Datasets:

h4iku
/

coconut_c2005_preprocessed

Dataset card Viewer Files Files and versions Community

Split (1)

train · 671k rows

rem stringlengths 0 274k	add stringlengths 0 169k	context stringlengths 9 471k
av=avma; uftot=0;	uftot = NULL;	thueinit(GEN poly, long flag, long prec){ GEN thueres,ALH,csts,c0; long av,tetpil,k,st; double d,dr; av=avma; uftot=0; if (checktnf(poly)) { uftot=(GEN)poly[2]; poly=(GEN)poly[1]; } else if (typ(poly)!=t_POL) err(notpoler,"thueinit"); if (degpol(poly)<=2) err(talker,"invalid polynomial in thue (need deg>2)"); if (!gisirreducible(poly)) err(redpoler,"thueinit"); st=sturm(poly); if (st) { dr=(double)((st+lgef(poly)-5)>>1); d=(double)degpol(poly); d=d(d-1)(d-2); /* Try to guess the precision by approximating Baker's bound. * Note that the guess is most of the time pretty generous, * ie 10 to 30 decimal digits above what is really necessary. * Note that the limiting step is the reduction. See paper. / Prec=3 + (long)((5.83 + (dr+4)5 + log(fact(dr+3)) + (dr+3)log(dr+2) + (dr+3)log(d) + log(log(2d(dr+2))) + (dr+1)) / 10.); ConstPrec=4; if (Prec<prec) Prec = prec; if (!checktnf(poly)) inithue(poly,flag); thueres=cgetg(8,t_VEC); thueres[1]=(long)poly; thueres[2]=(long)uftot; thueres[3]=(long)roo; Compute_Fund_Units(gmael(uftot,8,5)); ALH=cgetg(r+1,t_COL); for (k=1; k<=r; k++) ALH[k]=(long)Logarithmic_Height(k); thueres[4]=(long)ALH; thueres[5]=(long)MatFU; T_A_Matrices(); thueres[6]=(long)A; csts=cgetg(7,t_VEC); csts[1]=(long)c1; csts[2]=(long)c2; csts[3]=(long)halpha; csts[4]=(long)x0; csts[5]=(long)eps3; csts[6]=(long)stoi(Prec); thueres[7]=(long)csts; tetpil=avma; return gerepile(av,tetpil,gcopy(thueres)); } thueres=cgetg(3,t_VEC); c0=gun; Prec=4; roo=roots(poly,Prec); for (k=1; k<lg(roo); k++) c0=gmul(c0, gimag((GEN)roo[k])); c0=ginv(gabs(c0,Prec)); thueres[1]=(long)poly; thueres[2]=(long)c0; tetpil=avma; return gerepile(av,tetpil,gcopy(thueres));}
thueres[7]=(long)csts; tetpil=avma; return gerepile(av,tetpil,gcopy(thueres));	thueres[7]=(long)csts; return gerepilecopy(av,thueres);	thueinit(GEN poly, long flag, long prec){ GEN thueres,ALH,csts,c0; long av,tetpil,k,st; double d,dr; av=avma; uftot=0; if (checktnf(poly)) { uftot=(GEN)poly[2]; poly=(GEN)poly[1]; } else if (typ(poly)!=t_POL) err(notpoler,"thueinit"); if (degpol(poly)<=2) err(talker,"invalid polynomial in thue (need deg>2)"); if (!gisirreducible(poly)) err(redpoler,"thueinit"); st=sturm(poly); if (st) { dr=(double)((st+lgef(poly)-5)>>1); d=(double)degpol(poly); d=d(d-1)(d-2); /* Try to guess the precision by approximating Baker's bound. * Note that the guess is most of the time pretty generous, * ie 10 to 30 decimal digits above what is really necessary. * Note that the limiting step is the reduction. See paper. / Prec=3 + (long)((5.83 + (dr+4)5 + log(fact(dr+3)) + (dr+3)log(dr+2) + (dr+3)log(d) + log(log(2d(dr+2))) + (dr+1)) / 10.); ConstPrec=4; if (Prec<prec) Prec = prec; if (!checktnf(poly)) inithue(poly,flag); thueres=cgetg(8,t_VEC); thueres[1]=(long)poly; thueres[2]=(long)uftot; thueres[3]=(long)roo; Compute_Fund_Units(gmael(uftot,8,5)); ALH=cgetg(r+1,t_COL); for (k=1; k<=r; k++) ALH[k]=(long)Logarithmic_Height(k); thueres[4]=(long)ALH; thueres[5]=(long)MatFU; T_A_Matrices(); thueres[6]=(long)A; csts=cgetg(7,t_VEC); csts[1]=(long)c1; csts[2]=(long)c2; csts[3]=(long)halpha; csts[4]=(long)x0; csts[5]=(long)eps3; csts[6]=(long)stoi(Prec); thueres[7]=(long)csts; tetpil=avma; return gerepile(av,tetpil,gcopy(thueres)); } thueres=cgetg(3,t_VEC); c0=gun; Prec=4; roo=roots(poly,Prec); for (k=1; k<lg(roo); k++) c0=gmul(c0, gimag((GEN)roo[k])); c0=ginv(gabs(c0,Prec)); thueres[1]=(long)poly; thueres[2]=(long)c0; tetpil=avma; return gerepile(av,tetpil,gcopy(thueres));}
tetpil=avma; return gerepile(av,tetpil,gcopy(thueres));	return gerepilecopy(av,thueres);	thueinit(GEN poly, long flag, long prec){ GEN thueres,ALH,csts,c0; long av,tetpil,k,st; double d,dr; av=avma; uftot=0; if (checktnf(poly)) { uftot=(GEN)poly[2]; poly=(GEN)poly[1]; } else if (typ(poly)!=t_POL) err(notpoler,"thueinit"); if (degpol(poly)<=2) err(talker,"invalid polynomial in thue (need deg>2)"); if (!gisirreducible(poly)) err(redpoler,"thueinit"); st=sturm(poly); if (st) { dr=(double)((st+lgef(poly)-5)>>1); d=(double)degpol(poly); d=d(d-1)(d-2); /* Try to guess the precision by approximating Baker's bound. * Note that the guess is most of the time pretty generous, * ie 10 to 30 decimal digits above what is really necessary. * Note that the limiting step is the reduction. See paper. / Prec=3 + (long)((5.83 + (dr+4)5 + log(fact(dr+3)) + (dr+3)log(dr+2) + (dr+3)log(d) + log(log(2d(dr+2))) + (dr+1)) / 10.); ConstPrec=4; if (Prec<prec) Prec = prec; if (!checktnf(poly)) inithue(poly,flag); thueres=cgetg(8,t_VEC); thueres[1]=(long)poly; thueres[2]=(long)uftot; thueres[3]=(long)roo; Compute_Fund_Units(gmael(uftot,8,5)); ALH=cgetg(r+1,t_COL); for (k=1; k<=r; k++) ALH[k]=(long)Logarithmic_Height(k); thueres[4]=(long)ALH; thueres[5]=(long)MatFU; T_A_Matrices(); thueres[6]=(long)A; csts=cgetg(7,t_VEC); csts[1]=(long)c1; csts[2]=(long)c2; csts[3]=(long)halpha; csts[4]=(long)x0; csts[5]=(long)eps3; csts[6]=(long)stoi(Prec); thueres[7]=(long)csts; tetpil=avma; return gerepile(av,tetpil,gcopy(thueres)); } thueres=cgetg(3,t_VEC); c0=gun; Prec=4; roo=roots(poly,Prec); for (k=1; k<lg(roo); k++) c0=gmul(c0, gimag((GEN)roo[k])); c0=ginv(gabs(c0,Prec)); thueres[1]=(long)poly; thueres[2]=(long)c0; tetpil=avma; return gerepile(av,tetpil,gcopy(thueres));}
unsigned8 b[NUM_FIELDS];	uint8_t b[NUM_FIELDS];	command_port(FTPD_SessionInfo_t info, char const args){ enum { NUM_FIELDS = 6 }; unsigned int a[NUM_FIELDS]; int n; close_data_socket(info); n = sscanf(args, "%u,%u,%u,%u,%u,%u", a+0, a+1, a+2, a+3, a+4, a+5); if(NUM_FIELDS == n) { int i; unsigned8 b[NUM_FIELDS]; for(i = 0; i < NUM_FIELDS; ++i) { if(a[i] > 255) break; b[i] = (unsigned8)a[i]; } if(i == NUM_FIELDS) { /* Note: while it contradicts with RFC959, we don't allow PORT command * to specify IP address different than those of the originating client * for the sake of safety. / unsigned32 const ip = (unsigned32 )b; if(ip == info->def_addr.sin_addr.s_addr) { info->data_addr.sin_addr.s_addr = ip; info->data_addr.sin_port = (unsigned16 )(b + 4); info->data_addr.sin_family = AF_INET; memset(info->data_addr.sin_zero, 0, sizeof(info->data_addr.sin_zero)); info->use_default = 0; send_reply(info, 200, "PORT command successful."); return; / success */ } else { send_reply(info, 425, "Address doesn't match peer's IP."); return; } } } send_reply(info, 501, "Syntax error.");}
