File: [local] / OpenXM / src / asir-contrib / packages / src / noro_pd.rr (download)
Revision 1.10, Mon Nov 16 01:01:42 2020 UTC (3 years, 6 months ago) by noro
Branch: MAIN
CVS Tags: HEAD
Changes since 1.9: +3 -1
lines
Added an option "level=n" for setting the max level of primary components in syc_dec.
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/* $OpenXM: OpenXM/src/asir-contrib/packages/src/noro_pd.rr,v 1.10 2020/11/16 01:01:42 noro Exp $ */
import("gr")$
module noro_pd$
static GBF4,GBTrace,GBCheck,Chrem,Procs,IntGB,UsualInt,ContAlg,Competitive$
static MP_Serial$
localf radical_membership_sat$
localf witness$
localf get_lc,tomonic,aa,ideal_intersection_m,redbase$
localf para_exec,nd_gr_rat,nd_gr_elim,nd_gr_trace_elim,competitive_exec,call_func,call_func_serial$
localf call_ideal_list_intersection$
localf call_colon,call_prime_dec$
localf prime_dec2, prime_dec_main2$
localf first_second$
localf third$
localf locsat,iso_comp_para,extract_qj,colon_prime_dec,extract_comp$
localf separator$
localf member,subset,mingen,compute_gbsyz,redcoef,recompute_trace,dtop,topnum$
localf prepost$
localf monodec0,monodec,prod$
localf extract_qd,primary_check$
localf second$
localf gbrat,succsat,repcolon,comp_third_tdeg,comp_tord$
localf power$
localf syci_dec$
localf find_si0,find_si1,find_si2$
localf find_ssi0,find_ssi1,find_ssi2$
localf init_pprocs, init_procs, kill_procs, reset_procs$
localf iso_comp$
localf prime_dec, prime_dec_main, lex_predec1, zprimedec$
localf complete_decomp$
localf partial_decomp, partial_decomp0, zprimecomp$
localf fast_gb, incremental_gb, elim_gb, ldim, make_mod_subst$
localf rsgn, find_npos, gen_minipoly, indepset$
localf maxindep, maxindep2, contraction, contraction_m, contraction_succ, contraction_onetime$
localf ideal_list_intersection, ideal_intersection$
localf radical_membership, modular_radical_membership$
localf radical_membership_rep, ideal_product$
localf sat, sat_ind, sat_ind_var, colon, isat$
localf ideal_colon, ideal_sat, ideal_inclusion, qd_simp_comp, qd_remove_redundant_comp$
localf pd_simp_comp, remove_identical_comp$
localf pd_remove_redundant_comp, ppart, sq, gen_fctr, gen_nf, gen_gb_comp$
localf gen_mptop, lcfactor, compute_deg0, compute_deg, member$
localf elimination, setintersection, setminus, sep_list$
localf first, comp_tdeg, comp_tdeg_first, tdeg, comp_by_ord, comp_by_second$
localf gbcheck,sathomo,qd_check,qdb_check,intgb,gbtrace,gbf4,usualint$
localf zero_dim$
localf comp_by_deg,gen_minipoly_chr,gen_minipoly_leq,gen_minipoly_rat,gen_minipoly_rat1,gen_minipoly_elim$
localf comp_by_tdeg,redcont,nf_mlist,find_member_with_support$
localf contalg,competitive,competitive_setup$
GBCheck=1$
ContAlg=0$
IntGB=0$
UsualInt=0$
GBTrace=0$
GBF4=0$
Procs=0$
Competitive=0$
MP_Serial=0$
#define MAX(a,b) ((a)>(b)?(a):(b))
#define ACCUM_TIME(C,R) {T1 = time(); C += (T1[0]-T0[0])+(T1[1]-T0[1]); R += (T1[3]-T0[3]); }
def competitive_setup()
{
if ( type(NoX=getopt(nox)) == -1 ) NoX = 0;
init_procs(5|nox=NoX);
gbtrace(1);
gbf4(1);
competitive(1);
contalg(1);
}
def usualint(A)
{
UsualInt = A;
}
def gbf4(A)
{
GBF4 = A;
}
def gbtrace(A)
{
GBTrace = A;
}
def competitive(A)
{
Competitive = A;
}
/* A=0: onetime, A=1:successive, A=2:successive&colon */
def contalg(A)
{
ContAlg = A;
}
def gbcheck(A)
{
if ( A ) GBCheck = 1;
else GBCheck = -1;
}
def intgb(A)
{
if ( A ) IntGB = 1;
else IntGB = 0;
}
