Annotation of OpenXM/src/asir-contrib/testing/noro/obsolete/new_pd.rr, Revision 1.1
1.1 ! noro 1: /* $OpenXM$ */
! 2: import("gr")$
! 3: module noro_pd$
! 4: static GBCheck,F4,EProcs,Procs,SatHomo,GBRat,SuccSat,RepColon$
! 5:
! 6: localf radical_membership_sat$
! 7: localf witness$
! 8: localf get_lc,tomonic,aa,ideal_intersection_m,redbase$
! 9: localf para_exec,nd_gr_rat,competitive_exec,call_func,call_func_serial$
! 10: localf call_ideal_list_intersection$
! 11: localf call_colon,call_prime_dec$
! 12: localf prime_dec2, prime_dec_main2$
! 13: localf first_second$
! 14: localf third$
! 15: localf locsat,iso_comp_para,extract_qj,colon_prime_dec,extract_comp$
! 16: localf separator$
! 17: localf member,mingen,compute_gbsyz,redcoef,recompute_trace,dtop,topnum$
! 18: localf prepost$
! 19: localf monodec0,monodec,prod$
! 20: localf extract_qd,primary_check$
! 21: localf second$
! 22: localf gbrat,succsat,repcolon,comp_third_tdeg,comp_tord$
! 23: localf power$
! 24:
! 25: localf syci_dec, syc_dec$
! 26: localf syca_dec,syc0_dec$
! 27:
! 28: localf find_si0,find_si1,find_si2$
! 29: localf find_ssi0,find_ssi1,find_ssi2$
! 30:
! 31: localf init_pprocs, init_eprocs, init_procs, kill_procs$
! 32:
! 33: localf sy_dec, pseudo_dec, iso_comp, prima_dec$
! 34:
! 35: localf prime_dec, prime_dec_main, lex_predec1, zprimedec, zprimadec$
! 36: localf complete_qdecomp, partial_qdecomp, partial_qdecomp0, complete_decomp$
! 37: localf partial_decomp, partial_decomp0, zprimacomp, zprimecomp$
! 38: localf fast_gb, incremental_gb, elim_gb, ldim, make_mod_subst$
! 39: localf rsgn, find_npos, gen_minipoly, indepset$
! 40: localf maxindep, maxindep2, contraction, contraction_m, ideal_list_intersection, ideal_intersection$
! 41: localf radical_membership, modular_radical_membership$
! 42: localf radical_membership_rep, ideal_product, saturation$
! 43: localf sat, satind, sat_ind, sat_ind_var, colon, isat$
! 44: localf ideal_colon, ideal_sat, ideal_inclusion, qd_simp_comp, qd_remove_redundant_comp$
! 45: localf pd_simp_comp, remove_identical_comp$
! 46: localf pd_remove_redundant_comp, ppart, sq, gen_fctr, gen_nf, gen_gb_comp$
! 47: localf gen_mptop, lcfactor, compute_deg0, compute_deg, member$
! 48: localf elimination, setintersection, setminus, sep_list$
! 49: localf first, comp_tdeg, comp_tdeg_first, tdeg, comp_by_ord, comp_by_second$
! 50: localf gbcheck,f4,sathomo,qd_check,qdb_check$
! 51:
! 52: SatHomo=0$
! 53: GBCheck=1$
! 54: GBRat=0$
! 55: SuccSat=0$
! 56: RepColon=0$
! 57:
! 58: #define MAX(a,b) ((a)>(b)?(a):(b))
! 59: #define ACCUM_TIME(C,R) {T1 = time(); C += (T1[0]-T0[0])+(T1[1]-T0[1]); R += (T1[3]-T0[3]); }
! 60:
! 61: def gbrat(A)
! 62: {
! 63: GBRat = A;
! 64: }
! 65:
! 66: def succsat(A)
! 67: {
! 68: SuccSat = A;
! 69: }
! 70:
! 71: def repcolon(A)
! 72: {
! 73: RepColon = A;
! 74: }
! 75:
! 76: def gbcheck(A)
! 77: {
! 78: if ( A ) GBCheck = 1;
! 79: else GBCheck = -1;
! 80: }
! 81:
! 82: def f4(A)
! 83: {
! 84: if ( A ) F4 = 1;
! 85: else F4 = 0;
! 86: }
! 87:
! 88: def sathomo(A)
! 89: {
! 90: if ( A ) SatHomo = 1;
! 91: else SatHomo = 0;
! 92: }
! 93:
! 94: def init_eprocs()
! 95: {
! 96: if ( type(NoX=getopt(nox)) == -1 ) NoX = 0;
! 97: if ( !EProcs ) {
! 98: if ( NoX ) {
! 99: P0 = ox_launch_nox();
! 100: P1 = ox_launch_nox();
! 101: } else {
! 102: P0 = ox_launch();
! 103: P1 = ox_launch();
! 104: }
! 105: EProcs = [P0,P1];
! 106: }
! 107: }
! 108:
! 109: def init_pprocs(N)
! 110: {
! 111: if ( type(NoX=getopt(nox)) == -1 ) NoX = 0;
! 112: for ( R = [], I = 0; I < N; I++ ) {
! 113: P = NoX ? ox_launch_nox() : ox_launch();
! 114: R = cons(P,R);
! 115: }
! 116: return reverse(R);
! 117: }
! 118:
! 119: def init_procs()
! 120: {
! 121: if ( type(NoX=getopt(nox)) == -1 ) NoX = 0;
! 122: if ( !Procs ) {
! 123: if ( NoX ) {
! 124: P0 = ox_launch_nox();
! 125: P1 = ox_launch_nox();
! 126: } else {
! 127: P0 = ox_launch();
! 128: P1 = ox_launch();
! 129: }
! 130: Procs = [P0,P1];
! 131: }
! 132: }
! 133:
! 134: def kill_procs()
! 135: {
! 136: if ( Procs ) {
! 137: ox_shutdown(Procs[0]);
! 138: ox_shutdown(Procs[1]);
! 139: Procs = 0;
! 140: }
! 141: if ( EProcs ) {
! 142: ox_shutdown(EProcs[0]);
! 143: ox_shutdown(EProcs[1]);
! 144: EProcs = 0;
! 145: }
! 146: }
! 147:
! 148: def qd_check(B,V,QD)
! 149: {
! 150: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 151: G = nd_gr(B,V,Mod,0);
! 152: Iso = ideal_list_intersection(map(first,QD[0]),V,0|mod=Mod);
! 153: Emb = ideal_list_intersection(map(first,QD[1]),V,0|mod=Mod);
! 154: GG = ideal_intersection(Iso,Emb,V,0|mod=Mod);
! 155: return gen_gb_comp(G,GG,Mod);
! 156: }
! 157:
! 158: def primary_check(B,V)
! 159: {
! 160: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 161: G = nd_gr(B,V,Mod,0);
! 162: PL = prime_dec(G,V|indep=1,mod=Mod);
! 163: if ( length(PL) > 1 ) return 0;
! 164: P = PL[0][0]; Y = PL[0][1];
! 165: Z = setminus(V,Y);
! 166: H = elim_gb(G,Z,Y,Mod,[[0,length(Z)],[0,length(Y)]]);
! 167: H = contraction(H,Z|mod=Mod);
! 168: H = nd_gr(H,V,Mod,0);
! 169: if ( gen_gb_comp(G,H,Mod) ) return nd_gr(P,V,Mod,0);
! 170: else return 0;
! 171: }
! 172:
! 173: def qdb_check(B,V,QD)
! 174: {
! 175: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 176: G = nd_gr(B,V,Mod,0);
! 177: N = length(QD);
! 178: for ( I = 0, Q = [1]; I < N; I++ )
! 179: for ( J = 0, QL = map(first,QD[I]), L = length(QL);
! 180: J < L; J++ )
! 181: Q = ideal_intersection_m(Q,QL[J],V,0|mod=Mod);
! 182: Q = nd_gr(Q,V,0,0);
! 183: if ( !gen_gb_comp(G,Q,Mod) )
! 184: return 0;
! 185: for ( I = 0; I < N; I++ ) {
! 186: T = QD[I];
! 187: M = length(T);
! 188: for ( J = 0; J < M; J++ ) {
! 189: P = primary_check(T[J][0],V|mod=Mod);
! 190: if ( !P ) return 0;
! 191: PP = nd_gr(T[J][1],V,Mod,0);
! 192: if ( !gen_gb_comp(P,PP,Mod) ) return 0;
! 193: }
! 194: }
! 195: return 1;
! 196: }
! 197:
! 198: def extract_qd(QD,V,Ind)
! 199: {
! 200: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 201: N = length(Ind);
! 202: for ( I = 0, Q = [1]; I < N; I++ )
! 203: for ( J = 0, QL = map(first,QD[Ind[I]]), L = length(QL);
! 204: J < L; J++ )
! 205: Q = ideal_intersection(Q,QL[J],V,0|mod=Mod);
! 206: return Q;
! 207: }
! 208:
! 209: /* SYC primary decomositions */
! 210:
! 211: def syc_dec(B,V)
! 212: {
! 213: if ( type(SI=getopt(si)) == -1 ) SI = 2;
! 214: SIFList=[noro_pd.find_ssi0, noro_pd.find_ssi1, noro_pd.find_ssi2];
! 215: if ( SI<0 || SI>2 ) error("sycb_dec : si should be 0,1,2");
! 216: SIF = SIFList[SI];
! 217:
! 218: if ( type(MaxLevel=getopt(level)) == -1 ) MaxLevel = -1;
! 219: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 220: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
! 221: if ( type(Time=getopt(time)) == -1 ) Time = 0;
! 222: if ( type(Iso=getopt(iso)) == -1 ) Iso = 0;
! 223: if ( type(Colon=getopt(colon)) == -1 ) Colon = 1;
! 224: Ord = 0;
! 225: Tall = time();
! 226: C = Gt = G = fast_gb(B,V,Mod,Ord|trace=1);
! 227: Q = []; IntQ = [1]; First = 1;
! 228: Tpd = Tiso = Tsep = 0;
! 229: RTpd = RTiso = RTsep = 0;
! 230: for ( Level = 0; MaxLevel < 0 || Level <= MaxLevel; Level++ ) {
! 231: if ( type(Gt[0])==1 ) break;
! 232: T3 = T2 = T1 = T0 = time();
! 233: if ( First ) {
! 234: PtR = prime_dec(C,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1);
! 235: Pt = PtR[0]; IntPt = PtR[1];
! 236: if ( gen_gb_comp(Gt,IntPt,Mod) ) {
! 237: /* Gt is radical and Gt = cap Pt */
! 238: for ( T = Pt, Qt = []; T != []; T = cdr(T) )
! 239: Qt = cons([car(T)[0],car(T)[0]],Qt);
! 240: return append(Q,[Qt]);
! 241: }
! 242: }
! 243: T1 = time(); Tpd += (T1[0]-T0[0])+(T1[1]-T0[1]); RTpd += (T1[3]-T0[3]);
! 244: Qt = iso_comp(Gt,Pt,V,Ord|mod=Mod,first=First,iso=Iso);
! 245: Q = append(Q,[Qt]);
! 246: for ( T = Qt; T != []; T = cdr(T) )
! 247: IntQ = ideal_intersection(IntQ,car(T)[0],V,Ord
! 248: |mod=Mod,
! 249: gbblock=[[0,length(IntQ)],[length(IntQ),length(car(T)[0])]]);
! 250: if ( First ) { IntP = IntPt; First = 0; }
! 251: if ( gen_gb_comp(IntQ,G,Mod) ) break;
! 252:
! 253: M = mingen(IntQ,V);
! 254: for ( Pt = [], C = [1], T = M; T != []; T = cdr(T) ) {
! 255: Ci = colon(G,car(T),V|isgb=1);
! 256: if ( type(Ci[0]) != 1 ) {
! 257: Pi = prime_dec(Ci,V|indep=1,lexdec=Lexdec,radical=1,mod=Mod);
! 258: C = ideal_intersection(C,Pi[1],V,Ord);
! 259: Pt = append(Pt,Pi[0]);
! 260: }
! 261: }
! 262: Pt = pd_simp_comp(Pt,V|first=1,mod=Mod);
! 263: if ( Colon ) C = ideal_colon(G,IntQ,V|mod=Mod);
! 264: T2 = time(); Tiso += (T2[0]-T1[0])+(T2[1]-T1[1]); RTiso += (T2[3]-T1[3]);
! 265: Ok = (*SIF)(C,G,IntQ,IntP,V,Ord|mod=Mod);
! 266: Gt = append(Ok,G);
! 267: T3 = time(); Tsep += (T3[0]-T2[0])+(T3[1]-T2[1]); RTsep += (T3[3]-T2[3]);
! 268: }
! 269: T4 = time(); RTall = (T4[3]-Tall[3]); Tall = (T4[0]-Tall[0])+(T3[1]-Tall[1]);
! 270: if ( Time ) {
! 271: print(["cpu","total",Tall,"pd",Tpd,"iso",Tiso,"sep",Tsep]);
! 272: print(["elapsed","total",RTall,"pd",RTpd,"iso",RTiso,"sep",RTsep]);
! 273: }
! 274: return Q;
! 275: }
! 276:
! 277: static Tint2, RTint2$
! 278:
! 279: def syci_dec(B,V)
! 280: {
! 281: if ( type(SI=getopt(si)) == -1 ) SI = 1;
! 282: if ( SI<0 || SI>2 ) error("sycb_assdec : si should be 0,1,2");
! 283: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 284: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
! 285: if ( type(Time=getopt(time)) == -1 ) Time = 0;
! 286: if ( type(Iso=getopt(iso)) == -1 ) Iso = 0;
! 287: if ( type(Ass=getopt(ass)) == -1 ) Ass = 0;
! 288: if ( type(Colon=getopt(colon)) == -1 ) Colon = 0;
! 289: if ( type(Para=getopt(para)) == -1 ) Para = 0;
! 290: if ( type(Trace=getopt(trace)) == -1 ) Trace = 0;
! 291: Ord = 0;
! 292: Tiso = Tint = Tpd = Text = Tint2 = 0;
! 293: RTiso = RTint = RTpd = RText = RTint2 = 0;
! 294: T00 = time();
! 295: G = fast_gb(B,V,Mod,Ord|trace=Trace);
! 296: IntQ = [1]; QL = RL = []; First = 1;
! 297: for ( Level = 0; ; Level++ ) {
! 298: T0 = time();
! 299: if ( !Level ) {
! 300: PtR = prime_dec(G,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1);
! 301: ACCUM_TIME(Tfpd,RTfpd)
! 302: Pt = PtR[0]; IntPt = PtR[1]; Rad = IntPt;
! 303: if ( gen_gb_comp(G,Rad,Mod) ) {
! 304: /* Gt is radical and Gt = cap Pt */
! 305: for ( T = Pt, Qt = []; T != []; T = cdr(T) )
! 306: Qt = cons([car(T)[0],car(T)[0],car(T)[1]],Qt);
! 307: return [reverse(Qt)];
! 308: }
! 309: } else
! 310: Pt = colon_prime_dec(G,IntQ,V|lexdec=Lexdec,mod=Mod,para=Para);
! 311: ACCUM_TIME(Tpd,RTpd)
! 312: T0 = time();
! 313: Rt = iso_comp(G,Pt,V,Ord|mod=Mod,iso=Iso,para=Para,intq=IntQ);
! 314: ACCUM_TIME(Tiso,RTiso)
! 315: if ( !Level ) {
! 316: if ( Iso == 3 ) {
! 317: NI = length(Rt);
! 318: Q = IntQ;
! 319: T0 = time();
! 320: if ( Para ) {
! 321: for ( J = 0, Task = []; J < NI; J++ ) {
! 322: T = ["noro_pd.extract_qj",Q,V,Rt[J],Rad,Mod,SI,Colon,-1];
! 323: Task = cons(T,Task);
! 324: }
! 325: Task = reverse(Task);
! 326: print("comps:",2); print(length(Task),2);
! 327: Rt = para_exec(Para,Task);
! 328: } else {
! 329: for ( J = 0, T = []; J < NI; J++ ) {
! 330: TJ = extract_qj(Q,V,Rt[J],Rad,Mod,SI,Colon,-1);
! 331: T = cons(TJ,T);
! 332: }
! 333: Rt = reverse(T);
! 334: }
! 335: ACCUM_TIME(Text,RText)
! 336: }
! 337: print("");
! 338: T0 = time();
! 339: Int = Rad;
! 340: for ( T = Rt; T != []; T = cdr(T) )
! 341: if ( !gb_comp(car(T)[0],car(T)[1]) )
! 342: Int = ideal_intersection_m(Int,car(T)[0],V,Ord|mod=Mod);
! 343: IntQ = nd_gr(Int,V,Mod,Ord);
! 344: ACCUM_TIME(Tint,RTint)
! 345: RL = append(RL,[Rt]);
! 346: } else if ( Iso != 3 ) {
! 347: T0 = time();
! 348: IntQ = ideal_list_intersection(map(first,Rt),V,Ord|mod=Mod,isgb=1);
! 349: RL = append(RL,[Rt]);
! 350: ACCUM_TIME(Tint,RTint)
! 351: } else {
! 352: NI = length(Rt);
! 353: Q = IntQ;
! 354: if ( Para ) {
! 355: for ( J = 0, Task = []; J < NI; J++ ) {
! 356: T = ["noro_pd.extract_qj",Q,V,Rt[J],Rad,Mod,SI,Colon,-1];
! 357: Task = cons(T,Task);
! 358: }
! 359: Task = reverse(Task);
! 360: print("comps:",2); print(length(Task),2);
! 361: T0 = time();
! 362: R = para_exec(Para,Task);
! 363: ACCUM_TIME(Text,RText)
! 364: print("");
! 365: T0 = time();