b[i] = (unsigned8)a[i];	b[i] = (uint8_t)a[i];	command_port(FTPD_SessionInfo_t info, char const args){ enum { NUM_FIELDS = 6 }; unsigned int a[NUM_FIELDS]; int n; close_data_socket(info); n = sscanf(args, "%u,%u,%u,%u,%u,%u", a+0, a+1, a+2, a+3, a+4, a+5); if(NUM_FIELDS == n) { int i; unsigned8 b[NUM_FIELDS]; for(i = 0; i < NUM_FIELDS; ++i) { if(a[i] > 255) break; b[i] = (unsigned8)a[i]; } if(i == NUM_FIELDS) { /* Note: while it contradicts with RFC959, we don't allow PORT command * to specify IP address different than those of the originating client * for the sake of safety. / unsigned32 const ip = (unsigned32 )b; if(ip == info->def_addr.sin_addr.s_addr) { info->data_addr.sin_addr.s_addr = ip; info->data_addr.sin_port = (unsigned16 )(b + 4); info->data_addr.sin_family = AF_INET; memset(info->data_addr.sin_zero, 0, sizeof(info->data_addr.sin_zero)); info->use_default = 0; send_reply(info, 200, "PORT command successful."); return; / success */ } else { send_reply(info, 425, "Address doesn't match peer's IP."); return; } } } send_reply(info, 501, "Syntax error.");}
unsigned32 const ip = (unsigned32 )b;	uint32_t const ip = (uint32_t )b;	command_port(FTPD_SessionInfo_t info, char const args){ enum { NUM_FIELDS = 6 }; unsigned int a[NUM_FIELDS]; int n; close_data_socket(info); n = sscanf(args, "%u,%u,%u,%u,%u,%u", a+0, a+1, a+2, a+3, a+4, a+5); if(NUM_FIELDS == n) { int i; unsigned8 b[NUM_FIELDS]; for(i = 0; i < NUM_FIELDS; ++i) { if(a[i] > 255) break; b[i] = (unsigned8)a[i]; } if(i == NUM_FIELDS) { /* Note: while it contradicts with RFC959, we don't allow PORT command * to specify IP address different than those of the originating client * for the sake of safety. / unsigned32 const ip = (unsigned32 )b; if(ip == info->def_addr.sin_addr.s_addr) { info->data_addr.sin_addr.s_addr = ip; info->data_addr.sin_port = (unsigned16 )(b + 4); info->data_addr.sin_family = AF_INET; memset(info->data_addr.sin_zero, 0, sizeof(info->data_addr.sin_zero)); info->use_default = 0; send_reply(info, 200, "PORT command successful."); return; / success */ } else { send_reply(info, 425, "Address doesn't match peer's IP."); return; } } } send_reply(info, 501, "Syntax error.");}
info->data_addr.sin_port = (unsigned16 )(b + 4);	info->data_addr.sin_port = (uint16_t )(b + 4);	command_port(FTPD_SessionInfo_t info, char const args){ enum { NUM_FIELDS = 6 }; unsigned int a[NUM_FIELDS]; int n; close_data_socket(info); n = sscanf(args, "%u,%u,%u,%u,%u,%u", a+0, a+1, a+2, a+3, a+4, a+5); if(NUM_FIELDS == n) { int i; unsigned8 b[NUM_FIELDS]; for(i = 0; i < NUM_FIELDS; ++i) { if(a[i] > 255) break; b[i] = (unsigned8)a[i]; } if(i == NUM_FIELDS) { /* Note: while it contradicts with RFC959, we don't allow PORT command * to specify IP address different than those of the originating client * for the sake of safety. / unsigned32 const ip = (unsigned32 )b; if(ip == info->def_addr.sin_addr.s_addr) { info->data_addr.sin_addr.s_addr = ip; info->data_addr.sin_port = (unsigned16 )(b + 4); info->data_addr.sin_family = AF_INET; memset(info->data_addr.sin_zero, 0, sizeof(info->data_addr.sin_zero)); info->use_default = 0; send_reply(info, 200, "PORT command successful."); return; / success */ } else { send_reply(info, 425, "Address doesn't match peer's IP."); return; } } } send_reply(info, 501, "Syntax error.");}
if (!signe(x)) { y=cgetr(3); y[1]=x[1]; y[2]=0; return y; }	if (!signe(x)) return realzero_bit(expo(x));	mpsin(GEN x){ long mod8,av,tetpil; GEN y,p1; if (typ(x)!=t_REAL) err(typeer,"mpsin"); if (!signe(x)) { y=cgetr(3); y[1]=x[1]; y[2]=0; return y; } av=avma; p1=mpsc1(x,&mod8); tetpil=avma; switch(mod8) { case 0: case 6: y=mpaut(p1); break; case 1: case 5: y=addsr(1,p1); break; case 2: case 4: y=mpaut(p1); setsigne(y,-signe(y)); break; default: /* case 3: case 7: */ y=subsr(-1,p1); break; } return gerepile(av,tetpil,y);}
testx(GEN bnfz, GEN bnf, GEN X, GEN module, GEN subgroup, GEN vecMsup, GEN vecWB, long g, GEN U)	testx(GEN bnfz, GEN bnr, GEN X, GEN subgroup, GEN vecMsup, GEN vecWB, long g, GEN U)	testx(GEN bnfz, GEN bnf, GEN X, GEN module, GEN subgroup, GEN vecMsup, GEN vecWB, long g, GEN U){ long i,l,lX; GEN be,polrelbe,p1,nf; if (gcmp0(X)) return NULL; lX = lg(X); for (i=dv+1; i<lX; i++) if (gcmp0((GEN)X[i])) return NULL; l = lg(vecMsup); for (i=1; i<l; i++) if (gcmp0(FpV_red(gmul((GEN)vecMsup[i],X), gell))) return NULL; be = gun; for (i=1; i<lX; i++) be = gmul(be, powgi((GEN)vecWB[i], (GEN)X[i])); if (DEBUGLEVEL>1) fprintferr("reducing beta = %Z\n",be); be = reducebeta(bnfz, be); if (DEBUGLEVEL>1) fprintferr("beta reduced = %Z\n",be); nf = (GEN)bnf[7]; polrelbe = computepolrelbeta((GEN)nf[1],be,g,U); p1 = unifpol(nf,polrelbe,0); l = lg(p1); /* lift to Q rational coeffs */ for (i=2; i<l; i++) if (isnfscalar((GEN)p1[i])) polrelbe[i] = mael(p1,i,1); p1 = denom(gtovec(p1)); polrelbe = rescale_pol(polrelbe,p1); if (DEBUGLEVEL>1) fprintferr("polrelbe = %Z\n",polrelbe); p1 = rnfconductor(bnf,polrelbe,0); if (!gegal((GEN)p1[1],module) \|\| !gegal((GEN)p1[3],subgroup)) return NULL; return polrelbe;}
be = gun; for (i=1; i<lX; i++) be = gmul(be, powgi((GEN)vecWB[i], (GEN)X[i]));	be = factorback(vecWB, X);	testx(GEN bnfz, GEN bnf, GEN X, GEN module, GEN subgroup, GEN vecMsup, GEN vecWB, long g, GEN U){ long i,l,lX; GEN be,polrelbe,p1,nf; if (gcmp0(X)) return NULL; lX = lg(X); for (i=dv+1; i<lX; i++) if (gcmp0((GEN)X[i])) return NULL; l = lg(vecMsup); for (i=1; i<l; i++) if (gcmp0(FpV_red(gmul((GEN)vecMsup[i],X), gell))) return NULL; be = gun; for (i=1; i<lX; i++) be = gmul(be, powgi((GEN)vecWB[i], (GEN)X[i])); if (DEBUGLEVEL>1) fprintferr("reducing beta = %Z\n",be); be = reducebeta(bnfz, be); if (DEBUGLEVEL>1) fprintferr("beta reduced = %Z\n",be); nf = (GEN)bnf[7]; polrelbe = computepolrelbeta((GEN)nf[1],be,g,U); p1 = unifpol(nf,polrelbe,0); l = lg(p1); /* lift to Q rational coeffs */ for (i=2; i<l; i++) if (isnfscalar((GEN)p1[i])) polrelbe[i] = mael(p1,i,1); p1 = denom(gtovec(p1)); polrelbe = rescale_pol(polrelbe,p1); if (DEBUGLEVEL>1) fprintferr("polrelbe = %Z\n",polrelbe); p1 = rnfconductor(bnf,polrelbe,0); if (!gegal((GEN)p1[1],module) \|\| !gegal((GEN)p1[3],subgroup)) return NULL; return polrelbe;}