def init_pprocs(N)
{
if ( type(NoX=getopt(nox)) == -1 ) NoX = 0;
for ( R = [], I = 0; I < N; I++ ) {
P = NoX ? ox_launch_nox() : ox_launch();
R = cons(P,R);
}
return reverse(R);
}
def init_procs(N)
{
if ( N < 5 ) N = 5;
if ( type(NoX=getopt(nox)) == -1 ) NoX = 0;
if ( Procs ) kill_procs();
if ( NoX )
Procs = init_pprocs(N|nox=1);
else
Procs = init_pprocs(N);
}
def kill_procs()
{
if ( Procs ) {
map(ox_shutdown,Procs);
Procs = 0;
}
}
def reset_procs()
{
if ( Procs ) {
map(ox_reset,Procs);
}
}
def qd_check(B,V,QD)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
G = fast_gb(B,V,Mod,0);
Iso = ideal_list_intersection(map(first,QD[0]),V,0|mod=Mod);
Emb = ideal_list_intersection(map(first,QD[1]),V,0|mod=Mod);
GG = ideal_intersection(Iso,Emb,V,0|mod=Mod);
return gen_gb_comp(G,GG,Mod);
}
def primary_check(B,V)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
G = fast_gb(B,V,Mod,0);
PL = prime_dec(G,V|indep=1,mod=Mod);
if ( length(PL) > 1 ) return 0;
P = PL[0][0]; Y = PL[0][1];
Z = setminus(V,Y);
H = elim_gb(G,Z,Y,Mod,[[0,length(Z)],[0,length(Y)]]);
H = contraction(H,Z|mod=Mod);
H = fast_gb(H,V,Mod,0);
if ( gen_gb_comp(G,H,Mod) ) return fast_gb(P,V,Mod,0);
else return 0;
}
def qdb_check(B,V,QD)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
G = fast_gb(B,V,Mod,0);
N = length(QD);
for ( I = 0, Q = [1]; I < N; I++ )
for ( J = 0, QL = map(first,QD[I]), L = length(QL); J < L; J++ )
Q = ideal_intersection_m(Q,QL[J],V,0|mod=Mod);
Q = fast_gb(Q,V,0,0);
if ( !gen_gb_comp(G,Q,Mod) )
return 0;
for ( I = 0; I < N; I++ ) {
T = QD[I];
M = length(T);
for ( J = 0; J < M; J++ ) {
P = primary_check(T[J][0],V|mod=Mod);
if ( !P ) return 0;
PP = fast_gb(T[J][1],V,Mod,0);
if ( !gen_gb_comp(P,PP,Mod) ) return 0;
}
}
return 1;
}
def extract_qd(QD,V,Ind)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
N = length(Ind);
for ( I = 0, Q = [1]; I < N; I++ )
for ( J = 0, QL = map(first,QD[Ind[I]]), L = length(QL); J < L; J++ )
Q = ideal_intersection(Q,QL[J],V,0|mod=Mod);
return Q;
}
static Tint2, RTint2$
def syci_dec(B,V)
{
if ( type(SI=getopt(si)) == -1 ) SI = 1;
if ( SI<0 || SI>2 ) error("sycb_assdec : si should be 0,1,2");
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
if ( type(Time=getopt(time)) == -1 ) Time = 0;
if ( type(Iso=getopt(iso)) == -1 ) Iso = 0;
if ( type(IsoOnly=getopt(isoonly)) == -1 ) IsoOnly = 0;
if ( type(CompLevel=getopt(level)) == -1 ) CompLevel = x;
if ( type(Ass=getopt(ass)) == -1 ) Ass = 0;
if ( type(Colon=getopt(colon)) == -1 ) Colon = 0;
if ( type(Para=getopt(para)) == -1 ) Para = 0;
/* global options */
if ( type(Opt=getopt(f4)) != -1 ) GBF4 = Opt;
if ( type(Opt=getopt(trace)) != -1 ) GBTrace = Opt;
if ( type(Opt=getopt(intgb)) != -1 ) IntGB = Opt;
Ord = 0;
Tiso = Tint = Tpd = Text = Tint2 = 0;
RTiso = RTint = RTpd = RText = RTint2 = 0;
T00 = time();
G = fast_gb(B,V,Mod,Ord);
IntQ = [1]; QL = RL = []; First = 1;
for ( Level = 0; ; Level++ ) {
T0 = time();
if ( !Level ) {
PtR = prime_dec(G,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1);
ACCUM_TIME(Tfpd,RTfpd)
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);
ACCUM_TIME(Tiso,RTiso)
if ( !Level ) {
if ( Iso == 3 ) {
NI = length(Rt);
Q = IntQ;
T0 = time();
if ( Para ) {
for ( J = 0, Task = []; J < NI; J++ ) {
T = ["noro_pd.extract_qj",Q,V,Rt[J],Rad,Mod,SI,Colon,-1];
Task = cons(T,Task);
}
Task = reverse(Task);
print("comps:",2); print(length(Task),2);
