Annotation of OpenXM_contrib/pari-2.2/src/basemath/base5.c, Revision 1.1
1.1 ! noro 1: /* $Id: base5.c,v 1.17 2001/10/01 12:11:29 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: /* BASIC NF OPERATIONS */
! 19: /* (continued 2) */
! 20: /* */
! 21: /*******************************************************************/
! 22: #include "pari.h"
! 23: GEN mat_to_vecpol(GEN x, long v);
! 24:
! 25: GEN
! 26: matbasistoalg(GEN nf,GEN x)
! 27: {
! 28: long i,j,lx,li;
! 29: GEN p1,z;
! 30:
! 31: if (typ(x)!=t_MAT)
! 32: err(talker,"argument must be a matrix in matbasistoalg");
! 33: lx=lg(x); z=cgetg(lx,t_MAT); if (lx==1) return z;
! 34:
! 35: li=lg(x[1]);
! 36: for (j=1; j<lx; j++)
! 37: {
! 38: p1=cgetg(li,t_COL); z[j]=(long)p1;
! 39: for (i=1; i<li; i++) p1[i]=(long)basistoalg(nf,gcoeff(x,i,j));
! 40: }
! 41: return z;
! 42: }
! 43:
! 44: GEN
! 45: matalgtobasis(GEN nf,GEN x)
! 46: {
! 47: long i,j,lx,li;
! 48: GEN p1,z;
! 49:
! 50: if (typ(x)!=t_MAT)
! 51: err(talker,"argument must be a matrix in matalgtobasis");
! 52: lx=lg(x); z=cgetg(lx,t_MAT); if (lx==1) return z;
! 53:
! 54: li=lg(x[1]);
! 55: for (j=1; j<lx; j++)
! 56: {
! 57: p1=cgetg(li,t_COL); z[j]=(long)p1;
! 58: for (i=1; i<li; i++) p1[i]=(long)algtobasis(nf,gcoeff(x,i,j));
! 59: }
! 60: return z;
! 61: }
! 62:
! 63: static GEN
! 64: rnfmakematrices(GEN rnf)
! 65: {
! 66: long i,j,k,n,r1,r2,ru,ruk,r1rel,r2rel;
! 67: GEN nf,pol,rac,base,base1,racnf,sig,vecmat,vecM,vecMC,vecT2,rack;
! 68: GEN M,p2,p3,MC,sigk,T2,T,p1,MD,TI,MDI;
! 69:
! 70: nf=(GEN)rnf[10]; racnf=(GEN)nf[6]; pol=(GEN)rnf[1];
! 71: n=degpol(pol);
! 72: base=(GEN)rnf[7]; base1=(GEN)base[1]; rac=(GEN)rnf[6]; sig=(GEN)rnf[2];
! 73: r1 = nf_get_r1(nf);
! 74: r2 = nf_get_r2(nf); ru = r1+r2;
! 75: vecmat=cgetg(8,t_VEC);
! 76: vecM=cgetg(ru+1,t_VEC); vecmat[1]=(long)vecM;
! 77: vecMC=cgetg(ru+1,t_VEC); vecmat[2]=(long)vecMC;
! 78: vecT2=cgetg(ru+1,t_VEC); vecmat[3]=(long)vecT2;
! 79: for (k=1; k<=ru; k++)
! 80: {
! 81: rack=(GEN)rac[k]; ruk=lg(rack)-1;
! 82: M=cgetg(n+1,t_MAT); vecM[k]=(long)M;
! 83: for (j=1; j<=n; j++)
! 84: {
! 85: p2=cgetg(ruk+1,t_COL); M[j]=(long)p2; p3=lift((GEN)base1[j]);
! 86: p3=gsubst(p3,varn(nf[1]),(GEN)racnf[k]);
! 87: for (i=1; i<=ruk; i++) p2[i]=lsubst(p3,varn(rnf[1]),(GEN)rack[i]);
! 88: }
! 89: MC=gconj(gtrans(M)); vecMC[k]=(long)MC;
! 90: if (k<=r1)
! 91: {
! 92: sigk=(GEN)sig[k]; r1rel=itos((GEN)sigk[1]); r2rel=itos((GEN)sigk[2]);
! 93: if (r1rel+r2rel != lg(MC)-1) err(talker,"bug in rnfmakematrices");
! 94: for (j=r1rel+1; j<=r1rel+r2rel; j++) MC[j]=lmul2n((GEN)MC[j],1);
! 95: }
! 96: T2=gmul(MC,M); vecT2[k]=(long)T2;
! 97: }
! 98: T=cgetg(n+1,t_MAT); vecmat[4]=(long)T;
! 99: for (j=1; j<=n; j++)
! 100: {
! 101: p1=cgetg(n+1,t_COL); T[j]=(long)p1;
! 102: for (i=1; i<=n; i++)
! 103: p1[i]=ltrace(gmodulcp(gmul((GEN)base1[i],(GEN)base1[j]),pol));
! 104: }
! 105: MD=cgetg(1,t_MAT); vecmat[5]=(long)MD; /* matrice de la differente */
! 106: TI=cgetg(1,t_MAT); vecmat[6]=(long)TI; /* matrice .... ? */
! 107: MDI=cgetg(1,t_MAT); vecmat[7]=(long)MDI; /* matrice .... ? */
! 108: return vecmat;
! 109: }
! 110:
! 111: GEN