! 366: IntQ = ideal_list_intersection(cons(IntQ,map(first,R)),V,Ord|mod=Mod);
! 367: ACCUM_TIME(Tint,RTint)
! 368: RL = append(RL,[R]);
! 369: } else {
! 370: for ( J = 0, T = []; J < NI; J++ ) {
! 371: T0 = time();
! 372: TJ = extract_qj(Q,V,Rt[J],Rad,Mod,SI,Colon,-1);
! 373: ACCUM_TIME(Text,RText)
! 374: T = cons(TJ,T);
! 375: T0 = time();
! 376: IntQ = ideal_intersection_m(IntQ,TJ[0],V,Ord|mod=Mod);
! 377: ACCUM_TIME(Tint,RTint)
! 378: }
! 379: print("");
! 380: T0 = time();
! 381: IntQ = nd_gr(IntQ,V,Mod,Ord);
! 382: ACCUM_TIME(Tint,RTint)
! 383: T = reverse(T); RL = append(RL,[T]);
! 384: }
! 385: }
! 386: QL = append(QL,[IntQ]);
! 387: if ( gen_gb_comp(IntQ,G,Mod) ) break;
! 388: }
! 389: T0 = time();
! 390: if ( Iso != 3 && !Ass )
! 391: RL = extract_comp(QL,RL,V,Rad|mod=Mod,para=Para,si=SI,colon=Colon,ass=Ass);
! 392: ACCUM_TIME(Text,RText)
! 393: if ( Time ) {
! 394: T1 = time();
! 395: Tall = T1[0]-T00[0]+T1[1]-T00[1]; RTall += T1[3]-T00[3];
! 396: Tass = Tall-Text; RTass = RTall-RText;
! 397: print(["total",Tall,"ass",Tass,"pd",Tpd,"(fpd)",Tfpd,"iso",Tiso,"int",Tint,"ext",Text]);
! 398: print(["elapsed",RTall,"ass",RTass,"pd",RTpd,"(fpd)",RTfpd,"iso",RTiso,"int",RTint,"ext",RText]);
! 399: }
! 400: return RL;
! 401: }
! 402:
! 403: def extract_comp(QL,RL,V,Rad) {
! 404: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 405: if ( type(Para=getopt(para)) == -1 ) Para = 0;
! 406: if ( type(Colon=getopt(colon)) == -1 ) Colon = 0;
! 407: if ( type(SI=getopt(si)) == -1 ) SI = 1;
! 408: if ( type(Ass=getopt(ass)) == -1 ) Ass = 0;
! 409:
! 410: L = length(QL);
! 411: if ( Para ) {
! 412: for ( Task = [], I = 1; I < L; I++ ) {
! 413: QI = QL[I-1]; RI = RL[I]; NI = length(RI);
! 414: for ( J = 0, TI = []; J < NI; J++ ) {
! 415: T = ["noro_pd.extract_qj",QI,V,RI[J],Rad,Mod,SI,Colon,I];
! 416: Task = cons(T,Task);
! 417: }
! 418: }
! 419: Task = reverse(Task);
! 420: print("comps:",2); print(length(Task),2); print("");
! 421: R = para_exec(Para,Task);
! 422: S = vector(L);
! 423: for ( I = 1; I < L; I++ ) S[I] = [];
! 424: S[0] = RL[0];
! 425: for ( T = R; T != []; T = cdr(T) ) {
! 426: U = car(T); Level = U[0]; Body = U[1];
! 427: S[Level] = cons(Body,S[Level]);
! 428: }
! 429: return vtol(S);
! 430: } else {
! 431: TL = [RL[0]];
! 432: for ( I = 1; I < L; I++ ) {
! 433: print("level:",2); print(I,2);
! 434: print(" comps:",2); print(length(RL[I]),2); print("");
! 435: QI = QL[I-1]; RI = RL[I]; NI = length(RI);
! 436: for ( J = 0, TI = []; J < NI; J++ ) {
! 437: TIJ = extract_qj(QI,V,RI[J],Rad,Mod,SI,Colon,-1);
! 438: TI = cons(TIJ,TI);
! 439: }
! 440: TI = reverse(TI); TL = cons(TI,TL);
! 441: }
! 442: TL = reverse(TL);
! 443: }
! 444: return TL;
! 445: }
! 446:
! 447: def colon_prime_dec(G,IntQ,V) {
! 448: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 449: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
! 450: if ( type(Para=getopt(para)) == -1 ) Para = 0;
! 451: if ( !Para ) {
! 452: print("colon_pd:",2); print(length(IntQ),2);
! 453: }
! 454: if ( !Mod ) M = mingen(IntQ,V);
! 455: else M = IntQ;
! 456: if ( Para ) {
! 457: L = length(M);
! 458: for ( Task = [], J = 0; J < L; J++ )
! 459: if ( gen_nf(M[J],G,V,Ord,Mod) ) {
! 460: T = ["noro_pd.call_colon",G,M[J],V,Mod,1];
! 461: Task = cons(T,Task);
! 462: }
! 463: Task = reverse(Task);
! 464: R = para_exec(Para,Task);
! 465: R = pd_simp_comp(R,V|mod=Mod); L = length(R);
! 466:
! 467: for ( Task = [], J = 0; J < L; J++ ) {
! 468: T = ["noro_pd.call_prime_dec",R[J],V,1,Lexdec,Mod];
! 469: Task = cons(T,Task);
! 470: }
! 471: Task = reverse(Task);
! 472: R = para_exec(Para,Task);
! 473:
! 474: for ( Pt = [], T = R; T != []; T = cdr(T) ) Pt = append(Pt,car(T));
! 475: } else {
! 476: for ( R = [], T = M; T != []; T = cdr(T) ) {
! 477: Ci = colon(G,car(T),V|isgb=1,mod=Mod);
! 478: R = cons(Ci,R);
! 479: }
! 480: print("->",2); print(length(M),2);
! 481: R = pd_simp_comp(R,V|mod=Mod);
! 482: print("->",2); print(length(R));
! 483: #if 1
! 484: for ( Pt = [], T = R; T != []; T = cdr(T) ) {
! 485: Pi = prime_dec(car(T),V|indep=1,lexdec=Lexdec,mod=Mod);
! 486: Pt = append(Pt,Pi);
! 487: }
! 488: #else
! 489: J = ideal_list_intersection(R,V,0|mod=Mod);
! 490: Pt = prime_dec(J,V|indep=1,lexdec=Lexdec,mod=Mod);
! 491: #endif
! 492: }
! 493: #if 1
! 494: Pt = pd_simp_comp(Pt,V|first=1,mod=Mod);
! 495: #endif
! 496: return Pt;
! 497: }
! 498:
! 499: def call_colon(G,F,V,Mod,IsGB)
! 500: {
! 501: return colon(G,F,V|isgb=1,mod=Mod);
! 502: }
! 503:
! 504: def call_prime_dec(G,V,Indep,Lexdec,Mod)
! 505: {
! 506: if ( type(G[0]) != 1 )
! 507: Pi = prime_dec(G,V|indep=Indep,lexdec=Lexdec,mod=Mod);
! 508: else
! 509: Pi = [];
! 510: return Pi;
! 511: }
! 512:
! 513: def extract_qj(Q,V,QL,Rad,Mod,SI,Colon,Level)
! 514: {
! 515: SIFList=[noro_pd.find_ssi0, noro_pd.find_ssi1, noro_pd.find_ssi2];
! 516: SIF = SIFList[SI];
! 517: G = QL[0]; P = QL[1]; PV = QL[2];
! 518: if ( Q != [1] ) {
! 519: C = Colon ? ideal_colon(G,Q,V|mod=Mod) : P;
! 520: Ok = (*SIF)(C,G,Q,Rad,V,0|mod=Mod);
! 521: } else
! 522: Ok = [];
! 523: V0 = setminus(V,PV);
! 524: HJ = elim_gb(append(Ok,G),V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
! 525: HJ = contraction(HJ,V0|mod=Mod);
! 526: IJ = nd_gr(HJ,V,Mod,Ord);
! 527: return Level >= 0 ? [Level,[IJ,P]] : [IJ,P];
! 528: }
! 529:
! 530: def syca_dec(B,V)
! 531: {
! 532: T00 = time();
! 533: if ( type(SI=getopt(si)) == -1 ) SI = 2;
! 534: SIFList=[noro_pd.find_si0, noro_pd.find_si1, noro_pd.find_si2];
! 535: SIF = SIFList[SI];
! 536: if ( !SIF ) error("syca_dec : si should be 0,1,2");
! 537:
! 538: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 539: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
! 540: if ( type(NoSimp=getopt(nosimp)) == -1 ) NoSimp = 0;
! 541: if ( type(Time=getopt(time)) == -1 ) Time = 0;
! 542: if ( type(Iso=getopt(iso)) == -1 ) Iso = 0;
! 543: Ord = 0;
! 544: Gt = G0 = G = fast_gb(B,V,Mod,Ord|trace=1);
! 545: Q0 = Q = []; IntQ0 = IntQ = [1]; First = 1;
! 546: C = 0;
! 547:
! 548: Tass = Tiso = Tcolon = Tsep = Tirred = 0;
! 549: Rass = Riso = Rcolon = Rsep = Rirred = 0;
! 550: while ( 1 ) {
! 551: if ( type(Gt[0])==1 ) break;
! 552: T0 = time();
! 553: PtR = prime_dec(Gt,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1);
! 554: T1 = time(); Tass += T1[0]-T0[0]+T1[1]-T0[1]; Rass += T1[3]-T0[3];
! 555: Pt = PtR[0]; IntPt = PtR[1];
! 556: if ( gen_gb_comp(Gt,IntPt,Mod) ) {
! 557: /* Gt is radical and Gt = cap Pt */
! 558: for ( T = Pt, Qt = []; T != []; T = cdr(T) )
! 559: Qt = cons([car(T)[0],car(T)[0]],Qt);
! 560: if ( First )
! 561: return [Qt,[]];
! 562: else
! 563: Q0 = append(Qt,Q0);
! 564: break;
! 565: }
! 566: T0 = time();
! 567: Qt = iso_comp(Gt,Pt,V,Ord|mod=Mod,isgb=1,iso=Iso);
! 568: T1 = time(); Tiso += T1[0]-T0[0]+T1[1]-T0[1]; Riso += T1[3]-T0[3];
! 569: IntQt = ideal_list_intersection(map(first,Qt),V,Ord|mod=Mod);
! 570: if ( First ) {
! 571: IntQ0 = IntQ = IntQt; IntP = IntPt; Qi = Qt; First = 0;
! 572: } else {
! 573: IntQ1 = ideal_intersection(IntQ,IntQt,V,Ord|mod=Mod);
! 574: if ( gen_gb_comp(IntQ,IntQ1,Mod) ) {
! 575: G = Gt; IntP = IntPt; Q = []; IntQ = [1]; C = 0;
! 576: continue;
! 577: } else {
! 578: IntQ = IntQ1;
! 579: IntQ1 = ideal_intersection(IntQ0,IntQt,V,Ord|mod=Mod);
! 580: if ( !gen_gb_comp(IntQ0,IntQ1,Mod) ) {
! 581: Q = append(Qt,Q);
! 582: for ( T = Qt; T != []; T = cdr(T) )
! 583: if ( !ideal_inclusion(IntQ0,car(T)[0],V,Ord|mod=Mod) )
! 584: Q0 = append(Q0,[car(T)]);
! 585: IntQ0 = IntQ1;
! 586: }
! 587: }
! 588: }
! 589: if ( gen_gb_comp(IntQt,Gt,Mod) || gen_gb_comp(IntQ,G,Mod) || gen_gb_comp(IntQ0,G0,Mod) ) break;
! 590: T0 = time();
! 591: C1 = ideal_colon(G,IntQ,V|mod=Mod);
! 592: T1 = time(); Tcolon += T1[0]-T0[0]+T1[1]-T0[1]; Rcolon += T1[3]-T0[3];
! 593: if ( C && gen_gb_comp(C,C1,Mod) ) {
! 594: G = Gt; IntP = IntPt; Q = []; IntQ = [1]; C = 0;
! 595: continue;
! 596: } else C = C1;
! 597: T0 = time();
! 598: Ok = (*SIF)(C,G,IntQ,IntP,V,Ord|mod=Mod);
! 599: G1 = append(Ok,G);
! 600: Gt1 = incremental_gb(G1,V,Ord|mod=Mod);
! 601: T1 = time(); Tsep += T1[0]-T0[0]+T1[1]-T0[1]; Rsep += T1[3]-T0[3];
! 602: Gt = Gt1;
! 603: }
! 604: T0 = time();
! 605: if ( !NoSimp ) Q1 = qd_remove_redundant_comp(G0,Qi,Q0,V,Ord|mod=Mod);
! 606: else Q1 = Q0;
! 607: if ( Time ) {
! 608: T1 = time(); Tirred += T1[0]-T0[0]+T1[1]-T0[1]; Rirred += T1[3]-T0[3];
! 609: Tall = T1[0]-T00[0]+T1[1]-T00[1]; Rall += T1[3]-T00[3];
! 610: print(["total",Tall,"ass",Tass,"iso",Tiso, "colon",Tcolon,"sep",Tsep,"irred",Tirred]);
! 611: print(["Rtotal",Rall,"Rass",Rass,"Riso",Riso, "Rcolon",Rcolon,"Rsep",Rsep,"Rirred",Rirred]);
! 612: print(["iso",length(Qi),"emb",length(Q0),"->",length(Q1)]);
! 613: }
! 614: return [Qi,Q1];
! 615: }
! 616:
! 617: def syc0_dec(B,V)
! 618: {
! 619: T00 = time();
! 620: if ( type(SI=getopt(si)) == -1 ) SI = 1;
! 621: SIFList=[noro_pd.find_si0, noro_pd.find_si1, noro_pd.find_si2, noro_pd.find_ssi0, noro_pd.find_ssi1, noro_pd.find_ssi2];
! 622: SIF = SIFList[SI];
! 623: if ( !SIF ) error("syc0_dec : si should be 0,1,2");
! 624: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 625: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
! 626: if ( type(NoSimp=getopt(nosimp)) == -1 ) NoSimp = 0;
! 627: if ( type(Time=getopt(time)) == -1 ) Time = 0;
! 628: Ord = 0;
! 629: G = fast_gb(B,V,Mod,Ord);
! 630: Q = []; IntQ = [1]; Gt = G; First = 1;
! 631: Tass = Tiso = Tcolon = Tsep = Tirred = 0;
! 632: Rass = Riso = Rcolon = Rsep = Rirred = 0;
! 633: while ( 1 ) {
! 634: if ( type(Gt[0])==1 ) break;
! 635: T0 = time();
! 636: PtR = prime_dec(Gt,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1);
! 637: T1 = time(); Tass += T1[0]-T0[0]+T1[1]-T0[1]; Rass += T1[3]-T0[3];
! 638: Pt = PtR[0]; IntPt = PtR[1];
! 639: if ( gen_gb_comp(Gt,IntPt,Mod) ) {
! 640: /* Gt is radical and Gt = cap Pt */
! 641: for ( T = Pt, Qt = []; T != []; T = cdr(T) )
! 642: Qt = cons([car(T)[0],car(T)[0]],Qt);
! 643: if ( First )
! 644: return [Qt,[]];
! 645: else
! 646: Q = append(Qt,Q);
! 647: break;
! 648: }
! 649:
! 650: T0 = time();
! 651: Qt = iso_comp(Gt,Pt,V,Ord|mod=Mod,isgb=1);
! 652: T1 = time(); Tiso += T1[0]-T0[0]+T1[1]-T0[1]; Riso += T1[3]-T0[3];
! 653: IntQt = ideal_list_intersection(map(first,Qt),V,Ord|mod=Mod);
! 654: if ( First ) {
! 655: IntQ = IntQt; Qi = Qt; First = 0;
! 656: } else {
! 657: IntQ1 = ideal_intersection(IntQ,IntQt,V,Ord|mod=Mod);
! 658: if ( !gen_gb_comp(IntQ1,IntQ,Mod) )
! 659: Q = append(Qt,Q);
! 660: }
! 661: if ( gen_gb_comp(IntQ,G,Mod) || gen_gb_comp(IntQt,Gt,Mod) )
! 662: break;
! 663: T0 = time();
! 664: C = ideal_colon(Gt,IntQt,V|mod=Mod);
! 665: T1 = time(); Tcolon += T1[0]-T0[0]+T1[1]-T0[1]; Rcolon += T1[3]-T0[3];
! 666: T0 = time();
! 667: Ok = (*SIF)(C,Gt,IntQt,IntPt,V,Ord|mod=Mod);
! 668: G1 = append(Ok,Gt);
! 669: Gt = incremental_gb(G1,V,Ord|mod=Mod);
! 670: T1 = time(); Tsep += T1[0]-T0[0]+T1[1]-T0[1]; Rsep += T1[3]-T0[3];
! 671: }
! 672: T0 = time();
! 673: if ( !NoSimp ) Q1 = qd_remove_redundant_comp(G,Qi,Q,V,Ord|mod=Mod);
! 674: else Q1 = Q;
! 675: T1 = time(); Tirred += T1[0]-T0[0]+T1[1]-T0[1]; Rirred += T1[3]-T0[3];
! 676: Tall = T1[0]-T00[0]+T1[1]-T00[1]; Rall += T1[3]-T00[3];
! 677: if ( Time ) {
! 678: print(["total",Tall,"ass",Tass,"iso",Tiso, "colon",Tcolon,"sep",Tsep,"irred",Tirred]);
! 679: print(["Rtotal",Rall,"Rass",Rass,"Riso",Riso, "Rcolon",Rcolon,"Rsep",Rsep,"Rirred",Rirred]);
! 680: print(["iso",length(Qi),"emb",length(Q),"->",length(Q1)]);
! 681: }
! 682: return [Qi,Q1];
! 683: }
! 684:
! 685: def power(A,I) { return A^I; }
! 686:
! 687:
! 688: /* functions for computating a separing ideal */
! 689: /* C=G:Q, Rad=rad(Q), return J s.t. Q cap (G+J) = G */
! 690:
! 691: def find_si0(C,G,Q,Rad,V,Ord) {
! 692: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 693: for ( CI = C, I = 1; ; I++ ) {
! 694: for ( T = CI, S = []; T != []; T = cdr(T) )
! 695: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
! 696: if ( S == [] )
! 697: error("find_si0 : cannot happen");
