
! 767: }
! 768: }
! 769: err(talker,"indefinite invariant polynomial in gpoly()");
! 770: return NULL; /* not reached */
! 771: }
! 772:
! 773: extern GEN small_to_pol_i(GEN z, long l);
! 774: extern GEN ZX_caract_sqf(GEN A, GEN B, long *lambda, long v);
! 775:
! 776: static void
! 777: tschirn(GEN po, GEN *r, long pr)
! 778: {
! 779: long a[NMAX],i,k, v = varn(po), d = TSCHMAX + 1;
! 780: GEN h,u;
! 781:
! 782: if (d >= N) err(talker,"degree too large in tschirn");
! 783: if (DEBUGLEVEL)
! 784: fprintferr("\n$$$$$ Tschirnhaus transformation of degree %ld: $$$$$\n",d);
! 785:
! 786: do
! 787: {
! 788: for (i=0; i<d; i++) a[i] = ((mymyrand()>>4) & 7) + 1;
! 789: h = small_to_pol_i(a-2, d+2);
! 790: (void)normalizepol_i(h, d+2); setvarn(h,0);
! 791: } while (lgef(h) <= 3 || !ZX_is_squarefree(h));
! 792: setvarn(h, v);
! 793: k = 0; u = ZX_caract_sqf(h, po, &k, v);
! 794: a[1] += k; /* a may have been modified */
! 795: if (DEBUGLEVEL>2) outerr(u);
! 796:
! 797: d = TSCHMAX;
! 798: for (i=0; i<=d; i++) coeff[d][i] = a[i];
! 799: preci(r,PRMAX); r[d] = cgetg(N+1,t_VEC);
! 800: new_pol(r,a,d); preci(r,pr); TSCHMAX++;
! 801: }
! 802:
! 803: static GEN
! 804: get_pol_perm(PERM S1, PERM S2, GEN rr, RESOLVANTE a,
! 805: long nbm, long nbv)
! 806: {
! 807: static long r[NMAX+1];
! 808: long i;
! 809:
! 810: for (i=1; i<=N; i++) r[i] = rr[(int)S1[(int)S2[i]]];
! 811: return a? gpolynomial(r,a,nbm,nbv): gpoly(r,nbm,nbv);
! 812: }
! 813:
! 814: static void
! 815: dbg_rac(long nri,long nbracint,long numi[],GEN racint[],long multi[])
! 816: {
! 817: long k;
! 818: if (nbracint>nri+1)
! 819: fprintferr(" there are %ld rational integer roots:\n",nbracint-nri);
! 820: else if (nbracint==nri+1)
! 821: fprintferr(" there is 1 rational integer root:\n");
! 822: else
! 823: fprintferr(" there is no rational integer root.\n");
! 824: for (k=nri+1; k<=nbracint; k++)
! 825: {
! 826: fprintferr(" number%2ld: ",numi[k]);
! 827: bruterr(racint[k],'g',-1); fprintferr(", order %ld.\n",multi[k]);
! 828: }
! 829: flusherr();
! 830: }
! 831:
! 832: static GEN
! 833: is_int(GEN g)
! 834: {
! 835: GEN gint,p1;
! 836: long av;
! 837:
! 838: if (typ(g) == t_COMPLEX)
! 839: {
! 840: p1 = (GEN)g[2];
! 841: if (signe(p1) && expo(p1) >= - (bit_accuracy(lg(p1))>>1)) return NULL;
! 842: g = (GEN)g[1];
! 843: }
! 844: gint = ground(g); av=avma; p1 = subri(g,gint);
! 845: if (signe(p1) && expo(p1) >= - (bit_accuracy(lg(p1))>>1)) return NULL;
! 846: avma=av; return gint;
! 847: }
! 848:
! 849: static PERM
! 850: isin_end(PERM S, PERM uu, PERM s0, GEN gpol, long av1)
! 851: {
! 852: PERM vv = permmul(S,uu), ww = permmul(vv,s0);
! 853:
! 854: if (DEBUGLEVEL)
! 855: {
! 856: fprintferr(" testing roots reordering: ");
! 857: bruterr(gpol,'g',-1); flusherr();
! 858: }
! 859: free(vv); avma = av1; return ww;
! 860: }
! 861:
! 862: #define M 2521
! 863: /* return NULL if not included, the permutation of the roots otherwise */
! 864: static PERM
! 865: check_isin(GEN po,GEN *r,long nbm,long nbv, POBJ a, POBJ tau, POBJ ss, PERM s0)
! 866: {
! 867: long pr = PREC, av1 = avma, av2,nogr,nocos,init,i,j,k,l,d,nrm,nri,sp;
! 868: long nbgr,nbcos,nbracint,nbrac,lastnbri,lastnbrm;
! 869: static long numi[M],numj[M],lastnum[M],multi[M],norac[M],lastnor[M];
! 870: GEN rr,ro,roint,racint[M];
! 871: PERM uu;
! 872:
! 873: nbcos = getcard_obj(ss);
! 874: nbgr = getcard_obj(tau);
! 875: lastnbri = lastnbrm = -1; sp = nbracint = nbrac = 0; /* gcc -Wall*/
! 876: for (nogr=1; nogr<=nbgr; nogr++)
! 877: {
! 878: if (DEBUGLEVEL)
! 879: { fprintferr(" ----> Group # %ld/%ld:\n",nogr,nbgr); flusherr(); }
! 880: init = 0;
! 881: for (d=1; ; d++)
! 882: {
! 883: if (d > 1)
! 884: {
! 885: if (DEBUGLEVEL)
! 886: {
! 887: fprintferr(" all integer roots are double roots\n");
! 888: fprintferr(" Working with polynomial #%ld:\n", d); flusherr();
! 889: }
! 890: if (d > TSCHMAX) { tschirn(po,r,pr); av1 = avma; }
! 891: }
! 892: if (!init)
! 893: {
! 894: init = 1;
! 895: for(;;)
! 896: {
! 897: av2=avma; rr = r[d-1]; nbrac = nbracint = 0;
! 898: for (nocos=1; nocos<=nbcos; nocos++)
! 899: {
! 900: ro = get_pol_perm(tau[nogr], ss[nocos], rr,a,nbm,nbv);
! 901: sp = suffprec(ro); if (sp > 0) break;
! 902: roint = is_int(ro);
! 903: if (roint)
! 904: {
! 905: nbrac++;
! 906: if (nbrac >= M)
! 907: {
! 908: err(warner, "more than %ld rational integer roots\n", M);
! 909: avma = av1; init = 0; break;
! 910: }
! 911: for (j=1; j<=nbracint; j++)
! 912: if (gegal(roint,racint[j])) { multi[j]++; break; }
! 913: if (j > nbracint)
! 914: {
! 915: nbracint = j; multi[j]=1; numi[j]=nocos;
! 916: racint[j] = gerepileupto(av2,roint); av2=avma;
! 917: }
! 918: numj[nbrac]=nocos; norac[nbrac]=j;
! 919: }
! 920: avma=av2;
! 921: }
! 922: if (sp <= 0) break;
! 923: avma = av1; pr+=sp; moreprec(po,r,pr); av1 = avma;
! 924: }
! 925: if (!init) continue;
! 926:
! 927: if (DEBUGLEVEL) dbg_rac(0,nbracint,numi,racint,multi);
! 928: for (i=1; i<=nbracint; i++)
! 929: if (multi[i]==1)
! 930: {
! 931: uu = ss[numi[i]];
! 932: ro = DEBUGLEVEL? get_pol_perm(SID,uu,rr,a,nbm,nbv): (GEN)NULL;
! 933: return isin_end(tau[nogr], uu, s0, ro, av1);
! 934: }
! 935: }
! 936: else
! 937: {
! 938: nrm = nri = 0;
! 939: for (l=1; l<=lastnbri; l++)
! 940: {
! 941: for(;;)
! 942: {
! 943: av2=avma; rr = r[d-1]; nbrac=nrm; nbracint=nri;
! 944: for (k=1; k<=lastnbrm; k++)
! 945: if (lastnor[k]==l)
! 946: {
! 947: nocos = lastnum[k];
! 948: ro = get_pol_perm(tau[nogr], ss[nocos], rr,a,nbm,nbv);
! 949: sp = suffprec(ro); if (sp > 0) break;
! 950: roint = is_int(ro);
! 951: if (roint)
! 952: {
! 953: nbrac++;
! 954: for (j=nri+1; j<=nbracint; j++)
! 955: if (gegal(roint,racint[j])) { multi[j]++; break; }
! 956: if (j > nbracint)
! 957: {
! 958: nbracint = j; multi[j]=1; numi[j]=nocos;
! 959: racint[j] = gerepileupto(av2,roint); av2=avma;
! 960: }
! 961: numj[nbrac]=nocos; norac[nbrac]=j;
! 962: }
! 963: avma=av2;
! 964: }
! 965: if (sp <= 0) break;
! 966: avma = av1; pr+=sp; moreprec(po,r,pr); av1 = avma;
! 967: }
! 968: if (DEBUGLEVEL) dbg_rac(nri,nbracint,numi,racint,multi);
! 969: for (i=nri+1; i<=nbracint; i++)
! 970: if (multi[i]==1)
! 971: {
! 972: uu = ss[numi[i]];
! 973: ro = DEBUGLEVEL? get_pol_perm(SID,uu,rr,a,nbm,nbv): (GEN)NULL;
! 974: return isin_end(tau[nogr], uu, s0, ro, av1);
! 975: }
! 976: avma = av1; nri=nbracint; nrm=nbrac;
! 977: }
! 978: }
! 979: avma = av1; if (!nbracint) break;
! 980:
! 981: lastnbri=nbracint; lastnbrm=nbrac;
! 982: for (j=1; j<=nbrac; j++)
! 983: { lastnum[j]=numj[j]; lastnor[j]=norac[j]; }
! 984: }
! 985: }
! 986: return NULL;
! 987: }
! 988: #undef M
! 989:
! 990: /* BIBLIOTHEQUE POUR LE DEGRE 8 */
! 991:
! 992: static long
! 993: galoisprim8(GEN po, GEN *r)
! 994: {
! 995: long rep;