nf = (GEN)bnf[7];	nf = checknf(bnr);	testx(GEN bnfz, GEN bnf, GEN X, GEN module, GEN subgroup, GEN vecMsup, GEN vecWB, long g, GEN U){ long i,l,lX; GEN be,polrelbe,p1,nf; if (gcmp0(X)) return NULL; lX = lg(X); for (i=dv+1; i<lX; i++) if (gcmp0((GEN)X[i])) return NULL; l = lg(vecMsup); for (i=1; i<l; i++) if (gcmp0(FpV_red(gmul((GEN)vecMsup[i],X), gell))) return NULL; be = gun; for (i=1; i<lX; i++) be = gmul(be, powgi((GEN)vecWB[i], (GEN)X[i])); if (DEBUGLEVEL>1) fprintferr("reducing beta = %Z\n",be); be = reducebeta(bnfz, be); if (DEBUGLEVEL>1) fprintferr("beta reduced = %Z\n",be); nf = (GEN)bnf[7]; polrelbe = computepolrelbeta((GEN)nf[1],be,g,U); p1 = unifpol(nf,polrelbe,0); l = lg(p1); /* lift to Q rational coeffs */ for (i=2; i<l; i++) if (isnfscalar((GEN)p1[i])) polrelbe[i] = mael(p1,i,1); p1 = denom(gtovec(p1)); polrelbe = rescale_pol(polrelbe,p1); if (DEBUGLEVEL>1) fprintferr("polrelbe = %Z\n",polrelbe); p1 = rnfconductor(bnf,polrelbe,0); if (!gegal((GEN)p1[1],module) \|\| !gegal((GEN)p1[3],subgroup)) return NULL; return polrelbe;}
p1 = rnfconductor(bnf,polrelbe,0); if (!gegal((GEN)p1[1],module) \|\| !gegal((GEN)p1[3],subgroup)) return NULL;	p1 = rnfnormgroup(bnr,polrelbe); if (!gegal(p1,subgroup)) return NULL;	testx(GEN bnfz, GEN bnf, GEN X, GEN module, GEN subgroup, GEN vecMsup, GEN vecWB, long g, GEN U){ long i,l,lX; GEN be,polrelbe,p1,nf; if (gcmp0(X)) return NULL; lX = lg(X); for (i=dv+1; i<lX; i++) if (gcmp0((GEN)X[i])) return NULL; l = lg(vecMsup); for (i=1; i<l; i++) if (gcmp0(FpV_red(gmul((GEN)vecMsup[i],X), gell))) return NULL; be = gun; for (i=1; i<lX; i++) be = gmul(be, powgi((GEN)vecWB[i], (GEN)X[i])); if (DEBUGLEVEL>1) fprintferr("reducing beta = %Z\n",be); be = reducebeta(bnfz, be); if (DEBUGLEVEL>1) fprintferr("beta reduced = %Z\n",be); nf = (GEN)bnf[7]; polrelbe = computepolrelbeta((GEN)nf[1],be,g,U); p1 = unifpol(nf,polrelbe,0); l = lg(p1); /* lift to Q rational coeffs */ for (i=2; i<l; i++) if (isnfscalar((GEN)p1[i])) polrelbe[i] = mael(p1,i,1); p1 = denom(gtovec(p1)); polrelbe = rescale_pol(polrelbe,p1); if (DEBUGLEVEL>1) fprintferr("polrelbe = %Z\n",polrelbe); p1 = rnfconductor(bnf,polrelbe,0); if (!gegal((GEN)p1[1],module) \|\| !gegal((GEN)p1[3],subgroup)) return NULL; return polrelbe;}
const int pk = _pk(p,k), L = lg(tabaall)-1, lz = pk - L;	const int pk = u_pow(p,k), L = lg(tabaall)-1, lz = pk - L;	extendtabs(GEN N, int p, int k){ const int pk = _pk(p,k), L = lg(tabaall)-1, lz = pk - L; const ulong ltab = (NBITSN/kglob)+2; if (lz <= 0) { if (tabcyc[pk]==0) filltabs(N,p,k,ltab); return; } extend((GEN)&tabaall, lz); extend((GEN)&tabtall, lz); extend((GEN*)&tabcyc, lz); extend(&tabefin, lz); extend(&tabE, lz); extend(&tabTH, lz); extend(&tabeta, lz); extend(&sgt, lz); extend(&ctsgt, lz); filltabs(N,p,k, ltab);}
extend(&tabefin, lz);		extendtabs(GEN N, int p, int k){ const int pk = _pk(p,k), L = lg(tabaall)-1, lz = pk - L; const ulong ltab = (NBITSN/kglob)+2; if (lz <= 0) { if (tabcyc[pk]==0) filltabs(N,p,k,ltab); return; } extend((GEN)&tabaall, lz); extend((GEN)&tabtall, lz); extend((GEN*)&tabcyc, lz); extend(&tabefin, lz); extend(&tabE, lz); extend(&tabTH, lz); extend(&tabeta, lz); extend(&sgt, lz); extend(&ctsgt, lz); filltabs(N,p,k, ltab);}
pushtmatrix((SDL_svg_context *)closure);	pushtmatrix(c); c->minx = HUGE; c->miny = HUGE; c->maxx = -HUGE; c->maxy = -HUGE;	static svg_status_t _SDL_SVG_BeginElement (void closure){ dprintf("svg_BeginElement\n"); pushtmatrix((SDL_svg_context )closure); return SVG_STATUS_SUCCESS;}
	_extremes(c, x1, y1); _extremes(c, x2, y2); _extremes(c, x3, y3);	_SDL_SVG_CurveTo (void closure, double x1, double y1, double x2, double y2, double x3, double y3){SDL_svg_context c=closure;IPoint p1,p2,p3; dprintf("svg_CurveTo (x1=%5.5f, y1=%5.5f, x2=%5.5f, y2=%5.5f, x3=%5.5f, y3=%5.5f)\n", x1,y1,x2,y2,x3,y3); if(!c->path \|\| !c->numpoints) return SVG_STATUS_INVALID_CALL; p1 = FixCoords(c, (IPoint) {x1, y1}); p2 = FixCoords(c, (IPoint) {x2, y2}); p3 = FixCoords(c, (IPoint) {x3, y3}); _AddIPoint(c, (IPoint) {p1.x, p1.y}, TAG_CONTROL3); _AddIPoint(c, (IPoint) {p2.x, p2.y}, TAG_CONTROL3); _AddIPoint(c, (IPoint) {p3.x, p3.y}, TAG_ONPATH); c->at = (IPoint) {x3, y3}; return SVG_STATUS_SUCCESS;}
	_extremes(c, x, y);	_SDL_SVG_LineTo (void closure, double x, double y){SDL_svg_context c=closure; dprintf("svg_LineTo (x=%5.5f, y=%5.5f)\n",x,y); _AddIPoint(c, FixCoords(c, (IPoint) {x, y}), TAG_ONPATH); c->at = (IPoint) {x, y}; return SVG_STATUS_SUCCESS;}
	_extremes(c, x, y);	_SDL_SVG_MoveTo (void closure, double x, double y){SDL_svg_context c=closure; dprintf("svg_MoveTo (x=%5.5f, y=%5.5f)\n",x,y); if(c->numpoints && needs_path_stop(c)) _AddPathStop(c, 0); _AddIPoint(c, FixCoords(c, (IPoint) {x, y}), TAG_ONPATH); c->at = (IPoint) {x, y}; return SVG_STATUS_SUCCESS;}
	_extremes(c, x1, y1); _extremes(c, x2, y2);	_SDL_SVG_QuadraticCurveTo (void closure, double x1, double y1, double x2, double y2){SDL_svg_context c=closure;IPoint p1,p2; dprintf("svg_QuadraticCurveTo (x1=%5.5f, y1=%5.5f, x2=%5.5f, y2=%5.5f)\n", x1,y1,x2,y2); if(!c->path \|\| !c->numpoints) return SVG_STATUS_INVALID_CALL; p1 = FixCoords(c, (IPoint) {x1, y1}); p2 = FixCoords(c, (IPoint) {x2, y2}); _AddIPoint(c, (IPoint) {p1.x, p1.y}, TAG_CONTROL2); _AddIPoint(c, (IPoint) {p2.x, p2.y}, TAG_ONPATH); c->at = (IPoint) {x2, y2}; return SVG_STATUS_SUCCESS;}
	_extremes(c, x1, y1); _extremes(c, x2, y2);	_SDL_SVG_RenderRect (void closure, svg_length_t x_len, svg_length_t y_len, svg_length_t width_len, svg_length_t height_len, svg_length_t rx_len, svg_length_t ry_len){SDL_svg_context c=closure;float x1,y1;float x2,y2; dprintf("svg_RenderRect\n"); x1 = x_len->value; y1 = y_len->value; x2 = x1 + width_len->value; y2 = y1 + height_len->value; _AddIPoint(c, FixCoords(c, (IPoint) {x1, y1}), TAG_ONPATH); _AddIPoint(c, FixCoords(c, (IPoint) {x2, y1}), TAG_ONPATH); _AddIPoint(c, FixCoords(c, (IPoint) {x2, y2}), TAG_ONPATH); _AddIPoint(c, FixCoords(c, (IPoint) {x1, y2}), TAG_ONPATH); _SDL_SVG_RenderPath(closure); return SVG_STATUS_SUCCESS;}