! 698: G1 = append(S,G);
! 699: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
! 700: /* check whether (Q cap (G+S)) = G */
! 701: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
! 702: CI = ideal_product(CI,C,V|mod=Mod);
! 703: }
! 704: }
! 705:
! 706: def find_si1(C,G,Q,Rad,V,Ord) {
! 707: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 708: for ( T = C, S = []; T != []; T = cdr(T) )
! 709: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
! 710: if ( S == [] )
! 711: error("find_si1 : cannot happen");
! 712: G1 = append(S,G);
! 713: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
! 714: /* check whether (Q cap (G+S)) = G */
! 715: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
! 716:
! 717: C = qsort(C,noro_pd.comp_tdeg);
! 718:
! 719: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
! 720: Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
! 721: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
! 722: Dp = dp_gr_print(); dp_gr_print(0);
! 723: for ( T = C, S = []; T != []; T = cdr(T) ) {
! 724: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
! 725: Ui = U = car(T);
! 726: for ( I = 1; ; I++ ) {
! 727: G1 = cons(Ui,G);
! 728: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
! 729: if ( gen_gb_comp(Int,G,Mod) ) break;
! 730: else
! 731: Ui = gen_nf(Ui*U,G,V,Ord,Mod);
! 732: }
! 733: print([length(T),I],2);
! 734: Int1 = incremental_gb(append(Int0,[Tmp*Ui]),TV,Ord1
! 735: |gbblock=[[0,length(Int0)]],mod=Mod);
! 736: Int = elimination(Int1,V);
! 737: if ( !gen_gb_comp(Int,G,Mod) ) {
! 738: break;
! 739: } else {
! 740: Int0 = Int1;
! 741: S = cons(Ui,S);
! 742: }
! 743: }
! 744: print("");
! 745: dp_gr_print(Dp);
! 746: return reverse(S);
! 747: }
! 748:
! 749: def find_si2(C,G,Q,Rad,V,Ord) {
! 750: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 751: for ( T = C, S = []; T != []; T = cdr(T) )
! 752: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
! 753: if ( S == [] )
! 754: error("find_si2 : cannot happen");
! 755: G1 = append(S,G);
! 756: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
! 757: /* check whether (Q cap (G+S)) = G */
! 758: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
! 759:
! 760: C = qsort(C,noro_pd.comp_tdeg);
! 761:
! 762: Dp = dp_gr_print(); dp_gr_print(0);
! 763: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
! 764: Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
! 765: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
! 766: for ( T = C, S = []; T != []; T = cdr(T) ) {
! 767: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
! 768: Ui = U = car(T);
! 769: for ( I = 1; ; I++ ) {
! 770: Int1 = incremental_gb(append(Int0,[Tmp*Ui]),TV,Ord1
! 771: |gbblock=[[0,length(Int0)]],mod=Mod);
! 772: Int = elimination(Int1,V);
! 773: if ( gen_gb_comp(Int,G,Mod) ) break;
! 774: else
! 775: Ui = gen_nf(Ui*U,G,V,Ord,Mod);
! 776: }
! 777: print([length(T),I],2);
! 778: S = cons(Ui,S);
! 779: }
! 780: S = qsort(S,noro_pd.comp_tdeg);
! 781: print("");
! 782: End = Len = length(S);
! 783:
! 784: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
! 785: Prev = 1;
! 786: G1 = append(G,[S[0]]);
! 787: Int0 = incremental_gb(append(vtol(ltov(G1)*Tmp),vtol(ltov(Q)*(1-Tmp))),
! 788: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
! 789: if ( End > 1 ) {
! 790: Cur = 2;
! 791: while ( Prev < Cur ) {
! 792: for ( St = [], I = Prev; I < Cur; I++ ) St = cons(Tmp*S[I],St);
! 793: Int1 = incremental_gb(append(Int0,St),TV,Ord1
! 794: |gbblock=[[0,length(Int0)]],mod=Mod);
! 795: Int = elimination(Int1,V);
! 796: if ( gen_gb_comp(Int,G,Mod) ) {
! 797: print([Cur],2);
! 798: Prev = Cur;
! 799: Cur = Cur+idiv(End-Cur+1,2);
! 800: Int0 = Int1;
! 801: } else {
! 802: End = Cur;
! 803: Cur = Prev + idiv(Cur-Prev,2);
! 804: }
! 805: }
! 806: for ( St = [], I = 0; I < Prev; I++ ) St = cons(S[I],St);
! 807: } else
! 808: St = [S[0]];
! 809: print("");
! 810: for ( I = Prev; I < Len; I++ ) {
! 811: Int1 = incremental_gb(append(Int0,[Tmp*S[I]]),TV,Ord1
! 812: |gbblock=[[0,length(Int0)]],mod=Mod);
! 813: Int = elimination(Int1,V);
! 814: if ( gen_gb_comp(Int,G,Mod) ) {
! 815: print([I],2);
! 816: St = cons(S[I],St);
! 817: Int0 = Int1;
! 818: }
! 819: }
! 820: Ok = reverse(St);
! 821: print("");
! 822: print([length(S),length(Ok)]);
! 823: dp_gr_print(Dp);
! 824: return Ok;
! 825: }
! 826:
! 827: /* functions for computing a saturated separating ideal */
! 828:
! 829: def find_ssi0(C,G,Q,Rad,V,Ord) {
! 830: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 831: if ( type(Reduce=getopt(red)) == -1 ) Reduce = 0;
! 832: for ( T = C, S = []; T != []; T = cdr(T) )
! 833: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
! 834: if ( S == [] )
! 835: error("find_ssi0 : cannot happen");
! 836: G1 = append(S,G);
! 837: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
! 838: /* check whether (Q cap (G+S)) = G */
! 839: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
! 840:
! 841: if ( Reduce ) {
! 842: for ( T = C, U = []; T != []; T = cdr(T) )
! 843: if ( gen_nf(car(T),Rad,V,Ord,Mod) ) U = cons(car(T),U);
! 844: U = reverse(U);
! 845: } else
! 846: U = C;
! 847:
! 848: for ( I = 1; ; I++ ) {
! 849: print([I],2);
! 850: S = map(power,U,I);
! 851: G1 = append(S,G);
! 852: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
! 853: /* check whether (Q cap (G+S)) = G */
! 854: if ( gen_gb_comp(Int,G,Mod) ) { print(""); return reverse(S); }
! 855: }
! 856: }
! 857:
! 858: def find_ssi1(C,G,Q,Rad,V,Ord) {
! 859: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 860: if ( type(Reduce=getopt(red)) == -1 ) Reduce = 0;
! 861: for ( T = C, S = []; T != []; T = cdr(T) )
! 862: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
! 863: if ( S == [] )
! 864: error("find_ssi1 : cannot happen");
! 865: G1 = append(S,G);
! 866: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
! 867: /* check whether (Q cap (G+S)) = G */
! 868: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
! 869:
! 870: dp_ord(Ord); DC = map(dp_ptod,C,V);
! 871: DC = qsort(DC,noro_pd.comp_tord); C = map(dp_dtop,DC,V);
! 872: print(length(C),2);
! 873: if ( Reduce ) {
! 874: SC = map(sq,C,Mod);
! 875: SC = reverse(SC); C = reverse(C);
! 876: for ( T = C, C1 = [], R1 = append(SC,Rad); T != []; T = cdr(T) ) {
! 877: R0 = car(R1); R1 = cdr(R1);
! 878: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
! 879: if ( radical_membership(R0,R1,V|mod=Mod) ) {
! 880: C1 = cons(car(T),C1);
! 881: R1 = append(R1,[R0]);
! 882: }
! 883: }
! 884: print("->",0); print(length(C1),2);
! 885: C = C1;
! 886: }
! 887: print(" ",2);
! 888:
! 889: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
! 890: Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
! 891: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
! 892: Dp = dp_gr_print(); dp_gr_print(0);
! 893: for ( J = 0, T = C, S = [], GS = G; T != []; T = cdr(T), J++ ) {
! 894: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
! 895: Ui = U = car(T);
! 896: for ( I = 1; ; I++ ) {
! 897: Int1 = nd_gr(append(Int0,[Tmp*Ui]),TV,Mod,Ord1
! 898: |gbblock=[[0,length(Int0)]],newelim=1);
! 899: if ( Int1 ) {
! 900: Int = elimination(Int1,V);
! 901: if ( gen_gb_comp(Int,G,Mod) ) break;
! 902: }
! 903: print("x",2);
! 904: Ui = gen_nf(Ui*U,G,V,Ord,Mod);
! 905: }
! 906: print(J,2);
! 907: Int0 = Int1;
! 908: S = cons(Ui,S);
! 909: }
! 910: print("");
! 911: dp_gr_print(Dp);
! 912: return reverse(S);
! 913: }
! 914:
! 915: def find_ssi2(C,G,Q,Rad,V,Ord) {
! 916: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 917: if ( type(Reduce=getopt(red)) == -1 ) Reduce = 0;
! 918: for ( T = C, S = []; T != []; T = cdr(T) )
! 919: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
! 920: if ( S == [] )
! 921: error("find_ssi2 : cannot happen");
! 922: G1 = append(S,G);
! 923: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
! 924: /* check whether (Q cap (G+S)) = G */
! 925: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
! 926:
! 927: #if 0
! 928: dp_ord(Ord); DC = map(dp_ptod,C,V);
! 929: DC = qsort(DC,noro_pd.comp_tord); C = map(dp_dtop,DC,V);
! 930: #else
! 931: C = qsort(C,noro_pd.comp_tdeg);
! 932: #endif
! 933: if ( Reduce ) {
! 934: for ( T = C, C1 = [], R1 = Rad; T != []; T = cdr(T) ) {
! 935: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
! 936: if ( radical_membership(car(T),R1,V|mod=Mod) ) {
! 937: C1 = cons(car(T),C1);
! 938: R1 = cons(sq(car(T),Mod),R1);
! 939: }
! 940: }
! 941: print(["C",length(C),"->",length(C1)]);
! 942: C = reverse(C1);
! 943: }
! 944: for ( T = C, S = []; T != []; T = cdr(T) ) {
! 945: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
! 946: Ui = U = car(T);
! 947: S = cons([Ui,U],S);
! 948: }
! 949: S = qsort(S,noro_pd.comp_tdeg_first);
! 950: print("");
! 951:
! 952: Dp = dp_gr_print(); dp_gr_print(0);
! 953: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
! 954: Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
! 955: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
! 956: OK = [];
! 957: while ( S != [] ) {
! 958: Len = length(S); print("remaining gens : ",0); print(Len);
! 959: S1 = [];
! 960: for ( Start = Prev = 0; Start < Len; Start = Prev ) {
! 961: Cur = Start+1;
! 962: print(Start,2);
! 963: while ( Prev < Len ) {
! 964: for ( St = [], I = Prev; I < Cur; I++ ) St = cons(Tmp*S[I][0],St);
! 965: Int1 = nd_gr(append(Int0,St),TV,Mod,Ord1|gbblock=[[0,length(Int0)]],newelim=1);
! 966: if ( !Int1 ) {
! 967: print("x",0); break;
! 968: }
! 969: Int = elimination(Int1,V);
! 970: if ( gen_gb_comp(Int,G,Mod) ) {
! 971: print([Prev,Cur-1],2);
! 972: Prev = Cur;
! 973: Cur += (Prev-Start)+1;
! 974: if ( Cur > Len ) Cur = Len;
! 975: Int0 = Int1;
! 976: } else
! 977: break;
! 978: }
! 979: for ( I = Start; I < Prev; I++ ) OK = cons(S[I][0],OK);
! 980: if ( Prev == Start ) {
! 981: Ui = S[I][0]; U = S[I][1];
! 982: Ui = gen_nf(Ui*U,G,V,Ord,Mod);
! 983: S1 = cons([Ui,U],S1);
! 984: Prev++;
! 985: }
! 986: }
! 987: S = reverse(S1);
! 988: print("");
! 989: }
! 990: print("");
! 991: OK = reverse(OK);
! 992: dp_gr_print(Dp);
! 993: return OK;
! 994: }
! 995:
! 996: /* SY primary decompsition */
! 997:
! 998: def sy_dec(B,V)
! 999: {
! 1000: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1001: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
! 1002: Ord = 0;
! 1003: G = fast_gb(B,V,Mod,Ord);
! 1004: Q = [];
! 1005: IntQ = [1];
! 1006: Gt = G;
! 1007: First = 1;
! 1008: while ( 1 ) {
! 1009: if ( type(Gt[0]) == 1 ) break;
! 1010: Pt = prime_dec(Gt,V|indep=1,lexdec=Lexdec,mod=Mod);
! 1011: L = pseudo_dec(Gt,Pt,V,Ord|mod=Mod);
! 1012: Qt = L[0]; Rt = L[1]; St = L[2];
! 1013: IntQt = ideal_list_intersection(map(first,Qt),V,Ord|mod=Mod);
! 1014: if ( First ) {
! 1015: IntQ = IntQt;
! 1016: Qi = Qt;
! 1017: First = 0;
! 1018: } else {
! 1019: IntQ = ideal_intersection(IntQ,IntQt,V,Ord|mod=Mod);
! 1020: Q = append(Qt,Q);
! 1021: }
! 1022: if ( gen_gb_comp(IntQ,G,Mod) ) break;
! 1023: for ( T = Rt; T != []; T = cdr(T) ) {
! 1024: if ( type(car(T)[0]) == 1 ) continue;
! 1025: U = sy_dec(car(T),V|lexdec=Lexdec,mod=Mod);
! 1026: IntQ = ideal_list_intersection(cons(IntQ,map(first,U)),
! 1027: V,Ord|mod=Mod);
! 1028: Q = append(U,Q);
! 1029: if ( gen_gb_comp(IntQ,G,Mod) ) break;
! 1030: }
! 1031: Gt = fast_gb(append(Gt,St),V,Mod,Ord);
! 1032: }
! 1033: Q = qd_remove_redundant_comp(G,Qi,Q,V,Ord|mod=Mod);
! 1034: return append(Qi,Q);
! 1035: }
! 1036:
! 1037: def pseudo_dec(G,L,V,Ord)
! 1038: {
! 1039: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1040: N = length(L);
! 1041: S = vector(N);
! 1042: Q = vector(N);
! 1043: R = vector(N);
! 1044: L0 = map(first,L);
! 1045: for ( I = 0; I < N; I++ ) {
! 1046: LI = setminus(L0,[L0[I]]);
! 1047: PI = ideal_list_intersection(LI,V,Ord|mod=Mod);
! 1048: PI = qsort(PI,noro_pd.comp_tdeg);
! 1049: for ( T = PI; T != []; T = cdr(T) )
! 1050: if ( gen_nf(car(T),L0[I],V,Ord,Mod) ) break;
! 1051: if ( T == [] ) error("separator : cannot happen");
! 1052: SI = sat_ind(G,car(T),V|mod=Mod);
! 1053: QI = SI[0];