Rt = para_exec(Para,Task);
} else {
for ( J = 0, T = []; J < NI; J++ ) {
TJ = extract_qj(Q,V,Rt[J],Rad,Mod,SI,Colon,-1);
T = cons(TJ,T);
}
Rt = reverse(T);
}
ACCUM_TIME(Text,RText)
}
print("");
T0 = time();
if ( zero_dim(G,V,Ord) ) {
IntQ = G;
} else {
Int = Rad;
for ( T = Rt; T != []; T = cdr(T) )
if ( !gb_comp(car(T)[0],car(T)[1]) )
Int = ideal_intersection_m(Int,car(T)[0],V,Ord|mod=Mod);
IntQ = fast_gb(Int,V,Mod,Ord);
}
ACCUM_TIME(Tint,RTint)
RL = append(RL,[Rt]);
} else if ( Iso != 3 ) {
T0 = time();
IntQ = ideal_list_intersection(map(first,Rt),V,Ord|mod=Mod,isgb=1);
RL = append(RL,[Rt]);
ACCUM_TIME(Tint,RTint)
} else {
NI = length(Rt);
Q = IntQ;
if ( Para ) {
for ( J = 0, Task = []; J < NI; J++ ) {
T = ["noro_pd.extract_qj",Q,V,Rt[J],Rad,Mod,SI,Colon,-1];
Task = cons(T,Task);
}
Task = reverse(Task);
print("comps:",2); print(length(Task),2);
T0 = time();
R = para_exec(Para,Task);
ACCUM_TIME(Text,RText)
print("");
T0 = time();
IntQ = ideal_list_intersection(cons(IntQ,map(first,R)),V,Ord|mod=Mod);
ACCUM_TIME(Tint,RTint)
RL = append(RL,[R]);
} else {
for ( J = 0, T = []; J < NI; J++ ) {
T0 = time();
TJ = extract_qj(Q,V,Rt[J],Rad,Mod,SI,Colon,-1);
ACCUM_TIME(Text,RText)
T = cons(TJ,T);
T0 = time();
IntQ = ideal_intersection_m(IntQ,TJ[0],V,Ord|mod=Mod);
ACCUM_TIME(Tint,RTint)
}
print("");
T0 = time();
IntQ = fast_gb(IntQ,V,Mod,Ord);
ACCUM_TIME(Tint,RTint)
T = reverse(T); RL = append(RL,[T]);
}
}
QL = append(QL,[IntQ]);
if ( gen_gb_comp(IntQ,G,Mod) ) break;
if ( IsoOnly ) return RL;
if ( Level >= CompLevel ) break;
}
T0 = time();
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 ) {
T1 = time();
Tall = T1[0]-T00[0]+T1[1]-T00[1]; RTall += T1[3]-T00[3];
Tass = Tall-Text; RTass = RTall-RText;
print(["total",Tall,"ass",Tass,"pd",Tpd,"(fpd)",Tfpd,"iso",Tiso,"int",Tint,"ext",Text]);
print(["elapsed",RTall,"ass",RTass,"pd",RTpd,"(fpd)",RTfpd,"iso",RTiso,"int",RTint,"ext",RText]);
}
return RL;
}
def extract_comp(QL,RL,V,Rad) {
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(Para=getopt(para)) == -1 ) Para = 0;
if ( type(Colon=getopt(colon)) == -1 ) Colon = 0;
if ( type(SI=getopt(si)) == -1 ) SI = 1;
if ( type(Ass=getopt(ass)) == -1 ) Ass = 0;
L = length(QL);
if ( Para ) {
for ( Task = [], I = 1; I < L; I++ ) {
QI = QL[I-1]; RI = RL[I]; NI = length(RI);
for ( J = 0, TI = []; J < NI; J++ ) {
T = ["noro_pd.extract_qj",QI,V,RI[J],Rad,Mod,SI,Colon,I];
Task = cons(T,Task);
}
}
Task = reverse(Task);
print("comps:",2); print(length(Task),2); print("");
R = para_exec(Para,Task);
S = vector(L);
for ( I = 1; I < L; I++ ) S[I] = [];
S[0] = RL[0];
for ( T = R; T != []; T = cdr(T) ) {
U = car(T); Level = U[0]; Body = U[1];
S[Level] = cons(Body,S[Level]);
}
return vtol(S);
} else {
TL = [RL[0]];
for ( I = 1; I < L; I++ ) {
print("level:",2); print(I,2);
print(" comps:",2); print(length(RL[I]),2); print("");
QI = QL[I-1]; RI = RL[I]; NI = length(RI);
for ( J = 0, TI = []; J < NI; J++ ) {
TIJ = extract_qj(QI,V,RI[J],Rad,Mod,SI,Colon,-1);
TI = cons(TIJ,TI);
}
TI = reverse(TI); TL = cons(TI,TL);
}
TL = reverse(TL);
}
return TL;
}
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; J < L; J++ )
if ( gen_nf(M[J],G,V,Ord,Mod) ) {
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 ( 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));
#if 1
for ( Pt = [], T = R; T != []; T = cdr(T) ) {
Pi = prime_dec(car(T),V|indep=1,lexdec=Lexdec,mod=Mod);