dst.e = in->c * in->f - in->d * in->e; dst.f = in->b * in->e - in->a * in->f;	dst.e = (in->c * in->f - in->d * in->e)/det; dst.f = (in->b * in->e - in->a * in->f)/det;	svg_matrix_t svg_matrix_invert(svg_matrix_t in){float det;svg_matrix_t dst; det = in->a in->d - in->b * in->c; if(det == 0.0) return (svg_matrix_t) {1.0, 0.0, 0.0, 1.0, 0.0, 0.0}; dst.a = in->d/det; dst.b = -in->b/det; dst.c = -in->c/det; dst.d = in->a/det; dst.e = in->c * in->f - in->d * in->e; dst.f = in->b * in->e - in->a * in->f; return dst;}
the_object = _Objects_Get( information, id, OBJECTS_SEARCH_LOCAL_NODE );	the_object = _Objects_Get( information, id, &ignored_location );	Objects_Name_or_id_lookup_errors _Objects_Id_to_name ( Objects_Id id, Objects_Name name){ unsigned32 the_api; unsigned32 the_class; Objects_Information information; Objects_Control the_object = (Objects_Control ) 0; if ( !name ) return OBJECTS_INVALID_NAME; the_api = _Objects_Get_API( id ); if ( the_api && the_api > OBJECTS_APIS_LAST ) return OBJECTS_INVALID_ID; the_class = _Objects_Get_class( id ); information = _Objects_Information_table[ the_api ][ the_class ]; if ( !information ) return OBJECTS_INVALID_ID; if ( information->is_string ) return OBJECTS_INVALID_ID; the_object = _Objects_Get( information, id, OBJECTS_SEARCH_LOCAL_NODE ); if (!the_object) return OBJECTS_INVALID_ID; *name = the_object->name; return OBJECTS_NAME_OR_ID_LOOKUP_SUCCESSFUL;}
if (precision(p1)) return 1;	if (precision(p1)) res = 1;	use_maximal_pivot(GEN x){ long tx,i,j, lx = lg(x), ly = lg(x[1]); GEN p1; for (i=1; i<lx; i++) for (j=1; j<ly; j++) { p1 = gmael(x,i,j); tx = typ(p1); if (!is_scalar_t(tx)) return 0; if (precision(p1)) return 1; } return 0;}
return 0;	return res;	use_maximal_pivot(GEN x){ long tx,i,j, lx = lg(x), ly = lg(x[1]); GEN p1; for (i=1; i<lx; i++) for (j=1; j<ly; j++) { p1 = gmael(x,i,j); tx = typ(p1); if (!is_scalar_t(tx)) return 0; if (precision(p1)) return 1; } return 0;}
tmppool);	request->respool);	static apr_status_t read_from_connection(serf_connection_t conn){ apr_status_t status; apr_pool_t tmppool; /* Whatever is coming in on the socket corresponds to the first request * on our chain. / serf_request_t request = conn->requests; /* assert: request != NULL / if ((status = apr_pool_create(&tmppool, request->respool)) != APR_SUCCESS) goto error; / Invoke response handlers until we have no more work. / while (1) { apr_pool_clear(tmppool); / If the request doesn't have a response bucket, then call the * acceptor to get one created. / if (request->resp_bkt == NULL) { request->resp_bkt = (request->acceptor)(request, conn->skt, request->acceptor_baton, tmppool); apr_pool_clear(tmppool); } status = (request->handler)(request->resp_bkt, request->handler_baton, tmppool); if (!APR_STATUS_IS_EOF(status)) { / Whether success, or an error, there is no more to do unless * this request has been completed. / goto error; } / The request has been fully-delivered, and the response has * been fully-read. Remove it from our queue and loop to read * another response. / conn->requests = request->next; / The bucket is no longer needed, nor is the request's pool. / serf_bucket_destroy(request->resp_bkt); apr_pool_destroy(request->respool); request = conn->requests; / If we just ran out of requests, then update the pollset. We * don't want to read from this socket any more. We are definitely * done with this loop, too. */ if (request == NULL) { status = update_pollset(conn); goto error; } } error: apr_pool_destroy(tmppool); return status;}
unsigned32 erc32_sonic_read_register(	uint32_t erc32_sonic_read_register(	unsigned32 erc32_sonic_read_register( void base, unsigned32 regno){ volatile unsigned32 p = base; unsigned32 value; value = p[regno];#if (SONIC_DEBUG & SONIC_DEBUG_PRINT_REGISTERS) printf( "%p Read 0x%04x from %s (0x%02x)\n", &p[regno], value, SONIC_Reg_name[regno], regno ); fflush( stdout );#endif return 0x0ffff & value;}
unsigned32 regno	uint32_t regno	unsigned32 erc32_sonic_read_register( void base, unsigned32 regno){ volatile unsigned32 p = base; unsigned32 value; value = p[regno];#if (SONIC_DEBUG & SONIC_DEBUG_PRINT_REGISTERS) printf( "%p Read 0x%04x from %s (0x%02x)\n", &p[regno], value, SONIC_Reg_name[regno], regno ); fflush( stdout );#endif return 0x0ffff & value;}
volatile unsigned32 *p = base; unsigned32 value;	volatile uint32_t *p = base; uint32_t value;	unsigned32 erc32_sonic_read_register( void base, unsigned32 regno){ volatile unsigned32 p = base; unsigned32 value; value = p[regno];#if (SONIC_DEBUG & SONIC_DEBUG_PRINT_REGISTERS) printf( "%p Read 0x%04x from %s (0x%02x)\n", &p[regno], value, SONIC_Reg_name[regno], regno ); fflush( stdout );#endif return 0x0ffff & value;}
rtems_unsigned32 task_count = 0;	uint32_t task_count = 0;	void test1(){ boolean auto_extend; rtems_status_code result; rtems_unsigned32 task_count = 0; Objects_Information the_information; char c1 = 'a'; char c2 = 'a'; char c3 = '0'; char c4 = '0'; printf( "\n TEST1 : auto-extend disabled.\n" ); / * This is a major hack and only recommended for a test. Doing this * saves having another test. / the_information = _Objects_Information_table[OBJECTS_CLASSIC_API][OBJECTS_RTEMS_TASKS]; auto_extend = the_information->auto_extend; the_information->auto_extend = FALSE; while (task_count < MAX_TASKS) { rtems_name name; printf(" TEST1 : creating task '%c%c%c%c', ", c1, c2, c3, c4); name = rtems_build_name(c1, c2, c3, c4); result = rtems_task_create(name, 10, RTEMS_MINIMUM_STACK_SIZE, RTEMS_DEFAULT_ATTRIBUTES, RTEMS_LOCAL, &task_id[task_count]); if (status_code_bad(result)) break; printf("number = %3i, id = %08x, starting, ", task_count, task_id[task_count]); fflush(stdout); result = rtems_task_start(task_id[task_count], test_task, (rtems_task_argument) task_count); if (status_code_bad(result)) break; / * Update the name. */ NEXT_TASK_NAME(c1, c2, c3, c4); task_count++; } if (task_count >= MAX_TASKS) printf( "\nMAX_TASKS too small for work-space size, please make larger !!\n\n" ); if (task_count != (TASK_ALLOCATION_SIZE - 1)) { printf( " FAIL1 : the number of tasks does not equal the expected size -\n" " task created = %i, required number = %i\n", task_count, TASK_ALLOCATION_SIZE); exit( 1 ); } destory_all_tasks("TEST1"); the_information->auto_extend = auto_extend; printf( " TEST1 : completed\n" );}