! 996:
! 997: /* PRIM_8_1: */
! 998: rep=isin_G_H(po,r,50,43);
! 999: if (rep) return CAR? 37: 43;
! 1000: /* PRIM_8_2: */
! 1001: if (!CAR) return 50;
! 1002: /* PRIM_8_3: */
! 1003: rep=isin_G_H(po,r,49,48);
! 1004: if (!rep) return 49;
! 1005: /* PRIM_8_4: */
! 1006: rep=isin_G_H(po,r,48,36);
! 1007: if (!rep) return 48;
! 1008: /* PRIM_8_5: */
! 1009: rep=isin_G_H(po,r,36,25);
! 1010: return rep? 25: 36;
! 1011: }
! 1012:
! 1013: static long
! 1014: galoisimpodd8(GEN po, GEN *r, long nh)
! 1015: {
! 1016: long rep;
! 1017: /* IMPODD_8_1: */
! 1018: if (nh!=47) goto IMPODD_8_6;
! 1019: /* IMPODD_8_2: */
! 1020: rep=isin_G_H(po,r,47,46);
! 1021: if (!rep) goto IMPODD_8_5;
! 1022: /* IMPODD_8_4: */
! 1023: rep=isin_G_H(po,r,46,28);
! 1024: if (rep) goto IMPODD_8_7; else return 46;
! 1025:
! 1026: IMPODD_8_5:
! 1027: rep=isin_G_H(po,r,47,35);
! 1028: if (rep) goto IMPODD_8_9; else return 47;
! 1029:
! 1030: IMPODD_8_6:
! 1031: rep=isin_G_H(po,r,44,40);
! 1032: if (rep) goto IMPODD_8_10; else goto IMPODD_8_11;
! 1033:
! 1034: IMPODD_8_7:
! 1035: rep=isin_G_H(po,r,28,21);
! 1036: if (rep) return 21; else goto IMPODD_8_33;
! 1037:
! 1038: IMPODD_8_9:
! 1039: rep=isin_G_H(po,r,35,31);
! 1040: if (rep) goto IMPODD_8_13; else goto IMPODD_8_14;
! 1041:
! 1042: IMPODD_8_10:
! 1043: rep=isin_G_H(po,r,40,26);
! 1044: if (rep) goto IMPODD_8_15; else goto IMPODD_8_16;
! 1045:
! 1046: IMPODD_8_11:
! 1047: rep=isin_G_H(po,r,44,38);
! 1048: if (rep) goto IMPODD_8_17; else goto IMPODD_8_18;
! 1049:
! 1050: IMPODD_8_12:
! 1051: rep=isin_G_H(po,r,16,7);
! 1052: if (rep) goto IMPODD_8_19; else return 16;
! 1053:
! 1054: IMPODD_8_13:
! 1055: rep=isin_G_H(po,r,31,21);
! 1056: return rep? 21: 31;
! 1057:
! 1058: IMPODD_8_14:
! 1059: rep=isin_G_H(po,r,35,30);
! 1060: if (rep) goto IMPODD_8_34; else goto IMPODD_8_20;
! 1061:
! 1062: IMPODD_8_15:
! 1063: rep=isin_G_H(po,r,26,16);
! 1064: if (rep) goto IMPODD_8_12; else goto IMPODD_8_21;
! 1065:
! 1066: IMPODD_8_16:
! 1067: rep=isin_G_H(po,r,40,23);
! 1068: if (rep) goto IMPODD_8_22; else return 40;
! 1069:
! 1070: IMPODD_8_17:
! 1071: rep=isin_G_H(po,r,38,31);
! 1072: if (rep) goto IMPODD_8_13; else return 38;
! 1073:
! 1074: IMPODD_8_18:
! 1075: rep=isin_G_H(po,r,44,35);
! 1076: if (rep) goto IMPODD_8_9; else return 44;
! 1077:
! 1078: IMPODD_8_19:
! 1079: rep=isin_G_H(po,r,7,1);
! 1080: return rep? 1: 7;
! 1081:
! 1082: IMPODD_8_20:
! 1083: rep=isin_G_H(po,r,35,28);
! 1084: if (rep) goto IMPODD_8_7; else goto IMPODD_8_23;
! 1085:
! 1086: IMPODD_8_21:
! 1087: rep=isin_G_H(po,r,26,17);
! 1088: if (rep) goto IMPODD_8_24; else goto IMPODD_8_25;
! 1089:
! 1090: IMPODD_8_22:
! 1091: rep=isin_G_H(po,r,23,8);
! 1092: if (rep) goto IMPODD_8_26; else return 23;
! 1093:
! 1094: IMPODD_8_23:
! 1095: rep=isin_G_H(po,r,35,27);
! 1096: if (rep) goto IMPODD_8_27; else goto IMPODD_8_28;
! 1097:
! 1098: IMPODD_8_24:
! 1099: rep=isin_G_H(po,r,17,7);
! 1100: if (rep) goto IMPODD_8_19; else return 17;
! 1101:
! 1102: IMPODD_8_25:
! 1103: rep=isin_G_H(po,r,26,15);
! 1104: if (rep) goto IMPODD_8_29; else return 26;
! 1105:
! 1106: IMPODD_8_26:
! 1107: rep=isin_G_H(po,r,8,1);
! 1108: return rep? 1: 8;
! 1109:
! 1110: IMPODD_8_27:
! 1111: rep=isin_G_H(po,r,27,16);
! 1112: if (rep) goto IMPODD_8_12; else return 27;
! 1113:
! 1114: IMPODD_8_28:
! 1115: rep=isin_G_H(po,r,35,26);
! 1116: if (rep) goto IMPODD_8_15; else return 35;
! 1117:
! 1118: IMPODD_8_29:
! 1119: rep=isin_G_H(po,r,15,7);
! 1120: if (rep) goto IMPODD_8_19;
! 1121: /* IMPODD_8_30: */
! 1122: rep=isin_G_H(po,r,15,6);
! 1123: if (!rep) goto IMPODD_8_32;
! 1124: /* IMPODD_8_31: */
! 1125: rep=isin_G_H(po,r,6,1);
! 1126: return rep? 1: 6;
! 1127:
! 1128: IMPODD_8_32:
! 1129: rep=isin_G_H(po,r,15,8);
! 1130: if (rep) goto IMPODD_8_26; else return 15;
! 1131:
! 1132: IMPODD_8_33:
! 1133: rep=isin_G_H(po,r,28,16);
! 1134: if (rep) goto IMPODD_8_12; else return 28;
! 1135:
! 1136: IMPODD_8_34:
! 1137: rep=isin_G_H(po,r,30,21);
! 1138: return rep? 21: 30;
! 1139: }
! 1140:
! 1141: static long
! 1142: galoisimpeven8(GEN po, GEN *r, long nh)
! 1143: {
! 1144: long rep;
! 1145: /* IMPEVEN_8_1: */
! 1146: if (nh!=45) goto IMPEVEN_8_6;
! 1147: /* IMPEVEN_8_2: */
! 1148: rep=isin_G_H(po,r,45,42);
! 1149: if (!rep) goto IMPEVEN_8_5;
! 1150: /* IMPEVEN_8_4: */
! 1151: rep=isin_G_H(po,r,42,34);
! 1152: if (rep) goto IMPEVEN_8_7; else goto IMPEVEN_8_8;
! 1153:
! 1154: IMPEVEN_8_5:
! 1155: rep=isin_G_H(po,r,45,41);
! 1156: if (rep) goto IMPEVEN_8_9; else return 45;
! 1157:
! 1158: IMPEVEN_8_6:
! 1159: rep=isin_G_H(po,r,39,32);
! 1160: if (rep) goto IMPEVEN_8_10; else goto IMPEVEN_8_11;
! 1161:
! 1162: IMPEVEN_8_7:
! 1163: rep=isin_G_H(po,r,34,18);
! 1164: if (rep) goto IMPEVEN_8_21; else goto IMPEVEN_8_45;
! 1165:
! 1166: IMPEVEN_8_8:
! 1167: rep=isin_G_H(po,r,42,33);
! 1168: if (rep) goto IMPEVEN_8_14; else return 42;
! 1169:
! 1170: IMPEVEN_8_9:
! 1171: rep=isin_G_H(po,r,41,34);
! 1172: if (rep) goto IMPEVEN_8_7; else goto IMPEVEN_8_15;
! 1173:
! 1174: IMPEVEN_8_10:
! 1175: rep=isin_G_H(po,r,32,22);
! 1176: if (rep) goto IMPEVEN_8_16; else goto IMPEVEN_8_17;
! 1177:
! 1178: IMPEVEN_8_11:
! 1179: rep=isin_G_H(po,r,39,29);
! 1180: if (rep) goto IMPEVEN_8_18; else goto IMPEVEN_8_19;
! 1181:
! 1182: IMPEVEN_8_12:
! 1183: rep=isin_G_H(po,r,14,4);
! 1184: return rep? 4: 14;
! 1185:
! 1186: IMPEVEN_8_14:
! 1187: rep=isin_G_H(po,r,33,18);
! 1188: if (rep) goto IMPEVEN_8_21; else goto IMPEVEN_8_22;
! 1189:
! 1190: IMPEVEN_8_15:
! 1191: rep=isin_G_H(po,r,41,33);
! 1192: if (rep) goto IMPEVEN_8_14; else goto IMPEVEN_8_23;
! 1193:
! 1194: IMPEVEN_8_16:
! 1195: rep=isin_G_H(po,r,22,11);
! 1196: if (rep) goto IMPEVEN_8_24; else goto IMPEVEN_8_25;
! 1197:
! 1198: IMPEVEN_8_17:
! 1199: rep=isin_G_H(po,r,32,13);
! 1200: if (rep) goto IMPEVEN_8_26; else goto IMPEVEN_8_27;
! 1201:
! 1202: IMPEVEN_8_18:
! 1203: rep=isin_G_H(po,r,29,22);
! 1204: if (rep) goto IMPEVEN_8_16; else goto IMPEVEN_8_28;
! 1205:
! 1206: IMPEVEN_8_19:
! 1207: rep=isin_G_H(po,r,39,24);
! 1208: if (rep) goto IMPEVEN_8_29; else return 39;
! 1209:
! 1210: IMPEVEN_8_20:
! 1211: rep=isin_G_H(po,r,9,4);
! 1212: if (rep) return 4; else goto IMPEVEN_8_30;
! 1213:
! 1214: IMPEVEN_8_21:
! 1215: rep=isin_G_H(po,r,18,10);
! 1216: if (rep) goto IMPEVEN_8_31; else goto IMPEVEN_8_32;
! 1217:
! 1218: IMPEVEN_8_22:
! 1219: rep=isin_G_H(po,r,33,13);
! 1220: if (rep) goto IMPEVEN_8_26; else return 33;
! 1221:
! 1222: IMPEVEN_8_23:
! 1223: rep=isin_G_H(po,r,41,29);
! 1224: if (rep) goto IMPEVEN_8_18; else goto IMPEVEN_8_33;
! 1225:
! 1226: IMPEVEN_8_24:
! 1227: rep=isin_G_H(po,r,11,5);
! 1228: if (rep) return 5; else goto IMPEVEN_8_34;
! 1229:
! 1230: IMPEVEN_8_25:
! 1231: rep=isin_G_H(po,r,22,9);
