=================================================================== RCS file: /home/cvs/OpenXM/src/asir-contrib/testing/noro/Attic/new_pd.rr,v retrieving revision 1.1 retrieving revision 1.4 diff -u -p -r1.1 -r1.4 --- OpenXM/src/asir-contrib/testing/noro/Attic/new_pd.rr 2011/01/16 08:46:10 1.1 +++ OpenXM/src/asir-contrib/testing/noro/Attic/new_pd.rr 2011/02/18 02:59:04 1.4 @@ -1,18 +1,18 @@ -/* $OpenXM$ */ +/* $OpenXM: OpenXM/src/asir-contrib/testing/noro/new_pd.rr,v 1.3 2011/01/19 04:52:03 noro Exp $ */ import("gr")$ module noro_pd$ static GBCheck,F4,EProcs,Procs,SatHomo,GBRat$ -localf get_lc,tomonic$ +localf witness$ +localf get_lc,tomonic,aa,ideal_intersection_m,redbase$ localf para_exec,nd_gr_rat,competitive_exec,call_func$ localf call_ideal_list_intersection$ +localf call_colon,call_prime_dec$ localf first_second$ localf third$ localf locsat,iso_comp_para,extract_qj,colon_prime_dec,extract_comp$ -localf colon_prime_dec1$ localf separator$ -localf member,mingen,compute_gbsyz,redcoef,recompute_trace3,dtop,topnum$ -localf ideal_colon1$ +localf member,mingen,compute_gbsyz,redcoef,recompute_trace,dtop,topnum$ localf prepost$ localf monodec0,monodec,prod$ localf extract_qd,primary_check$ @@ -38,7 +38,7 @@ localf rsgn, find_npos, gen_minipoly, indepset$ localf maxindep, contraction, ideal_list_intersection, ideal_intersection$ localf radical_membership, modular_radical_membership$ localf radical_membership_rep, ideal_product, saturation$ -localf sat, satind, sat_ind, colon$ +localf sat, satind, sat_ind, colon, isat$ localf ideal_colon, ideal_sat, ideal_inclusion, qd_simp_comp, qd_remove_redundant_comp$ localf pd_simp_comp$ localf pd_remove_redundant_comp, ppart, sq, gen_fctr, gen_nf, gen_gb_comp$ @@ -284,22 +284,41 @@ T0 = time(); if ( First ) { PtR = prime_dec(G,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1); Pt = PtR[0]; IntPt = PtR[1]; Rad = IntPt; + if ( gen_gb_comp(G,Rad,Mod) ) { + /* Gt is radical and Gt = cap Pt */ + for ( T = Pt, Qt = []; T != []; T = cdr(T) ) + Qt = cons([car(T)[0],car(T)[0],car(T)[1]],Qt); + return [reverse(Qt)]; + } } else Pt = colon_prime_dec(G,IntQ,V|lexdec=Lexdec,mod=Mod,para=Para); ACCUM_TIME(Tpd,RTpd) T0 = time(); Rt = iso_comp(G,Pt,V,Ord|mod=Mod,iso=Iso,para=Para,intq=IntQ); - RL = append(RL,[Rt]); ACCUM_TIME(Tiso,RTiso) T0 = time(); - IntQ = ideal_list_intersection(map(first,Rt),V,Ord|mod=Mod,para=Para); + if ( Iso != 3 ) { + IntQ = ideal_list_intersection(map(first,Rt),V,Ord|mod=Mod,para=Para,isgb=1); + RL = append(RL,[Rt]); + } else { + NI = length(Rt); + Q = IntQ; + for ( J = 0, T = []; J < NI; J++ ) { + TJ = extract_qj(Q,V,Rt[J],Rad,Mod,SI,Colon,-1); + T = cons(TJ,T); + IntQ = ideal_intersection_m(IntQ,TJ[0],V,Ord|mod=Mod); + } + print(""); + IntQ = nd_gr(IntQ,V,Mod,Ord); + T = reverse(T); RL = append(RL,[T]); + } QL = append(QL,[IntQ]); ACCUM_TIME(Tint,RTint) if ( gen_gb_comp(IntQ,G,Mod) ) break; First = 0; } T0 = time(); - if ( !Ass ) + if ( Iso != 3 && !Ass ) RL = extract_comp(QL,RL,V,Rad|mod=Mod,para=Para,si=SI,colon=Colon,ass=Ass); ACCUM_TIME(Text,RText) if ( Time ) { @@ -359,21 +378,40 @@ def colon_prime_dec(G,IntQ,V) { if ( type(Mod=getopt(mod)) == -1 ) Mod = 0; if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0; if ( type(Para=getopt(para)) == -1 ) Para = 0; + if ( !Para ) { + print("colon_pd:",2); print(length(IntQ),2); + } if ( !Mod ) M = mingen(IntQ,V); else M = IntQ; if ( Para ) { L = length(M); - for ( Task = [], J = 0, RI = []; J < L; J++ ) + for ( Task = [], J = 0; J < L; J++ ) if ( gen_nf(M[J],G,V,Ord,Mod) ) { - T = ["noro_pd.colon_prime_dec1",G,M[J],Mod,V]; + T = ["noro_pd.call_colon",G,M[J],V,Mod,1]; Task = cons(T,Task); } Task = reverse(Task); R = para_exec(Para,Task); + R = pd_simp_comp(R,V|mod=Mod); L = length(R); + + for ( Task = [], J = 0; J < L; J++ ) { + T = ["noro_pd.call_prime_dec",R[J],V,1,Lexdec,Mod]; + Task = cons(T,Task); + } + Task = reverse(Task); + R = para_exec(Para,Task); + for ( Pt = [], T = R; T != []; T = cdr(T) ) Pt = append(Pt,car(T)); } else { - for ( Pt = [], T = M; T != []; T = cdr(T) ) { - Pi = colon_prime_dec1(G,car(T),Mod,V); + for ( R = [], T = M; T != []; T = cdr(T) ) { + Ci = colon(G,car(T),V|isgb=1,mod=Mod); + R = cons(Ci,R); + } + print("->",2); print(length(M),2); + R = pd_simp_comp(R,V|mod=Mod); + print("->",2); print(length(R)); + for ( Pt = [], T = R; T != []; T = cdr(T) ) { + Pi = prime_dec(car(T),V|indep=1,lexdec=Lexdec,mod=Mod); Pt = append(Pt,Pi); } } @@ -381,11 +419,15 @@ def colon_prime_dec(G,IntQ,V) { return Pt; } -def colon_prime_dec1(G,F,Mod,V) +def call_colon(G,F,V,Mod,IsGB) { - Ci = colon(G,F,V|isgb=1,mod=Mod); - if ( type(Ci[0]) != 1 ) - Pi = prime_dec(Ci,V|indep=1,lexdec=Lexdec,mod=Mod); + return colon(G,F,V|isgb=1,mod=Mod); +} + +def call_prime_dec(G,V,Indep,Lexdec,Mod) +{ + if ( type(G[0]) != 1 ) + Pi = prime_dec(G,V|indep=Indep,lexdec=Lexdec,mod=Mod); else Pi = []; return Pi; @@ -396,8 +438,11 @@ def extract_qj(Q,V,QL,Rad,Mod,SI,Colon,Level) SIFList=[find_ssi0, find_ssi1,find_ssi2]; SIF = SIFList[SI]; G = QL[0]; P = QL[1]; PV = QL[2]; - C = Colon ? ideal_colon(G,Q,V|mod=Mod) : P; - Ok = (*SIF)(C,G,Q,Rad,V,0|mod=Mod); + if ( Q != [1] ) { + C = Colon ? ideal_colon(G,Q,V|mod=Mod) : P; + Ok = (*SIF)(C,G,Q,Rad,V,0|mod=Mod); + } else + Ok = []; V0 = setminus(V,PV); HJ = elim_gb(append(Ok,G),V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]); HJ = contraction(HJ,V0|mod=Mod); @@ -809,7 +854,7 @@ def find_ssi2(C,G,Q,Rad,V,Ord) { if ( Reduce ) { for ( T = C, C1 = [], R1 = Rad; T != []; T = cdr(T) ) { if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue; - if ( radical_membership(car(T),R1,V) ) { + if ( radical_membership(car(T),R1,V|mod=Mod) ) { C1 = cons(car(T),C1); R1 = cons(sq(car(T),Mod),R1); } @@ -955,8 +1000,9 @@ def iso_comp(G,L,V,Ord) if ( type(Iso=getopt(iso)) == -1 ) Iso = 0; if ( type(Para=getopt(para)) == -1 ) Para = 0; if ( type(Q=getopt(intq)) == -1 ) Q = 0; + if ( type(S=getopt(sep)) == -1 ) S = 0; - S = separator(L,V|mod=Mod); + if ( !S ) S = separator(L,V|mod=Mod); N = length(L); print("comps : ",2); print(N); print("",2); if ( Para ) { @@ -1002,6 +1048,8 @@ def locsat(G,V,L,S,Mod,IsGB,Iso,Q) 1,1,[[0,1],[0,length(V0)]]|gbblock=[[0,length(HI)]]); GI = elimination(GI,V); GI = nd_gr(contraction(GI,V0|mod=Mod),V,Mod,0); + } else if ( Iso==3 ) { + GI = sat(G,S,V|isgb=IsGB,mod=Mod); } if ( Q ) GI = ideal_intersection(Q,GI,V,0|mod=Mod); @@ -1081,11 +1129,15 @@ def prime_dec_main(B,V) G = fast_gb(B,V,Mod,0); IntP = [1]; PD = []; + DG = ltov(map(dp_ptod,G,V)); + for ( Ind = [], I = length(G)-1; I >= 0; I-- ) Ind = cons(I,Ind); + if ( Mod ) DG = map(dp_mod,DG,Mod,[]); while ( 1 ) { /* rad(G) subset IntP */ /* check if IntP subset rad(G) */ + /* print([length(PD),length(IntP)],2); */ for ( T = IntP; T != []; T = cdr(T) ) { - if ( (GNV = radical_membership(car(T),G,V|mod=Mod,isgb=1)) ) { + if ( (GNV = radical_membership(car(T),G,V|mod=Mod,isgb=1,dg=[DG,Ind])) ) { F = car(T); break; } @@ -1106,7 +1158,12 @@ def prime_dec_main(B,V) Int = ideal_list_intersection(PD0,V,0|mod=Mod); PD = append(PD,PD0); } - IntP = ideal_intersection(IntP,Int,V,0|mod=Mod); +#if 0 + IntP = ideal_intersection_m(IntP,Int,V,0|mod=Mod); +#else + IntP = ideal_intersection(IntP,Int,V,0 + |mod=Mod,gbblock=[[0,length(IntP)]]); +#endif } } @@ -1458,7 +1515,7 @@ def elim_gb(G,V,PV,Mod,Ord) return G1; } else #if 1 -#if 1 +#if 0 G = dp_gr_main(G,V,0,0,Ord); #else G = nd_gr_trace(G,V,1,1,Ord); @@ -1652,29 +1709,37 @@ def contraction(G,V) def ideal_list_intersection(L,V,Ord) { if ( type(Mod=getopt(mod)) == -1 ) Mod = 0; + if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0; if ( type(Para=getopt(para)) == -1 || type(Para) != 4 ) Para = []; N = length(L); if ( N == 0 ) return [1]; - if ( N == 1 ) return fast_gb(L[0],V,Mod,Ord); - N2 = idiv(N,2); - for ( L1 = [], I = 0; I < N2; I++ ) L1 = cons(L[I],L1); - for ( L2 = []; I < N; I++ ) L2 = cons(L[I],L2); - if ( length(Para) >= 2 ) { - T1 = ["noro_pd.call_ideal_list_intersection",L1,V,Mod,Ord]; - T2 = ["noro_pd.call_ideal_list_intersection",L2,V,Mod,Ord]; - R = para_exec(Para,[T1,T2]); - I1 = R[0]; I2 = R[1]; + if ( N == 1 ) + return IsGB ? L[0] : fast_gb(L[0],V,Mod,Ord); + if ( N > 2 && (Len = length(Para)) >= 2 ) { + Div = N >= 2*Len ? Len : 2; + QR = iqr(N,Div); Q = QR[0]; R = QR[1]; + T = []; K = 0; + for ( I = 0; I < Div; I++ ) { + LenI = I= 0; I-- ) Ind = cons(I,Ind); + for ( T = DA, C = []; T != []; T = cdr(T) ) { + L = Mod?dp_true_nf_mod(Ind,car(T),DB,1,Mod):dp_true_nf(Ind,car(T),DB,1); + R = dp_dtop(L[0],V); Q = dp_dtop(car(T)*L[1]-L[0],V); + C = cons([R,-Q],C); + } + G = nd_gr(append(C,map(aa,B)),V,Mod,[1,Ord]|intersect=1); + G = map(second,G); + return G; +} + /* returns GB if F notin rad(G) */ def radical_membership(F,G,V) { if ( type(Mod=getopt(mod)) == -1 ) Mod = 0; if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0; - F = gen_nf(F,G,V,0,Mod); - if ( !F ) return 0; - F2 = gen_nf(F*F,G,V,0,Mod); - if ( !F2 ) return 0; - F3 = gen_nf(F2*F,G,V,0,Mod); - if ( !F3 ) return 0; + if ( type(L=getopt(dg)) == -1 ) L = 0; + dp_ord(0); + if ( L ) { DG = L[0]; Ind = L[1]; } + else { + DG = ltov(map(dp_ptod,G,V)); + if ( Mod ) DG = map(dp_mod,DG,Mod,[]); + for ( Ind = [], I = length(G)-1; I >= 0; I-- ) Ind = cons(I,Ind); + } + DF = dp_ptod(F,V); DFI = dp_ptod(1,V); + if ( Mod ) { + DF = dp_mod(DF,Mod,[]); DFI = dp_mod(DFI,Mod,[]); + setmod(Mod); + } + for ( I = 0; I < 3; I++ ) { + DFI = Mod?dp_nf_mod(Ind,DF*DFI,DG,0,Mod):dp_nf(Ind,DF*DFI,DG,0); + if ( !DFI ) return 0; + } NV = ttttt; if ( IsGB ) T = nd_gr(append(G,[NV*F-1]),cons(NV,V),Mod,0 @@ -1844,6 +1945,17 @@ def sat(G,F,V) return elimination(G1,V); } +def isat(B,S,V) +{ + if ( type(Mod=getopt(mod)) == -1 ) Mod = 0; + if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0; + F = cdr(fctr(S)); + R = B; + for ( T = F; T != []; T = cdr(T) ) + R = sat(R,car(T)[0],V|mod=Mod,isgb=IsGB); + return R; +} + def satind(G,F,V) { if ( type(Block=getopt(gbblock)) == -1 ) Block = 0; @@ -1907,7 +2019,8 @@ def colon(G,F,V) T = ideal_intersection(G,[F],V,Ord|gbblock=[[0,length(G)]],mod=Mod); else T = ideal_intersection(G,[F],V,Ord|mod=Mod); - return Mod?map(sdivm,T,F,Mod):map(ptozp,map(sdiv,T,F)); + Gen = Mod?map(sdivm,T,F,Mod):map(ptozp,map(sdiv,T,F)); + return nd_gr(Gen,V,Mod,Ord); } #if 1 @@ -1943,14 +2056,6 @@ def ideal_colon(G,F,V) #endif -def ideal_colon1(G,F,V) -{ - if ( type(Mod=getopt(mod)) == -1 ) Mod = 0; - F = qsort(F,comp_tdeg); - T = mingen(F,V|mod=Mod); - return ideal_colon(G,T,V|mod=Mod); -} - def member(A,L) { for ( ; L != []; L = cdr(L) ) @@ -1961,85 +2066,41 @@ def member(A,L) def mingen(B,V) { if ( type(Mod=getopt(mod)) == -1 ) Mod = 0; Data = nd_gr(B,V,Mod,O|gentrace=1,gensyz=1); - G = Data[0]; - S = compute_gbsyz(V,Data); - S = dtop(S,V); - R = topnum(S); + G = Data[0]; STrace = Data[6]; N = length(G); - U = []; - for ( I = 0; I < N; I++ ) - if ( !member(I,R) ) U = cons(G[I],U); + S = compute_gbsyz(N,V,STrace,Mod); + for ( T = S, R = []; T != []; T = cdr(T) ) { + for ( A = car(T); A1 = dp_rest(A); A = A1); + if ( type(dp_hc(A)) ==1 ) R = cons(dp_etov(A)[0],R); + } + for ( I = 0, U = []; I < N; I++ ) if ( !member(I,R) ) U = cons(G[I],U); return U; } -def compute_gbsyz(V,Data) +def compute_gbsyz(N,V,Trace,Mod) { - G = Data[0]; - Homo = Data[1]; - Trace = Data[2]; - IntRed = Data[3]; - Ind = Data[4]; - InputRed = Data[5]; - SpairTrace = Data[6]; - DB = map(dp_ptod,G,V); - N = length(G); P = vector(N); - for ( I = 0; I < N; I++ ) { - C = vector(N); C[I] = 1; P[I] = C; - } - U = []; - for ( T = SpairTrace; T != []; T = cdr(T) ) { + for ( I = 0; I < N; I++ ) P[I] = dp_ptod(x^I,[x]); + for ( U = [], T = Trace; T != []; T = cdr(T) ) { Ti = car(T); if ( Ti[0] != -1 ) error("Input is not a GB"); - R = recompute_trace3(Ti[1],P,0); - U = cons(redcoef(R)[0],U); + R = recompute_trace(Ti[1],P,V,Mod); + U = cons(R,U); } return reverse(U); } -def redcoef(L) { - N =L[0]$ D = L[1]$ Len = length(N)$ - for ( I = 0; I < Len; I++ ) if ( N[I] ) break; - if ( I == Len ) return [N,0]; - for ( I = 0, G = D; I < Len; I++ ) - if ( N[I] ) G = igcd(G,dp_hc(N[I])/dp_hc(dp_ptozp(N[I]))); - return [N/G,D/G]; -} - -def recompute_trace3(Ti,P,C) +def recompute_trace(Ti,P,V,Mod) { for ( Num = 0, Den = 1; Ti != []; Ti = cdr(Ti) ) { - Sj = car(Ti); Dj = Sj[0]; Ij =Sj[1]; Mj = Sj[2]; Cj = Sj[3]; - /* Num/Den <- (Dj*(Num/Den)+Mj*P[Ij])/Cj */ + Sj = car(Ti); Dj = Sj[0]; Ij =Sj[1]; Mj = dp_dtop(Sj[2],V); Cj = Sj[3]; /* Num/Den <- (Dj*Num+Den*Mj*P[Ij])/(Den*Cj) */ - if ( Dj ) - Num = (Dj*Num+Den*Mj*P[Ij]); + if ( Dj ) Num = (Dj*Num+Den*Mj*P[Ij]); Den *= Cj; - if ( C ) C *= Dj; } - return [Num,C]; + return Num; } -def dtop(A,V) -{ - T = type(A); - if ( T == 4 || T == 5 || T == 6 ) - return map(dtop,A,V); - else if ( T == 9 ) return dp_dtop(A,V); - else return A; -} - -def topnum(L) -{ - for ( R = [], T = L; T != []; T = cdr(T) ) { - V = car(T); - N = length(V); - for ( I = 0; I < N && !V[I]; I++ ); - if ( type(V[I])==1 ) R = cons(I,R); - } - return reverse(R); -} - def ideal_sat(G,F,V) { if ( type(Mod=getopt(mod)) == -1 ) Mod = 0; @@ -2464,11 +2525,15 @@ def monodec(B,V) T0 = map(dp_ptod,D0,W); D1 = monodec(map(subst,B,X,1),W); T1 = map(dp_ptod,D1,W); +#if 0 for ( T = T1; T != []; T = cdr(T) ) { for ( M = car(T), S1 = [], S = T0; S != []; S = cdr(S) ) if ( !dp_redble(car(S),M) ) S1= cons(car(S),S1); T0 = S1; } +#else + T0 = dp_mono_reduce(T0,T1); +#endif D0 = map(dp_dtop,T0,W); D0 = vtol(X*ltov(D0)); return append(D0,D1); @@ -2478,30 +2543,40 @@ def separator(P,V) { if ( type(Mod=getopt(mod)) == -1 ) Mod = 0; N = length(P); - M = matrix(N,N); + dp_ord(0); + DP = vector(N); + for ( I = 0; I < N; I++ ) DP[I] = qsort(ltov(map(dp_ptod,P[I][0],V)),comp_tord); + if ( Mod ) + for ( I = 0; I < N; I++ ) DP[I] = map(dp_mod,DP[I],Mod,[]); + Ind = vector(N); for ( I = 0; I < N; I++ ) { - /* M[I][J] is an element of P[I]-P[J] */ - PI = qsort(P[I][0],comp_tdeg); + for ( K = [], J = length(DP[I])-1; J >= 0; J-- ) K = cons(J,K); + Ind[I] = K; + } + S = vector(N); + for ( I = 0; I < N; I++ ) S[I] = 1; + for ( I = 0; I < N; I++ ) { + print(".",2); for ( J = 0; J < N; J++ ) { if ( J == I ) continue; - for ( T = PI; T != []; T = cdr(T) ) - if ( gen_nf(car(T),P[J][0],V,0,Mod) ) break; - M[I][J] = sq(car(T),Mod); + T = DP[I]; L = length(T); + if ( Mod ) { + for ( K = 0; K < L; K++ ) + if ( dp_nf_mod(Ind[J],T[K],DP[J],0,Mod) ) break; + } else { + for ( K = 0; K < L; K++ ) + if ( dp_nf(Ind[J],T[K],DP[J],0) ) break; + } + S[J] = lcm(S[J],dp_dtop(T[K],V)); } } - S = vector(N); - for ( J = 0; J < N; J++ ) { - for ( I = 0, T = 1; I < N; I++ ) { - if ( I == J ) continue; - T = sq(T*M[I][J],Mod); - } - S[J] = T; - } + print(""); return S; } def prepost(PL,V) -{ +{ + if ( type(Mod=getopt(mod)) == -1 ) Mod = 0; A = ltov(PL); N = length(A); Pre = vector(N); Post = vector(N); @@ -2509,20 +2584,16 @@ def prepost(PL,V) Pre[0] = [1]; print("pre ",2); for ( I = 1; I < N; I++, print(".",2) ) - Pre[I] = ideal_intersection(Pre[I-1],A[I-1][0],V,0 - |gbblock=[[0,length(Pre[I-1])]],mod=Mod); + Pre[I] = ideal_intersection_m(Pre[I-1],A[I-1],V,0|mod=Mod); print("done"); print("post ",2); Post[N-1] = [1]; for ( I = N-2; I >= 0; I--, print(".",2) ) - Post[I] = ideal_intersection(Post[I+1],A[I+1][0],V,0 - |gbblock=[[0,length(Post[I+1])]],mod=Mod); + Post[I] = ideal_intersection_m(Post[I+1],A[I+1],V,0|mod=Mod); print("done"); print("int ",2); for ( I = 0; I < N; I++, print(".",2) ) - R[I] = ideal_intersection(Pre[I],Post[I],V,0 - |gbblock=[[0,length(Pre[I])],[length(Pre[I]),length(Post[I])]], - mod=Mod); + R[I] = ideal_intersection_m(Pre[I],Post[I],V,0|mod=Mod); print("done"); return R; } @@ -2582,6 +2653,57 @@ def para_exec(Proc,Task) { } print(""); return reverse(R); +} + +def redbase(B,V,Mod,Ord) +{ + M = nd_gr_postproc(B,V,Mod,Ord,0); + dp_ord(Ord); + DM = ltov(map(dp_ptod,M,V)); + if ( Mod ) DM = map(dp_mod,DM,Mod,[]); + N = length(DM); + for ( Ind = [], I = N-1; I >= 0; I-- ) Ind = cons(I,Ind); + for ( T = B, R = vtol(DM); T != []; T = cdr(T) ) { + D = dp_ptod(car(T),V); + if ( Mod ) D = dp_mod(D,Mod,[]); + D = Mod?dp_nf_mod(Ind,D,DM,1,Mod):dp_nf(Ind,D,DM,1); + if ( D ) R = cons(D,R); + } + D = qsort(R,comp_tord); + return map(dp_dtop,D,V); +} + +def witness(A,B,V) +{ + G = nd_gr(B,V,0,Mod); + L = length(A); + QL = []; PL = []; + for ( I = L-1; I >= 0; I-- ) { + QL = append(map(first,A[I]),QL); + PL = append(map(second,A[I]),PL); + } + N = length(QL); + Qhat = prepost(QL,V); + for ( I = 0, W = []; I < N; I++ ) { + for ( T = Qhat[I]; T != []; T = cdr(T) ) + if ( gen_nf(car(T),QL[I],V,0,Mod) ) break; + Ai = car(T); + Ji = colon(G,Ai,V|isgb=1,mod=Mod); + Ji = nd_gr(Ji,V,Mod,0); + if ( gen_gb_comp(Ji,PL[I],Mod) ) Bi = 1; + else { + Ki = ideal_colon(Ji,PL[I],V|mod=Mod); + for ( T = Ki; T != []; T = cdr(T) ) + if ( gen_nf(car(T),Ji,V,0,Mod) ) break; + Bi = car(T); + } + W = cons(Ai*Bi,W); + Li = colon(G,W[0],V|isgb=1,mod=Mod); + Li = nd_gr(Li,V,Mod,0); + if ( !gen_gb_comp(Li,PL[I],Mod) ) + error("afo"); + } + return reverse(W); } endmodule$ end$