	puts("");	void stat_a_file( const char *file){ int status; struct stat statbuf; assert( file ); printf( "stat( %s ) returned ", file ); fflush( stdout ); status = stat( file, &statbuf ); if ( status == -1 ) { printf( ": %s\n", strerror( errno ) ); } else { dump_statbuf( &statbuf ); }}
long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf;	long ell, i, j, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, vnf; long l, lSp, lSml2, lSl2, lW;	rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); / step 7 / if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); / step 1 of alg 5.3.5. / if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; / step 2 / if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ellell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* / / step reduction of R / if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG\|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); / step 3 / / one could factor disc(R) using th. 2.1.6. / if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); / computation of the uu(j) (see remark 5.2.15.) / uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; / step 4 / if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((jd)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 / if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); / famat / Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); / step 6 / if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; / step 7 done above / / step 8 / if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); / left inverse / T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { / l \| N(ideal) / GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } / step 9 / if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); / step 10 and step 11 / if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; / step 12 / if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } / step 13 / if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); / step 14, 15, and 17 / if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 / if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } / step 18 / if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; / step 19 / for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); / step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}
GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp;	GEN polnf,bnf,nf,bnfz,nfz,bid,ideal,cycgen,gell,p1,p2,wk,U,vselmer; GEN clgp,fununits,torsunit,Tc,Tv,P; GEN Q,idealz,gothf,factgothf; GEN M,K,y,vecMsup,vecW,vecWA,vecWB,vecB,vecC; GEN u,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp,listprSp;	rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); / step 7 / if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); / step 1 of alg 5.3.5. / if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; / step 2 / if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ellell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* / / step reduction of R / if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG\|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); / step 3 / / one could factor disc(R) using th. 2.1.6. / if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); / computation of the uu(j) (see remark 5.2.15.) / uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; / step 4 / if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((jd)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 / if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); / famat / Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); / step 6 / if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; / step 7 done above / / step 8 / if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); / left inverse / T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { / l \| N(ideal) / GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } / step 9 / if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); / step 10 and step 11 / if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; / step 12 / if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } / step 13 / if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); / step 14, 15, and 17 / if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 / if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } / step 18 / if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; / step 19 / for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); / step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}
p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4];	compositum_red(&COMPO, polnf, cyclo(ell,vnf));	rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); / step 7 / if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); / step 1 of alg 5.3.5. / if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; / step 2 / if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ellell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* / / step reduction of R / if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG\|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); / step 3 / / one could factor disc(R) using th. 2.1.6. / if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); / computation of the uu(j) (see remark 5.2.15.) / uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; / step 4 / if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((jd)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 / if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); / famat / Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); / step 6 / if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; / step 7 done above / / step 8 / if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); / left inverse / T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { / l \| N(ideal) / GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } / step 9 / if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); / step 10 and step 11 / if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; / step 12 / if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } / step 13 / if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); / step 14, 15, and 17 / if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 / if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } / step 18 / if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; / step 19 / for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); / step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}