Pt = append(Pt,Pi);
}
#else
J = ideal_list_intersection(R,V,0|mod=Mod);
Pt = prime_dec(J,V|indep=1,lexdec=Lexdec,mod=Mod);
#endif
}
#if 1
Pt = pd_simp_comp(Pt,V|first=1,mod=Mod);
#endif
return Pt;
}
def call_colon(G,F,V,Mod,IsGB)
{
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;
}
def extract_qj(Q,V,QL,Rad,Mod,SI,Colon,Level)
{
SIFList=[noro_pd.find_ssi0, noro_pd.find_ssi1, noro_pd.find_ssi2];
SIF = SIFList[SI];
G = QL[0]; P = QL[1]; PV = QL[2];
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);
IJ = fast_gb(HJ,V,Mod,Ord);
return Level >= 0 ? [Level,[IJ,P]] : [IJ,P];
}
def power(A,I) { return A^I; }
/* functions for computating a separing ideal */
/* C=G:Q, Rad=rad(Q), return J s.t. Q cap (G+J) = G */
def find_si0(C,G,Q,Rad,V,Ord) {
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
for ( CI = C, I = 1; ; I++ ) {
for ( T = CI, S = []; T != []; T = cdr(T) )
if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
if ( S == [] )
error("find_si0 : cannot happen");
G1 = append(S,G);
Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
/* check whether (Q cap (G+S)) = G */
if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
CI = ideal_product(CI,C,V|mod=Mod);
}
}
def find_si1(C,G,Q,Rad,V,Ord) {
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
for ( T = C, S = []; T != []; T = cdr(T) )
if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
if ( S == [] )
error("find_si1 : cannot happen");
G1 = append(S,G);
Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
/* check whether (Q cap (G+S)) = G */
if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
C = qsort(C,noro_pd.comp_tdeg);
Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
Dp = dp_gr_print(); dp_gr_print(0);
for ( T = C, S = []; T != []; T = cdr(T) ) {
if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
Ui = U = car(T);
for ( I = 1; ; I++ ) {
G1 = cons(Ui,G);
Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
if ( gen_gb_comp(Int,G,Mod) ) break;
else
Ui = gen_nf(Ui*U,G,V,Ord,Mod);
}
print([length(T),I],2);
Int1 = incremental_gb(append(Int0,[Tmp*Ui]),TV,Ord1
|gbblock=[[0,length(Int0)]],mod=Mod);
Int = elimination(Int1,V);
if ( !gen_gb_comp(Int,G,Mod) ) {
break;
} else {
Int0 = Int1;
S = cons(Ui,S);
}
}
print("");
dp_gr_print(Dp);
return reverse(S);
}
def find_si2(C,G,Q,Rad,V,Ord) {
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
for ( T = C, S = []; T != []; T = cdr(T) )
if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
if ( S == [] )
error("find_si2 : cannot happen");
G1 = append(S,G);
Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
/* check whether (Q cap (G+S)) = G */
if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
C = qsort(C,noro_pd.comp_tdeg);
Dp = dp_gr_print(); dp_gr_print(0);
Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
for ( T = C, S = []; T != []; T = cdr(T) ) {
if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
Ui = U = car(T);
for ( I = 1; ; I++ ) {
Int1 = incremental_gb(append(Int0,[Tmp*Ui]),TV,Ord1
|gbblock=[[0,length(Int0)]],mod=Mod);
Int = elimination(Int1,V);
if ( gen_gb_comp(Int,G,Mod) ) break;
else
Ui = gen_nf(Ui*U,G,V,Ord,Mod);
}
print([length(T),I],2);
S = cons(Ui,S);
}
S = qsort(S,noro_pd.comp_tdeg);
print("");
End = Len = length(S);
Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
Prev = 1;
G1 = append(G,[S[0]]);
Int0 = incremental_gb(append(vtol(ltov(G1)*Tmp),vtol(ltov(Q)*(1-Tmp))),
TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
if ( End > 1 ) {
Cur = 2;
while ( Prev < Cur ) {
for ( St = [], I = Prev; I < Cur; I++ ) St = cons(Tmp*S[I],St);
Int1 = incremental_gb(append(Int0,St),TV,Ord1
|gbblock=[[0,length(Int0)]],mod=Mod);
Int = elimination(Int1,V);
if ( gen_gb_comp(Int,G,Mod) ) {
print([Cur],2);
Prev = Cur;
Cur = Cur+idiv(End-Cur+1,2);
Int0 = Int1;
} else {
End = Cur;
Cur = Prev + idiv(Cur-Prev,2);
}
}
for ( St = [], I = 0; I < Prev; I++ ) St = cons(S[I],St);
} else
St = [S[0]];
print("");
for ( I = Prev; I < Len; I++ ) {
Int1 = incremental_gb(append(Int0,[Tmp*S[I]]),TV,Ord1
|gbblock=[[0,length(Int0)]],mod=Mod);
Int = elimination(Int1,V);
if ( gen_gb_comp(Int,G,Mod) ) {
print([I],2);
St = cons(S[I],St);
Int0 = Int1;
}
}
Ok = reverse(St);
print("");
print([length(S),length(Ok)]);
dp_gr_print(Dp);
return Ok;
}
/* functions for computing a saturated separating ideal */
def find_ssi0(C,G,Q,Rad,V,Ord) {
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(Reduce=getopt(red)) == -1 ) Reduce = 0;
for ( T = C, S = []; T != []; T = cdr(T) )
if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
if ( S == [] )
error("find_ssi0 : cannot happen");
G1 = append(S,G);
Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
/* check whether (Q cap (G+S)) = G */
if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
if ( Reduce ) {
for ( T = C, U = []; T != []; T = cdr(T) )
if ( gen_nf(car(T),Rad,V,Ord,Mod) ) U = cons(car(T),U);
U = reverse(U);
} else
U = C;
for ( I = 1; ; I++ ) {
print([I],2);
S = map(power,U,I);
G1 = append(S,G);
Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
/* check whether (Q cap (G+S)) = G */
if ( gen_gb_comp(Int,G,Mod) ) { print(""); return reverse(S); }
}
}
def find_ssi1(C,G,Q,Rad,V,Ord) {
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(Reduce=getopt(red)) == -1 ) Reduce = 0;
for ( T = C, S = []; T != []; T = cdr(T) )
if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
if ( S == [] )
error("find_ssi1 : cannot happen");
G1 = append(S,G);
Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
/* check whether (Q cap (G+S)) = G */
if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
dp_ord(Ord); DC = map(dp_ptod,C,V);
DC = qsort(DC,noro_pd.comp_tord); C = map(dp_dtop,DC,V);
print(length(C),2);
if ( Reduce ) {
SC = map(sq,C,Mod);
SC = reverse(SC); C = reverse(C);
for ( T = C, C1 = [], R1 = append(SC,Rad); T != []; T = cdr(T) ) {
R0 = car(R1); R1 = cdr(R1);
if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
if ( radical_membership(R0,R1,V|mod=Mod) ) {
C1 = cons(car(T),C1);
R1 = append(R1,[R0]);
}
}
print("->",0); print(length(C1),2);
C = C1;
}
print(" ",2);
Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
Dp = dp_gr_print(); dp_gr_print(0);
for ( J = 0, T = C, S = [], GS = G; T != []; T = cdr(T), J++ ) {
if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
Ui = U = car(T);
for ( I = 1; ; I++ ) {
Int1 = nd_gr(append(Int0,[Tmp*Ui]),TV,Mod,Ord1
|gbblock=[[0,length(Int0)]],newelim=1);
if ( Int1 ) {
Int = elimination(Int1,V);
if ( gen_gb_comp(Int,G,Mod) ) break;
}
print("x",2);
Ui = gen_nf(Ui*U,G,V,Ord,Mod);
}
print(J,2);
Int0 = Int1;
S = cons(Ui,S);
}
print("");
dp_gr_print(Dp);
return reverse(S);
}
def find_ssi2(C,G,Q,Rad,V,Ord) {
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(Reduce=getopt(red)) == -1 ) Reduce = 0;