! 1054: S[I] = car(T)^SI[1];
! 1055: PV = L[I][1];
! 1056: V0 = setminus(V,PV);
! 1057: #if 0
! 1058: GI = fast_gb(QI,append(V0,PV),Mod,
! 1059: [[Ord,length(V0)],[Ord,length(PV)]]);
! 1060: #else
! 1061: GI = fast_gb(QI,append(V0,PV),Mod,
! 1062: [[2,length(V0)],[Ord,length(PV)]]);
! 1063: #endif
! 1064: LCFI = lcfactor(GI,V0,Ord,Mod);
! 1065: for ( F = 1, T = LCFI, Gt = QI; T != []; T = cdr(T) ) {
! 1066: St = sat_ind(Gt,T[0],V|mod=Mod);
! 1067: Gt = St[0]; F *= T[0]^St[1];
! 1068: }
! 1069: Q[I] = [Gt,L0[I]];
! 1070: R[I] = fast_gb(cons(F,QI),V,Mod,Ord);
! 1071: }
! 1072: return [vtol(Q),vtol(R),vtol(S)];
! 1073: }
! 1074:
! 1075: def iso_comp(G,L,V,Ord)
! 1076: {
! 1077: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1078: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
! 1079: if ( type(Iso=getopt(iso)) == -1 ) Iso = 0;
! 1080: if ( type(Para=getopt(para)) == -1 ) Para = 0;
! 1081: if ( type(Q=getopt(intq)) == -1 ) Q = 0;
! 1082: if ( type(S=getopt(sep)) == -1 ) S = 0;
! 1083:
! 1084: if ( !S ) S = separator(L,V|mod=Mod);
! 1085: N = length(L);
! 1086: print("comps : ",2); print(N); print("",2);
! 1087: if ( Para ) {
! 1088: Task = [];
! 1089: for ( I = 0; I < N; I++ ) {
! 1090: T = ["noro_pd.locsat",G,V,L[I],S[I],Mod,IsGB,Iso,Q];
! 1091: Task = cons(T,Task);
! 1092: }
! 1093: Task = reverse(Task);
! 1094: R = para_exec(Para,Task);
! 1095: return R;
! 1096: } else {
! 1097: for ( I = 0, R = []; I < N; I++ ) {
! 1098: QI = locsat(G,V,L[I],S[I],Mod,IsGB,Iso,Q);
! 1099: if ( type(QI[0][0])==1 )
! 1100: error("iso_comp : cannot happen");
! 1101: print(".",2);
! 1102: R = cons(QI,R);
! 1103: }
! 1104: print("");
! 1105: return reverse(R);
! 1106: }
! 1107: }
! 1108:
! 1109: def locsat(G,V,L,S,Mod,IsGB,Iso,Q)
! 1110: {
! 1111: P = L[0]; PV = L[1]; V0 = setminus(V,PV);
! 1112: if ( Iso==1 ) {
! 1113: QI = sat(G,S,V|isgb=IsGB,mod=Mod);
! 1114: GI = elim_gb(QI,V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
! 1115: GI = nd_gr(contraction(GI,V0|mod=Mod,allv=V),V,Mod,0);
! 1116: } else if ( Iso==0 ) {
! 1117: HI = elim_gb(G,V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
! 1118: GI = nd_gr(contraction(HI,V0|mod=Mod,allv=V),V,Mod,0);
! 1119: GI = sat(GI,S,V|isgb=IsGB,mod=Mod);
! 1120: } else if ( Iso==2 ) {
! 1121: HI = elim_gb(G,V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
! 1122: TV = ttttt;
! 1123: if ( Mod )
! 1124: GI = nd_gr(cons(TV*S-1,HI),cons(TV,V0),Mod,[[0,1],[0,length(V0)]]);
! 1125: else
! 1126: GI = nd_gr_trace(append(HI,[TV*S-1]),cons(TV,V0),
! 1127: 1,1,[[0,1],[0,length(V0)]]|gbblock=[[0,length(HI)]]);
! 1128: GI = elimination(GI,V);
! 1129: GI = nd_gr(contraction(GI,V0|mod=Mod,allv=V),V,Mod,0);
! 1130: } else if ( Iso==3 ) {
! 1131: GI = sat(G,S,V|isgb=IsGB,mod=Mod);
! 1132: }
! 1133: if ( Q )
! 1134: GI = ideal_intersection(Q,GI,V,0|mod=Mod);
! 1135: return [GI,P,PV];
! 1136: }
! 1137:
! 1138: /* GTZ primary decompsition */
! 1139:
! 1140: def prima_dec(B,V)
! 1141: {
! 1142: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1143: if ( type(Ord=getopt(ord)) == -1 ) Ord = 0;
! 1144: G0 = fast_gb(B,V,Mod,0);
! 1145: G = fast_gb(G0,V,Mod,Ord);
! 1146: IntP = [1];
! 1147: QD = [];
! 1148: while ( 1 ) {
! 1149: if ( type(G[0])==1 || ideal_inclusion(IntP,G0,V,0|mod=Mod) )
! 1150: break;
! 1151: W = maxindep(G,V,Ord); NP = length(W);
! 1152: V0 = setminus(V,W); N = length(V0);
! 1153: V1 = append(V0,W);
! 1154: G1 = fast_gb(G,V1,Mod,[[Ord,N],[Ord,NP]]);
! 1155: LCF = lcfactor(G1,V0,Ord,Mod);
! 1156: L = zprimacomp(G,V0|mod=Mod);
! 1157: F = 1;
! 1158: for ( T = LCF, G2 = G; T != []; T = cdr(T) ) {
! 1159: S = sat_ind(G2,T[0],V1|mod=Mod);
! 1160: G2 = S[0]; F *= T[0]^S[1];
! 1161: }
! 1162: for ( T = L, QL = []; T != []; T = cdr(T) )
! 1163: QL = cons(car(T)[0],QL);
! 1164: Int = ideal_list_intersection(QL,V,0|mod=Mod);
! 1165: IntP = ideal_intersection(IntP,Int,V,0|mod=Mod);
! 1166: QD = append(QD,L);
! 1167: F = gen_nf(F,G,V,0,Mod);
! 1168: G = fast_gb(cons(F,G),V,Mod,Ord);
! 1169: }
! 1170: QD = qd_remove_redundant_comp(G0,[],QD,V,0);
! 1171: return QD;
! 1172: }
! 1173:
! 1174: /* SL prime decomposition */
! 1175:
! 1176: def prime_dec(B,V)
! 1177: {
! 1178: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1179: if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
! 1180: if ( type(LexDec=getopt(lexdec)) == -1 ) LexDec = 0;
! 1181: if ( type(Rad=getopt(radical)) == -1 ) Rad = 0;
! 1182: B = map(sq,B,Mod);
! 1183: if ( LexDec )
! 1184: PD = lex_predec1(B,V|mod=Mod);
! 1185: else
! 1186: PD = [B];
! 1187: if ( length(PD) > 1 ) {
! 1188: G = ideal_list_intersection(PD,V,0|mod=Mod);
! 1189: PD = pd_remove_redundant_comp(G,PD,V,0|mod=Mod);
! 1190: }
! 1191: R = []; RL = [];
! 1192: for ( T = PD; T != []; T = cdr(T) ) {
! 1193: PDT = prime_dec_main(car(T),V|indep=Indep,mod=Mod);
! 1194: R = append(R,PDT[0]);
! 1195: GT = nd_gr(PDT[1],V,Mod,0);
! 1196: RL = append(RL,[GT]);
! 1197: }
! 1198: if ( LexDec ) R = pd_simp_comp(R,V|first=Indep,mod=Mod);
! 1199: if ( Rad ) {
! 1200: G = ideal_list_intersection(RL,V,0|mod=Mod);
! 1201: return [R,G];
! 1202: } else return R;
! 1203: }
! 1204:
! 1205: def prime_dec2(B,V)
! 1206: {
! 1207: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1208: if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
! 1209: if ( type(LexDec=getopt(lexdec)) == -1 ) LexDec = 0;
! 1210: if ( type(Rad=getopt(radical)) == -1 ) Rad = 0;
! 1211: if ( type(Para=getopt(para)) == -1 || type(Para) != 4 ) Para = [];
! 1212: B = map(sq,B,Mod);
! 1213: if ( LexDec )
! 1214: PD = lex_predec1(B,V|mod=Mod);
! 1215: else
! 1216: PD = [B];
! 1217: if ( length(PD) > 1 ) {
! 1218: G = ideal_list_intersection(PD,V,0|mod=Mod);
! 1219: PD = pd_remove_redundant_comp(G,PD,V,0|mod=Mod);
! 1220: }
! 1221: R = [];
! 1222: for ( T = PD; T != []; T = cdr(T) )
! 1223: R = append(prime_dec_main2(car(T),V|indep=Indep,mod=Mod,para=Para),R);
! 1224: if ( Indep ) {
! 1225: G = ideal_list_intersection(map(first,R),V,0|mod=Mod);
! 1226: R = pd_simp_comp(R,V|first=1,mod=Mod);
! 1227: } else {
! 1228: G = ideal_list_intersection(R,V,0|mod=Mod);
! 1229: R = pd_simp_comp(R,V|mod=Mod);
! 1230: }
! 1231: return Rad ? [R,G] : R;
! 1232: }
! 1233:
! 1234: /* returns [PD,rad(I)] */
! 1235:
! 1236: def prime_dec_main(B,V)
! 1237: {
! 1238: Tpint = RTpint = 0;
! 1239: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1240: if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
! 1241: G = fast_gb(B,V,Mod,0);
! 1242: IntP = [1];
! 1243: PD = [];
! 1244: DG = ltov(map(dp_ptod,G,V));
! 1245: for ( Ind = [], I = length(G)-1; I >= 0; I-- ) Ind = cons(I,Ind);
! 1246: if ( Mod ) DG = map(dp_mod,DG,Mod,[]);
! 1247: while ( 1 ) {
! 1248: print([length(PD)],2);
! 1249: /* rad(G) subset IntP */
! 1250: /* check if IntP subset rad(G) */
! 1251: /* print([length(PD),length(IntP)],2); */
! 1252: for ( T = IntP; T != []; T = cdr(T) )
! 1253: if ( (G0 = radical_membership_sat(car(T),G,V|mod=Mod,isgb=1,dg=[DG,Ind])) ) {
! 1254: F = car(T);
! 1255: break;
! 1256: }
! 1257: if ( T == [] ) {
! 1258: print(["pint",Tpint,"rpint",RTpint]);
! 1259: return [PD,IntP];
! 1260: }
! 1261: PD0 = zprimecomp(G0,V,Indep|mod=Mod);
! 1262: Int = ideal_list_intersection(Indep?map(first,PD0):PD0,V,0|mod=Mod);
! 1263: PD = append(PD,PD0);
! 1264: #if 1
! 1265: T0=time();
! 1266: IntP = ideal_intersection_m(IntP,Int,V,0|mod=Mod);
! 1267: dp_ord(0); DC = map(dp_ptod,IntP,V);
! 1268: DC = qsort(DC,noro_pd.comp_tord); IntP = map(dp_dtop,DC,V);
! 1269: ACCUM_TIME(Tpint,RTpint)
! 1270: #else
! 1271: IntP = ideal_intersection(IntP,Int,V,0|mod=Mod,gbblock=[[0,length(IntP)]]);
! 1272: #endif
! 1273: }
! 1274: }
! 1275:
! 1276: localf callsat,callzcomp;
! 1277:
! 1278: def callsat(F,G,V,Mod,DG)
! 1279: {
! 1280: return radical_membership(F,G,V|mod=Mod,isgb=1,dg=DG,sat=1);
! 1281: }
! 1282:
! 1283: def callzcomp(F,V,Indep,Mod)
! 1284: {
! 1285: PD0 = zprimecomp(F,V,Indep|mod=Mod);
! 1286: Int = ideal_list_intersection(Indep?map(first,PD0):PD0,V,0|mod=Mod);
! 1287: return [PD0,Int];
! 1288: }
! 1289:
! 1290: def prime_dec_main2(B,V)
! 1291: {
! 1292: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1293: if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
! 1294: if ( type(Para=getopt(para)) == -1 || type(Para) != 4 ) Para = [];
! 1295: NPara = length(Para);
! 1296:
! 1297: G = fast_gb(B,V,Mod,0);
! 1298: IntP = [1];
! 1299: PD = [];
! 1300: DG = ltov(map(dp_ptod,G,V));
! 1301: for ( Ind = [], I = length(G)-1; I >= 0; I-- ) Ind = cons(I,Ind);
! 1302: if ( Mod ) DG = map(dp_mod,DG,Mod,[]);
! 1303: if ( NPara )
! 1304: while ( 1 ) {
! 1305: IntPM = mingen(IntP,V);
! 1306: for ( T = IntPM, CallSat = []; T != []; T = cdr(T) )
! 1307: CallSat = cons(["noro_pd.callsat",car(T),G,V,Mod,[DG,Ind]],CallSat);
! 1308: CallSat = reverse(CallSat);
! 1309: /* SatL = [[..],0,[...],...] */
! 1310: SatL = para_exec(Para,CallSat);
! 1311: for ( T = SatL, Sat = []; T != []; T = cdr(T) ) if ( car(T) ) Sat = cons(car(T),Sat);
! 1312: if ( Sat == [] ) return PD;
! 1313: print(length(Sat),2); print("->",2);
! 1314: Sat = remove_identical_comp(Sat|mod=Mod);
! 1315: print(length(Sat));
! 1316: for ( T = Sat, CallComp = []; T != []; T = cdr(T) )
! 1317: CallComp = cons(["noro_pd.callzcomp",car(T),V,Indep,Mod],CallComp);
! 1318: CallComp = reverse(CallComp);
! 1319: /* PDL = [[PD0,Int],...] */
! 1320: PDL = para_exec(Para,CallComp);
! 1321: for ( T = PDL; T != []; T = cdr(T) ) PD = append(PD,car(T)[0]);
! 1322: Int = ideal_list_intersection(map(second,PDL),V,0|mod=Mod);
! 1323: IntP = ideal_intersection(IntP,Int,V,0|mod=Mod,gbblock=[[0,length(IntP)]]);
! 1324: }
! 1325: else
! 1326: while ( 1 ) {
! 1327: /* rad(G) subset IntP */
! 1328: /* check if IntP subset rad(G) */
! 1329: /* print([length(PD),length(IntP)],2); */
! 1330: Sat = [];
! 1331: IntPM = mingen(IntP,V);
! 1332: for ( T = IntPM; T != [] && length(Sat) < 16; T = cdr(T) )
! 1333: if ( G0 = radical_membership(car(T),G,V|mod=Mod,isgb=1,dg=[DG,Ind],sat=1) )
! 1334: Sat = cons(G0,Sat);
! 1335: if ( Sat == [] ) return PD;
! 1336: print(length(Sat),2); print("->",2);
! 1337: Sat = remove_identical_comp(Sat|mod=Mod);
! 1338: print(length(Sat));
! 1339: for ( T = Sat; T != []; T = cdr(T) ) {
! 1340: PD0 = zprimecomp(car(T),V,Indep|mod=Mod); PD = append(PD,PD0);
! 1341: Int = ideal_list_intersection(Indep?map(first,PD0):PD0,V,0|mod=Mod);
! 1342: IntP = ideal_intersection(IntP,Int,V,0|mod=Mod,gbblock=[[0,length(IntP)]]);
! 1343: }
! 1344: }
! 1345: }
! 1346:
! 1347: /* pre-decomposition */
! 1348:
! 1349: def lex_predec1(B,V)
! 1350: {
! 1351: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1352: G = fast_gb(B,V,Mod,2);
! 1353: for ( T = G; T != []; T = cdr(T) ) {
! 1354: F = gen_fctr(car(T),Mod);
! 1355: if ( length(F) > 2 || length(F) == 2 && F[1][1] > 1 ) {
! 1356: for ( R = [], S = cdr(F); S != []; S = cdr(S) ) {
! 1357: Ft = car(S)[0];
! 1358: Gt = map(ptozp,map(gen_nf,G,[Ft],V,0,Mod));
! 1359: R1 = fast_gb(cons(Ft,Gt),V,Mod,0);
! 1360: R = cons(R1,R);
! 1361: }
! 1362: return R;
! 1363: }
! 1364: }
! 1365: return [G];
! 1366: }
! 1367:
! 1368: /* zero-dimensional prime/primary decomosition */
! 1369:
! 1370: def zprimedec(B,V,Mod)
! 1371: {
! 1372: L = partial_decomp(B,V,Mod);
! 1373: P = L[0]; NP = L[1];
! 1374: R = [];
! 1375: for ( ; P != []; P = cdr(P) ) R = cons(car(car(P)),R);
! 1376: for ( T = NP; T != []; T = cdr(T) ) {
! 1377: R1 = complete_decomp(car(T),V,Mod);
! 1378: R = append(R1,R);
! 1379: }
! 1380: return R;
! 1381: }
! 1382:
! 1383: def zprimadec(B,V,Mod)
! 1384: {
! 1385: L = partial_qdecomp(B,V,Mod);
! 1386: Q = L[0]; NQ = L[1];
! 1387: R = [];
! 1388: for ( ; Q != []; Q = cdr(Q) ) {
! 1389: T = car(Q); R = cons([T[0],T[1]],R);
! 1390: }
! 1391: for ( T = NQ; T != []; T = cdr(T) ) {
! 1392: R1 = complete_qdecomp(car(T),V,Mod);
! 1393: R = append(R1,R);
! 1394: }
! 1395: return R;
! 1396: }
! 1397:
! 1398: def complete_qdecomp(GD,V,Mod)
! 1399: {
! 1400: GQ = GD[0]; GP = GD[1]; D = GD[2];
! 1401: W = vars(GP);