! 1232: if (rep) goto IMPEVEN_8_20; else return 22;
! 1233:
! 1234: IMPEVEN_8_26:
! 1235: rep=isin_G_H(po,r,13,3);
! 1236: return rep? 3: 13;
! 1237:
! 1238: IMPEVEN_8_27:
! 1239: rep=isin_G_H(po,r,32,12);
! 1240: if (rep) goto IMPEVEN_8_35; else return 32;
! 1241:
! 1242: IMPEVEN_8_28:
! 1243: rep=isin_G_H(po,r,29,20);
! 1244: if (rep) goto IMPEVEN_8_36; else goto IMPEVEN_8_37;
! 1245:
! 1246: IMPEVEN_8_29:
! 1247: rep=isin_G_H(po,r,24,14);
! 1248: if (rep) goto IMPEVEN_8_12; else goto IMPEVEN_8_38;
! 1249:
! 1250: IMPEVEN_8_30:
! 1251: rep=isin_G_H(po,r,9,3);
! 1252: if (rep) return 3; else goto IMPEVEN_8_39;
! 1253:
! 1254: IMPEVEN_8_31:
! 1255: rep=isin_G_H(po,r,10,2);
! 1256: return rep? 2: 10;
! 1257:
! 1258: IMPEVEN_8_32:
! 1259: rep=isin_G_H(po,r,18,9);
! 1260: if (rep) goto IMPEVEN_8_20; else return 18;
! 1261:
! 1262: IMPEVEN_8_33:
! 1263: rep=isin_G_H(po,r,41,24);
! 1264: if (rep) goto IMPEVEN_8_29; else return 41;
! 1265:
! 1266: IMPEVEN_8_34:
! 1267: rep=isin_G_H(po,r,11,4);
! 1268: if (rep) return 4; else goto IMPEVEN_8_44;
! 1269:
! 1270: IMPEVEN_8_35:
! 1271: rep=isin_G_H(po,r,12,5);
! 1272: return rep? 5: 12;
! 1273:
! 1274: IMPEVEN_8_36:
! 1275: rep=isin_G_H(po,r,20,10);
! 1276: if (rep) goto IMPEVEN_8_31; else return 20;
! 1277:
! 1278: IMPEVEN_8_37:
! 1279: rep=isin_G_H(po,r,29,19);
! 1280: if (rep) goto IMPEVEN_8_40; else goto IMPEVEN_8_41;
! 1281:
! 1282: IMPEVEN_8_38:
! 1283: rep=isin_G_H(po,r,24,13);
! 1284: if (rep) goto IMPEVEN_8_26; else goto IMPEVEN_8_42;
! 1285:
! 1286: IMPEVEN_8_39:
! 1287: rep=isin_G_H(po,r,9,2);
! 1288: return rep? 2: 9;
! 1289:
! 1290: IMPEVEN_8_40:
! 1291: rep=isin_G_H(po,r,19,10);
! 1292: if (rep) goto IMPEVEN_8_31; else goto IMPEVEN_8_43;
! 1293:
! 1294: IMPEVEN_8_41:
! 1295: rep=isin_G_H(po,r,29,18);
! 1296: if (rep) goto IMPEVEN_8_21; else return 29;
! 1297:
! 1298: IMPEVEN_8_42:
! 1299: rep=isin_G_H(po,r,24,9);
! 1300: if (rep) goto IMPEVEN_8_20; else return 24;
! 1301:
! 1302: IMPEVEN_8_43:
! 1303: rep=isin_G_H(po,r,19,9);
! 1304: if (rep) goto IMPEVEN_8_20; else return 19;
! 1305:
! 1306: IMPEVEN_8_44:
! 1307: rep=isin_G_H(po,r,11,2);
! 1308: return rep? 2: 11;
! 1309:
! 1310: IMPEVEN_8_45:
! 1311: rep=isin_G_H(po,r,34,14);
! 1312: if (rep) goto IMPEVEN_8_12; else return 34;
! 1313: }
! 1314:
! 1315: static long
! 1316: closure8(GEN po)
! 1317: {
! 1318: long rep;
! 1319: GEN r[NMAX];
! 1320:
! 1321: r[0] = myroots(po,PRMAX); preci(r,PREC);
! 1322: if (!CAR)
! 1323: {
! 1324: /* CLOS_8_1: */
! 1325: rep=isin_G_H(po,r,50,47);
! 1326: if (rep) return galoisimpodd8(po,r,47);
! 1327: /* CLOS_8_2: */
! 1328: rep=isin_G_H(po,r,50,44);
! 1329: if (rep) return galoisimpodd8(po,r,44);
! 1330: }
! 1331: else
! 1332: {
! 1333: /* CLOS_8_3: */
! 1334: rep=isin_G_H(po,r,49,45);
! 1335: if (rep) return galoisimpeven8(po,r,45);
! 1336: /* CLOS_8_4: */
! 1337: rep=isin_G_H(po,r,49,39);
! 1338: if (rep) return galoisimpeven8(po,r,39);
! 1339: }
! 1340: return galoisprim8(po,r);
! 1341: }
! 1342:
! 1343: static GROUP
! 1344: initgroup(long n, long nbgr)
! 1345: {
! 1346: GROUP t = allocgroup(n,nbgr);
! 1347: t[1] = SID; return t;
! 1348: }
! 1349:
! 1350: static PERM
! 1351: data8(long n1, long n2, GROUP *t)
! 1352: {
! 1353: switch(n1)
! 1354: {
! 1355: case 7: if (n2!=1) break;
! 1356: *t=initgroup(N,2);
! 1357: _aff((*t)[2], 1, 2, 3, 4, 6, 5, 8, 7);
! 1358: return SID;
! 1359: case 9: if (n2!=4) break;
! 1360: *t=initgroup(N,2);
! 1361: _aff((*t)[2], 1, 2, 4, 3, 5, 6, 8, 7);
! 1362: return SID;
! 1363: case 10: if (n2!=2) break;
! 1364: *t=initgroup(N,2);
! 1365: _aff((*t)[2], 1, 2, 3, 4, 6, 5, 8, 7);
! 1366: return SID;
! 1367: case 11:
! 1368: switch(n2)
! 1369: {
! 1370: case 2:
! 1371: *t=initgroup(N,2);
! 1372: _aff((*t)[2], 1, 2, 5, 6, 3, 4, 8, 7);
! 1373: return _cr(1, 3, 5, 8, 2, 4, 6, 7);
! 1374: case 4:
! 1375: *t=initgroup(N,1);
! 1376: return _cr(1, 3, 7, 5, 2, 4, 8, 6);
! 1377: }break;
! 1378: case 14: if (n2!=4) break;
! 1379: *t=initgroup(N,1);
! 1380: return _cr(1, 2, 4, 3, 5, 6, 8, 7);
! 1381: case 15: if (n2!=6 && n2!=8) break;
! 1382: *t=initgroup(N,2);
! 1383: _aff((*t)[2], 1, 2, 3, 4, 6, 5, 8, 7);
! 1384: return SID;
! 1385: case 16: if (n2!=7) break;
! 1386: *t=initgroup(N,2);
! 1387: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
! 1388: return SID;
! 1389: case 18:
! 1390: switch(n2)
! 1391: {
! 1392: case 9: *t=initgroup(N,3);
! 1393: _aff((*t)[2], 1, 5, 3, 7, 2, 6, 4, 8);
! 1394: _aff((*t)[3], 1, 2, 3, 4, 6, 5, 8, 7);
! 1395: return SID;
! 1396: case 10: *t=initgroup(N,3);
! 1397: _aff((*t)[2], 1, 6, 3, 8, 2, 5, 4, 7);
! 1398: _aff((*t)[3], 1, 5, 3, 7, 2, 6, 4, 8);
! 1399: return SID;
! 1400: }break;
! 1401: case 19: if (n2!=9) break;
! 1402: *t=initgroup(N,1);
! 1403: return _cr(1, 5, 3, 8, 2, 6, 4, 7);
! 1404: case 20: if (n2!=10) break;
! 1405: *t=initgroup(N,2);
! 1406: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
! 1407: return SID;
! 1408: case 22:
! 1409: switch(n2)
! 1410: {
! 1411: case 9: *t=initgroup(N,6);
! 1412: _aff((*t)[2], 1, 2, 7, 8, 3, 4, 6, 5);
! 1413: _aff((*t)[3], 1, 2, 7, 8, 3, 4, 5, 6);
! 1414: _aff((*t)[4], 1, 2, 5, 6, 3, 4, 8, 7);
! 1415: _aff((*t)[5], 1, 2, 5, 6, 3, 4, 7, 8);
! 1416: _aff((*t)[6], 1, 2, 3, 4, 5, 6, 8, 7);
! 1417: return _cr(1, 3, 5, 7, 2, 4, 6, 8);
! 1418: case 11: *t=initgroup(N,6);
! 1419: _aff((*t)[2], 1, 2, 5, 6, 7, 8, 4, 3);
! 1420: _aff((*t)[3], 1, 2, 5, 6, 7, 8, 3, 4);
! 1421: _aff((*t)[4], 1, 2, 3, 4, 7, 8, 6, 5);
! 1422: _aff((*t)[5], 1, 2, 3, 4, 7, 8, 5, 6);
! 1423: _aff((*t)[6], 1, 2, 3, 4, 5, 6, 8, 7);
! 1424: return SID;
! 1425: }break;
! 1426: case 23: if (n2!=8) break;
! 1427: *t=initgroup(N,1);
! 1428: return _cr(1, 2, 3, 4, 6, 5, 8, 7);
! 1429: case 26: if (n2!=15 && n2!=17) break;
! 1430: *t=initgroup(N,2);
! 1431: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
! 1432: return SID;
! 1433: case 28: if (n2!=21) break;
! 1434: *t=initgroup(N,1);
! 1435: return _cr(1, 2, 3, 4, 7, 8, 5, 6);
! 1436: case 29: if (n2!=18 && n2!=19) break;
! 1437: *t=initgroup(N,2);
! 1438: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
! 1439: return SID;
! 1440: case 30: if (n2!=21) break;
! 1441: *t=initgroup(N,1);
! 1442: return _cr(1, 2, 3, 4, 7, 8, 5, 6);
! 1443: case 31: if (n2!=21) break;
! 1444: *t=initgroup(N,3);
! 1445: _aff((*t)[2], 1, 2, 3, 4, 7, 8, 5, 6);
! 1446: _aff((*t)[3], 1, 2, 5, 6, 7, 8, 3, 4);
! 1447: return SID;
! 1448: case 32: if (n2!=12 && n2!=13) break;
! 1449: *t=initgroup(N,2);
! 1450: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
! 1451: return SID;
! 1452: case 33:
! 1453: switch(n2)
! 1454: {
! 1455: case 13: *t=initgroup(N,1);
! 1456: return _cr(1, 5, 2, 6, 3, 7, 4, 8);
! 1457: case 18: *t=initgroup(N,1);
! 1458: return _cr(1, 2, 5, 6, 3, 4, 7, 8);