for ( T = C, S = []; T != []; T = cdr(T) )
if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
if ( S == [] )
error("find_ssi2 : cannot happen");
G1 = append(S,G);
Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
/* check whether (Q cap (G+S)) = G */
if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
#if 0
dp_ord(Ord); DC = map(dp_ptod,C,V);
DC = qsort(DC,noro_pd.comp_tord); C = map(dp_dtop,DC,V);
#else
C = qsort(C,noro_pd.comp_tdeg);
#endif
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|mod=Mod) ) {
C1 = cons(car(T),C1);
R1 = cons(sq(car(T),Mod),R1);
}
}
print(["C",length(C),"->",length(C1)]);
C = reverse(C1);
}
for ( T = C, S = []; T != []; T = cdr(T) ) {
if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
Ui = U = car(T);
S = cons([Ui,U],S);
}
S = qsort(S,noro_pd.comp_tdeg_first);
print("");
Dp = dp_gr_print(); dp_gr_print(0);
Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
OK = [];
while ( S != [] ) {
Len = length(S); print("remaining gens : ",0); print(Len);
S1 = [];
for ( Start = Prev = 0; Start < Len; Start = Prev ) {
Cur = Start+1;
print(Start,2);
while ( Prev < Len ) {
for ( St = [], I = Prev; I < Cur; I++ ) St = cons(Tmp*S[I][0],St);
Int1 = nd_gr(append(Int0,St),TV,Mod,Ord1|gbblock=[[0,length(Int0)]],newelim=1);
if ( !Int1 ) {
print("x",0); break;
}
Int = elimination(Int1,V);
if ( gen_gb_comp(Int,G,Mod) ) {
print([Prev,Cur-1],2);
Prev = Cur;
Cur += (Prev-Start)+1;
if ( Cur > Len ) Cur = Len;
Int0 = Int1;
} else
break;
}
for ( I = Start; I < Prev; I++ ) OK = cons(S[I][0],OK);
if ( Prev == Start ) {
Ui = S[I][0]; U = S[I][1];
Ui = gen_nf(Ui*U,G,V,Ord,Mod);
S1 = cons([Ui,U],S1);
Prev++;
}
}
S = reverse(S1);
print("");
}
print("");
OK = reverse(OK);
dp_gr_print(Dp);
return OK;
}
def iso_comp(G,L,V,Ord)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
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;
if ( !S ) S = separator(L,V|mod=Mod);
N = length(L);
print("comps : ",2); print(N); print("",2);
if ( Para ) {
Task = [];
for ( I = 0; I < N; I++ ) {
T = ["noro_pd.locsat",G,V,L[I],S[I],Mod,IsGB,Iso,Q];
Task = cons(T,Task);
}
Task = reverse(Task);
R = para_exec(Para,Task);
return R;
} else {
for ( I = 0, R = []; I < N; I++ ) {
QI = locsat(G,V,L[I],S[I],Mod,IsGB,Iso,Q);
if ( type(QI[0][0])==1 )
error("iso_comp : cannot happen");
print(".",2);
R = cons(QI,R);
}
print("");
return reverse(R);
}
}
def locsat(G,V,L,S,Mod,IsGB,Iso,Q)
{
P = L[0]; PV = L[1]; V0 = setminus(V,PV);
if ( Iso==1 ) {
QI = sat(G,S,V|isgb=IsGB,mod=Mod);
GI = elim_gb(QI,V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
GI = fast_gb(contraction(GI,V0|mod=Mod,allv=V),V,Mod,0);
} else if ( Iso==0 ) {
HI = elim_gb(G,V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
GI = fast_gb(contraction(HI,V0|mod=Mod,allv=V),V,Mod,0);
GI = sat(GI,S,V|isgb=IsGB,mod=Mod);
} else if ( Iso==2 ) {
HI = elim_gb(G,V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
TV = ttttt;
if ( Mod )
GI = fast_gb(cons(TV*S-1,HI),cons(TV,V0),Mod,[[0,1],[0,length(V0)]]);
else
GI = nd_f4_trace(append(HI,[TV*S-1]),cons(TV,V0),
1,1,[[0,1],[0,length(V0)]]|gbblock=[[0,length(HI)]]);
GI = elimination(GI,V);
GI = fast_gb(contraction(GI,V0|mod=Mod,allv=V),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);
return [GI,P,PV];
}
/* SL prime decomposition */
def prime_dec(B,V)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