! 1402: PV = setminus(W,V);
! 1403: N = length(V); PN = length(PV);
! 1404: U = find_npos([GP,D],V,PV,Mod);
! 1405: NV = ttttt;
! 1406: M = gen_minipoly(cons(NV-U,GQ),cons(NV,V),PV,0,NV,Mod);
! 1407: M = ppart(M,NV,Mod);
! 1408: MF = Mod ? modfctr(M,Mod) : fctr(M);
! 1409: R = [];
! 1410: for ( T = cdr(MF); T != []; T = cdr(T) ) {
! 1411: S = car(T);
! 1412: Mt = subst(S[0],NV,U);
! 1413: GP1 = fast_gb(cons(Mt,GP),W,Mod,0);
! 1414: GQ1 = fast_gb(cons(Mt^S[1],GQ),W,Mod,0);
! 1415: if ( PV != [] ) {
! 1416: GP1 = elim_gb(GP1,V,PV,Mod,[[0,N],[0,PN]]);
! 1417: GQ1 = elim_gb(GQ1,V,PV,Mod,[[0,N],[0,PN]]);
! 1418: }
! 1419: R = cons([GQ1,GP1],R);
! 1420: }
! 1421: return R;
! 1422: }
! 1423:
! 1424: def partial_qdecomp(B,V,Mod)
! 1425: {
! 1426: Elim = (Elim=getopt(elim))&&type(Elim)!=-1 ? 1 : 0;
! 1427: N = length(V);
! 1428: W = vars(B);
! 1429: PV = setminus(W,V);
! 1430: NP = length(PV);
! 1431: W = append(V,PV);
! 1432: if ( Elim && PV != [] ) Ord = [[0,N],[0,NP]];
! 1433: else Ord = 0;
! 1434: if ( Mod )
! 1435: B = nd_f4(B,W,Mod,Ord);
! 1436: else
! 1437: B = nd_gr_trace(B,W,1,GBCheck,Ord);
! 1438: Q = []; NQ = [[B,B,vector(N+1)]];
! 1439: for ( I = length(V)-1; I >= 0; I-- ) {
! 1440: NQ1 = [];
! 1441: for ( T = NQ; T != []; T = cdr(T) ) {
! 1442: L = partial_qdecomp0(car(T),V,PV,Ord,I,Mod);
! 1443: Q = append(L[0],Q);
! 1444: NQ1 = append(L[1],NQ1);
! 1445: }
! 1446: NQ = NQ1;
! 1447: }
! 1448: return [Q,NQ];
! 1449: }
! 1450:
! 1451: def partial_qdecomp0(GD,V,PV,Ord,I,Mod)
! 1452: {
! 1453: GQ = GD[0]; GP = GD[1]; D = GD[2];
! 1454: N = length(V); PN = length(PV);
! 1455: W = append(V,PV);
! 1456: VI = V[I];
! 1457: M = gen_minipoly(GQ,V,PV,Ord,VI,Mod);
! 1458: M = ppart(M,VI,Mod);
! 1459: if ( Mod )
! 1460: MF = modfctr(M,Mod);
! 1461: else
! 1462: MF = fctr(M);
! 1463: Q = []; NQ = [];
! 1464: if ( length(MF) == 2 && MF[1][1] == 1 ) {
! 1465: D1 = D*1; D1[I] = M;
! 1466: GQelim = elim_gb(GQ,V,PV,Mod,Ord);
! 1467: GPelim = elim_gb(GP,V,PV,Mod,Ord);
! 1468: LD = ldim(GQelim,V);
! 1469: if ( deg(M,VI) == LD )
! 1470: Q = cons([GQelim,GPelim,D1],Q);
! 1471: else
! 1472: NQ = cons([GQelim,GPelim,D1],NQ);
! 1473: return [Q,NQ];
! 1474: }
! 1475: for ( T = cdr(MF); T != []; T = cdr(T) ) {
! 1476: S = car(T); Mt = S[0]; D1 = D*1; D1[I] = Mt;
! 1477:
! 1478: GQ1 = fast_gb(cons(Mt^S[1],GQ),W,Mod,Ord);
! 1479: GQelim = elim_gb(GQ1,V,PV,Mod,Ord);
! 1480: GP1 = fast_gb(cons(Mt,GP),W,Mod,Ord);
! 1481: GPelim = elim_gb(GP1,V,PV,Mod,Ord);
! 1482:
! 1483: D1[N] = LD = ldim(GPelim,V);
! 1484:
! 1485: for ( J = 0; J < N; J++ )
! 1486: if ( D1[J] && deg(D1[J],V[J]) == LD ) break;
! 1487: if ( J < N )
! 1488: Q = cons([GQelim,GPelim,D1],Q);
! 1489: else
! 1490: NQ = cons([GQelim,GPelim,D1],NQ);
! 1491: }
! 1492: return [Q,NQ];
! 1493: }
! 1494:
! 1495: def complete_decomp(GD,V,Mod)
! 1496: {
! 1497: G = GD[0]; D = GD[1];
! 1498: W = vars(G);
! 1499: PV = setminus(W,V);
! 1500: N = length(V); PN = length(PV);
! 1501: U = find_npos(GD,V,PV,Mod);
! 1502: NV = ttttt;
! 1503: M = gen_minipoly(cons(NV-U,G),cons(NV,V),PV,0,NV,Mod);
! 1504: M = ppart(M,NV,Mod);
! 1505: MF = Mod ? modfctr(M,Mod) : fctr(M);
! 1506: if ( length(MF) == 2 ) return [G];
! 1507: R = [];
! 1508: for ( T = cdr(MF); T != []; T = cdr(T) ) {
! 1509: Mt = subst(car(car(T)),NV,U);
! 1510: G1 = fast_gb(cons(Mt,G),W,Mod,0);
! 1511: if ( PV != [] ) G1 = elim_gb(G1,V,PV,Mod,[[0,N],[0,PN]]);
! 1512: R = cons(G1,R);
! 1513: }
! 1514: return R;
! 1515: }
! 1516:
! 1517: def partial_decomp(B,V,Mod)
! 1518: {
! 1519: Elim = (Elim=getopt(elim))&&type(Elim)!=-1 ? 1 : 0;
! 1520: N = length(V);
! 1521: W = vars(B);
! 1522: PV = setminus(W,V);
! 1523: NP = length(PV);
! 1524: W = append(V,PV);
! 1525: if ( Elim && PV != [] ) Ord = [[0,N],[0,NP]];
! 1526: else Ord = 0;
! 1527: if ( Mod )
! 1528: B = nd_f4(B,W,Mod,Ord);
! 1529: else
! 1530: B = nd_gr_trace(B,W,1,GBCheck,Ord);
! 1531: P = []; NP = [[B,vector(N+1)]];
! 1532: for ( I = length(V)-1; I >= 0; I-- ) {
! 1533: NP1 = [];
! 1534: for ( T = NP; T != []; T = cdr(T) ) {
! 1535: L = partial_decomp0(car(T),V,PV,Ord,I,Mod);
! 1536: P = append(L[0],P);
! 1537: NP1 = append(L[1],NP1);
! 1538: }
! 1539: NP = NP1;
! 1540: }
! 1541: return [P,NP];
! 1542: }
! 1543:
! 1544: def partial_decomp0(GD,V,PV,Ord,I,Mod)
! 1545: {
! 1546: G = GD[0]; D = GD[1];
! 1547: N = length(V); PN = length(PV);
! 1548: W = append(V,PV);
! 1549: VI = V[I];
! 1550: M = gen_minipoly(G,V,PV,Ord,VI,Mod);
! 1551: M = ppart(M,VI,Mod);
! 1552: if ( Mod )
! 1553: MF = modfctr(M,Mod);
! 1554: else
! 1555: MF = fctr(M);
! 1556: if ( length(MF) == 2 && MF[1][1] == 1 ) {
! 1557: D1 = D*1;
! 1558: D1[I] = M;
! 1559: Gelim = elim_gb(G,V,PV,Mod,Ord);
! 1560: D1[N] = LD = ldim(Gelim,V);
! 1561: GD1 = [Gelim,D1];
! 1562: for ( J = 0; J < N; J++ )
! 1563: if ( D1[J] && deg(D1[J],V[J]) == LD )
! 1564: return [[GD1],[]];
! 1565: return [[],[GD1]];
! 1566: }
! 1567: P = []; NP = [];
! 1568: GI = elim_gb(G,V,PV,Mod,Ord);
! 1569: for ( T = cdr(MF); T != []; T = cdr(T) ) {
! 1570: Mt = car(car(T));
! 1571: D1 = D*1;
! 1572: D1[I] = Mt;
! 1573: GIt = map(gen_nf,GI,[Mt],V,Ord,Mod);
! 1574: G1 = cons(Mt,GIt);
! 1575: Gelim = elim_gb(G1,V,PV,Mod,Ord);
! 1576: D1[N] = LD = ldim(Gelim,V);
! 1577: for ( J = 0; J < N; J++ )
! 1578: if ( D1[J] && deg(D1[J],V[J]) == LD ) break;
! 1579: if ( J < N )
! 1580: P = cons([Gelim,D1],P);
! 1581: else
! 1582: NP = cons([Gelim,D1],NP);
! 1583: }
! 1584: return [P,NP];
! 1585: }
! 1586:
! 1587: /* prime/primary components over rational function field */
! 1588:
! 1589: def zprimacomp(G,V) {
! 1590: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1591: L = zprimadec(G,V,0|mod=Mod);
! 1592: R = [];
! 1593: dp_ord(0);
! 1594: for ( T = L; T != []; T = cdr(T) ) {
! 1595: S = car(T);
! 1596: UQ = contraction(S[0],V|mod=Mod);
! 1597: UP = contraction(S[1],V|mod=Mod);
! 1598: R = cons([UQ,UP],R);
! 1599: }
! 1600: return R;
! 1601: }
! 1602:
! 1603: def zprimecomp(G,V,Indep) {
! 1604: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1605: W = maxindep(G,V,0|mod=Mod);
! 1606: V0 = setminus(V,W);
! 1607: V1 = append(V0,W);
! 1608: #if 0
! 1609: O1 = [[0,length(V0)],[0,length(W)]];
! 1610: G1 = fast_gb(G,V1,Mod,O1);
! 1611: dp_ord(0);
! 1612: #else
! 1613: G1 = G;
! 1614: #endif
! 1615: PD = zprimedec(G1,V0,Mod);
! 1616: dp_ord(0);
! 1617: R = [];
! 1618: for ( T = PD; T != []; T = cdr(T) ) {
! 1619: U = contraction(car(T),V0|mod=Mod);
! 1620: U = nd_gr(U,V,Mod,0);
! 1621: R = cons(Indep?[U,W]:U,R);
! 1622: }
! 1623: return R;
! 1624: }
! 1625:
! 1626: def fast_gb(B,V,Mod,Ord)
! 1627: {
! 1628: if ( type(Block=getopt(gbblock)) == -1 ) Block = 0;
! 1629: if ( type(NoRA=getopt(nora)) == -1 ) NoRA = 0;
! 1630: if ( type(Trace=getopt(trace)) == -1 ) Trace = 0;
! 1631: if ( Mod )
! 1632: G = nd_f4(B,V,Mod,Ord|nora=NoRA);
! 1633: else if ( F4 )
! 1634: G = map(ptozp,f4_chrem(B,V,Ord));
! 1635: else if ( Trace ) {
! 1636: if ( Block )
! 1637: G = nd_gr_trace(B,V,1,1,Ord|nora=NoRA,gbblock=Block);
! 1638: else
! 1639: G = nd_gr_trace(B,V,1,1,Ord|nora=NoRA);
! 1640: } else {
! 1641: if ( Block )
! 1642: G = nd_gr(B,V,0,Ord|nora=NoRA,gbblock=Block);
! 1643: else
! 1644: G = nd_gr(B,V,0,Ord|nora=NoRA);
! 1645: }
! 1646: return G;
! 1647: }
! 1648:
! 1649: def incremental_gb(A,V,Ord)
! 1650: {
! 1651: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1652: if ( type(Block=getopt(gbblock)) == -1 ) Block = 0;
! 1653: if ( Mod ) {
! 1654: if ( Block )
! 1655: G = nd_gr(A,V,Mod,Ord|gbblock=Block);
! 1656: else
! 1657: G = nd_gr(A,V,Mod,Ord);
! 1658: } else if ( Procs ) {
! 1659: Arg0 = ["nd_gr",A,V,0,Ord];
! 1660: Arg1 = ["nd_gr_trace",A,V,1,GBCheck,Ord];
! 1661: G = competitive_exec(Procs,Arg0,Arg1);
! 1662: } else if ( Block )
! 1663: G = nd_gr(A,V,0,Ord|gbblock=Block);
! 1664: else
! 1665: G = nd_gr(A,V,0,Ord);
! 1666: return G;
! 1667: }
! 1668:
! 1669: def elim_gb(G,V,PV,Mod,Ord)
! 1670: {
! 1671: N = length(V); PN = length(PV);
! 1672: O1 = [[0,N],[0,PN]];
! 1673: if ( Ord == O1 )
! 1674: Ord = Ord[0][0];
! 1675: if ( Mod ) /* XXX */ {
! 1676: for ( T = G, H = []; T != []; T = cdr(T) )
! 1677: if ( car(T) ) H = cons(car(T),H);
! 1678: G = reverse(H);
! 1679: G = dp_gr_mod_main(G,V,0,Mod,Ord);
! 1680: } else if ( EProcs ) {
! 1681: #if 1
! 1682: Arg0 = ["dp_gr_main",G,V,0,0,Ord];
! 1683: #else
! 1684: Arg0 = ["nd_gr",G,V,0,Ord];
! 1685: #endif
! 1686: Arg1 = ["noro_pd.nd_gr_rat",G,V,PV,O1,Ord];
! 1687: G = competitive_exec(EProcs,Arg0,Arg1);
! 1688: } else if ( GBRat ) {
! 1689: G1 = nd_gr(G,append(V,PV),0,O1);
! 1690: if ( GBRat == 1 )
! 1691: G1 = nd_gr_postproc(G1,V,0,Ord,0|nora=1);
! 1692: return G1;
! 1693: } else
! 1694: #if 1
! 1695: #if 0
! 1696: G = dp_gr_main(G,V,0,0,Ord);
! 1697: #else
! 1698: G = nd_gr_trace(G,V,1,1,Ord);
! 1699: #endif
! 1700: #else
! 1701: G = nd_gr(G,V,0,Ord);
! 1702: #endif
! 1703: return G;
! 1704: }
! 1705:
! 1706: def ldim(G,V)
! 1707: {
! 1708: O0 = dp_ord(); dp_ord(0);
! 1709: D = length(dp_mbase(map(dp_ptod,G,V)));
! 1710: dp_ord(O0);
! 1711: return D;
! 1712: }
! 1713:
! 1714: /* over Q only */
! 1715:
! 1716: def make_mod_subst(GD,V,PV,HC)
! 1717: {
! 1718: N = length(V);
! 1719: PN = length(PV);
! 1720: G = GD[0]; D = GD[1];
! 1721: for ( I = 0; ; I = (I+1)%100 ) {
! 1722: Mod = lprime(I);
! 1723: S = [];
! 1724: for ( J = PN-1; J >= 0; J-- )
! 1725: S = append([PV[J],random()%Mod],S);
! 1726: for ( T = HC; T != []; T = cdr(T) )
! 1727: if ( !(subst(car(T),S)%Mod) ) break;
! 1728: if ( T != [] ) continue;
! 1729: for ( J = 0; J < N; J++ ) {
! 1730: M = subst(D[J],S);
! 1731: F = modsqfr(M,Mod);
! 1732: if ( length(F) != 2 || F[1][1] != 1 ) break;
! 1733: }
! 1734: if ( J < N ) continue;
! 1735: G0 = map(subst,G,S);
! 1736: return [G0,Mod];
! 1737: }
! 1738: }
! 1739:
! 1740: def rsgn()
! 1741: {
! 1742: return random()%2 ? 1 : -1;
! 1743: }
! 1744:
! 1745: def find_npos(GD,V,PV,Mod)
! 1746: {
! 1747: N = length(V); PN = length(PV);
! 1748: G = GD[0]; D = GD[1]; LD = D[N];
! 1749: DH = map(dp_dtop,map(dp_ht,map(dp_ptod,D,V)),V);
! 1750: Ord0 = dp_ord(); dp_ord(0);
! 1751: HC = map(dp_hc,map(dp_ptod,G,V));
! 1752: dp_ord(Ord0);
! 1753: if ( !Mod ) {
! 1754: W = append(V,PV);
! 1755: G1 = nd_gr_trace(G,W,1,GBCheck,[[0,N],[0,PN]]);
! 1756: L = make_mod_subst([G1,D],V,PV,HC);
! 1757: return find_npos([L[0],D],V,[],L[1]);
! 1758: }
! 1759: N = length(V);
! 1760: NV = ttttt;
! 1761: for ( B = 2; ; B++ ) {
! 1762: for ( J = N-2; J >= 0; J-- ) {
! 1763: for ( U = 0, K = J; K < N; K++ ) {
! 1764: if ( DH[K] == V[K] ) continue;
! 1765: U += rsgn()*((random()%B+1))*V[K];
! 1766: }
! 1767: #if 0
! 1768: M = minipolym(G,V,0,U,NV,Mod);
! 1769: #else
! 1770: M = gen_minipoly(cons(NV-U,G),cons(NV,V),PV,0,NV,Mod);
! 1771: #endif
! 1772: if ( deg(M,NV) == LD ) return U;
! 1773: }
! 1774: }
! 1775: }
! 1776:
! 1777: def gen_minipoly(G,V,PV,Ord,VI,Mod)
! 1778: {
! 1779: O0 = dp_ord();
! 1780: if ( PV == [] ) {
! 1781: NV = sssss;
! 1782: if ( Mod )
! 1783: M = minipolym(G,V,Ord,VI,NV,Mod);
! 1784: else
! 1785: M = minipoly(G,V,Ord,VI,NV);
! 1786: dp_ord(O0);
! 1787: return subst(M,NV,VI);
! 1788: }
! 1789: W = setminus(V,[VI]);
! 1790: PV1 = cons(VI,PV);
! 1791: #if 0
! 1792: while ( 1 ) {
! 1793: V1 = append(W,PV1);
! 1794: if ( Mod )
! 1795: G = nd_gr(G,V1,Mod,[[0,1],[0,length(V1)-1]]|nora=1);
! 1796: else
! 1797: G = nd_gr_trace(G,V1,1,GBCheck,[[0,1],[0,length(V1)-1]]|nora=1);
! 1798: if ( W == [] ) break;
! 1799: else {
! 1800: W = cdr(W);
! 1801: G = elimination(G,cdr(V1));
! 1802: }
! 1803: }
! 1804: #elif 1
! 1805: if ( Mod ) {
! 1806: V1 = append(W,PV1);
! 1807: G = nd_gr(G,V1,Mod,[[0,length(W)],[0,length(PV1)]]);
! 1808: G = elimination(G,PV1);
! 1809: } else {
! 1810: PV2 = setminus(PV1,[PV1[length(PV1)-1]]);
! 1811: V2 = append(W,PV2);
! 1812: G = nd_gr_trace(G,V2,1,GBCheck,[[0,length(W)],[0,length(PV2)]]|nora=1);
! 1813: G = elimination(G,PV1);
! 1814: }
! 1815: #else
! 1816: V1 = append(W,PV1);
! 1817: if ( Mod )
! 1818: G = nd_gr(G,V1,Mod,[[0,length(W)],[0,length(PV1)]]|nora=1);