! 1459: }break;
! 1460: case 34:
! 1461: switch(n2)
! 1462: {
! 1463: case 14: *t=initgroup(N,3);
! 1464: _aff((*t)[2], 1, 2, 3, 4, 5, 8, 6, 7);
! 1465: _aff((*t)[3], 1, 2, 3, 4, 5, 7, 8, 6);
! 1466: return _cr(1, 5, 2, 6, 3, 7, 4, 8);
! 1467: case 18: *t=initgroup(N,1);
! 1468: return _cr(1, 2, 5, 6, 3, 4, 8, 7);
! 1469: }break;
! 1470: case 39: if (n2!=24) break;
! 1471: *t=initgroup(N,2);
! 1472: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
! 1473: return SID;
! 1474: case 40: if (n2!=23) break;
! 1475: *t=initgroup(N,2);
! 1476: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
! 1477: return SID;
! 1478: case 41:
! 1479: switch(n2)
! 1480: {
! 1481: case 24: *t=initgroup(N,1);
! 1482: return _cr(1, 5, 2, 6, 3, 7, 4, 8);
! 1483: case 29: *t=initgroup(N,1);
! 1484: return _cr(1, 2, 5, 6, 3, 4, 7, 8);
! 1485: }break;
! 1486: case 42: if (n2!=34) break;
! 1487: *t=initgroup(N,1);
! 1488: return _cr(1, 2, 3, 4, 5, 6, 8, 7);
! 1489: case 45: if (n2!=41 && n2!=42) break;
! 1490: *t=initgroup(N,2);
! 1491: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
! 1492: return SID;
! 1493: case 46: if (n2!=28) break;
! 1494: *t=initgroup(N,1);
! 1495: return _cr(1, 2, 5, 6, 3, 4, 7, 8);
! 1496: case 47: if (n2!=35) break;
! 1497: *t=initgroup(N,1);
! 1498: return _cr(1, 2, 5, 6, 3, 4, 7, 8);
! 1499: case 49: if (n2!=48) break;
! 1500: *t=initgroup(N,2);
! 1501: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
! 1502: return SID;
! 1503: }
! 1504: *t=initgroup(N,1); return SID;
! 1505: }
! 1506:
! 1507: static long
! 1508: galoismodulo8(GEN pol, GEN dpol)
! 1509: {
! 1510: long av = avma, res, gr[51];
! 1511: long **TYP = partitions(8), **GR = (long**)cgeti(49);
! 1512:
! 1513: /* List of possible types in group j: GR[j][0] = #GR[j] if
! 1514: * the group is odd, - #GR[j] if even */
! 1515: GR[ 1]= _gr( 4, 1,5,15,22);
! 1516: GR[ 2]= _gr( -3, 1,5,15);
! 1517: GR[ 3]= _gr( -2, 1,5);
! 1518: GR[ 4]= _gr( -3, 1,5,15);
! 1519: GR[ 5]= _gr( -3, 1,5,15);
! 1520: GR[ 6]= _gr( 5, 1,4,5,15,22);
! 1521: GR[ 7]= _gr( 5, 1,3,5,15,22);
! 1522: GR[ 8]= _gr( 5, 1,4,5,15,22);
! 1523: GR[ 9]= _gr( -4, 1,3,5,15);
! 1524: GR[10]= _gr( -4, 1,3,5,15);
! 1525: GR[11]= _gr( -4, 1,3,5,15);
! 1526: GR[12]= _gr( -5, 1,5,9,15,20);
! 1527: GR[13]= _gr( -4, 1,5,9,20);
! 1528: GR[14]= _gr( -4, 1,5,9,15);
! 1529: GR[15]= _gr( 6, 1,3,4,5,15,22);
! 1530: GR[16]= _gr( 5, 1,3,5,15,22);
! 1531: GR[17]= _gr( 7, 1,3,5,11,13,15,22);
! 1532: GR[18]= _gr( -4, 1,3,5,15);
! 1533: GR[19]= _gr( -5, 1,3,5,12,15);
! 1534: GR[20]= _gr( -4, 1,3,5,15);
! 1535: GR[21]= _gr( 5, 1,3,5,13,15);
! 1536: GR[22]= _gr( -4, 1,3,5,15);
! 1537: GR[23]= _gr( 7, 1,4,5,9,15,20,22);
! 1538: GR[24]= _gr( -6, 1,3,5,9,15,20);
! 1539: GR[25]= _gr( -3, 1,5,21);
! 1540: GR[26]= _gr( 8, 1,3,4,5,11,13,15,22);
! 1541: GR[27]= _gr( 8, 1,2,3,4,5,13,15,22);
! 1542: GR[28]= _gr( 7, 1,3,5,12,13,15,22);
! 1543: GR[29]= _gr( -5, 1,3,5,12,15);
! 1544: GR[30]= _gr( 7, 1,3,4,5,11,13,15);
! 1545: GR[31]= _gr( 7, 1,2,3,4,5,13,15);
! 1546: GR[32]= _gr( -6, 1,3,5,9,15,20);
! 1547: GR[33]= _gr( -6, 1,3,5,9,15,20);
! 1548: GR[34]= _gr( -5, 1,3,5,9,15);
! 1549: GR[35]= _gr( 10, 1,2,3,4,5,11,12,13,15,22);
! 1550: GR[36]= _gr( -5, 1,5,9,20,21);
! 1551: GR[37]= _gr( -5, 1,5,9,15,21);
! 1552: GR[38]= _gr( 11, 1,2,3,4,5,9,10,13,15,19,20);
! 1553: GR[39]= _gr( -7, 1,3,5,9,12,15,20);
! 1554: GR[40]= _gr( 10, 1,3,4,5,9,11,13,15,20,22);
! 1555: GR[41]= _gr( -7, 1,3,5,9,12,15,20);
! 1556: GR[42]= _gr( -8, 1,3,5,6,8,9,15,20);
! 1557: GR[43]= _gr( 8, 1,4,5,9,15,19,21,22);
! 1558: GR[44]= _gr( 14, 1,2,3,4,5,9,10,11,12,13,15,19,20,22);
! 1559: GR[45]= _gr( -9, 1,3,5,6,8,9,12,15,20);
! 1560: GR[46]= _gr( 10, 1,3,5,6,8,9,12,13,15,22);
! 1561: GR[47]= _gr( 16, 1,2,3,4,5,6,7,8,9,11,12,13,14,15,20,22);
! 1562: GR[48]= _gr( -8, 1,3,5,9,12,15,20,21);
! 1563:
! 1564: gr[0]=51; res = galmodp(pol,dpol,TYP,gr,GR);
! 1565: avma=av; if (!res) return 0;
! 1566: return CAR? 49: 50;
! 1567: }
! 1568:
! 1569: /* BIBLIOTHEQUE POUR LE DEGRE 9 */
! 1570: static long
! 1571: galoisprim9(GEN po, GEN *r)
! 1572: {
! 1573: long rep;
! 1574:
! 1575: if (!CAR)
! 1576: {
! 1577: /* PRIM_9_1: */
! 1578: rep=isin_G_H(po,r,34,26);
! 1579: if (!rep) return 34;
! 1580: /* PRIM_9_2: */
! 1581: rep=isin_G_H(po,r,26,19);
! 1582: if (!rep) return 26;
! 1583: /* PRIM_9_3: */
! 1584: rep=isin_G_H(po,r,19,16);
! 1585: if (rep) return 16;
! 1586: /* PRIM_9_4: */
! 1587: rep=isin_G_H(po,r,19,15);
! 1588: return rep? 15: 19;
! 1589: }
! 1590: /* PRIM_9_5: */
! 1591: rep=isin_G_H(po,r,33,32);
! 1592: if (!rep) goto PRIM_9_7;
! 1593: /* PRIM_9_6: */
! 1594: rep=isin_G_H(po,r,32,27);
! 1595: return rep? 27: 32;
! 1596:
! 1597: PRIM_9_7:
! 1598: rep=isin_G_H(po,r,33,23);
! 1599: if (!rep) return 33;
! 1600: /* PRIM_9_8: */
! 1601: rep=isin_G_H(po,r,23,14);
! 1602: if (!rep) return 23;
! 1603: /* PRIM_9_9: */
! 1604: rep=isin_G_H(po,r,14,9);
! 1605: return rep? 9: 14;
! 1606: }
! 1607:
! 1608: static long
! 1609: galoisimpodd9(GEN po, GEN *r)
! 1610: {
! 1611: long rep;
! 1612:
! 1613: /* IMPODD_9_1: */
! 1614: rep=isin_G_H(po,r,31,29);
! 1615: if (!rep) goto IMPODD_9_5;
! 1616: /* IMPODD_9_2: */
! 1617: rep=isin_G_H(po,r,29,20);
! 1618: if (!rep) return 29;
! 1619: IMPODD_9_3:
! 1620: rep=isin_G_H(po,r,20,12);
! 1621: if (!rep) return 20;
! 1622: IMPODD_9_4:
! 1623: rep=isin_G_H(po,r,12,4);
! 1624: return rep? 4: 12;
! 1625:
! 1626: IMPODD_9_5:
! 1627: rep=isin_G_H(po,r,31,28);
! 1628: if (!rep) goto IMPODD_9_9;
! 1629: /* IMPODD_9_6: */
! 1630: rep=isin_G_H(po,r,28,22);
! 1631: if (!rep) return 28;
! 1632: IMPODD_9_7:
! 1633: rep=isin_G_H(po,r,22,13);
! 1634: if (!rep) return 22;
! 1635: IMPODD_9_8:
! 1636: rep=isin_G_H(po,r,13,4);
! 1637: return rep? 4: 13;
! 1638:
! 1639: IMPODD_9_9:
! 1640: rep=isin_G_H(po,r,31,24);
! 1641: if (!rep) return 31;
! 1642: /* IMPODD_9_10: */
! 1643: rep=isin_G_H(po,r,24,22);
! 1644: if (rep) goto IMPODD_9_7;
! 1645: /* IMPODD_9_11: */
! 1646: rep=isin_G_H(po,r,24,20);
! 1647: if (rep) goto IMPODD_9_3;
! 1648: /* IMPODD_9_12: */
! 1649: rep=isin_G_H(po,r,24,18);
! 1650: if (!rep) return 24;
! 1651: /* IMPODD_9_13: */
! 1652: rep=isin_G_H(po,r,18,13);
! 1653: if (rep) goto IMPODD_9_8;
! 1654: /* IMPODD_9_14: */
! 1655: rep=isin_G_H(po,r,18,12);
! 1656: if (rep) goto IMPODD_9_4;
! 1657: /* IMPODD_9_15: */
! 1658: rep=isin_G_H(po,r,18,8);
! 1659: if (!rep) return 18;
! 1660: /* IMPODD_9_16: */
! 1661: rep=isin_G_H(po,r,8,4);
! 1662: return rep? 4: 8;
! 1663: }
! 1664:
! 1665: static long
! 1666: galoisimpeven9(GEN po, GEN *r)
! 1667: {
! 1668: long rep;
! 1669:
! 1670: /* IMPEVEN_9_1: */
! 1671: rep=isin_G_H(po,r,30,25);
! 1672: if (!rep) goto IMPEVEN_9_7;
! 1673: /* IMPEVEN_9_2: */