if ( type(LexDec=getopt(lexdec)) == -1 ) LexDec = 0;
if ( type(Rad=getopt(radical)) == -1 ) Rad = 0;
B = map(sq,B,Mod);
if ( LexDec )
PD = lex_predec1(B,V|mod=Mod);
else
PD = [B];
if ( length(PD) > 1 ) {
G = ideal_list_intersection(PD,V,0|mod=Mod);
PD = pd_remove_redundant_comp(G,PD,V,0|mod=Mod);
}
R = []; RL = [];
for ( T = PD; T != []; T = cdr(T) ) {
PDT = prime_dec_main(car(T),V|indep=Indep,mod=Mod,radical=Rad);
if ( Rad ) {
R = append(R,PDT[0]);
GT = fast_gb(PDT[1],V,Mod,0);
RL = append(RL,[GT]);
} else {
R = append(R,PDT);
}
}
if ( LexDec ) R = pd_simp_comp(R,V|first=Indep,mod=Mod);
if ( Rad ) {
G = ideal_list_intersection(RL,V,0|mod=Mod);
return [R,G];
} else return R;
}
def prime_dec2(B,V)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
if ( type(LexDec=getopt(lexdec)) == -1 ) LexDec = 0;
if ( type(Rad=getopt(radical)) == -1 ) Rad = 0;
if ( type(Para=getopt(para)) == -1 || type(Para) != 4 ) Para = [];
B = map(sq,B,Mod);
if ( LexDec )
PD = lex_predec1(B,V|mod=Mod);
else
PD = [B];
if ( length(PD) > 1 ) {
G = ideal_list_intersection(PD,V,0|mod=Mod);
PD = pd_remove_redundant_comp(G,PD,V,0|mod=Mod);
}
R = [];
for ( T = PD; T != []; T = cdr(T) )
R = append(prime_dec_main2(car(T),V|indep=Indep,mod=Mod,para=Para),R);
if ( Indep ) {
G = ideal_list_intersection(map(first,R),V,0|mod=Mod);
R = pd_simp_comp(R,V|first=1,mod=Mod);
} else {
G = ideal_list_intersection(R,V,0|mod=Mod);
R = pd_simp_comp(R,V|mod=Mod);
}
return Rad ? [R,G] : R;
}
/* returns [PD,rad(I)] */
def prime_dec_main(B,V)
{
Tpint = RTpint = 0;
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
if ( type(Rad=getopt(radical)) == -1 ) Rad = 0;
G = fast_gb(B,V,Mod,0);
if ( zero_dim(G,V,0) ) {
PD = zprimecomp(G,V,Indep|mod=Mod);
if ( Rad ) {
Int = ideal_list_intersection(map(first,PD),V,0|mod=Mod);
return [PD,Int];
} else
return PD;
}
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 ) {
print([length(PD)],2);
/* rad(G) subset IntP */
/* check if IntP subset rad(G) */
/* print([length(PD),length(IntP)],2); */
for ( T = IntP; T != []; T = cdr(T) )
if ( (G0 = radical_membership_sat(car(T),G,V|mod=Mod,isgb=1,dg=[DG,Ind])) ) {
F = car(T);
break;
}
if ( T == [] ) {
print(["pint",Tpint,"rpint",RTpint]);
return Rad ? [PD,IntP] : PD;
}
PD0 = zprimecomp(G0,V,Indep|mod=Mod);
Int = ideal_list_intersection(Indep?map(first,PD0):PD0,V,0|mod=Mod);
PD = append(PD,PD0);
#if 1
T0=time();
IntP = ideal_intersection_m(IntP,Int,V,0|mod=Mod);
dp_ord(0); DC = map(dp_ptod,IntP,V);
DC = qsort(DC,noro_pd.comp_tord); IntP = map(dp_dtop,DC,V);
ACCUM_TIME(Tpint,RTpint)
#else
IntP = ideal_intersection(IntP,Int,V,0|mod=Mod,gbblock=[[0,length(IntP)]]);
#endif
}
}
localf callsat,callzcomp;
def callsat(F,G,V,Mod,DG)
{
return radical_membership(F,G,V|mod=Mod,isgb=1,dg=DG,sat=1);
}
def callzcomp(F,V,Indep,Mod)
{
PD0 = zprimecomp(F,V,Indep|mod=Mod);
Int = ideal_list_intersection(Indep?map(first,PD0):PD0,V,0|mod=Mod);
return [PD0,Int];
}
def prime_dec_main2(B,V)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
if ( type(Para=getopt(para)) == -1 || type(Para) != 4 ) Para = [];
NPara = length(Para);
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,[]);
if ( NPara )
while ( 1 ) {
IntPM = mingen(IntP,V);
for ( T = IntPM, CallSat = []; T != []; T = cdr(T) )
CallSat = cons(["noro_pd.callsat",car(T),G,V,Mod,[DG,Ind]],CallSat);
CallSat = reverse(CallSat);
/* SatL = [[..],0,[...],...] */
SatL = para_exec(Para,CallSat);