! 112: rnfinitalg(GEN nf,GEN pol,long prec)
! 113: {
! 114: ulong av = avma;
! 115: long m,n,r1,r2,vnf,i,j,k,vpol,v1,r1j,r2j,lfac,degabs;
! 116: GEN RES,sig,rac,p1,p2,liftpol,delta,RAC,ro,p3,bas;
! 117: GEN f,f2,fac,fac1,fac2,id,p4,p5;
! 118:
! 119: if (typ(pol)!=t_POL) err(notpoler,"rnfinitalg");
! 120: nf=checknf(nf); n=degpol(pol); vpol=varn(pol);
! 121: vnf=0;
! 122: for (i=0; i<=n; i++)
! 123: {
! 124: long tp1;
! 125:
! 126: p1=(GEN)pol[i+2];
! 127: tp1=typ(p1);
! 128: if (! is_const_t(tp1))
! 129: {
! 130: if (tp1!=t_POLMOD) err(typeer,"rnfinitalg");
! 131: p1 = checknfelt_mod(nf, p1, "rnfinitalg");
! 132: if (! is_const_t(typ(p1)))
! 133: {
! 134: v1=varn(p1);
! 135: if (vnf && vnf!=v1) err(talker,"different variables in rnfinitalg");
! 136: if (!vnf) vnf=v1;
! 137: }
! 138: }
! 139: }
! 140: if (!vnf) vnf=varn(nf[1]);
! 141: if (vpol>=vnf)
! 142: err(talker,"main variable must be of higher priority in rnfinitalg");
! 143: RES=cgetg(12,t_VEC);
! 144: RES[1]=(long)pol;
! 145: m=degpol(nf[1]); degabs=n*m;
! 146: r1 = nf_get_r1(nf); r2 = (m-r1) >> 1;
! 147: sig=cgetg(r1+r2+1,t_VEC); RES[2]=(long)sig;
! 148: rac=(GEN)nf[6]; liftpol=lift(pol);
! 149: RAC=cgetg(r1+r2+1,t_VEC); RES[6]=(long)RAC;
! 150: for (j=1; j<=r1; j++)
! 151: {
! 152: p1=gsubst(liftpol,vnf,(GEN)rac[j]);
! 153: ro=roots(p1,prec);
! 154: r1j=0;
! 155: while (r1j<n && gcmp0(gimag((GEN)ro[r1j+1]))) r1j++;
! 156: p2=cgetg(3,t_VEC); p2[1]=lstoi(r1j); p2[2]=lstoi(r2j=((n-r1j)>>1));
! 157: sig[j]=(long)p2;
! 158: p3=cgetg(r1j+r2j+1,t_VEC);
! 159: for (i=1; i<=r1j; i++) p3[i]=lreal((GEN)ro[i]);
! 160: for (; i<=r1j+r2j; i++) p3[i]=(long)ro[(i<<1)-r1j];
! 161: RAC[j]=(long)p3;
! 162: }
! 163: for (; j<=r1+r2; j++)
! 164: {
! 165: p2=cgetg(3,t_VEC); p2[1]=zero; p2[2]=lstoi(n); sig[j]=(long)p2;
! 166: p1=gsubst(liftpol,vnf,(GEN)rac[j]);
! 167: RAC[j]=(long)roots(p1,prec);
! 168: }
! 169: p1 = rnfpseudobasis(nf,pol);
! 170:
! 171: delta = cgetg(3,t_VEC);
! 172: delta[1]=p1[3];
! 173: delta[2]=p1[4];
! 174: RES[3]=(long)delta;
! 175: p2 = matbasistoalg(nf,(GEN)p1[1]);
! 176: bas = cgetg(3,t_VEC);
! 177: bas[1]=(long)mat_to_vecpol(p2,vpol);
! 178: bas[2]=(long)p1[2];
! 179: RES[7]=(long)bas;
! 180: RES[8]=linvmat(p2);
! 181:
! 182: f2=idealdiv(nf,discsr(pol),(GEN)p1[3]);
! 183: fac=idealfactor(nf,f2);
! 184: fac1=(GEN)fac[1]; fac2=(GEN)fac[2]; lfac=lg(fac1)-1;
! 185: f=idmat(m);
! 186: for (i=1; i<=lfac; i++)
! 187: {
! 188: if (mpodd((GEN)fac2[i])) err(bugparier,"rnfinitalg (odd exponent)");
! 189: f=idealmul(nf,f,idealpow(nf,(GEN)fac1[i],gmul2n((GEN)fac2[i],-1)));
! 190: }
! 191: RES[4]=(long)f;
! 192: RES[10]=(long)nf;
! 193: RES[5]=(long)rnfmakematrices(RES);
! 194: if (DEBUGLEVEL>1) msgtimer("matrices");
! 195: RES[9]=lgetg(1,t_VEC); /* table de multiplication */
! 196: p2=cgetg(6,t_VEC); RES[11]=(long)p2;
! 197: p1=rnfequation2(nf,pol); for (i=1; i<=3; i++) p2[i]=p1[i];
! 198: p4=cgetg(degabs+1,t_MAT);
! 199: for (i=1; i<=n; i++)
! 200: { /* removing denominators speeds up multiplication */
! 201: GEN cop3,com, om = rnfelementreltoabs(RES,gmael(bas,1,i));
! 202:
! 203: if (DEBUGLEVEL>1) msgtimer("i = %ld",i);