! 1674: rep=isin_G_H(po,r,25,17);
! 1675: if (!rep) return 25;
! 1676: IMPEVEN_9_3:
! 1677: rep=isin_G_H(po,r,17,7);
! 1678: if (!rep) goto IMPEVEN_9_5;
! 1679: IMPEVEN_9_4:
! 1680: rep=isin_G_H(po,r,7,2);
! 1681: return rep? 2: 7;
! 1682:
! 1683: IMPEVEN_9_5:
! 1684: rep=isin_G_H(po,r,17,6);
! 1685: if (!rep) return 17;
! 1686: IMPEVEN_9_6:
! 1687: rep=isin_G_H(po,r,6,1);
! 1688: return rep? 1: 6;
! 1689:
! 1690: IMPEVEN_9_7:
! 1691: rep=isin_G_H(po,r,30,21);
! 1692: if (!rep) return 30;
! 1693: /* IMPEVEN_9_8: */
! 1694: rep=isin_G_H(po,r,21,17);
! 1695: if (rep) goto IMPEVEN_9_3;
! 1696: /* IMPEVEN_9_9: */
! 1697: rep=isin_G_H(po,r,21,11);
! 1698: if (!rep) goto IMPEVEN_9_13;
! 1699: /* IMPEVEN_9_10: */
! 1700: rep=isin_G_H(po,r,11,7);
! 1701: if (rep) goto IMPEVEN_9_4;
! 1702: /* IMPEVEN_9_11: */
! 1703: rep=isin_G_H(po,r,11,5);
! 1704: if (!rep) return 11;
! 1705: /* IMPEVEN_9_12: */
! 1706: rep=isin_G_H(po,r,5,2);
! 1707: return rep? 2: 5;
! 1708:
! 1709: IMPEVEN_9_13:
! 1710: rep=isin_G_H(po,r,21,10);
! 1711: if (!rep) return 21;
! 1712: /* IMPEVEN_9_14: */
! 1713: rep=isin_G_H(po,r,10,6);
! 1714: if (rep) goto IMPEVEN_9_6;
! 1715: /* IMPEVEN_9_15: */
! 1716: rep=isin_G_H(po,r,10,3);
! 1717: if (!rep) return 10;
! 1718: /* IMPEVEN_9_16: */
! 1719: rep=isin_G_H(po,r,3,1);
! 1720: return rep? 1: 3;
! 1721: }
! 1722:
! 1723: static long
! 1724: closure9(GEN po)
! 1725: {
! 1726: long rep;
! 1727: GEN r[NMAX];
! 1728:
! 1729: r[0] = myroots(po,PRMAX); preci(r,PREC);
! 1730: if (!CAR)
! 1731: {
! 1732: /* CLOS_9_1: */
! 1733: rep=isin_G_H(po,r,34,31);
! 1734: if (rep) return galoisimpodd9(po,r);
! 1735: }
! 1736: else
! 1737: {
! 1738: /* CLOS_9_2: */
! 1739: rep=isin_G_H(po,r,33,30);
! 1740: if (rep) return galoisimpeven9(po,r);
! 1741: }
! 1742: return galoisprim9(po,r);
! 1743: }
! 1744:
! 1745: static PERM
! 1746: data9(long n1, long n2, GROUP *t)
! 1747: {
! 1748: switch(n1)
! 1749: {
! 1750: case 6: if (n2!=1) break;
! 1751: *t=initgroup(N,3);
! 1752: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 9, 7);
! 1753: _aff((*t)[3], 1, 2, 3, 4, 5, 6, 9, 7, 8);
! 1754: return SID;
! 1755: case 7: if (n2!=2) break;
! 1756: *t=initgroup(N,3);
! 1757: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 9, 7);
! 1758: _aff((*t)[3], 1, 2, 3, 4, 5, 6, 9, 7, 8);
! 1759: return SID;
! 1760: case 8: if (n2!=4) break;
! 1761: *t=initgroup(N,2);
! 1762: _aff((*t)[2], 1, 4, 7, 2, 5, 8, 3, 6, 9);
! 1763: return SID;
! 1764: case 12: if (n2!=4) break;
! 1765: *t=initgroup(N,3);
! 1766: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 9, 7);
! 1767: _aff((*t)[3], 1, 2, 3, 4, 5, 6, 9, 7, 8);
! 1768: return SID;
! 1769: case 13: if (n2!=4) break;
! 1770: *t=initgroup(N,1);
! 1771: return _cr(1, 4, 7, 2, 5, 8, 3, 6, 9);
! 1772: case 14: if (n2!=9) break;
! 1773: *t=initgroup(N,3);
! 1774: _aff((*t)[2], 1, 2, 3, 5, 6, 4, 9, 7, 8);
! 1775: _aff((*t)[3], 1, 2, 3, 6, 4, 5, 8, 9, 7);
! 1776: return SID;
! 1777: case 17: if (n2!=6) break;
! 1778: *t=initgroup(N,2);
! 1779: _aff((*t)[2], 1, 2, 3, 7, 8, 9, 4, 5, 6);
! 1780: return SID;
! 1781: case 21: if (n2!=10) break;
! 1782: *t=initgroup(N,2);
! 1783: _aff((*t)[2], 1, 2, 3, 7, 8, 9, 4, 5, 6);
! 1784: return SID;
! 1785: case 33: if (n2!=32) break;
! 1786: *t=initgroup(N,2);
! 1787: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 7, 9, 8);
! 1788: return SID;
! 1789: }
! 1790: *t=initgroup(N,1); return SID;
! 1791: }
! 1792:
! 1793: static long
! 1794: galoismodulo9(GEN pol, GEN dpol)
! 1795: {
! 1796: long av = avma, res, gr[35];
! 1797: long **TYP = partitions(9), **GR = (long**) cgeti(33);
! 1798:
! 1799: /* 42 TYPES ORDONNES CROISSANT (T[1],...,T[30])*/
! 1800:
! 1801: GR[ 1]= _gr( -3, 1,12,30);
! 1802: GR[ 2]= _gr( -2, 1,12);
! 1803: GR[ 3]= _gr( -4, 1,5,12,30);
! 1804: GR[ 4]= _gr( 4, 1,4,12,26);
! 1805: GR[ 5]= _gr( -3, 1,5,12);
! 1806: GR[ 6]= _gr( -4, 1,10,12,30);
! 1807: GR[ 7]= _gr( -3, 1,10,12);
! 1808: GR[ 8]= _gr( 5, 1,4,5,12,26);
! 1809: GR[ 9]= _gr( -4, 1,5,12,18);
! 1810: GR[10]= _gr( -6, 1,5,10,12,25,30);
! 1811: GR[11]= _gr( -5, 1,5,10,12,25);
! 1812: GR[12]= _gr( 5, 1,4,10,12,26);
! 1813: GR[13]= _gr( 5, 1,4,10,12,26);
! 1814: GR[14]= _gr( -4, 1,5,12,18);
! 1815: GR[15]= _gr( 5, 1,5,12,18,29);
! 1816: GR[16]= _gr( 6, 1,4,5,12,18,26);
! 1817: GR[17]= _gr( -5, 1,6,10,12,30);
! 1818: GR[18]= _gr( 7, 1,4,5,10,12,25,26);
! 1819: GR[19]= _gr( 7, 1,4,5,12,18,26,29);
! 1820: GR[20]= _gr( 9, 1,4,6,9,10,12,24,26,30);
! 1821: GR[21]= _gr( -7, 1,5,6,10,12,25,30);
! 1822: GR[22]= _gr( 7, 1,4,6,10,12,26,30);
! 1823: GR[23]= _gr( -6, 1,5,10,12,18,25);
! 1824: GR[24]= _gr( 11, 1,4,5,6,9,10,12,24,25,26,30);
! 1825: GR[25]= _gr( -7, 1,3,6,8,10,12,30);
! 1826: GR[26]= _gr( 9, 1,4,5,10,12,18,25,26,29);
! 1827: GR[27]= _gr( -5, 1,5,12,27,30);
! 1828: GR[28]= _gr( 12, 1,2,3,4,6,7,8,10,11,12,26,30);
! 1829: GR[29]= _gr( 12, 1,3,4,6,8,9,10,12,15,24,26,30);
! 1830: GR[30]= _gr(-11, 1,3,5,6,8,10,12,14,17,25,30);
! 1831: GR[31]= _gr( 19, 1,2,3,4,5,6,7,8,9,10,11,12,14,15,17,24,25,26,30);
! 1832: GR[32]= _gr( -7, 1,5,10,12,25,27,30);
! 1833:
! 1834: gr[0]=35; res = galmodp(pol,dpol,TYP,gr,GR);
! 1835: avma=av; if (!res) return 0;
! 1836: return CAR? 33: 34;
! 1837: }
! 1838:
! 1839: /* BIBLIOTHEQUE POUR LE DEGRE 10 */
! 1840: static long
! 1841: galoisprim10(GEN po, GEN *r)
! 1842: {
! 1843: long rep;
! 1844: if (CAR)
! 1845: {
! 1846: /* PRIM_10_1: */
! 1847: rep=isin_G_H(po,r,44,31);
! 1848: if (!rep) return 44;
! 1849: /* PRIM_10_2: */
! 1850: rep=isin_G_H(po,r,31,26);
! 1851: if (!rep) return 31;
! 1852: /* PRIM_10_3: */
! 1853: rep=isin_G_H(po,r,26,7);
! 1854: return rep? 7: 26;
! 1855: }
! 1856: else
! 1857: {
! 1858: /* PRIM_10_4: */
! 1859: rep=isin_G_H(po,r,45,35);
! 1860: if (!rep) return 45;
! 1861: /* PRIM_10_5: */
! 1862: rep=isin_G_H(po,r,35,32);
! 1863: if (!rep) goto PRIM_10_7;
! 1864: /* PRIM_10_6: */
! 1865: rep=isin_G_H(po,r,32,13);
! 1866: return rep? 13: 32;
! 1867:
! 1868: PRIM_10_7:
! 1869: rep=isin_G_H(po,r,35,30);
! 1870: return rep? 30: 35;
! 1871: }
! 1872: }
! 1873:
! 1874: static long
! 1875: galoisimpeven10(GEN po, GEN *r, long nogr)
! 1876: {
! 1877: long rep;
! 1878: if (nogr==42)
! 1879: {
! 1880: /* IMPEVEN_10_1: */
! 1881: rep=isin_G_H(po,r,42,28);
! 1882: if (!rep) return 42;
! 1883: /* IMPEVEN_10_2: */
! 1884: rep=isin_G_H(po,r,28,18);
! 1885: return rep? 18: 28;
! 1886: }
! 1887: else
! 1888: {
! 1889: /* IMPEVEN_10_3: */
! 1890: rep=isin_G_H(po,r,37,34);
! 1891: if (!rep) goto IMPEVEN_10_5;
! 1892: /* IMPEVEN_10_4: */
! 1893: rep=isin_G_H(po,r,34,15);
! 1894: if (rep) goto IMPEVEN_10_7; else return 34;
! 1895:
! 1896: IMPEVEN_10_5:
! 1897: rep=isin_G_H(po,r,37,24);
! 1898: if (!rep) return 37;
! 1899: /* IMPEVEN_10_6: */