degKz = degpol(R); m = degKz/degK; d = (ell-1)/m;	degKz = degpol(COMPO.R); m = degKz / degK; d = (ell-1) / m;	rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); / step 7 / if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); / step 1 of alg 5.3.5. / if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; / step 2 / if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ellell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* / / step reduction of R / if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG\|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); / step 3 / / one could factor disc(R) using th. 2.1.6. / if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); / computation of the uu(j) (see remark 5.2.15.) / uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; / step 4 / if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((jd)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 / if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); / famat / Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); / step 6 / if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; / step 7 done above / / step 8 / if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); / left inverse / T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { / l \| N(ideal) / GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } / step 9 / if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); / step 10 and step 11 / if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; / step 12 / if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } / step 13 / if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); / step 14, 15, and 17 / if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 / if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } / step 18 / if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; / step 19 / for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); / step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}
if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG\|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U);		rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); / step 7 / if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); / step 1 of alg 5.3.5. / if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; / step 2 / if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ellell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* / / step reduction of R / if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG\|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); / step 3 / / one could factor disc(R) using th. 2.1.6. / if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); / computation of the uu(j) (see remark 5.2.15.) / uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; / step 4 / if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((jd)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 / if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); / famat / Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); / step 6 / if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; / step 7 done above / / step 8 / if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); / left inverse / T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { / l \| N(ideal) / GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } / step 9 / if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); / step 10 and step 11 / if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; / step 12 / if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } / step 13 / if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); / step 14, 15, and 17 / if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 / if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } / step 18 / if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; / step 19 / for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); / step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}
bnfz = bnfinit0(R,1,NULL,prec);	bnfz = bnfinit0(COMPO.R,1,NULL,prec); cycgen = check_and_build_cycgen(bnfz);	rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); / step 7 / if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); / step 1 of alg 5.3.5. / if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; / step 2 / if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ellell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* / / step reduction of R / if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG\|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); / step 3 / / one could factor disc(R) using th. 2.1.6. / if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); / computation of the uu(j) (see remark 5.2.15.) / uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; / step 4 / if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((jd)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 / if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); / famat / Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); / step 6 / if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; / step 7 done above / / step 8 / if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); / left inverse / T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { / l \| N(ideal) / GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } / step 9 / if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); / step 10 and step 11 / if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; / step 12 / if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } / step 13 / if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); / step 14, 15, and 17 / if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 / if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } / step 18 / if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; / step 19 / for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); / step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}