! 204: com = content(om); om = gdiv(om,com);
! 205: id=gmael(bas,2,i);
! 206: for (j=1; j<=m; j++)
! 207: {
! 208: p5=cgetg(degabs+1,t_COL); p4[(i-1)*m+j]=(long)p5;
! 209: p1=gmul((GEN)nf[7],(GEN)id[j]);
! 210: p3 = gsubst(p1,varn(nf[1]), (GEN)p2[2]);
! 211: cop3 = content(p3); p3 = gdiv(p3,cop3);
! 212: p3 = gmul(gmul(com,cop3), lift_intern(gmul(om,p3)));
! 213:
! 214: for (k=1; k<lgef(p3)-1; k++) p5[k]=p3[k+1];
! 215: for ( ; k<=degabs; k++) p5[k]=zero;
! 216: }
! 217: }
! 218: if (DEBUGLEVEL>1) msgtimer("p4");
! 219: p3 = denom(p4);
! 220: p4 = hnfmodid(gmul(p3,p4), p3);
! 221: if (DEBUGLEVEL>1) msgtimer("hnfmod");
! 222: for (j=degabs-1; j>0; j--)
! 223: if (cmpis(gcoeff(p4,j,j),2) > 0)
! 224: {
! 225: p1=shifti(gcoeff(p4,j,j),-1);
! 226: for (k=j+1; k<=degabs; k++)
! 227: if (cmpii(gcoeff(p4,j,k),p1) > 0)
! 228: for (i=1; i<=j; i++)
! 229: coeff(p4,i,k)=lsubii(gcoeff(p4,i,k),gcoeff(p4,i,j));
! 230: }
! 231: p4 = gdiv(p4,p3);
! 232: p2[4]=(long)mat_to_vecpol(p4,vpol);
! 233: p2[5]=linvmat(p4);
! 234: return gerepilecopy(av,RES);
! 235: }
! 236:
! 237: GEN
! 238: rnfbasistoalg(GEN rnf,GEN x)
! 239: {
! 240: long tx=typ(x),lx=lg(x),av=avma,tetpil,i,n;
! 241: GEN p1,z,nf;
! 242:
! 243: checkrnf(rnf); nf=(GEN)rnf[10];
! 244: switch(tx)
! 245: {
! 246: case t_VEC:
! 247: x=gtrans(x); /* fall through */
! 248: case t_COL:
! 249: n=lg(x)-1; p1=cgetg(n+1,t_COL);
! 250: for (i=1; i<=n; i++)
! 251: {
! 252: if (typ(x[i])==t_COL) p1[i]=(long)basistoalg(nf,(GEN)x[i]);
! 253: else p1[i]=x[i];
! 254: }
! 255: p1=gmul(gmael(rnf,7,1),p1); tetpil=avma;
! 256: return gerepile(av,tetpil,gmodulcp(p1,(GEN)rnf[1]));
! 257:
! 258: case t_MAT:
! 259: z=cgetg(lx,tx);
! 260: for (i=1; i<lx; i++) z[i]=(long)rnfbasistoalg(rnf,(GEN)x[i]);
! 261: return z;
! 262:
! 263: case t_POLMOD:
! 264: return gcopy(x);
! 265:
! 266: default:
! 267: z=cgetg(3,t_POLMOD); z[1]=lcopy((GEN)rnf[1]);
! 268: z[2]=lmul(x,polun[varn(rnf[1])]); return z;
! 269: }
! 270: }
! 271:
! 272: extern long polegal_spec(GEN x, GEN y);
! 273:
! 274: /* assume x is a t_POLMOD */
! 275: GEN
! 276: lift_to_pol(GEN x)
! 277: {
! 278: GEN y = (GEN)x[2];
! 279: return (typ(y) != t_POL)? gtopoly(y,varn(x[1])): y;
! 280: }
! 281:
! 282: extern GEN mulmat_pol(GEN A, GEN x);
! 283:
! 284: GEN
! 285: rnfalgtobasis(GEN rnf,GEN x)
! 286: {
! 287: long av=avma,tx=typ(x), i,lx;
! 288: GEN z;
! 289:
! 290: checkrnf(rnf);
! 291: switch(tx)
! 292: {
! 293: case t_VEC: case t_COL: case t_MAT:
! 294: lx = lg(x); z = cgetg(lx,tx);
! 295: for (i=1; i<lx; i++) z[i]=(long)rnfalgtobasis(rnf,(GEN)x[i]);
! 296: return z;
! 297:
! 298: case t_POLMOD:
! 299: if (!polegal_spec((GEN)rnf[1],(GEN)x[1]))
! 300: err(talker,"not the same number field in rnfalgtobasis");
! 301: x = lift_to_pol(x); /* fall through */
! 302: case t_POL:
! 303: { /* cf algtobasis_intern */
! 304: GEN P = (GEN)rnf[1];
! 305: long N = degpol(P);
! 306: if (degpol(x) >= N) x = gres(x,P);
! 307: return gerepileupto(av, mulmat_pol((GEN)rnf[8], x));
! 308: }
! 309: }
! 310: return gscalcol(x, degpol(rnf[1]));
! 311: }
! 312:
! 313: /* x doit etre un polymod ou un polynome ou un vecteur de tels objets... */