! 1900: rep=isin_G_H(po,r,24,15);
! 1901: if (!rep) return 24;
! 1902: IMPEVEN_10_7:
! 1903: rep=isin_G_H(po,r,15,8);
! 1904: return rep? 8: 15;
! 1905: }
! 1906: }
! 1907:
! 1908: static long
! 1909: galoisimpodd10(GEN po, GEN *r, long nogr)
! 1910: {
! 1911: long rep;
! 1912: if (nogr==43)
! 1913: {
! 1914: /* IMPODD_10_1: */
! 1915: rep=isin_G_H(po,r,43,41);
! 1916: if (!rep) goto IMPODD_10_3;
! 1917: /* IMPODD_10_2: */
! 1918: rep=isin_G_H(po,r,41,40);
! 1919: if (rep) goto IMPODD_10_4; else goto IMPODD_10_5;
! 1920:
! 1921: IMPODD_10_3:
! 1922: rep=isin_G_H(po,r,43,33);
! 1923: if (rep) goto IMPODD_10_6; else return 43;
! 1924:
! 1925: IMPODD_10_4:
! 1926: rep=isin_G_H(po,r,40,21);
! 1927: if (rep) goto IMPODD_10_7; else goto IMPODD_10_8;
! 1928:
! 1929: IMPODD_10_5:
! 1930: rep=isin_G_H(po,r,41,27);
! 1931: if (rep) goto IMPODD_10_9; else goto IMPODD_10_10;
! 1932:
! 1933: IMPODD_10_6:
! 1934: rep=isin_G_H(po,r,33,27);
! 1935: if (rep) goto IMPODD_10_9; else return 33;
! 1936:
! 1937: IMPODD_10_7:
! 1938: rep=isin_G_H(po,r,21,10);
! 1939: if (rep) goto IMPODD_10_12; else goto IMPODD_10_13;
! 1940:
! 1941: IMPODD_10_8:
! 1942: rep=isin_G_H(po,r,40,12);
! 1943: if (rep) goto IMPODD_10_14; else goto IMPODD_10_15;
! 1944:
! 1945: IMPODD_10_9:
! 1946: rep=isin_G_H(po,r,27,21);
! 1947: if (rep) goto IMPODD_10_7; else goto IMPODD_10_16;
! 1948:
! 1949: IMPODD_10_10:
! 1950: rep=isin_G_H(po,r,41,22);
! 1951: if (!rep) return 41;
! 1952: /* IMPODD_10_11: */
! 1953: rep=isin_G_H(po,r,22,12);
! 1954: if (rep) goto IMPODD_10_14; else goto IMPODD_10_18;
! 1955:
! 1956: IMPODD_10_12:
! 1957: rep=isin_G_H(po,r,10,4);
! 1958: return rep? 4: 10;
! 1959:
! 1960: IMPODD_10_13:
! 1961: rep=isin_G_H(po,r,21,9);
! 1962: if (rep) goto IMPODD_10_19; else return 21;
! 1963: IMPODD_10_14:
! 1964: rep=isin_G_H(po,r,12,4);
! 1965: return rep? 4: 12;
! 1966:
! 1967: IMPODD_10_15:
! 1968: rep=isin_G_H(po,r,40,11);
! 1969: if (rep) goto IMPODD_10_20; else return 40;
! 1970: IMPODD_10_16:
! 1971: rep=isin_G_H(po,r,27,20);
! 1972: if (!rep) goto IMPODD_10_21;
! 1973: /* IMPODD_10_17: */
! 1974: rep=isin_G_H(po,r,20,10);
! 1975: if (rep) goto IMPODD_10_12; return 20;
! 1976:
! 1977: IMPODD_10_18:
! 1978: rep=isin_G_H(po,r,22,11);
! 1979: if (rep) goto IMPODD_10_20; else goto IMPODD_10_23;
! 1980:
! 1981: IMPODD_10_19:
! 1982: rep=isin_G_H(po,r,9,6);
! 1983: if (rep) goto IMPODD_10_24; else goto IMPODD_10_25;
! 1984:
! 1985: IMPODD_10_20:
! 1986: rep=isin_G_H(po,r,11,3);
! 1987: if (rep) goto IMPODD_10_26; else return 11;
! 1988:
! 1989: IMPODD_10_21:
! 1990: rep=isin_G_H(po,r,27,19);
! 1991: if (rep) goto IMPODD_10_27;
! 1992: /* IMPODD_10_22: */
! 1993: rep=isin_G_H(po,r,27,17);
! 1994: if (rep) goto IMPODD_10_28; else return 27;
! 1995:
! 1996: IMPODD_10_23:
! 1997: rep=isin_G_H(po,r,22,5);
! 1998: if (rep) goto IMPODD_10_29; else return 22;
! 1999:
! 2000: IMPODD_10_24:
! 2001: rep=isin_G_H(po,r,6,2);
! 2002: if (rep) return 2; else goto IMPODD_10_30;
! 2003:
! 2004: IMPODD_10_25:
! 2005: rep=isin_G_H(po,r,9,3);
! 2006: if (!rep) return 9;
! 2007: IMPODD_10_26:
! 2008: rep=isin_G_H(po,r,3,2);
! 2009: if (rep) return 2; else goto IMPODD_10_31;
! 2010:
! 2011: IMPODD_10_27:
! 2012: rep=isin_G_H(po,r,19,9);
! 2013: if (rep) goto IMPODD_10_19; else return 19;
! 2014:
! 2015: IMPODD_10_28:
! 2016: rep=isin_G_H(po,r,17,10);
! 2017: if (rep) goto IMPODD_10_12; else goto IMPODD_10_32;
! 2018:
! 2019: IMPODD_10_29:
! 2020: rep=isin_G_H(po,r,5,4);
! 2021: if (rep) return 4; else goto IMPODD_10_33;
! 2022:
! 2023: IMPODD_10_30:
! 2024: rep=isin_G_H(po,r,6,1);
! 2025: return rep? 1: 6;
! 2026:
! 2027: IMPODD_10_31:
! 2028: rep=isin_G_H(po,r,3,1);
! 2029: return rep? 1: 3;
! 2030:
! 2031: IMPODD_10_32:
! 2032: rep=isin_G_H(po,r,17,9);
! 2033: if (rep) goto IMPODD_10_19; else goto IMPODD_10_60;
! 2034:
! 2035: IMPODD_10_33:
! 2036: rep=isin_G_H(po,r,5,3);
! 2037: if (rep) goto IMPODD_10_26; else return 5;
! 2038:
! 2039: IMPODD_10_60:
! 2040: rep=isin_G_H(po,r,17,5);
! 2041: if (rep) goto IMPODD_10_29; else return 17;
! 2042: }
! 2043: else
! 2044: {
! 2045: /* IMPODD_10_34: */
! 2046: rep=isin_G_H(po,r,39,38);
! 2047: if (!rep) goto IMPODD_10_36;
! 2048: /* IMPODD_10_35: */
! 2049: rep=isin_G_H(po,r,38,25);
! 2050: if (rep) goto IMPODD_10_37; else goto IMPODD_10_38;
! 2051:
! 2052: IMPODD_10_36:
! 2053: rep=isin_G_H(po,r,39,36);
! 2054: if (rep) goto IMPODD_10_39; else goto IMPODD_10_40;
! 2055:
! 2056: IMPODD_10_37:
! 2057: rep=isin_G_H(po,r,25,4);
! 2058: return rep? 4: 25;
! 2059:
! 2060: IMPODD_10_38:
! 2061: rep=isin_G_H(po,r,38,12);
! 2062: if (rep) goto IMPODD_10_41; else return 38;
! 2063:
! 2064: IMPODD_10_39:
! 2065: rep=isin_G_H(po,r,36,23);
! 2066: if (rep) goto IMPODD_10_42; else goto IMPODD_10_43;
! 2067:
! 2068: IMPODD_10_40:
! 2069: rep=isin_G_H(po,r,39,29);
! 2070: if (rep) goto IMPODD_10_44; else goto IMPODD_10_45;
! 2071:
! 2072: IMPODD_10_41:
! 2073: rep=isin_G_H(po,r,12,4);
! 2074: return rep? 4: 12;
! 2075:
! 2076: IMPODD_10_42:
! 2077: rep=isin_G_H(po,r,23,16);
! 2078: if (rep) goto IMPODD_10_46; else goto IMPODD_10_47;
! 2079:
! 2080: IMPODD_10_43:
! 2081: rep=isin_G_H(po,r,36,11);
! 2082: if (rep) goto IMPODD_10_48; else return 36;
! 2083:
! 2084: IMPODD_10_44:
! 2085: rep=isin_G_H(po,r,29,25);
! 2086: if (rep) goto IMPODD_10_37; else goto IMPODD_10_49;
! 2087:
! 2088: IMPODD_10_45:
! 2089: rep=isin_G_H(po,r,39,22);
! 2090: if (rep) goto IMPODD_10_50; else return 39;
! 2091:
! 2092: IMPODD_10_46:
! 2093: rep=isin_G_H(po,r,16,2);
! 2094: return rep? 2: 16;
! 2095:
! 2096: IMPODD_10_47:
! 2097: rep=isin_G_H(po,r,23,14);
! 2098: if (rep) goto IMPODD_10_51; else goto IMPODD_10_52;
! 2099:
! 2100: IMPODD_10_48:
! 2101: rep=isin_G_H(po,r,11,3);
! 2102: if (rep) goto IMPODD_10_53; else return 11;
! 2103:
! 2104: IMPODD_10_49:
! 2105: rep=isin_G_H(po,r,29,23);
! 2106: if (rep) goto IMPODD_10_42; else goto IMPODD_10_54;
! 2107:
! 2108: IMPODD_10_50:
! 2109: rep=isin_G_H(po,r,22,12);
! 2110: if (rep) goto IMPODD_10_41; else goto IMPODD_10_55;
! 2111:
! 2112: IMPODD_10_51:
! 2113: rep=isin_G_H(po,r,14,1);
! 2114: return rep? 1: 14;
! 2115:
! 2116: IMPODD_10_52:
! 2117: rep=isin_G_H(po,r,23,3);
! 2118: if (!rep) return 23;
! 2119: IMPODD_10_53:
! 2120: rep=isin_G_H(po,r,3,2);
! 2121: if (rep) return 2; else goto IMPODD_10_57;
! 2122:
! 2123: IMPODD_10_54:
! 2124: rep=isin_G_H(po,r,29,5);
! 2125: if (rep) goto IMPODD_10_58; else return 29;
! 2126:
! 2127: IMPODD_10_55:
! 2128: rep=isin_G_H(po,r,22,11);
! 2129: if (rep) goto IMPODD_10_48;
! 2130: /* IMPODD_10_56: */
! 2131: rep=isin_G_H(po,r,22,5);
! 2132: if (rep) goto IMPODD_10_58; else return 22;
! 2133:
! 2134: IMPODD_10_57:
! 2135: rep=isin_G_H(po,r,3,1);
! 2136: return rep? 1: 3;