! 1819: else
! 1820: G = nd_gr_trace(G,V1,1,GBCheck,[[0,length(W)],[0,length(PV1)]]|nora=1);
! 1821: G = elimination(G,PV1);
! 1822: #endif
! 1823: if ( Mod )
! 1824: G = nd_gr(G,PV1,Mod,[[0,1],[0,length(PV)]]|nora=1);
! 1825: else
! 1826: G = nd_gr_trace(G,PV1,1,GBCheck,[[0,1],[0,length(PV)]]|nora=1);
! 1827: for ( M = car(G), T = cdr(G); T != []; T = cdr(T) )
! 1828: if ( deg(car(T),VI) < deg(M,VI) ) M = car(T);
! 1829: dp_ord(O0);
! 1830: return M;
! 1831: }
! 1832:
! 1833: def indepset(V,H)
! 1834: {
! 1835: if ( H == [] ) return V;
! 1836: N = -1;
! 1837: for ( T = V; T != []; T = cdr(T) ) {
! 1838: VI = car(T);
! 1839: HI = [];
! 1840: for ( S = H; S != []; S = cdr(S) )
! 1841: if ( !tdiv(car(S),VI) ) HI = cons(car(S),HI);
! 1842: RI = indepset(setminus(V,[VI]),HI);
! 1843: if ( length(RI) > N ) {
! 1844: R = RI; N = length(RI);
! 1845: }
! 1846: }
! 1847: return R;
! 1848: }
! 1849:
! 1850: def maxindep(B,V,O)
! 1851: {
! 1852: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1853: G = fast_gb(B,V,Mod,O);
! 1854: Old = dp_ord();
! 1855: dp_ord(O);
! 1856: H = map(dp_dtop,map(dp_ht,map(dp_ptod,G,V)),V);
! 1857: H = map(sq,H,0);
! 1858: H = nd_gr(H,V,0,0);
! 1859: H = monodec0(H,V);
! 1860: N = length(V);
! 1861: Dep = [];
! 1862: for ( T = H, Len = N+1; T != []; T = cdr(T) ) {
! 1863: M = length(car(T));
! 1864: if ( M < Len ) {
! 1865: Dep = [car(T)];
! 1866: Len = M;
! 1867: } else if ( M == Len )
! 1868: Dep = cons(car(T),Dep);
! 1869: }
! 1870: R = setminus(V,Dep[0]);
! 1871: dp_ord(Old);
! 1872: return R;
! 1873: }
! 1874:
! 1875: def maxindep2(B,V,O)
! 1876: {
! 1877: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1878: G = fast_gb(B,V,Mod,O);
! 1879: Old = dp_ord();
! 1880: dp_ord(O);
! 1881: H = map(dp_dtop,map(dp_ht,map(dp_ptod,G,V)),V);
! 1882: H = map(sq,H,0);
! 1883: H = nd_gr(H,V,0,0);
! 1884: H = monodec0(H,V);
! 1885: N = length(V);
! 1886: Dep = [];
! 1887: for ( T = H, Len = N+1; T != []; T = cdr(T) ) {
! 1888: M = length(car(T));
! 1889: if ( M < Len ) {
! 1890: Dep = [car(T)];
! 1891: Len = M;
! 1892: } else if ( M == Len )
! 1893: Dep = cons(car(T),Dep);
! 1894: }
! 1895: R = [];
! 1896: for ( T = Dep; T != []; T = cdr(T) )
! 1897: R = cons(setminus(V,car(T)),R);
! 1898: dp_ord(Old);
! 1899: return reverse(R);
! 1900: }
! 1901:
! 1902:
! 1903: /* ideal operations */
! 1904: def contraction(G,V)
! 1905: {
! 1906: if ( type(AllV=getopt(allv)) == -1 ) AllV = 0;
! 1907: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1908:
! 1909: if ( RepColon ) return contraction_m(G,V|allv=AllV,mod=Mod);
! 1910:
! 1911: C = [];
! 1912: for ( T = G; T != []; T = cdr(T) ) {
! 1913: C1 = dp_hc(dp_ptod(car(T),V));
! 1914: S = gen_fctr(C1,Mod);
! 1915: for ( S = cdr(S); S != []; S = cdr(S) )
! 1916: if ( !member(S[0][0],C) ) C = cons(S[0][0],C);
! 1917: }
! 1918: W = vars(G);
! 1919: PV = setminus(W,V);
! 1920: if ( AllV ) W = AllV;
! 1921: else W = append(V,PV);
! 1922: NV = ttttt;
! 1923: if ( SuccSat ) {
! 1924: W1 = cons(NV,W);
! 1925: O1 = [[0,1],[0,length(W)]];
! 1926: Block = [];
! 1927: for ( T = C; T != []; T = cdr(T) ) {
! 1928: G1 = nd_gr(append(G,[NV*car(T)-1]),W1,Mod,O1|gbblock=Block);
! 1929: G = elimination(G1,W);
! 1930: Block = [[0,length(G)]];
! 1931: }
! 1932: } else {
! 1933: for ( T = C, S = 1; T != []; T = cdr(T) )
! 1934: S *= car(T);
! 1935: G = saturation([G,NV],S,W|mod=Mod);
! 1936: }
! 1937: return G;
! 1938: }
! 1939:
! 1940: def contraction_m(G,V)
! 1941: {
! 1942: if ( type(AllV=getopt(allv)) == -1 ) AllV = 0;
! 1943: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1944: C = [];
! 1945: for ( T = G; T != []; T = cdr(T) ) {
! 1946: C1 = dp_hc(dp_ptod(car(T),V));
! 1947: S = gen_fctr(C1,Mod);
! 1948: for ( S = cdr(S); S != []; S = cdr(S) )
! 1949: if ( !member(S[0][0],C) ) C = cons(S[0][0],C);
! 1950: }
! 1951: W = vars(G);
! 1952: PV = setminus(W,V);
! 1953: if ( AllV ) W = AllV;
! 1954: else W = append(V,PV);
! 1955: H = H0 = G;
! 1956: while ( 1 ) {
! 1957: for ( T = C; T != []; T = cdr(T) )
! 1958: H = map(sdiv,ideal_intersection_m([car(T)],H,W,0),car(T));
! 1959: H = nd_gr(H,W,0,0);
! 1960: if ( gb_comp(H0,H) ) break;
! 1961: else H0 = H;
! 1962: }
! 1963: return H;
! 1964: }
! 1965:
! 1966: def ideal_list_intersection(L,V,Ord)
! 1967: {
! 1968: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1969: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
! 1970: N = length(L);
! 1971: if ( N == 0 ) return [1];
! 1972: if ( N == 1 )
! 1973: return IsGB ? L[0] : fast_gb(L[0],V,Mod,Ord);
! 1974: else {
! 1975: for ( I = 0, T = [1]; I < N; I++ )
! 1976: T = ideal_intersection_m(T,L[I],V,Ord|mod=Mod);
! 1977: T = nd_gr(T,V,Mod,Ord);
! 1978: return T;
! 1979: }
! 1980: }
! 1981:
! 1982: def call_ideal_list_intersection(L,V,Mod,Ord,IsGB)
! 1983: {
! 1984: return ideal_list_intersection(L,V,Ord|mod=Mod,isgb=IsGB);
! 1985: }
! 1986:
! 1987: def ideal_intersection(A,B,V,Ord)
! 1988: {
! 1989: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 1990: if ( type(Block=getopt(gbblock)) == -1 ) Block = 0;
! 1991: T = ttttt;
! 1992: if ( Mod ) {
! 1993: if ( Block )
! 1994: G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
! 1995: cons(T,V),Mod,[[0,1],[Ord,length(V)]]|gbblock=Block,nora=0);
! 1996: else
! 1997: G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
! 1998: cons(T,V),Mod,[[0,1],[Ord,length(V)]]|nora=0);
! 1999: } else
! 2000: if ( Procs ) {
! 2001: Arg0 = ["nd_gr",
! 2002: append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
! 2003: cons(T,V),0,[[0,1],[Ord,length(V)]]];
! 2004: Arg1 = ["nd_gr_trace",
! 2005: append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
! 2006: cons(T,V),1,GBCheck,[[0,1],[Ord,length(V)]]];
! 2007: G = competitive_exec(Procs,Arg0,Arg1);
! 2008: } else {
! 2009: if ( Block )
! 2010: G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
! 2011: cons(T,V),0,[[0,1],[Ord,length(V)]]|gbblock=Block,nora=0);
! 2012: else
! 2013: G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
! 2014: cons(T,V),0,[[0,1],[Ord,length(V)]]|nora=0);
! 2015: }
! 2016: G0 = elimination(G,V);
! 2017: if ( 0 && !Procs )
! 2018: G0 = nd_gr_postproc(G0,V,Mod,Ord,0);
! 2019: return G0;
! 2020: }
! 2021:
! 2022:
! 2023: def aa(A) { return [A,A]; }
! 2024:
! 2025: def ideal_intersection_m(A,B,V,Ord)
! 2026: {
! 2027: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2028:
! 2029: dp_ord(Ord);
! 2030: DA = map(dp_ptod,A,V); DB = ltov(map(dp_ptod,B,V));
! 2031: if ( Mod ) {
! 2032: DA = map(dp_mod,DA,Mod,[]); DB = map(dp_mod,DB,Mod,[]);
! 2033: setmod(Mod);
! 2034: }
! 2035: N = length(B);
! 2036: for ( Ind = [], I = N-1; I >= 0; I-- ) Ind = cons(I,Ind);
! 2037: for ( T = DA, C = []; T != []; T = cdr(T) ) {
! 2038: L = Mod?dp_true_nf_mod(Ind,car(T),DB,1,Mod):dp_true_nf(Ind,car(T),DB,1);
! 2039: R = dp_dtop(L[0],V); Q = dp_dtop(car(T)*L[1]-L[0],V);
! 2040: C = cons([R,-Q],C);
! 2041: }
! 2042: G = nd_gr(append(C,map(aa,B)),V,Mod,[1,Ord]|intersect=1);
! 2043: G = map(second,G);
! 2044: return G;
! 2045: }
! 2046:
! 2047: /* returns GB if F notin rad(G) */
! 2048:
! 2049: def radical_membership(F,G,V) {
! 2050: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2051: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
! 2052: if ( type(L=getopt(dg)) == -1 ) L = 0;
! 2053: if ( type(Sat=getopt(sat)) == -1 ) Sat = 0;
! 2054: dp_ord(0);
! 2055: if ( L ) { DG = L[0]; Ind = L[1]; }
! 2056: else {
! 2057: DG = ltov(map(dp_ptod,G,V));
! 2058: if ( Mod ) DG = map(dp_mod,DG,Mod,[]);
! 2059: for ( Ind = [], I = length(G)-1; I >= 0; I-- ) Ind = cons(I,Ind);
! 2060: }
! 2061: DF = dp_ptod(F,V); DFI = dp_ptod(1,V);
! 2062: if ( Mod ) {
! 2063: DF = dp_mod(DF,Mod,[]); DFI = dp_mod(DFI,Mod,[]);
! 2064: setmod(Mod);
! 2065: }
! 2066: for ( I = 0; I < 3; I++ ) {
! 2067: DFI = Mod?dp_nf_mod(Ind,DF*DFI,DG,0,Mod):dp_nf(Ind,DF*DFI,DG,0);
! 2068: if ( !DFI ) return 0;
! 2069: }
! 2070: NV = ttttt;
! 2071: if ( IsGB )
! 2072: T = nd_gr(append(G,[NV*F-1]),cons(NV,V),Mod,0
! 2073: |gbblock=[[0,length(G)]]);
! 2074: else
! 2075: T = nd_gr(append(G,[NV*F-1]),cons(NV,V),Mod,0);
! 2076: if ( type(car(T)) == 1 ) return 0;
! 2077: else if ( Sat ) {
! 2078: G1 = fast_gb(T,cons(NV,V),Mod,[[0,1],[0,length(V)]]);
! 2079: G0 = elimination(G1,V);
! 2080: return G0;
! 2081: } else return [T,NV];
! 2082: }
! 2083:
! 2084: def radical_membership_sat(F,G,V) {
! 2085: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2086: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
! 2087: if ( type(L=getopt(dg)) == -1 ) L = 0;
! 2088: dp_ord(0);
! 2089: if ( L ) { DG = L[0]; Ind = L[1]; }
! 2090: else {
! 2091: DG = ltov(map(dp_ptod,G,V));
! 2092: if ( Mod ) DG = map(dp_mod,DG,Mod,[]);
! 2093: for ( Ind = [], I = length(G)-1; I >= 0; I-- ) Ind = cons(I,Ind);
! 2094: }
! 2095: DF = dp_ptod(F,V); DFI = dp_ptod(1,V);
! 2096: if ( Mod ) {
! 2097: DF = dp_mod(DF,Mod,[]); DFI = dp_mod(DFI,Mod,[]);
! 2098: setmod(Mod);
! 2099: }
! 2100: for ( I = 0; I < 3; I++ ) {
! 2101: DFI = Mod?dp_nf_mod(Ind,DF*DFI,DG,0,Mod):dp_nf(Ind,DF*DFI,DG,0);
! 2102: if ( !DFI ) return 0;
! 2103: }
! 2104: NV = ttttt;
! 2105: if ( IsGB )
! 2106: T = nd_gr(append(G,[NV*F-1]),cons(NV,V),Mod,[[0,1],[0,length(V)]]
! 2107: |gbblock=[[0,length(G)]]);
! 2108: else
! 2109: T = nd_gr(append(G,[NV*F-1]),cons(NV,V),Mod,[[0,1],[0,length(V)]]);
! 2110: if ( type(car(T)) == 1 ) return 0;
! 2111: G0 = elimination(T,V);
! 2112: return G0;
! 2113: }
! 2114:
! 2115: def modular_radical_membership(F,G,V) {
! 2116: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2117: if ( Mod )
! 2118: return radical_membership(F,G,V|mod=Mod);
! 2119:
! 2120: F = gen_nf(F,G,V,0,0);
! 2121: if ( !F ) return 0;
! 2122: NV = ttttt;
! 2123: for ( J = 0; ; J++ ) {
! 2124: Mod = lprime(J);
! 2125: H = map(dp_hc,map(dp_ptod,G,V));
! 2126: for ( ; H != []; H = cdr(H) ) if ( !(car(H)%Mod) ) break;
! 2127: if ( H != [] ) continue;
! 2128:
! 2129: T = nd_f4(cons(NV*F-1,G),cons(NV,V),Mod,0);
! 2130: if ( type(car(T)) == 1 ) {
! 2131: I = radical_membership_rep(F,G,V,-1,0,Mod);
! 2132: I1 = radical_membership_rep(F,G,V,I,0,0);
! 2133: if ( I1 > 0 ) return 0;
! 2134: }
! 2135: return radical_membership(F,G,V);
! 2136: }
! 2137: }
! 2138:
! 2139: def radical_membership_rep(F,G,V,Max,Ord,Mod) {
! 2140: Ft = F;
! 2141: I = 1;
! 2142: while ( Max < 0 || I <= Max ) {
! 2143: Ft = gen_nf(Ft,G,V,Ord,Mod);
! 2144: if ( !Ft ) return I;
! 2145: Ft *= F;
! 2146: I++;
! 2147: }
! 2148: return -1;
! 2149: }
! 2150:
! 2151: def ideal_product(A,B,V)
! 2152: {
! 2153: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2154: dp_ord(0);
! 2155: DA = map(dp_ptod,A,V);
! 2156: DB = map(dp_ptod,B,V);
! 2157: DegA = map(dp_td,DA);
! 2158: DegB = map(dp_td,DB);
! 2159: for ( PA = [], T = A, DT = DegA; T != []; T = cdr(T), DT = cdr(DT) )
! 2160: PA = cons([car(T),car(DT)],PA);
! 2161: PA = reverse(PA);
! 2162: for ( PB = [], T = B, DT = DegB; T != []; T = cdr(T), DT = cdr(DT) )
! 2163: PB = cons([car(T),car(DT)],PB);
! 2164: PB = reverse(PB);
! 2165: R = [];
! 2166: for ( T = PA; T != []; T = cdr(T) )
! 2167: for ( S = PB; S != []; S = cdr(S) )
! 2168: R = cons([car(T)[0]*car(S)[0],car(T)[1]+car(S)[1]],R);
! 2169: T = qsort(R,noro_pd.comp_by_second);
! 2170: T = map(first,T);
! 2171: Len = length(A)>length(B)?length(A):length(B);
! 2172: Len *= 2;
! 2173: L = sep_list(T,Len); B0 = L[0]; B1 = L[1];
! 2174: R = fast_gb(B0,V,Mod,0);
! 2175: while ( B1 != [] ) {
! 2176: print(length(B1));
! 2177: L = sep_list(B1,Len);
! 2178: B0 = L[0]; B1 = L[1];
! 2179: R = fast_gb(append(R,B0),V,Mod,0|gbblock=[[0,length(R)]],nora=1);
! 2180: }
! 2181: return R;
! 2182: }
! 2183:
! 2184: def saturation(GNV,F,V)
! 2185: {
! 2186: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2187: G = GNV[0]; NV = GNV[1];
! 2188: if ( Mod )
! 2189: G1 = nd_gr(cons(NV*F-1,G),cons(NV,V),Mod,[[0,1],[0,length(V)]]);
! 2190: else if ( Procs ) {
! 2191: Arg0 = ["nd_gr_trace",
! 2192: cons(NV*F-1,G),cons(NV,V),0,GBCheck,[[0,1],[0,length(V)]]];
! 2193: Arg1 = ["nd_gr_trace",