! 314: GEN
! 315: rnfelementreltoabs(GEN rnf,GEN x)
! 316: {
! 317: long av=avma,tx,i,lx,va,tp3;
! 318: GEN z,p1,p2,p3,polabs,teta,alpha,s,k;
! 319:
! 320: checkrnf(rnf); tx=typ(x); lx=lg(x); va=varn((GEN)rnf[1]);
! 321: switch(tx)
! 322: {
! 323: case t_VEC: case t_COL: case t_MAT:
! 324: z=cgetg(lx,tx);
! 325: for (i=1; i<lx; i++) z[i]=(long)rnfelementreltoabs(rnf,(GEN)x[i]);
! 326: return z;
! 327:
! 328: case t_POLMOD:
! 329: x=lift_to_pol(x); /* fall through */
! 330: case t_POL:
! 331: if (gvar(x) > va) x = scalarpol(x,va);
! 332: p1=(GEN)rnf[11]; polabs=(GEN)p1[1]; alpha=(GEN)p1[2]; k=(GEN)p1[3];
! 333: if (typ(alpha) == t_INT)
! 334: teta=gmodulcp(gsub(polx[va],gmul(k,alpha)),polabs);
! 335: else
! 336: teta=gmodulcp(gsub(polx[va],gmul(k,(GEN)alpha[2])),polabs);
! 337: s=gzero;
! 338: for (i=lgef(x)-1; i>1; i--)
! 339: {
! 340: p3=(GEN)x[i]; tp3=typ(p3);
! 341: if (is_const_t(tp3)) p2 = p3;
! 342: else
! 343: switch(tp3)
! 344: {
! 345: case t_POLMOD:
! 346: p3 = (GEN)p3[2]; /* fall through */
! 347: case t_POL:
! 348: p2 = poleval(p3,alpha);
! 349: break;
! 350: default: err(talker, "incorrect data in rnfelementreltoabs");
! 351: return NULL; /* not reached */
! 352: }
! 353: s=gadd(p2,gmul(teta,s));
! 354: }
! 355: return gerepileupto(av,s);
! 356:
! 357: default: return gcopy(x);
! 358: }
! 359: }
! 360:
! 361: GEN
! 362: rnfelementabstorel(GEN rnf,GEN x)
! 363: {
! 364: long av=avma,tx,i,lx;
! 365: GEN z,p1,s,tetap,k,nf;
! 366:
! 367: checkrnf(rnf); tx=typ(x); lx=lg(x);
! 368: switch(tx)
! 369: {
! 370: case t_VEC: case t_COL: case t_MAT:
! 371: z=cgetg(lx,tx);
! 372: for (i=1; i<lx; i++) z[i]=(long)rnfelementabstorel(rnf,(GEN)x[i]);
! 373: return z;
! 374:
! 375: case t_POLMOD:
! 376: x=lift_to_pol(x); /* fall through */
! 377: case t_POL:
! 378: p1=(GEN)rnf[11]; k=(GEN)p1[3]; nf=(GEN)rnf[10];
! 379: tetap=gmodulcp(gadd(polx[varn(rnf[1])],
! 380: gmul(k,gmodulcp(polx[varn(nf[1])],(GEN)nf[1]))),(GEN)rnf[1]);
! 381: s=gzero;
! 382: for (i=lgef(x)-1; i>1; i--) s=gadd((GEN)x[i],gmul(tetap,s));
! 383: return gerepileupto(av,s);
! 384:
! 385: default: return gcopy(x);
! 386: }
! 387: }
! 388:
! 389: /* x doit etre un polymod ou un polynome ou un vecteur de tels objets... */
! 390: GEN
! 391: rnfelementup(GEN rnf,GEN x)
! 392: {
! 393: long i,lx,tx;
! 394: GEN z;
! 395:
! 396: checkrnf(rnf); tx=typ(x); lx=lg(x);
! 397: switch(tx)
! 398: {
! 399: case t_VEC: case t_COL: case t_MAT:
! 400: z=cgetg(lx,tx);
! 401: for (i=1; i<lx; i++) z[i]=(long)rnfelementup(rnf,(GEN)x[i]);
! 402: return z;
! 403:
! 404: case t_POLMOD:
! 405: x=(GEN)x[2]; /* fall through */
! 406: case t_POL:
! 407: return poleval(x,gmael(rnf,11,2));
! 408:
! 409: default: return gcopy(x);
! 410: }
! 411: }
! 412:
! 413: /* x doit etre un polymod ou un polynome ou un vecteur de tels objets..*/
! 414: GEN
! 415: rnfelementdown(GEN rnf,GEN x)
! 416: {
! 417: ulong av = avma;
! 418: long i,lx,tx;
! 419: GEN p1,z;
! 420:
! 421: checkrnf(rnf); tx=typ(x); lx=lg(x);
! 422: switch(tx)
! 423: {
! 424: case t_VEC: case t_COL: case t_MAT:
! 425: z=cgetg(lx,tx);