! 2137:
! 2138: IMPODD_10_58:
! 2139: rep=isin_G_H(po,r,5,4);
! 2140: if (rep) return 4;
! 2141: /* IMPODD_10_59: */
! 2142: rep=isin_G_H(po,r,5,3);
! 2143: if (rep) goto IMPODD_10_53; else return 5;
! 2144: }
! 2145: }
! 2146:
! 2147: static long
! 2148: closure10(GEN po)
! 2149: {
! 2150: long rep;
! 2151: GEN r[NMAX];
! 2152:
! 2153: r[0] = myroots(po,PRMAX); preci(r,PREC);
! 2154: if (CAR)
! 2155: {
! 2156: /* CLOS_10_1: */
! 2157: rep=isin_G_H(po,r,44,42);
! 2158: if (rep) return galoisimpeven10(po,r,42);
! 2159: /* CLOS_10_2: */
! 2160: rep=isin_G_H(po,r,44,37);
! 2161: if (rep) return galoisimpeven10(po,r,37);
! 2162: }
! 2163: else
! 2164: {
! 2165: /* CLOS_10_3: */
! 2166: rep=isin_G_H(po,r,45,43);
! 2167: if (rep) return galoisimpodd10(po,r,43);
! 2168: /* CLOS_10_4: */
! 2169: rep=isin_G_H(po,r,45,39);
! 2170: if (rep) return galoisimpodd10(po,r,39);
! 2171: }
! 2172: return galoisprim10(po,r);
! 2173: }
! 2174:
! 2175: static PERM
! 2176: data10(long n1,long n2,GROUP *t)
! 2177: {
! 2178: switch(n1)
! 2179: {
! 2180: case 6: if (n2!=2) break;
! 2181: *t=initgroup(N,1);
! 2182: return _cr(1, 2, 3, 4, 5, 6, 10, 9, 8, 7);
! 2183: case 9: if (n2!=3 && n2!=6) break;
! 2184: *t=initgroup(N,2);
! 2185: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 10, 9, 8, 7);
! 2186: return SID;
! 2187: case 10: *t=initgroup(N,2);
! 2188: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 10, 9, 8, 7);
! 2189: return SID;
! 2190: case 14: case 16:*t=initgroup(N,1);
! 2191: return _cr(1, 3, 5, 7, 9, 2, 4, 6, 8, 10);
! 2192: case 17: if (n2!=5) break;
! 2193: *t=initgroup(N,2);
! 2194: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 10, 9, 8, 7);
! 2195: return SID;
! 2196: case 19: case 20: *t=initgroup(N,2);
! 2197: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 10, 7, 9);
! 2198: return SID;
! 2199: case 21: if (n2!=10) break;
! 2200: *t=initgroup(N,1);
! 2201: return _cr(1, 2, 3, 4, 5, 6, 8, 10, 7, 9);
! 2202: case 23: if (n2!=3) break;
! 2203: *t=initgroup(N,1);
! 2204: return _cr(1, 3, 5, 7, 9, 2, 4, 6, 8, 10);
! 2205: case 25: *t=initgroup(N,1);
! 2206: return _cr(1, 3, 5, 7, 9, 2, 4, 6, 8, 10);
! 2207: case 26: *t=initgroup(N,2);
! 2208: _aff((*t)[2], 1, 2, 4, 9, 6, 8, 10, 3, 7, 5);
! 2209: return _cr(1, 2, 3, 10, 6, 5, 7, 4, 8, 9);
! 2210: case 27: if (n2!=17 && n2!=21) break;
! 2211: *t=initgroup(N,2);
! 2212: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 10, 7, 9);
! 2213: return SID;
! 2214: case 28: *t=initgroup(N,2);
! 2215: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 10, 7, 9);
! 2216: return SID;
! 2217: case 29: if (n2!=5) break;
! 2218: *t=initgroup(N,1);
! 2219: return _cr(1, 3, 5, 7, 9, 2, 4, 6, 8, 10);
! 2220: case 32: *t=initgroup(N,2);
! 2221: _aff((*t)[2], 1, 2, 4, 9, 6, 8, 10, 3, 7, 5);
! 2222: return _cr(1, 2, 3, 10, 6, 5, 7, 4, 8, 9);
! 2223: case 36: if (n2!=11) break;
! 2224: *t=initgroup(N,1);
! 2225: return _cr(1, 3, 5, 7, 9, 2, 4, 6, 8, 10);
! 2226: case 38: if (n2!=12) break;
! 2227: *t=initgroup(N,1);
! 2228: return _cr(1, 3, 5, 7, 9, 2, 4, 6, 8, 10);
! 2229: case 39: if (n2!=22) break;
! 2230: *t=initgroup(N,1);
! 2231: return _cr(1, 3, 5, 7, 9, 2, 4, 6, 8, 10);
! 2232: case 40: if (n2!=12) break;
! 2233: *t=initgroup(N,1);
! 2234: return _cr(1, 2, 3, 4, 5, 6, 7, 8, 10, 9);
! 2235: case 41: if (n2!=22 && n2!=40) break;
! 2236: *t=initgroup(N,2);
! 2237: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 7, 8, 10, 9);
! 2238: return SID;
! 2239: }
! 2240: *t=initgroup(N,1); return SID;
! 2241: }
! 2242:
! 2243: static long
! 2244: galoismodulo10(GEN pol, GEN dpol)
! 2245: {
! 2246: long av = avma, res, gr[46];
! 2247: long **TYP = partitions(10), **GR = (long**) cgeti(45);
! 2248:
! 2249: GR[ 1]= _gr( 4, 1,6,30,42);
! 2250: GR[ 2]= _gr( 3, 1,6,30);
! 2251: GR[ 3]= _gr( 5, 1,5,6,30,42);
! 2252: GR[ 4]= _gr( 4, 1,5,23,30);
! 2253: GR[ 5]= _gr( 7, 1,5,6,22,23,30,42);
! 2254: GR[ 6]= _gr( 5, 1,6,24,30,42);
! 2255: GR[ 7]= _gr( -4, 1,5,14,30);
! 2256: GR[ 8]= _gr( -4, 1,3,5,30);
! 2257: GR[ 9]= _gr( 6, 1,5,6,24,30,42);
! 2258: GR[10]= _gr( 5, 1,5,23,24,30);
! 2259: GR[11]= _gr( 7, 1,5,6,11,30,33,42);
! 2260: GR[12]= _gr( 7, 1,5,6,11,23,30,33);
! 2261: GR[13]= _gr( 7, 1,4,5,14,23,30,34);
! 2262: GR[14]= _gr( 8, 1,2,3,4,5,6,30,42);
! 2263: GR[15]= _gr( -6, 1,3,5,18,22,30);
! 2264: GR[16]= _gr( 7, 1,3,5,6,17,23,30);
! 2265: GR[17]= _gr( 8, 1,5,6,22,23,24,30,42);
! 2266: GR[18]= _gr( -6, 1,5,22,24,30,40);
! 2267: GR[19]= _gr( 7, 1,5,6,22,24,30,42);
! 2268: GR[20]= _gr( 6, 1,5,22,23,24,30);
! 2269: GR[21]= _gr( 9, 1,3,5,6,23,24,26,30,42);
! 2270: GR[22]= _gr( 11, 1,3,5,6,11,13,22,23,30,33,42);
! 2271: GR[23]= _gr( 12, 1,2,3,4,5,6,17,18,22,23,30,42);
! 2272: GR[24]= _gr( -7, 1,3,5,18,22,30,40);
! 2273: GR[25]= _gr( 8, 1,3,5,18,22,23,30,39);
! 2274: GR[26]= _gr( -5, 1,5,14,22,30);
! 2275: GR[27]= _gr( 10, 1,3,5,6,22,23,24,26,30,42);
! 2276: GR[28]= _gr( -8, 1,3,5,22,24,26,30,40);
! 2277: GR[29]= _gr( 14, 1,2,3,4,5,6,17,18,22,23,30,39,40,42);
! 2278: GR[30]= _gr( 8, 1,5,6,14,22,30,39,42);
! 2279: GR[31]= _gr( -6, 1,5,14,22,30,40);
! 2280: GR[32]= _gr( 8, 1,4,5,14,22,23,30,34);
! 2281: GR[33]= _gr( 14, 1,3,5,6,15,17,22,23,24,26,29,30,40,42);
! 2282: GR[34]= _gr( -9, 1,3,5,11,13,18,22,30,32);
! 2283: GR[35]= _gr( 12, 1,4,5,6,14,22,23,30,34,39,40,42);
! 2284: GR[36]= _gr( 18, 1,2,3,4,5,6,11,12,13,17,18,22,23,30,31,32,33,42);
! 2285: GR[37]= _gr(-12, 1,3,5,11,13,16,18,22,30,32,35,40);
! 2286: GR[38]= _gr( 18, 1,3,4,5,6,11,13,15,17,18,21,22,23,30,32,33,35,39);
! 2287: GR[39]= _gr( 24, 1,2,3,4,5,6,11,12,13,15,16,17,18,21,22,23,30,31,32,33,35,39,40,42);
! 2288: GR[40]= _gr( 14, 1,3,5,6,7,9,11,23,24,26,27,30,33,42);
! 2289: GR[41]= _gr( 18, 1,3,5,6,7,9,11,13,16,20,22,23,24,26,27,30,33,42);
! 2290: GR[42]= _gr(-17, 1,3,5,7,9,11,13,16,18,20,22,24,26,27,30,35,40);
! 2291: GR[43]= _gr( 32, 1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,22,23,24,25,26,27,28,29,30,33,35,40,42);
! 2292: GR[44]= _gr(-22, 1,3,5,7,9,11,13,14,16,18,20,22,24,26,27,30,32,35,36,38,40,41);
! 2293:
! 2294: gr[0]=46; res = galmodp(pol,dpol,TYP,gr,GR);
! 2295: avma=av; if (!res) return 0;
! 2296: return CAR? 44: 45;
! 2297: }
! 2298:
! 2299: /* BIBLIOTHEQUE POUR LE DEGRE 11 */
! 2300:
! 2301: static long
! 2302: closure11(GEN po)
! 2303: {
! 2304: long rep;
! 2305: GEN r[NMAX];
! 2306:
! 2307: r[0] = myroots(po,PRMAX); preci(r,PREC);
! 2308: if (CAR)
! 2309: {
! 2310: /* EVEN_11_1: */
! 2311: rep=isin_G_H(po,r,7,6);
! 2312: if (!rep) return 7;
! 2313: /* EVEN_11_2: */
! 2314: rep=isin_G_H(po,r,6,5);
! 2315: if (!rep) return 6;
! 2316: /* EVEN_11_3: */
! 2317: rep=isin_G_H(po,r,5,3);
! 2318: if (!rep) return 5;
! 2319: /* EVEN_11_4: */
! 2320: rep=isin_G_H(po,r,3,1);