tau = get_tau(&_tau, nfz, U);		rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); / step 7 / if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); / step 1 of alg 5.3.5. / if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; / step 2 / if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ellell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* / / step reduction of R / if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG\|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); / step 3 / / one could factor disc(R) using th. 2.1.6. / if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); / computation of the uu(j) (see remark 5.2.15.) / uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; / step 4 / if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((jd)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 / if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); / famat / Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); / step 6 / if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; / step 7 done above / / step 8 / if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); / left inverse / T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { / l \| N(ideal) / GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } / step 9 / if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); / step 10 and step 11 / if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; / step 12 / if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } / step 13 / if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); / step 14, 15, and 17 / if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 / if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } / step 18 / if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; / step 19 / for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); / step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}
cycgen = check_and_build_cycgen(bnfz);		rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); / step 7 / if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); / step 1 of alg 5.3.5. / if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; / step 2 / if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ellell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* / / step reduction of R / if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG\|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); / step 3 / / one could factor disc(R) using th. 2.1.6. / if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); / computation of the uu(j) (see remark 5.2.15.) / uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; / step 4 / if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((jd)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 / if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); / famat / Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); / step 6 / if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; / step 7 done above / / step 8 / if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); / left inverse / T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { / l \| N(ideal) / GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } / step 9 / if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); / step 10 and step 11 / if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; / step 12 / if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } / step 13 / if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); / step 14, 15, and 17 / if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 / if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } / step 18 / if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; / step 19 / for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); / step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}
uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell);	u = cgetg(l,t_VEC); for (j=1; j<=rc; j++) u[j] = zero; for ( ; j< l; j++) u[j] = lmpinvmod((GEN)cyc[j], gell);	rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); / step 7 / if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); / step 1 of alg 5.3.5. / if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; / step 2 / if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ellell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* / / step reduction of R / if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG\|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); / step 3 / / one could factor disc(R) using th. 2.1.6. / if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); / computation of the uu(j) (see remark 5.2.15.) / uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; / step 4 / if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((jd)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 / if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); / famat / Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); / step 6 / if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; / step 7 done above / / step 8 / if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); / left inverse / T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { / l \| N(ideal) / GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } / step 9 / if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); / step 10 and step 11 / if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; / step 12 / if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } / step 13 / if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); / step 14, 15, and 17 / if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 / if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } / step 18 / if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; / step 19 / for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); / step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}