! 426: for (i=1; i<lx; i++) z[i]=(long)rnfelementdown(rnf,(GEN)x[i]);
! 427: return z;
! 428:
! 429: case t_POLMOD:
! 430: x=(GEN)x[2]; /* fall through */
! 431: case t_POL:
! 432: if (gcmp0(x)) return gzero;
! 433:
! 434: p1=rnfelementabstorel(rnf,x);
! 435: if (typ(p1)==t_POLMOD && varn(p1[1])==varn(rnf[1])) p1=(GEN)p1[2];
! 436: if (gvar(p1)>varn(rnf[1])) return gerepilecopy(av,p1);
! 437: if (lgef(p1)==3) return gerepilecopy(av,(GEN)p1[2]);
! 438: err(talker,"element is not in the base field in rnfelementdown");
! 439:
! 440: default: return gcopy(x);
! 441: }
! 442: }
! 443:
! 444: /* x est exprime sur la base relative */
! 445: static GEN
! 446: rnfprincipaltohermite(GEN rnf,GEN x)
! 447: {
! 448: long av=avma,tetpil;
! 449: GEN nf,bas,bas1,p1,z;
! 450:
! 451: x=rnfbasistoalg(rnf,x); nf=(GEN)rnf[10];
! 452: bas=(GEN)rnf[7]; bas1=(GEN)bas[1];
! 453: p1=rnfalgtobasis(rnf,gmul(x,gmodulcp(bas1,(GEN)rnf[1])));
! 454: z=cgetg(3,t_VEC); z[2]=bas[2];
! 455: settyp(p1,t_MAT); z[1]=(long)matalgtobasis(nf,p1);
! 456:
! 457: tetpil=avma;
! 458: return gerepile(av,tetpil,nfhermite(nf,z));
! 459: }
! 460:
! 461: GEN
! 462: rnfidealhermite(GEN rnf,GEN x)
! 463: {
! 464: long tx=typ(x),lx=lg(x),av=avma,tetpil,i,j,n,m;
! 465: GEN z,p1,p2,x1,x2,x1j,nf,bas,unnf,zeronf;
! 466:
! 467: checkrnf(rnf);
! 468: n=degpol(rnf[1]); nf=(GEN)rnf[10]; bas=(GEN)rnf[7];
! 469:
! 470: switch(tx)
! 471: {
! 472: case t_INT: case t_FRAC: case t_FRACN: z=cgetg(3,t_VEC);
! 473: m=degpol(nf[1]); zeronf=gscalcol_i(gzero,m); unnf=gscalcol_i(gun,m);
! 474: p1=cgetg(n+1,t_MAT); z[1]=(long)p1;
! 475: for (j=1; j<=n; j++)
! 476: {
! 477: p2=cgetg(n+1,t_COL); p1[j]=(long)p2;
! 478: for (i=1; i<=n; i++) p2[i]=(i==j)?(long)unnf:(long)zeronf;
! 479: }
! 480: z[2]=lmul(x,(GEN)bas[2]); return z;
! 481:
! 482: case t_POLMOD: case t_POL:
! 483: p1=rnfalgtobasis(rnf,x); tetpil=avma;
! 484: return gerepile(av,tetpil,rnfprincipaltohermite(rnf,p1));
! 485:
! 486: case t_VEC:
! 487: switch(lx)
! 488: {
! 489: case 3:
! 490: x1=(GEN)x[1];
! 491: if (typ(x1)!=t_MAT || lg(x1) < n+1 || lg(x1[1]) != n+1)
! 492: err(talker,"incorrect type in rnfidealhermite");
! 493: p1=cgetg(n+1,t_MAT);
! 494: for (j=1; j<=n; j++)
! 495: {
! 496: p2=cgetg(n+1,t_COL); p1[j]=(long)p2; x1j=(GEN)x1[j];
! 497: for (i=1; i<=n; i++)
! 498: {
! 499: tx = typ(x1j[i]);
! 500: if (is_const_t(tx)) p2[i] = x1j[i];
! 501: else
! 502: switch(tx)
! 503: {
! 504: case t_POLMOD: case t_POL:
! 505: p2[i]=(long)algtobasis(nf,(GEN)x1j[i]); break;
! 506: case t_COL:
! 507: p2[i]=x1j[i]; break;
! 508: default: err(talker,"incorrect type in rnfidealhermite");
! 509: }
! 510: }
! 511: }
! 512: x2=(GEN)x[2];
! 513: if (typ(x2)!=t_VEC || lg(x2)!=lg(x1))
! 514: err(talker,"incorrect type in rnfidealhermite");
! 515: tetpil=avma; z=cgetg(3,t_VEC); z[1]=lcopy(p1); z[2]=lcopy(x2);
! 516: z=gerepile(av,tetpil,nfhermite(nf,z));
! 517: if (lg(z[1]) != n+1)
! 518: err(talker,"not an ideal in rnfidealhermite");
! 519: return z;
! 520:
! 521: case 6:
! 522: err(impl,"rnfidealhermite for prime ideals");
! 523: default:
! 524: err(typeer,"rnfidealhermite");
! 525: }
! 526:
! 527: case t_COL:
! 528: if (lx!=(n+1)) err(typeer,"rnfidealhermite");
! 529: return rnfprincipaltohermite(rnf,x);
! 530:
! 531: case t_MAT:
! 532: return rnfidealabstorel(rnf,x);
! 533: }
! 534: err(typeer,"rnfidealhermite");
! 535: return NULL; /* not reached */
! 536: }
! 537:
! 538: GEN
! 539: rnfidealnormrel(GEN rnf,GEN id)
! 540: {
! 541: long av=avma,i,n;
! 542: GEN z,id2,nf;
! 543:
! 544: checkrnf(rnf);
! 545: id=rnfidealhermite(rnf,id); id2=(GEN)id[2];
! 546: n=degpol(rnf[1]); nf=(GEN)rnf[10];
! 547: if (n==1) { avma=av; return idmat(degpol(nf[1])); }
! 548: z=(GEN)id2[1]; for (i=2; i<=n; i++) z=idealmul(nf,z,(GEN)id2[i]);
! 549: return gerepileupto(av,z);
! 550: }
! 551:
! 552: GEN
! 553: rnfidealnormabs(GEN rnf,GEN id)
! 554: {
! 555: long av=avma,i,n;
! 556: GEN z,id2;
! 557:
! 558: checkrnf(rnf);
! 559: id=rnfidealhermite(rnf,id); id2=(GEN)id[2];
! 560: n=degpol(rnf[1]);
! 561: z=gun; for (i=1; i<=n; i++) z=gmul(z,dethnf((GEN)id2[i]));
! 562: return gerepileupto(av,z);
! 563: }
! 564:
! 565: GEN
! 566: rnfidealreltoabs(GEN rnf,GEN x)
! 567: {
! 568: long av=avma,i,j,k,n,m;
! 569: GEN nf,basinv,om,id,p1,p2,p3,p4,p5,c;
! 570:
! 571: checkrnf(rnf);
! 572: x = rnfidealhermite(rnf,x);
! 573: n=degpol(rnf[1]); nf=(GEN)rnf[10]; m=degpol(nf[1]);
! 574: basinv = gmael(rnf,11,5);
! 575: p3=cgetg(n*m+1,t_MAT); p2=gmael(rnf,11,2);
! 576: for (i=1; i<=n; i++)
! 577: {
! 578: om=rnfbasistoalg(rnf,gmael(x,1,i)); id=gmael(x,2,i);
! 579: om=rnfelementreltoabs(rnf,om);
! 580: for (j=1; j<=m; j++)
! 581: {
! 582: p1=gmul((GEN)nf[7],(GEN)id[j]);
! 583: p4=lift_intern(gmul(om,gsubst(p1,varn(nf[1]),p2)));
! 584: p5=cgetg(n*m+1,t_COL);
! 585: for (k=0; k<n*m; k++) p5[k+1]=(long)truecoeff(p4,k);
! 586: p3[(i-1)*m+j]=(long)p5;
! 587: }
! 588: }
! 589: p1 = gmul(basinv,p3); c = content(p1);
! 590: p2 = gmael(p1,1,1); /* x \cap Z */
! 591: if (is_pm1(c)) c = NULL; else { p1 = gdiv(p1, c); p2 = gdiv(p2, c); }
! 592: p1 = hnfmodid(p1, p2);
! 593: if (c) p1 = gmul(p1, c);
! 594: return gerepileupto(av, p1);
! 595: }
! 596:
! 597: GEN
! 598: rnfidealabstorel(GEN rnf,GEN x)
! 599: {
! 600: long av=avma,tetpil,n,m,j,k;
! 601: GEN nf,basabs,ma,xj,p1,p2,id;
! 602:
! 603: checkrnf(rnf); n=degpol(rnf[1]); nf=(GEN)rnf[10]; m=degpol(nf[1]);
! 604: if (typ(x)!=t_MAT || lg(x)!=(n*m+1) || lg(x[1])!=(n*m+1))
! 605: err(impl,"rnfidealabstorel for an ideal not in HNF");
! 606: basabs=gmael(rnf,11,4); ma=cgetg(n*m+1,t_MAT);
! 607: for (j=1; j<=n*m; j++)
! 608: {
! 609: p2=cgetg(n+1,t_COL); ma[j]=(long)p2;
! 610: xj=gmul(basabs,(GEN)x[j]);
! 611: xj=lift_intern(rnfelementabstorel(rnf,xj));
! 612: for (k=0; k<n; k++)
! 613: p2[k+1]=(long)truecoeff(xj,k);
! 614: }
! 615: ma=gmul((GEN)rnf[8],ma);
! 616: ma=matalgtobasis(nf,ma);
! 617: p1=cgetg(n*m+1,t_VEC); id=idmat(m);
! 618: for (j=1; j<=n*m; j++) p1[j]=(long)id;
! 619: p2=cgetg(3,t_VEC); p2[1]=(long)ma; p2[2]=(long)p1;
! 620: tetpil=avma; return gerepile(av,tetpil,nfhermite(nf,p2));
! 621: }
! 622:
! 623: GEN
! 624: rnfidealdown(GEN rnf,GEN x)
! 625: {
! 626: long av=avma;
! 627:
! 628: checkrnf(rnf); x=rnfidealhermite(rnf,x);
! 629: return gerepilecopy(av,gmael(x,2,1));
! 630: }
! 631:
! 632: /* lift ideal x to the relative extension, returns a Z-basis */
! 633: GEN
! 634: rnfidealup(GEN rnf,GEN x)
! 635: {
! 636: long av=avma,tetpil,i,n,m;
! 637: GEN nf,bas,bas2,p1,p2,zeronf,unnf;
! 638:
! 639: checkrnf(rnf);
! 640: bas=(GEN)rnf[7]; bas2=(GEN)bas[2];
! 641: n=lg(bas2)-1; nf=(GEN)rnf[10]; m=degpol((GEN)nf[1]);
! 642: zeronf=zerocol(m); unnf=gscalcol_i(gun,m);
! 643: p2=cgetg(3,t_VEC); p1=cgetg(n+1,t_VEC);
! 644: p2[1]=(long)idmat_intern(n,unnf,zeronf);
! 645: p2[2]=(long)p1;
! 646: for (i=1; i<=n; i++) p1[i]=(long)idealmul(nf,x,(GEN)bas2[i]);
! 647: tetpil=avma; return gerepile(av,tetpil,rnfidealreltoabs(rnf,p2));
! 648: }
! 649:
! 650: /* x a relative HNF ---> vector of 2 generators (relative polymods) */
! 651: GEN
! 652: rnfidealtwoelement(GEN rnf,GEN x)
! 653: {
! 654: long av=avma,tetpil,j;
! 655: GEN p1,p2,p3,res,polabs,nfabs,z;
! 656:
! 657: checkrnf(rnf);
! 658: res=(GEN)rnf[11]; polabs=(GEN)res[1];
! 659: nfabs=cgetg(10,t_VEC); nfabs[1]=(long)polabs;
! 660: for (j=2; j<=9; j++) nfabs[j]=zero;
! 661: nfabs[7]=(long)lift((GEN)res[4]); nfabs[8]=res[5];
! 662: p1=rnfidealreltoabs(rnf,x);
! 663: p2=ideal_two_elt(nfabs,p1);
! 664: p3=rnfelementabstorel(rnf,gmul((GEN)res[4],(GEN)p2[2]));
! 665: tetpil=avma; z=cgetg(3,t_VEC); z[1]=lcopy((GEN)p2[1]);
! 666: z[2]=(long)rnfalgtobasis(rnf,p3);
! 667: return gerepile(av,tetpil,z);
! 668: }
! 669:
! 670: GEN
! 671: rnfidealmul(GEN rnf,GEN x,GEN y) /* x et y sous HNF relative uniquement */
! 672: {
! 673: long av=avma,tetpil,i,j,n;
! 674: GEN z,nf,x1,x2,p1,p2,p3,p4,p5,res;
! 675:
! 676: z=rnfidealtwoelement(rnf,y);
! 677: nf=(GEN)rnf[10]; n=degpol(rnf[1]);
! 678: x=rnfidealhermite(rnf,x);
! 679: x1=gmodulcp(gmul(gmael(rnf,7,1),matbasistoalg(nf,(GEN)x[1])),(GEN) rnf[1]);
! 680: x2=(GEN)x[2]; p1=gmul((GEN)z[1],(GEN)x[1]);
! 681: p2=lift_intern(gmul(rnfbasistoalg(rnf,(GEN)z[2]),x1));
! 682: p3=cgetg(n+1,t_MAT);
! 683: for (j=1; j<=n; j++)
! 684: {
! 685: p4=cgetg(n+1,t_COL); p3[j]=(long)p4; p5=(GEN)p2[j];
! 686: for (i=1; i<=n; i++)
! 687: p4[i]=(long)algtobasis(nf,truecoeff((GEN)p5,i-1));
! 688: }
! 689: res=cgetg(3,t_VEC);
! 690: res[1]=(long)concatsp(p1,p3);
! 691: res[2]=(long)concatsp(x2,x2);
! 692: tetpil=avma; return gerepile(av,tetpil,nfhermite(nf,res));
! 693: }
! 694:
! 695: /*********************************************************************/
! 696: /** **/
! 697: /** LIBRARY FOR POLYNOMIALS WITH COEFFS. IN Z_K/P **/
! 698: /** An element in Z_K/P is a t_COL with degree(nf[1]) components. **/
! 699: /** These are integers modulo the prime p under prime ideal P **/
! 700: /** (only f(P/p) elements are non zero). These components are **/
! 701: /** given on the integer basis of K. **/
! 702: /** **/
! 703: /*********************************************************************/
! 704:
! 705: /* K.B: What follows is not meant to work (yet?) */
! 706:
! 707: GEN
! 708: polnfmulscal(GEN nf,GEN s,GEN x)
! 709: {
! 710: long i,lx=lgef(x);
! 711: GEN z;
! 712:
! 713: if (lx<3) return gcopy(x);
! 714: if (gcmp0(s))
! 715: {
! 716: z=cgetg(2,t_POL); z[1]=evallgef(2) | evalvarn(varn(x));
! 717: return z;