! 2194: cons(NV*F-1,G),cons(NV,V),1,GBCheck,[[0,1],[0,length(V)]]];
! 2195: G1 = competitive_exec(Procs,Arg0,Arg1);
! 2196: } else
! 2197: G1 = nd_gr(cons(NV*F-1,G),cons(NV,V),0,[[0,1],[0,length(V)]]);
! 2198: return elimination(G1,V);
! 2199: }
! 2200:
! 2201: def sat(G,F,V)
! 2202: {
! 2203: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2204: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
! 2205: NV = ttttt;
! 2206: if ( Mod )
! 2207: G1 = nd_gr(cons(NV*F-1,G),cons(NV,V),Mod,[[0,1],[0,length(V)]]);
! 2208: else if ( Procs ) {
! 2209: Arg0 = ["nd_gr_trace",
! 2210: cons(NV*F-1,G),cons(NV,V),0,GBCheck,[[0,1],[0,length(V)]]];
! 2211: Arg1 = ["nd_gr_trace",
! 2212: cons(NV*F-1,G),cons(NV,V),1,GBCheck,[[0,1],[0,length(V)]]];
! 2213: G1 = competitive_exec(Procs,Arg0,Arg1);
! 2214: } else {
! 2215: B1 = append(G,[NV*F-1]);
! 2216: V1 = cons(NV,V);
! 2217: Ord1 = [[0,1],[0,length(V)]];
! 2218: if ( IsGB )
! 2219: G1 = nd_gr(B1,V1,0,Ord1|gbblock=[[0,length(G)]]);
! 2220: else
! 2221: G1 = nd_gr(B1,V1,0,Ord1);
! 2222: }
! 2223: return elimination(G1,V);
! 2224: }
! 2225:
! 2226: def isat(B,S,V)
! 2227: {
! 2228: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2229: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
! 2230: F = cdr(fctr(S));
! 2231: R = B;
! 2232: for ( T = F; T != []; T = cdr(T) )
! 2233: R = sat(R,car(T)[0],V|mod=Mod,isgb=IsGB);
! 2234: return R;
! 2235: }
! 2236:
! 2237: /* buggy; do not use */
! 2238: def satind(G,F,V)
! 2239: {
! 2240: if ( type(Block=getopt(gbblock)) == -1 ) Block = 0;
! 2241: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2242: NV = ttttt;
! 2243: N = length(V);
! 2244: B = append(G,[NV*F-1]);
! 2245: V1 = cons(NV,V);
! 2246: Ord1 = [[0,1],[0,N]];
! 2247: if ( Mod )
! 2248: if ( Block )
! 2249: D = nd_gr(B,V1,Mod,Ord1|nora=1,gentrace=1,gbblock=Block);
! 2250: else
! 2251: D = nd_gr(B,V1,Mod,Ord1|nora=1,gentrace=1);
! 2252: else
! 2253: if ( Block )
! 2254: D = nd_gr_trace(B,V1,SatHomo,GBCheck,Ord1
! 2255: |nora=1,gentrace=1,gbblock=Block);
! 2256: else
! 2257: D = nd_gr_trace(B,V1,SatHomo,GBCheck,Ord1
! 2258: |nora=1,gentrace=1);
! 2259: G1 = D[0];
! 2260: Len = length(G1);
! 2261: Deg = compute_deg(B,V1,NV,D);
! 2262: D1 = 0;
! 2263: R = [];
! 2264: M = length(B);
! 2265: for ( I = 0; I < Len; I++ ) {
! 2266: if ( !member(NV,vars(G1[I])) ) {
! 2267: for ( J = 1; J < M; J++ )
! 2268: D1 = MAX(D1,Deg[I][J]);
! 2269: R = cons(G1[I],R);
! 2270: }
! 2271: }
! 2272: return [reverse(R),D1];
! 2273: }
! 2274:
! 2275: /* homogeneous case only */
! 2276:
! 2277: def sat_ind_var(G,F,V)
! 2278: {
! 2279: if ( type(Ord=getopt(ord)) == -1 ) Ord = 0;
! 2280: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2281: V0 = append(setminus(V,[F]),[F]);
! 2282: G0 = nd_gr(G,V0,Mod,0);
! 2283: M = 0;
! 2284: for ( G1 = [], T = G0; T != []; T = cdr(T) ) {
! 2285: S = car(T);
! 2286: M1 = mindeg(S,F);
! 2287: S = sdiv(S,F^M1);
! 2288: G1 = cons(S,G1);
! 2289: if ( M1 > M ) M = M1;
! 2290: }
! 2291: G1 = nd_gr(G1,V,Mod,Ord);
! 2292: return [G1,M];
! 2293: }
! 2294:
! 2295: def sat_ind(G,F,V)
! 2296: {
! 2297: if ( type(Ord=getopt(ord)) == -1 ) Ord = 0;
! 2298: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2299: NV = ttttt;
! 2300: F = gen_nf(F,G,V,Ord,Mod);
! 2301: for ( I = 0, GI = G; ; I++ ) {
! 2302: G1 = colon(GI,F,V|mod=Mod,ord=Ord);
! 2303: if ( ideal_inclusion(G1,GI,V,Ord|mod=Mod) ) {
! 2304: return [GI,I];
! 2305: }
! 2306: else GI = G1;
! 2307: }
! 2308: }
! 2309:
! 2310: def colon(G,F,V)
! 2311: {
! 2312: if ( type(Ord=getopt(ord)) == -1 ) Ord = 0;
! 2313: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2314: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
! 2315: F = gen_nf(F,G,V,Ord,Mod);
! 2316: if ( !F ) return [1];
! 2317: if ( IsGB )
! 2318: T = ideal_intersection(G,[F],V,Ord|gbblock=[[0,length(G)]],mod=Mod);
! 2319: else
! 2320: T = ideal_intersection(G,[F],V,Ord|mod=Mod);
! 2321: Gen = Mod?map(sdivm,T,F,Mod):map(ptozp,map(sdiv,T,F));
! 2322: return nd_gr(Gen,V,Mod,Ord);
! 2323: }
! 2324:
! 2325: #if 1
! 2326: def ideal_colon(G,F,V)
! 2327: {
! 2328: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2329: G = nd_gr(G,V,Mod,0);
! 2330: C = [1];
! 2331: TV = ttttt;
! 2332: F = qsort(F,noro_pd.comp_tdeg);
! 2333: for ( T = F; T != []; T = cdr(T) ) {
! 2334: S = colon(G,car(T),V|isgb=1,mod=Mod);
! 2335: if ( type(S[0])!= 1 ) {
! 2336: C = nd_gr(append(vtol(ltov(C)*TV),vtol(ltov(S)*(1-TV))),
! 2337: cons(TV,V),Mod,[[0,1],[Ord,length(V)]]|gbblock=[[0,length(C)]]);
! 2338: C = elimination(C,V);
! 2339: }
! 2340: }
! 2341: return C;
! 2342: }
! 2343: #else
! 2344: def ideal_colon(G,F,V)
! 2345: {
! 2346: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2347: G = nd_gr(G,V,Mod,0);
! 2348: for ( T = F, L = []; T != []; T = cdr(T) ) {
! 2349: C = colon(G,car(T),V|isgb=1,mod=Mod);
! 2350: if ( type(C[0]) != 1 ) L = cons(C,L);
! 2351: }
! 2352: L = reverse(L);
! 2353: return ideal_list_intersection(L,V,0|mod=Mod);
! 2354: }
! 2355:
! 2356: #endif
! 2357:
! 2358: def member(A,L)
! 2359: {
! 2360: for ( ; L != []; L = cdr(L) )
! 2361: if ( car(L) == A ) return 1;
! 2362: return 0;
! 2363: }
! 2364:
! 2365: def mingen(B,V) {
! 2366: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2367: Data = nd_gr(B,V,Mod,O|gentrace=1,gensyz=1);
! 2368: G = Data[0]; STrace = Data[6];
! 2369: N = length(G);
! 2370: S = compute_gbsyz(N,V,STrace,Mod);
! 2371: for ( T = S, R = []; T != []; T = cdr(T) ) {
! 2372: for ( A = car(T); A1 = dp_rest(A); A = A1);
! 2373: if ( type(dp_hc(A)) ==1 ) R = cons(dp_etov(A)[0],R);
! 2374: }
! 2375: for ( I = 0, U = []; I < N; I++ ) if ( !member(I,R) ) U = cons(G[I],U);
! 2376: return U;
! 2377: }
! 2378:
! 2379: def compute_gbsyz(N,V,Trace,Mod)
! 2380: {
! 2381: P = vector(N);
! 2382: for ( I = 0; I < N; I++ ) P[I] = dp_ptod(x^I,[x]);
! 2383: for ( U = [], T = Trace; T != []; T = cdr(T) ) {
! 2384: Ti = car(T);
! 2385: if ( Ti[0] != -1 ) error("Input is not a GB");
! 2386: R = recompute_trace(Ti[1],P,V,Mod);
! 2387: U = cons(R,U);
! 2388: }
! 2389: return reverse(U);
! 2390: }
! 2391:
! 2392: def recompute_trace(Ti,P,V,Mod)
! 2393: {
! 2394: for ( Num = 0, Den = 1; Ti != []; Ti = cdr(Ti) ) {
! 2395: Sj = car(Ti); Dj = Sj[0]; Ij =Sj[1]; Mj = dp_dtop(Sj[2],V); Cj = Sj[3];
! 2396: /* Num/Den <- (Dj*Num+Den*Mj*P[Ij])/(Den*Cj) */
! 2397: if ( Dj ) Num = (Dj*Num+Den*Mj*P[Ij]);
! 2398: Den *= Cj;
! 2399: }
! 2400: return Num;
! 2401: }
! 2402:
! 2403: def ideal_sat(G,F,V)
! 2404: {
! 2405: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2406: G = nd_gr(G,V,Mod,0);
! 2407: for ( T = F, L = []; T != []; T = cdr(T) )
! 2408: L = cons(sat(G,car(T),V|mod=Mod),L);
! 2409: L = reverse(L);
! 2410: return ideal_list_intersection(L,V,0|mod=Mod);
! 2411: }
! 2412:
! 2413: def ideal_inclusion(F,G,V,O)
! 2414: {
! 2415: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2416: for ( T = F; T != []; T = cdr(T) )
! 2417: if ( gen_nf(car(T),G,V,O,Mod) ) return 0;
! 2418: return 1;
! 2419: }
! 2420:
! 2421: /* remove redundant components */
! 2422:
! 2423: def qd_simp_comp(QP,V)
! 2424: {
! 2425: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2426: R = ltov(QP);
! 2427: N = length(R);
! 2428: for ( I = 0; I < N; I++ ) {
! 2429: if ( R[I] ) {
! 2430: QI = R[I][0]; PI = R[I][1];
! 2431: for ( J = I+1; J < N; J++ )
! 2432: if ( R[J] && gen_gb_comp(PI,R[J][1],Mod) ) {
! 2433: QI = ideal_intersection(QI,R[J][0],V,0|mod=Mod);
! 2434: R[J] = 0;
! 2435: }
! 2436: R[I] = [QI,PI];
! 2437: }
! 2438: }
! 2439: for ( I = N-1, S = []; I >= 0; I-- )
! 2440: if ( R[I] ) S = cons(R[I],S);
! 2441: return S;
! 2442: }
! 2443:
! 2444: def qd_remove_redundant_comp(G,Iso,Emb,V,Ord)
! 2445: {
! 2446: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2447: IsoInt = ideal_list_intersection(map(first,Iso),V,Ord|mod=Mod);
! 2448: Emb = qd_simp_comp(Emb,V|mod=Mod);
! 2449: Emb = reverse(qsort(Emb));
! 2450: A = ltov(Emb); N = length(A);
! 2451: Pre = IsoInt; Post = vector(N+1);
! 2452: for ( Post[N] = IsoInt, I = N-1; I >= 1; I-- )
! 2453: Post[I] = ideal_intersection(Post[I+1],A[I][0],V,Ord|mod=Mod);
! 2454: for ( I = 0; I < N; I++ ) {
! 2455: print(".",2);
! 2456: Int = ideal_intersection(Pre,Post[I+1],V,Ord|mod=Mod);
! 2457: if ( gen_gb_comp(Int,G,Mod) ) A[I] = 0;
! 2458: else
! 2459: Pre = ideal_intersection(Pre,A[I][0],V,Ord|mod=Mod);
! 2460: }
! 2461: for ( T = [], I = 0; I < N; I++ )
! 2462: if ( A[I] ) T = cons(A[I],T);
! 2463: return reverse(T);
! 2464: }
! 2465:
! 2466: def pd_simp_comp(PL,V)
! 2467: {
! 2468: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2469: if ( type(First=getopt(first)) == -1 ) First = 0;
! 2470: A = ltov(PL); N = length(A);
! 2471: if ( N == 1 ) return PL;
! 2472: for ( I = 0; I < N; I++ ) {
! 2473: if ( !A[I] ) continue;
! 2474: AI = First?A[I][0]:A[I];
! 2475: for ( J = 0; J < N; J++ ) {
! 2476: if ( J == I || !A[J] ) continue;
! 2477: AJ = First?A[J][0]:A[J];
! 2478: if ( gen_gb_comp(AI,AJ,Mod) || ideal_inclusion(AI,AJ,V,Ord|mod=Mod) )
! 2479: A[J] = 0;
! 2480: }
! 2481: }
! 2482: for ( I = 0, T = []; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
! 2483: return reverse(T);
! 2484: }
! 2485:
! 2486: def pd_remove_redundant_comp(G,P,V,Ord)
! 2487: {
! 2488: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2489: if ( type(First=getopt(first)) == -1 ) First = 0;
! 2490: if ( length(P) == 1 ) return P;
! 2491:
! 2492: A = ltov(P); N = length(A);
! 2493: for ( I = 0; I < N; I++ ) {
! 2494: if ( !A[I] ) continue;
! 2495: for ( J = I+1; J < N; J++ )
! 2496: if ( A[J] &&
! 2497: gen_gb_comp(First?A[I][0]:A[I],First?A[J][0]:A[J],Mod) ) A[J] = 0;
! 2498: }
! 2499: for ( I = 0, T = []; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
! 2500: A = ltov(reverse(T)); N = length(A);
! 2501: Pre = [1]; Post = vector(N+1);
! 2502: for ( Post[N] = [1], I = N-1; I >= 1; I-- )
! 2503: Post[I] = ideal_intersection(Post[I+1],First?A[I][0]:A[I],V,Ord|mod=Mod);
! 2504: for ( I = 0; I < N; I++ ) {
! 2505: Int = ideal_intersection(Pre,Post[I+1],V,Ord|mod=Mod);
! 2506: if ( gen_gb_comp(Int,G,Mod) ) A[I] = 0;
! 2507: else
! 2508: Pre = ideal_intersection(Pre,First?A[I][0]:A[I],V,Ord|mod=Mod);
! 2509: }
! 2510: for ( T = [], I = 0; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
! 2511: return reverse(T);
! 2512: }
! 2513:
! 2514: def remove_identical_comp(L)
! 2515: {
! 2516: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2517: if ( length(L) == 1 ) return L;
! 2518:
! 2519: A = ltov(L); N = length(A);
! 2520: for ( I = 0; I < N; I++ ) {
! 2521: if ( !A[I] ) continue;
! 2522: for ( J = I+1; J < N; J++ )
! 2523: if ( A[J] &&
! 2524: gen_gb_comp(A[I],A[J],Mod) ) A[J] = 0;
! 2525: }
! 2526: for ( I = 0, T = []; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
! 2527: return reverse(T);
! 2528: }
! 2529:
! 2530: /* polynomial operations */
! 2531:
! 2532: def ppart(F,V,Mod)
! 2533: {
! 2534: if ( !Mod )
! 2535: G = nd_gr([F],[V],0,0);
! 2536: else
! 2537: G = dp_gr_mod_main([F],[V],0,Mod,0);
! 2538: return G[0];
! 2539: }
! 2540:
! 2541:
! 2542: def sq(F,Mod)
! 2543: {
! 2544: if ( !F ) return 0;
! 2545: A = cdr(gen_fctr(F,Mod));
! 2546: for ( R = 1; A != []; A = cdr(A) )
! 2547: R *= car(car(A));
! 2548: return R;
! 2549: }
! 2550:
! 2551: def lcfactor(G,V,O,Mod)
! 2552: {
! 2553: O0 = dp_ord(); dp_ord(O);
! 2554: C = [];
! 2555: for ( T = G; T != []; T = cdr(T) ) {
! 2556: C1 = dp_hc(dp_ptod(car(T),V));
! 2557: S = gen_fctr(C1,Mod);
! 2558: for ( S = cdr(S); S != []; S = cdr(S) )
! 2559: if ( !member(S[0][0],C) ) C = cons(S[0][0],C);
! 2560: }
! 2561: dp_ord(O0);
! 2562: return C;
! 2563: }
! 2564:
! 2565: def gen_fctr(F,Mod)
! 2566: {
! 2567: if ( Mod ) return modfctr(F,Mod);
! 2568: else return fctr(F);
! 2569: }
! 2570:
! 2571: def gen_mptop(F)
! 2572: {
! 2573: if ( !F ) return F;
! 2574: else if ( type(F)==1 )
! 2575: if ( ntype(F)==5 ) return mptop(F);
! 2576: else return F;
! 2577: else {
! 2578: V = var(F);
! 2579: D = deg(F,V);
! 2580: for ( R = 0, I = 0; I <= D; I++ )