! 2321: return rep? 1: 3;
! 2322: }
! 2323: else
! 2324: {
! 2325: /* ODD_11_1: */
! 2326: rep=isin_G_H(po,r,8,4);
! 2327: if (!rep) return 8;
! 2328: /* ODD_11_2: */
! 2329: rep=isin_G_H(po,r,4,2);
! 2330: return rep? 2: 4;
! 2331: }
! 2332: }
! 2333:
! 2334: static PERM
! 2335: data11(long n1, GROUP *t)
! 2336: {
! 2337: switch(n1)
! 2338: {
! 2339: case 5: *t=initgroup(N,1);
! 2340: return _cr(1, 2, 3, 7, 8, 6, 11, 5, 9, 4, 10);
! 2341: case 6: *t=initgroup(N,1);
! 2342: return _cr(1, 2, 3, 4, 6, 10, 11, 9, 7, 5, 8);
! 2343: case 7: *t=initgroup(N,2);
! 2344: _aff((*t)[2], 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 10);
! 2345: return SID;
! 2346: }
! 2347: *t=initgroup(N,1); return SID;
! 2348: }
! 2349:
! 2350: static long
! 2351: galoismodulo11(GEN pol, GEN dpol)
! 2352: {
! 2353: long av = avma, res, gr[6] = {0, 1,1,1,1,1};
! 2354: long **TYP = (long**) cgeti(9);
! 2355:
! 2356: TYP[0] = new_chunk(1);
! 2357: TYP[1] = _gr(11, 11,0,0,0,0,0,0,0,0,0,0);
! 2358: if (CAR)
! 2359: {
! 2360: TYP[2] = _gr(11, 8,2,1,0,0,0,0,0,0,0,0);
! 2361: TYP[3] = _gr(11, 6,3,2,0,0,0,0,0,0,0,0);
! 2362: TYP[4] = _gr(11, 5,5,1,0,0,0,0,0,0,0,0);
! 2363: TYP[5] = _gr(11, 4,4,1,1,1,0,0,0,0,0,0);
! 2364: TYP[6] = _gr(11, 3,3,3,1,1,0,0,0,0,0,0);
! 2365: TYP[7] = _gr(11, 2,2,2,2,1,1,1,0,0,0,0);
! 2366: TYP[8] = _gr(11, 1,1,1,1,1,1,1,1,1,1,1);
! 2367: TYP[0][0] = 8;
! 2368: }
! 2369: else
! 2370: {
! 2371: TYP[2] = _gr(11,10,1,0,0,0,0,0,0,0,0,0);
! 2372: TYP[3] = _gr(11, 5,5,1,0,0,0,0,0,0,0,0);
! 2373: TYP[4] = _gr(11, 2,2,2,2,2,1,0,0,0,0,0);
! 2374: TYP[5] = _gr(11, 1,1,1,1,1,1,1,1,1,1,1);
! 2375: TYP[0][0] = 5;
! 2376: }
! 2377: res = galmodp(pol,dpol,TYP,gr,NULL);
! 2378: avma=av; if (!res) return 0;
! 2379: return CAR? 7: 8;
! 2380: }
! 2381:
! 2382: /* return 1 iff we need to read a resolvent */
! 2383: static long
! 2384: init_isin(long n1, long n2, GROUP *tau, GROUP *ss, PERM *s0)
! 2385: {
! 2386: long fl = 1;
! 2387: if (DEBUGLEVEL) {
! 2388: fprintferr("\n*** Entering isin_%ld_G_H_(%ld,%ld)\n",N,n1,n2); flusherr();
! 2389: }
! 2390: switch(N)
! 2391: {
! 2392: case 8:
! 2393: if ((n1==47 && n2==46) || (n1==44 && n2==40)) fl=0;
! 2394: *s0=data8(n1,n2,tau); break;
! 2395: case 9:
! 2396: if ((n1==31 && n2==29) || (n1==34 && n2==31) || (n1==33 && n2==30)) fl=0;
! 2397: *s0=data9(n1,n2,tau); break;
! 2398: case 10:
! 2399: if ((n1==45 && (n2==43||n2==39))
! 2400: || (n1==44 && (n2==42||n2==37))
! 2401: || (n1==43 && (n2==41||n2==33))
! 2402: || (n1==42 && n2==28)
! 2403: || (n1==41 && (n2==40||n2==27||n2==22))
! 2404: || (n1==40 && (n2==21||n2==11))
! 2405: || (n1==39 && (n2==38||n2==36||n2==29||n2==22))
! 2406: || (n1==38 && (n2==25||n2==12))
! 2407: || (n1==37 && (n2==34||n2==24))
! 2408: || (n1==36 && (n2==23||n2==11))
! 2409: || (n1==34 && n2==15)
! 2410: || (n1==33 && n2==27)
! 2411: || (n1==29 && (n2==25||n2==23||n2==5))
! 2412: || (n1==28 && n2==18)
! 2413: || (n1==27 && (n2==20||n2==19||n2==17))
! 2414: || (n1==25 && n2==4)
! 2415: || (n1==24 && n2==15)
! 2416: || (n1==23 && (n2==16||n2==3))
! 2417: || (n1==22 && (n2==12||n2==11||n2==5))
! 2418: || (n1==21 && (n2==10||n2==9))
! 2419: || (n1==17 && n2==5)
! 2420: || (n1==16 && n2==2)
! 2421: || (n1==14 && n2==1)
! 2422: || (n1==12 && n2==4)
! 2423: || (n1==11 && n2==3)
! 2424: || (n1==10 && n2==4)
! 2425: || (n1== 9 && n2==3)
! 2426: || (n1== 6 && n2==1)
! 2427: || (n1== 5 && n2==3)) fl = 0;
! 2428: *s0=data10(n1,n2,tau); break;
! 2429: case 11:
! 2430: *s0=data11(n1,tau); break;
! 2431: }
! 2432: *ss = lirecoset(n1,n2,N); return fl;
! 2433: }
! 2434:
! 2435: static long
! 2436: isin_G_H(GEN po, GEN *r, long n1, long n2)
! 2437: {
! 2438: long nbv,nbm,i,j;
! 2439: PERM s0, ww;
! 2440: RESOLVANTE a;
! 2441: GROUP ss,tau;
! 2442:
! 2443: if (init_isin(n1,n2, &tau, &ss, &s0))
! 2444: a = lireresolv(n1,n2,N,&nbv,&nbm);
! 2445: else
! 2446: { a = NULL; nbm=n1; nbv=n2; }
! 2447: ww = check_isin(po,r,nbm,nbv,a,tau,ss,s0);
! 2448: if (getpreci(r) != PREC) preci(r,PREC);
! 2449: free(ss); free(tau); if (a) free(a);
! 2450: if (ww)
! 2451: {
! 2452: long z[NMAX+1];
! 2453:
! 2454: if (DEBUGLEVEL)
! 2455: {
! 2456: fprintferr("\n Output of isin_%ld_G_H(%ld,%ld): %ld",N,n1,n2,n2);
! 2457: fprintferr("\n Reordering of the roots: "); printperm(ww);
! 2458: flusherr();
! 2459: }
! 2460: for (i=0; i<TSCHMAX; i++)
! 2461: {
! 2462: GEN p1 = r[i];
! 2463: for (j=1; j<=N; j++) z[j]=p1[(int)ww[j]];
! 2464: for (j=1; j<=N; j++) p1[j]=z[j];
! 2465: }
! 2466: free(ww); return n2;
! 2467: }
! 2468: if (DEBUGLEVEL)
! 2469: {
! 2470: fprintferr(" Output of isin_%ld_G_H(%ld,%ld): not included.\n",N,n1,n2);
! 2471: flusherr();
! 2472: }
! 2473: return 0;
! 2474: }
! 2475:
! 2476: GEN
! 2477: galoisbig(GEN pol, long prec)
! 2478: {
! 2479: GEN dpol, res = cgetg(4,t_VEC);
! 2480: long *tab,t, av = avma;
! 2481: long tab8[]={0,
! 2482: 8,8,8,8,8,16,16,16,16,16, 16,24,24,24,32,32,32,32,32,32,
! 2483: 32,32,48,48,56,64,64,64,64,64, 64,96,96,96,128,168,168,192,192,192,
! 2484: 192,288,336,384,576,576,1152,1344,20160,40320};
! 2485: long tab9[]={0,
! 2486: 9,9,18,18,18,27,27,36,36,54, 54,54,54,72,72,72,81,108,144,162,
! 2487: 162,162,216,324,324,432,504,648,648,648, 1296,1512,181440,362880};
! 2488: long tab10[]={0,
! 2489: 10,10,20,20,40,50,60,80,100,100, 120,120,120,160,160,160,200,200,200,200,
! 2490: 200,240,320,320,320,360,400,400,640,720, 720,720,800,960,1440,
! 2491: 1920,1920,1920,3840,7200,14400,14400,28800,1814400,3628800};
! 2492: long tab11[]={0, 11,22,55,110,660,7920,19958400,39916800};
! 2493:
! 2494: N = degpol(pol); dpol = discsr(pol); CAR = carreparfait(dpol);
! 2495: prec += 2 * (MEDDEFAULTPREC-2);
! 2496: PREC = prec;
! 2497: if (DEBUGLEVEL)
! 2498: {
! 2499: fprintferr("Galoisbig (prec=%ld): reduced polynomial #1 = %Z\n",prec,pol);
! 2500: fprintferr("discriminant = %Z\n", dpol);
! 2501: fprintferr("%s group\n", CAR? "EVEN": "ODD"); flusherr();
! 2502: }
! 2503: PRMAX = prec+5; TSCHMAX = 1; SID[0] = N;
! 2504: switch(N)
! 2505: {
! 2506: case 8: t = galoismodulo8(pol,dpol);
! 2507: if (!t) t = closure8(pol);
! 2508: tab=tab8; break;
! 2509:
! 2510: case 9: t = galoismodulo9(pol,dpol);
! 2511: if (!t) t = closure9(pol);
! 2512: tab=tab9; break;
! 2513:
! 2514: case 10: t = galoismodulo10(pol,dpol);
! 2515: if (!t) t = closure10(pol);
! 2516: tab=tab10; break;
! 2517:
! 2518: case 11: t = galoismodulo11(pol,dpol);
! 2519: if (!t) t = closure11(pol);
! 2520: tab=tab11; break;
! 2521:
! 2522: default: err(impl,"galois in degree > 11");
! 2523: return NULL; /* not reached */
! 2524: }
! 2525: avma = av;
! 2526: res[1]=lstoi(tab[t]);
! 2527: res[2]=lstoi(CAR? 1 : -1);
! 2528: res[3]=lstoi(t); return res;
! 2529: }
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