	U = gadd(gpowgs(COMPO.q, g), gmul(COMPO.k, COMPO.p)); U = poleval(COMPO.rev, U); tau = get_tau(&_tau, nfz, U);	rnfkummer(GEN bnr, GEN subgroup, long all, long prec){ long i, j, l, m, d, dK, dc, rc, ru, rv, g, mginv, degK, degKz, ell; long lSp, lSl2, lSml2, lW, vnf; gpmem_t av = avma; GEN p1,p2,p3,wk,U,R,gell; GEN polnf,nf,bnf,bnfz,bid,ideal,cycgen,vselmer; GEN kk,clgp,fununits,torsunit,vecB,vecC,Tc,Tv,P; GEN Q,idealz,gothf,factgothf,nfz; GEN listprSp,vecW,vecWA,vecWB; GEN M,K,y,A1,A2,A3,A3rev,vecMsup; GEN uu,gen,cyc,vecalpha,vecalphap,vecbetap,matP,Sp; primlist L; toK_s T; tau_s _tau, tau; checkbnrgen(bnr); bnf = (GEN)bnr[1]; nf = (GEN)bnf[7]; polnf = (GEN)nf[1]; vnf = varn(polnf); if (!vnf) err(talker,"main variable in kummer must not be x"); wk = gmael3(bnf,8,4,1); / step 7 / if (all) subgroup = NULL; p1 = conductor(bnr, subgroup, 2); bnr = (GEN)p1[2]; subgroup = (GEN)p1[3]; gell = get_gell(bnr,subgroup,all); if (gcmp1(gell)) { avma = av; return polx[vnf]; } if (!isprime(gell)) err(impl,"kummer for composite relative degree"); if (divise(wk,gell)) return gerepilecopy(av, rnfkummersimple(bnr,subgroup,all)); if (all) err(impl,"extensions by degree in kummer when zeta not in K"); bid = (GEN)bnr[2]; ideal = gmael(bid,1,1); ell = itos(gell); / step 1 of alg 5.3.5. / if (DEBUGLEVEL>2) fprintferr("Step 1\n"); p1 = (GEN)compositum2(polnf, cyclo(ell,vnf))[1]; R = (GEN)p1[1]; A1= (GEN)p1[2]; A2= (GEN)p1[3]; kk= (GEN)p1[4]; / step 2 / if (DEBUGLEVEL>2) fprintferr("Step 2\n"); degK = degpol(polnf); degKz = degpol(R); m = degKz/degK; d = (ell-1)/m; g = powuumod(u_gener(ell), d, ell); if (powuumod(g, m, ellell) == 1) g += ell; /* ord(g)=m in all (Z/ell^k)^* / / step reduction of R / if (DEBUGLEVEL>2) fprintferr("Step reduction\n"); p1 = polredabs0(R, nf_ORIG\|nf_PARTIALFACT); R = (GEN)p1[1]; if (DEBUGLEVEL>2) fprintferr("polredabs = %Z",R); A3= (GEN)p1[2]; A1 = poleval(lift(A1), A3); A2 = poleval(lift(A2), A3); A3rev= modreverse_i((GEN)A3[2], (GEN)A3[1]); U = gadd(gpowgs(A2,g), gmul(kk,A1)); U = poleval(A3rev, U); / step 3 / / one could factor disc(R) using th. 2.1.6. / if (DEBUGLEVEL>2) fprintferr("Step 3\n"); bnfz = bnfinit0(R,1,NULL,prec); nfz = (GEN)bnfz[7]; tau = get_tau(&_tau, nfz, U); clgp = gmael(bnfz,8,1); cyc = (GEN)clgp[2]; rc = prank(cyc,ell); gen = (GEN)clgp[3]; l = lg(cyc); vecalpha = cgetg(l,t_VEC); cycgen = check_and_build_cycgen(bnfz); for (j=1; j<l; j++) vecalpha[j] = (long)basistoalg(nfz, famat_to_nf(nfz, (GEN)cycgen[j])); / computation of the uu(j) (see remark 5.2.15.) / uu = cgetg(l,t_VEC); for (j=1; j<=rc; j++) uu[j] = zero; for ( ; j< l; j++) uu[j] = lmpinvmod((GEN)cyc[j], gell); fununits = check_units(bnfz,"rnfkummer"); torsunit = gmael3(bnfz,8,4,2); ru = (degKz>>1)-1; rv = rc+ru+1; vselmer = cgetg(rv+1,t_VEC); for (j=1; j<=rc; j++) vselmer[j] = cycgen[j]; for ( ; j< rv; j++) vselmer[j] = fununits[j-rc]; vselmer[rv]=(long)torsunit; / step 4 / if (DEBUGLEVEL>2) fprintferr("Step 4\n"); vecB=cgetg(rc+1,t_VEC); Tc=cgetg(rc+1,t_MAT); for (j=1; j<=rc; j++) { p1 = tauofideal(nfz,(GEN)gen[j], tau); p1 = isprincipalell(bnfz, p1, cycgen,uu,gell,rc); Tc[j] = p1[1]; vecB[j]= p1[2]; } p1 = cgetg(m,t_VEC); p1[1] = (long)idmat(rc); for (j=2; j<=m-1; j++) p1[j] = lmul((GEN)p1[j-1],Tc); p2 = cgetg(rc+1,t_VEC); for (j=1; j<=rc; j++) p2[j] = lgetg(1, t_MAT); p3 = vecB; for (j=1; j<=m-1; j++) { GEN T = FpM_red(gmulsg((jd)%ell,(GEN)p1[m-j]), gell); p3 = tauofvec(p3, tau); for (i=1; i<=rc; i++) p2[i] = (long)famat_mul((GEN)p2[i], famat_factorback(p3, (GEN)T[i])); } vecC = p2; for (i=1; i<=rc; i++) vecC[i] = (long)famat_reduce((GEN)vecC[i]); /* step 5 / if (DEBUGLEVEL>2) fprintferr("Step 5\n"); Tv = cgetg(rv+1,t_MAT); for (j=1; j<=rv; j++) { p1 = tauofelt((GEN)vselmer[j], tau); if (typ(p1) == t_MAT) p1 = factorbackelt(p1, nfz, NULL); / famat / Tv[j] = isvirtualunit(bnfz, p1, vecalpha,cyc,gell,rc)[1]; } P = FpM_ker(gsubgs(Tv, g), gell); lW = lg(P); vecW = cgetg(lW,t_VEC); for (j=1; j<lW; j++) vecW[j] = (long)famat_factorback(vselmer, (GEN)P[j]); / step 6 / if (DEBUGLEVEL>2) fprintferr("Step 6\n"); Q = FpM_ker(gsubgs(gtrans(Tc), g), gell); dc = lg(Q)-1; / step 7 done above / / step 8 / if (DEBUGLEVEL>2) fprintferr("Step 7 and 8\n"); idealz = lifttoKz(nfz, nf, ideal, A1); A1 = lift_intern(A1); p1 = polun[vnf]; p2 = cgetg(degK+1,t_MAT); for (j=1; j<=degK; j++) { p2[j] = (long)pol_to_vec(p1, degKz); if (j<degK) p1 = gmod(gmul(p1,A1), R); } T.invexpoteta1 = invmat(p2); / left inverse / T.polnf = polnf; T.tau = tau; T.m = m; if (smodis(idealnorm(nf,ideal), ell)) gothf = idealz; else { / l \| N(ideal) / GEN bnrz = buchrayinitgen(bnfz, idealz); GEN subgroupz = invimsubgroup(&T, bnrz,bnr,subgroup); gothf = conductor(bnrz,subgroupz,0); } / step 9 / if (DEBUGLEVEL>2) fprintferr("Step 9\n"); factgothf = idealfactor(nfz,gothf); / step 10 and step 11 / if (DEBUGLEVEL>2) fprintferr("Step 10 and 11\n"); i = build_list_Hecke(&L, nfz, factgothf, gothf, gell, tau); if (i) return no_sol(all,i); lSml2 = lg(L.Sml2)-1; Sp = concatsp(L.Sm, L.Sml1); lSp = lg(Sp)-1; listprSp = concatsp(L.Sml2, L.Sl); lSl2 = lg(listprSp)-1; / step 12 / if (DEBUGLEVEL>2) fprintferr("Step 12\n"); vecbetap = cgetg(lSp+1,t_VEC); vecalphap= cgetg(lSp+1,t_VEC); matP = cgetg(lSp+1,t_MAT); for (j=1; j<=lSp; j++) { GEN e, a; p1 = isprincipalell(bnfz, (GEN)Sp[j], cycgen,uu,gell,rc); e = (GEN)p1[1]; a = (GEN)p1[2]; matP[j] = (long)e; p3 = famat_mul(famat_factorback(vecC, gneg(e)), a); vecbetap[j] = (long)p3; p2 = cgetg(1, t_MAT); for (i=0; i<m; i++) { p2 = famat_mul(p2, famat_pow(p3, utoi(powuumod(g,m-1-i,ell)))); if (i < m-1) p3 = tauofelt(p3, tau); } vecalphap[j] = (long)p2; } / step 13 / if (DEBUGLEVEL>2) fprintferr("Step 13\n"); vecWB = concatsp(vecW, vecbetap); vecWA = concatsp(vecW, vecalphap); / step 14, 15, and 17 / if (DEBUGLEVEL>2) fprintferr("Step 14, 15 and 17\n"); mginv = (m u_invmod(g,ell)) % ell; vecMsup = cgetg(lSml2+1,t_VEC); M = NULL; for (i=1; i<=lSl2; i++) { GEN pr = (GEN)listprSp[i]; long e = itos((GEN)pr[3]), z = ell * (e / (ell-1)); if (i <= lSml2) { z += 1 - L.ESml2[i]; vecMsup[i] = (long)logall(nfz, vecWA,lW,mginv,ell,pr, z+1); } M = vconcat(M, logall(nfz, vecWA,lW,mginv,ell,pr, z)); } if (dc) { GEN QtP = gmul(gtrans_i(Q),matP); M = vconcat(M, concatsp(zeromat(dc,lW-1), QtP)); } if (!M) M = zeromat(1, lSp + lW - 1); /* step 16 / if (DEBUGLEVEL>2) fprintferr("Step 16\n"); K = FpM_ker(M, gell); dK= lg(K)-1; if (!dK) { avma=av; return gzero; } / step 18 / if (DEBUGLEVEL>2) fprintferr("Step 18\n"); y = cgetg(dK,t_VECSMALL); do { for (i=1; i<dK; i++) y[i] = 0; / step 19 / for(;;) { GEN res, X = (GEN)K[dK]; for (j=1; j<dK; j++) X = gadd(X, gmulsg(y[j],(GEN)K[j])); res = testx(&T,bnfz,bnr,X,subgroup,vecMsup,vecWB,g,gell,lW); if (res) return gerepilecopy(av, res); / step 20,21,22 */ i = dK; do { i--; if (!i) goto DECREASE; if (i < dK-1) y[i+1] = 0; y[i]++; } while (y[i] >= ell); }DECREASE: dK--; } while (dK); avma = av; return gzero;}