! 2581: if ( C = coef(F,I,V) ) R += gen_mptop(C)*V^I;
! 2582: return R;
! 2583: }
! 2584: }
! 2585:
! 2586: def gen_nf(F,G,V,Ord,Mod)
! 2587: {
! 2588: if ( !Mod ) return p_nf(F,G,V,Ord);
! 2589:
! 2590: setmod(Mod);
! 2591: dp_ord(Ord); DF = dp_mod(dp_ptod(F,V),Mod,[]);
! 2592: N = length(G); DG = newvect(N);
! 2593: for ( I = N-1, IL = []; I >= 0; I-- ) {
! 2594: DG[I] = dp_mod(dp_ptod(G[I],V),Mod,[]);
! 2595: IL = cons(I,IL);
! 2596: }
! 2597: T = dp_nf_mod(IL,DF,DG,1,Mod);
! 2598: for ( R = 0; T; T = dp_rest(T) )
! 2599: R += gen_mptop(dp_hc(T))*dp_dtop(dp_ht(T),V);
! 2600: return R;
! 2601: }
! 2602:
! 2603: /* Ti = [D,I,M,C] */
! 2604:
! 2605: def compute_deg0(Ti,P,V,TV)
! 2606: {
! 2607: N = length(P[0]);
! 2608: Num = vector(N);
! 2609: for ( I = 0; I < N; I++ ) Num[I] = -1;
! 2610: for ( ; Ti != []; Ti = cdr(Ti) ) {
! 2611: Sj = car(Ti);
! 2612: Dj = Sj[0];
! 2613: Ij =Sj[1];
! 2614: Mj = deg(type(Sj[2])==9?dp_dtop(Sj[2],V):Sj[2],TV);
! 2615: Pj = P[Ij];
! 2616: if ( Dj )
! 2617: for ( I = 0; I < N; I++ )
! 2618: if ( Pj[I] >= 0 ) {
! 2619: T = Mj+Pj[I];
! 2620: Num[I] = MAX(Num[I],T);
! 2621: }
! 2622: }
! 2623: return Num;
! 2624: }
! 2625:
! 2626: def compute_deg(B,V,TV,Data)
! 2627: {
! 2628: GB = Data[0];
! 2629: Homo = Data[1];
! 2630: Trace = Data[2];
! 2631: IntRed = Data[3];
! 2632: Ind = Data[4];
! 2633: DB = map(dp_ptod,B,V);
! 2634: if ( Homo ) {
! 2635: DB = map(dp_homo,DB);
! 2636: V0 = append(V,[hhh]);
! 2637: } else
! 2638: V0 = V;
! 2639: Perm = Trace[0]; Trace = cdr(Trace);
! 2640: for ( I = length(Perm)-1, T = Trace; T != []; T = cdr(T) )
! 2641: if ( (J=car(T)[0]) > I ) I = J;
! 2642: N = I+1;
! 2643: N0 = length(B);
! 2644: P = vector(N);
! 2645: for ( T = Perm, I = 0; T != []; T = cdr(T), I++ ) {
! 2646: Pi = car(T);
! 2647: C = vector(N0);
! 2648: for ( J = 0; J < N0; J++ ) C[J] = -1;
! 2649: C[Pi[1]] = 0;
! 2650: P[Pi[0]] = C;
! 2651: }
! 2652: for ( T = Trace; T != []; T = cdr(T) ) {
! 2653: Ti = car(T); P[Ti[0]] = compute_deg0(Ti[1],P,V0,TV);
! 2654: }
! 2655: M = length(Ind);
! 2656: for ( T = IntRed; T != []; T = cdr(T) ) {
! 2657: Ti = car(T); P[Ti[0]] = compute_deg0(Ti[1],P,V,TV);
! 2658: }
! 2659: R = [];
! 2660: for ( J = 0; J < M; J++ ) {
! 2661: U = P[Ind[J]];
! 2662: R = cons(U,R);
! 2663: }
! 2664: return reverse(R);
! 2665: }
! 2666:
! 2667: /* set theoretic functions */
! 2668:
! 2669: def member(A,S)
! 2670: {
! 2671: for ( ; S != []; S = cdr(S) )
! 2672: if ( car(S) == A ) return 1;
! 2673: return 0;
! 2674: }
! 2675:
! 2676: def elimination(G,V) {
! 2677: for ( R = [], T = G; T != []; T = cdr(T) )
! 2678: if ( setminus(vars(car(T)),V) == [] ) R =cons(car(T),R);
! 2679: return R;
! 2680: }
! 2681:
! 2682: def setintersection(A,B)
! 2683: {
! 2684: for ( L = []; A != []; A = cdr(A) )
! 2685: if ( member(car(A),B) )
! 2686: L = cons(car(A),L);
! 2687: return L;
! 2688: }
! 2689:
! 2690: def setminus(A,B) {
! 2691: for ( T = reverse(A), R = []; T != []; T = cdr(T) ) {
! 2692: for ( S = B, M = car(T); S != []; S = cdr(S) )
! 2693: if ( car(S) == M ) break;
! 2694: if ( S == [] ) R = cons(M,R);
! 2695: }
! 2696: return R;
! 2697: }
! 2698:
! 2699: def sep_list(L,N)
! 2700: {
! 2701: if ( length(L) <= N ) return [L,[]];
! 2702: R = [];
! 2703: for ( T = L, I = 0; I < N; I++, T = cdr(T) )
! 2704: R = cons(car(T),R);
! 2705: return [reverse(R),T];
! 2706: }
! 2707:
! 2708: def first(L)
! 2709: {
! 2710: return L[0];
! 2711: }
! 2712:
! 2713: def second(L)
! 2714: {
! 2715: return L[1];
! 2716: }
! 2717:
! 2718: def third(L)
! 2719: {
! 2720: return L[2];
! 2721: }
! 2722:
! 2723: def first_second(L)
! 2724: {
! 2725: return [L[0],L[1]];
! 2726: }
! 2727:
! 2728: def comp_tord(A,B)
! 2729: {
! 2730: DA = dp_ht(A);
! 2731: DB = dp_ht(B);
! 2732: if ( DA > DB ) return 1;
! 2733: else if ( DA < DB ) return -1;
! 2734: else return 0;
! 2735: }
! 2736:
! 2737: def comp_tdeg(A,B)
! 2738: {
! 2739: DA = tdeg(A);
! 2740: DB = tdeg(B);
! 2741: if ( DA > DB ) return 1;
! 2742: else if ( DA < DB ) return -1;
! 2743: else return 0;
! 2744: }
! 2745:
! 2746: def comp_tdeg_first(A,B)
! 2747: {
! 2748: DA = tdeg(A[0]);
! 2749: DB = tdeg(B[0]);
! 2750: if ( DA > DB ) return 1;
! 2751: else if ( DA < DB ) return -1;
! 2752: else return 0;
! 2753: }
! 2754:
! 2755: def comp_third_tdeg(A,B)
! 2756: {
! 2757: if ( A[2] > B[2] ) return 1;
! 2758: if ( A[2] < B[2] ) return -1;
! 2759: DA = tdeg(A[0]);
! 2760: DB = tdeg(B[0]);
! 2761: if ( DA > DB ) return 1;
! 2762: else if ( DA < DB ) return -1;
! 2763: else return 0;
! 2764: }
! 2765:
! 2766: def tdeg(P)
! 2767: {
! 2768: dp_ord(0);
! 2769: return dp_td(dp_ptod(P,vars(P)));
! 2770: }
! 2771:
! 2772: def comp_by_ord(A,B)
! 2773: {
! 2774: if ( dp_ht(A) > dp_ht(B) ) return 1;
! 2775: else if ( dp_ht(A) < dp_ht(B) ) return -1;
! 2776: else return 0;
! 2777: }
! 2778:
! 2779: def comp_by_second(A,B)
! 2780: {
! 2781: if ( A[1] > B[1] ) return 1;
! 2782: else if ( A[1] < B[1] ) return -1;
! 2783: else return 0;
! 2784: }
! 2785:
! 2786: def get_lc(F)
! 2787: {
! 2788: if ( type(F)==1 ) return F;
! 2789: V = var(F);
! 2790: D = deg(F,V);
! 2791: return get_lc(coef(F,D,V));
! 2792: }
! 2793:
! 2794: def tomonic(F,Mod)
! 2795: {
! 2796: C = get_lc(F);
! 2797: IC = inv(C,Mod);
! 2798: return (IC*F)%Mod;
! 2799: }
! 2800:
! 2801: def gen_gb_comp(A,B,Mod)
! 2802: {
! 2803: if ( !Mod ) return gb_comp(A,B);
! 2804: LA = length(A); LB = length(B);
! 2805: if ( LA != LB ) return 0;
! 2806: A = map(tomonic,A,Mod);
! 2807: B = map(tomonic,B,Mod);
! 2808: A = qsort(A); B = qsort(B);
! 2809: if ( A != B ) return 0;
! 2810: return 1;
! 2811: }
! 2812:
! 2813: def prod(L)
! 2814: {
! 2815: for ( R = 1; L != []; L = cdr(L) )
! 2816: R *= car(L);
! 2817: return R;
! 2818: }
! 2819:
! 2820: def monodec0(B,V)
! 2821: {
! 2822: M = monodec(B,V);
! 2823: return map(vars,M);
! 2824: }
! 2825:
! 2826: def monodec(B,V)
! 2827: {
! 2828: B = map(sq,B,0);
! 2829: G = nd_gr_postproc(B,V,0,0,0);
! 2830: V = vars(G);
! 2831: N = length(V);
! 2832: if ( N == 0 ) return G == [] ? [[]] : [];
! 2833: if ( N == 1 ) return G;
! 2834: if ( N < 20 ) {
! 2835: T = dp_mono_raddec(G,V);
! 2836: return map(prod,T);
! 2837: }
! 2838: X = car(V); W = cdr(V);
! 2839: D0 = monodec(map(subst,B,X,0),W);
! 2840: T0 = map(dp_ptod,D0,W);
! 2841: D1 = monodec(map(subst,B,X,1),W);
! 2842: T1 = map(dp_ptod,D1,W);
! 2843: #if 0
! 2844: for ( T = T1; T != []; T = cdr(T) ) {
! 2845: for ( M = car(T), S1 = [], S = T0; S != []; S = cdr(S) )
! 2846: if ( !dp_redble(car(S),M) ) S1= cons(car(S),S1);
! 2847: T0 = S1;
! 2848: }
! 2849: #else
! 2850: T0 = dp_mono_reduce(T0,T1);
! 2851: #endif
! 2852: D0 = map(dp_dtop,T0,W);
! 2853: D0 = vtol(X*ltov(D0));
! 2854: return append(D0,D1);
! 2855: }
! 2856:
! 2857: def separator(P,V)
! 2858: {
! 2859: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2860: N = length(P);
! 2861: dp_ord(0);
! 2862: DP = vector(N);
! 2863: for ( I = 0; I < N; I++ ) DP[I] = qsort(ltov(map(dp_ptod,P[I][0],V)),noro_pd.comp_tord);
! 2864: if ( Mod )
! 2865: for ( I = 0; I < N; I++ ) DP[I] = map(dp_mod,DP[I],Mod,[]);
! 2866: Ind = vector(N);
! 2867: for ( I = 0; I < N; I++ ) {
! 2868: for ( K = [], J = length(DP[I])-1; J >= 0; J-- ) K = cons(J,K);
! 2869: Ind[I] = K;
! 2870: }
! 2871: S = vector(N);
! 2872: for ( I = 0; I < N; I++ ) S[I] = 1;
! 2873: for ( I = 0; I < N; I++ ) {
! 2874: print(".",2);
! 2875: for ( J = 0; J < N; J++ ) {
! 2876: if ( J == I ) continue;
! 2877: T = DP[I]; L = length(T);
! 2878: if ( Mod ) {
! 2879: for ( K = 0; K < L; K++ )
! 2880: if ( dp_nf_mod(Ind[J],T[K],DP[J],0,Mod) ) break;
! 2881: } else {
! 2882: for ( K = 0; K < L; K++ )
! 2883: if ( dp_nf(Ind[J],T[K],DP[J],0) ) break;
! 2884: }
! 2885: S[J] = lcm(S[J],dp_dtop(T[K],V));
! 2886: }
! 2887: }
! 2888: print("");
! 2889: return S;
! 2890: }
! 2891:
! 2892: def prepost(PL,V)
! 2893: {
! 2894: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
! 2895: A = ltov(PL); N = length(A);
! 2896: Pre = vector(N);
! 2897: Post = vector(N);
! 2898: R = vector(N);
! 2899: Pre[0] = [1];
! 2900: print("pre ",2);
! 2901: for ( I = 1; I < N; I++, print(".",2) )
! 2902: Pre[I] = ideal_intersection_m(Pre[I-1],A[I-1],V,0|mod=Mod);
! 2903: print("done");
! 2904: print("post ",2);
! 2905: Post[N-1] = [1];
! 2906: for ( I = N-2; I >= 0; I--, print(".",2) )
! 2907: Post[I] = ideal_intersection_m(Post[I+1],A[I+1],V,0|mod=Mod);
! 2908: print("done");
! 2909: print("int ",2);
! 2910: for ( I = 0; I < N; I++, print(".",2) )
! 2911: R[I] = ideal_intersection_m(Pre[I],Post[I],V,0|mod=Mod);
! 2912: print("done");
! 2913: return R;
! 2914: }
! 2915:
! 2916: /* XXX */
! 2917:
! 2918: def call_func(Arg)
! 2919: {
! 2920: F = car(Arg);
! 2921: return call(strtov(F),cdr(Arg));
! 2922: }
! 2923:
! 2924: def call_func_serial(Arg,Serial)
! 2925: {
! 2926: F = car(Arg);
! 2927: return [call(strtov(F),cdr(Arg)),Serial];
! 2928: }
! 2929:
! 2930: def competitive_exec(P,Arg0,Arg1)
! 2931: {
! 2932: P0 = P[0]; P1 = P[1];
! 2933: ox_cmo_rpc(P0,"noro_pd.call_func",Arg0|sync=1);
! 2934: ox_cmo_rpc(P1,"noro_pd.call_func",Arg1|sync=1);
! 2935: F = ox_select(P);
! 2936: R = ox_get(F[0]);
! 2937: if ( length(F) == 2 ) {
! 2938: ox_get(F[1]);
! 2939: } else {
! 2940: U = setminus(P,F);
! 2941: ox_reset(U[0]);
! 2942: }
! 2943: return R;
! 2944: }
! 2945:
! 2946:
! 2947: def nd_gr_rat(B,V,PV,Ord1,Ord)
! 2948: {
! 2949: G = nd_gr(B,append(V,PV),0,Ord1);
! 2950: G1 = nd_gr_postproc(G,V,0,Ord,0);
! 2951: return G1;
! 2952: }
! 2953:
! 2954: /* Task[i] = [fname,[arg0,...,argn]] */
! 2955:
! 2956: def para_exec(Proc,Task) {
! 2957: Free = Proc;
! 2958: N = length(Task);
! 2959: R = [];
! 2960: print([N],2); print("->",2);
! 2961: Serial = 0;
! 2962: while ( N ) {
! 2963: while ( Task != [] && Free != [] ) {
! 2964: T = car(Task); Task = cdr(Task);
! 2965: ox_rpc(car(Free),"noro_pd.call_func_serial",T,Serial++);
! 2966: ox_push_cmd(car(Free),258); Free = cdr(Free);
! 2967: }
! 2968: Finish0 = Finish = ox_select(Proc);
! 2969: for ( ; Finish != []; Finish = cdr(Finish) ) {
! 2970: print(".",2);
! 2971: L = ox_get(car(Finish));
! 2972: R = cons(L,R);
! 2973: N--;
! 2974: }
! 2975: print([N],2);
! 2976: Free = append(Free,Finish0);
! 2977: }
! 2978: print("");
! 2979: R = qsort(R,noro_pd.comp_by_second);
! 2980: R = map(first,R);
! 2981: return R;
! 2982: }
! 2983:
! 2984: def redbase(B,V,Mod,Ord)
! 2985: {
! 2986: M = nd_gr_postproc(B,V,Mod,Ord,0);
! 2987: dp_ord(Ord);
! 2988: DM = ltov(map(dp_ptod,M,V));
! 2989: if ( Mod ) DM = map(dp_mod,DM,Mod,[]);
! 2990: N = length(DM);
! 2991: for ( Ind = [], I = N-1; I >= 0; I-- ) Ind = cons(I,Ind);
! 2992: for ( T = B, R = vtol(DM); T != []; T = cdr(T) ) {
! 2993: D = dp_ptod(car(T),V);
! 2994: if ( Mod ) D = dp_mod(D,Mod,[]);
! 2995: D = Mod?dp_nf_mod(Ind,D,DM,1,Mod):dp_nf(Ind,D,DM,1);
! 2996: if ( D ) R = cons(D,R);
! 2997: }
! 2998: D = qsort(R,noro_pd.comp_tord);
! 2999: return map(dp_dtop,D,V);
! 3000: }
! 3001:
! 3002: def witness(A,B,V)
! 3003: {
! 3004: G = nd_gr(B,V,0,Mod);
! 3005: L = length(A);
! 3006: QL = []; PL = [];
! 3007: for ( I = L-1; I >= 0; I-- ) {
! 3008: QL = append(map(first,A[I]),QL);
! 3009: PL = append(map(second,A[I]),PL);
! 3010: }
! 3011: N = length(QL);
! 3012: Qhat = prepost(QL,V);
! 3013: for ( I = 0, W = []; I < N; I++ ) {
! 3014: for ( T = Qhat[I]; T != []; T = cdr(T) )
! 3015: if ( gen_nf(car(T),QL[I],V,0,Mod) ) break;
! 3016: Ai = car(T);
! 3017: Ji = colon(G,Ai,V|isgb=1,mod=Mod);
! 3018: Ji = nd_gr(Ji,V,Mod,0);
! 3019: if ( gen_gb_comp(Ji,PL[I],Mod) ) Bi = 1;
! 3020: else {
! 3021: Ki = ideal_colon(Ji,PL[I],V|mod=Mod);
! 3022: for ( T = Ki; T != []; T = cdr(T) )
! 3023: if ( gen_nf(car(T),Ji,V,0,Mod) ) break;
! 3024: Bi = car(T);
! 3025: }
! 3026: W = cons(Ai*Bi,W);
! 3027: Li = colon(G,W[0],V|isgb=1,mod=Mod);
! 3028: Li = nd_gr(Li,V,Mod,0);
! 3029: if ( !gen_gb_comp(Li,PL[I],Mod) )
! 3030: error("afo");
! 3031: }
! 3032: return reverse(W);
! 3033: }
! 3034: endmodule$
! 3035: end$
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