! 718: }
! 719: z=cgetg(lx,t_POL); z[1]=x[1];
! 720: for (i=2; i<lx; i++) z[i]=(long)element_mul(nf,s,(GEN)x[i]);
! 721: return z;
! 722: }
! 723:
! 724: GEN
! 725: polnfmul(GEN nf, GEN x, GEN y)
! 726: {
! 727: ulong av;
! 728: long m,i,d,imin,imax,lx,ly,lz;
! 729: GEN p1,z,zeronf;
! 730:
! 731: if (gcmp0(x) || gcmp0(y)) return zeropol(varn(x));
! 732: m=degpol(nf[1]); av=avma;
! 733: lx=degpol(x); ly=degpol(y); lz=lx+ly;
! 734: zeronf=gscalcol_i(gzero,m);
! 735: z=cgetg(lz+3,t_POL);
! 736: z[1] = evallgef(lz+3) | evalvarn(x) | evalsigne(1);
! 737: for (d=0; d<=lz; d++)
! 738: {
! 739: p1=zeronf; imin=max(0,d-ly); imax=min(d,lx);
! 740: for (i=imin; i<=imax; i++)
! 741: p1=gadd(p1,element_mul(nf,(GEN)x[i+2],(GEN)y[d-i+2]));
! 742: z[d+2]=(long)p1;
! 743: }
! 744: return gerepilecopy(av,z);
! 745: }
! 746:
! 747: /* division euclidienne */
! 748: GEN
! 749: polnfdeuc(GEN nf, GEN x, GEN y, GEN *ptr)
! 750: {
! 751: long av=avma,m,i,d,tx,lx,ly,lz,fl;
! 752: GEN z,unnf,lcy,r;
! 753: GEN *gptr[2];
! 754:
! 755: if (gcmp0(y)) err(talker,"division by zero in polnfdiv");
! 756: lx=lgef(x); ly=lgef(y); lz=lx-ly;
! 757: if (gcmp0(x) || lz<0) { *ptr=gcopy(x); return zeropol(varn(x)); }
! 758:
! 759: m=degpol(nf[1]); unnf=gscalcol_i(gun,m);
! 760: x=dummycopy(x); y=dummycopy(y);
! 761: for (i=2; i<lx; i++)
! 762: {
! 763: tx=typ(x[i]);
! 764: if (is_intreal_t(tx) || tx == t_INTMOD || is_frac_t(tx))
! 765: x[i]=lmul((GEN)x[i],unnf);
! 766: }
! 767: for (i=2; i<ly; i++)
! 768: {
! 769: tx=typ(y[i]);
! 770: if (is_intreal_t(tx) || tx == t_INTMOD || is_frac_t(tx))
! 771: y[i]=lmul((GEN)y[i],unnf);
! 772: }
! 773:
! 774: lz += 3;
! 775: z=cgetg(lz,t_POL); z[1]=evallgef(lz) | evalvarn(x) | evalsigne(1);
! 776: lcy=(GEN)y[ly-1];
! 777: if (gegal(lift(lcy),unnf)) fl=0;
! 778: else
! 779: {
! 780: fl=1; y=polnfmulscal(nf,element_inv(nf,lcy),y);
! 781: }
! 782: for (d=lz-1; d>=2; d--)
! 783: {
! 784: z[d]=x[d+ly-3];
! 785: for (i=d; i<d+ly-3; i++)
! 786: x[i]=lsub((GEN)x[i],element_mul(nf,(GEN)z[d],(GEN)y[i-d-2]));
! 787: }
! 788: if (fl) z=polnfmulscal(nf,lcy,z);
! 789:
! 790: for(;;)
! 791: {
! 792: if (!gcmp0((GEN)x[d]))
! 793: {
! 794: r=cgetg(d,t_POL);
! 795: r[1] = evallgef(d) | evalvarn(varn(x)) | evalsigne(1);
! 796: for (i=2; i<d; i++) r[i]=x[i];
! 797: break;
! 798: }
! 799: if (d==2) { r = zeropol(varn(x)); break; }
! 800: d--;
! 801: }
! 802: *ptr=r; gptr[0]=ptr; gptr[1]=&z;
! 803: gerepilemany(av,gptr,2); return z;
! 804: }
! 805:
! 806: GEN
! 807: polnfpow(GEN nf,GEN x,GEN k)
! 808: {
! 809: long s,av=avma,m;
! 810: GEN y,z;
! 811:
! 812: m=degpol(nf[1]);
! 813: if (typ(k)!=t_INT) err(talker,"not an integer exponent in nfpow");
! 814: s=signe(k); if (s<0) err(impl,"polnfpow for negative exponents");
! 815:
! 816: z=x; y=cgetg(3,t_POL);
! 817: y[1] = evallgef(3) | evalvarn(varn(x)) | evalsigne(1);
! 818: y[2] = (long)gscalcol_i(gun,m);
! 819: for(;;)
! 820: {
! 821: if (mpodd(k)) y=polnfmul(nf,z,y);
! 822: k=shifti(k,-1);
! 823: if (!signe(k)) { cgiv(k); return gerepileupto(av,y); }
! 824: z=polnfmul(nf,z,z);
! 825: }
! 826: }
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