for ( T = SatL, Sat = []; T != []; T = cdr(T) ) if ( car(T) ) Sat = cons(car(T),Sat);
if ( Sat == [] ) return PD;
print(length(Sat),2); print("->",2);
Sat = remove_identical_comp(Sat|mod=Mod);
print(length(Sat));
for ( T = Sat, CallComp = []; T != []; T = cdr(T) )
CallComp = cons(["noro_pd.callzcomp",car(T),V,Indep,Mod],CallComp);
CallComp = reverse(CallComp);
/* PDL = [[PD0,Int],...] */
PDL = para_exec(Para,CallComp);
for ( T = PDL; T != []; T = cdr(T) ) PD = append(PD,car(T)[0]);
Int = ideal_list_intersection(map(second,PDL),V,0|mod=Mod);
IntP = ideal_intersection(IntP,Int,V,0|mod=Mod,gbblock=[[0,length(IntP)]]);
}
else
while ( 1 ) {
/* rad(G) subset IntP */
/* check if IntP subset rad(G) */
/* print([length(PD),length(IntP)],2); */
Sat = [];
IntPM = mingen(IntP,V);
for ( T = IntPM; T != [] && length(Sat) < 16; T = cdr(T) )
if ( G0 = radical_membership(car(T),G,V|mod=Mod,isgb=1,dg=[DG,Ind],sat=1) )
Sat = cons(G0,Sat);
if ( Sat == [] ) return PD;
print(length(Sat),2); print("->",2);
Sat = remove_identical_comp(Sat|mod=Mod);
print(length(Sat));
for ( T = Sat; T != []; T = cdr(T) ) {
PD0 = zprimecomp(car(T),V,Indep|mod=Mod); PD = append(PD,PD0);
Int = ideal_list_intersection(Indep?map(first,PD0):PD0,V,0|mod=Mod);
IntP = ideal_intersection(IntP,Int,V,0|mod=Mod,gbblock=[[0,length(IntP)]]);
}
}
}
/* pre-decomposition */
def lex_predec1(B,V)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
G = fast_gb(B,V,Mod,2);
for ( T = G; T != []; T = cdr(T) ) {
F = gen_fctr(car(T),Mod);
if ( length(F) > 2 || length(F) == 2 && F[1][1] > 1 ) {
for ( R = [], S = cdr(F); S != []; S = cdr(S) ) {
Ft = car(S)[0];
Gt = map(ptozp,map(gen_nf,G,[Ft],V,0,Mod));
R1 = fast_gb(cons(Ft,Gt),V,Mod,0);
R = cons(R1,R);
}
return R;
}
}
return [G];
}
/* zero-dimensional prime/primary decomosition */
def zprimedec(B,V,Mod)
{
L = partial_decomp(B,V,Mod);
P = L[0]; NP = L[1];
R = [];
for ( ; P != []; P = cdr(P) ) R = cons(car(car(P)),R);
for ( T = NP; T != []; T = cdr(T) ) {
R1 = complete_decomp(car(T),V,Mod);
R = append(R1,R);
}
return R;
}
def complete_decomp(GD,V,Mod)
{
G = GD[0]; D = GD[1];
W = vars(G);
PV = setminus(W,V);
N = length(V); PN = length(PV);
U = find_npos(GD,V,PV,Mod);
NV = ttttt;
M = gen_minipoly(cons(NV-U,G),cons(NV,V),PV,0,NV,Mod);
M = ppart(M,NV,Mod);
MF = Mod ? modfctr(M,Mod) : fctr(M);
if ( length(MF) == 2 ) return [G];
R = [];
for ( T = cdr(MF); T != []; T = cdr(T) ) {
Mt = subst(car(car(T)),NV,U);
G1 = fast_gb(cons(Mt,G),W,Mod,0);
if ( PV != [] ) G1 = elim_gb(G1,V,PV,Mod,[[0,N],[0,PN]]);
R = cons(G1,R);
}
return R;
}
def partial_decomp(B,V,Mod)
{
Elim = (Elim=getopt(elim))&&type(Elim)!=-1 ? 1 : 0;
N = length(V);
W = vars(B);
PV = setminus(W,V);
NP = length(PV);
W = append(V,PV);
if ( Elim && PV != [] ) Ord = [[0,N],[0,NP]];
else Ord = 0;
if ( Mod )
B = nd_f4(B,W,Mod,Ord);
else
B = nd_f4_trace(B,W,1,GBCheck,Ord);
P = []; NP = [[B,vector(N+1)]];
for ( I = length(V)-1; I >= 0; I-- ) {
NP1 = [];
for ( T = NP; T != []; T = cdr(T) ) {
L = partial_decomp0(car(T),V,PV,Ord,I,Mod);
P = append(L[0],P);
NP1 = append(L[1],NP1);
}
NP = NP1;
}
return [P,NP];
}
def partial_decomp0(GD,V,PV,Ord,I,Mod)
{
G = GD[0]; D = GD[1];
N = length(V); PN = length(PV);
W = append(V,PV);
VI = V[I];
M = gen_minipoly(G,V,PV,Ord,VI,Mod);
M = ppart(M,VI,Mod);
if ( Mod )
MF = modfctr(M,Mod);
else
MF = fctr(M);
if ( length(MF) == 2 && MF[1][1] == 1 ) {
D1 = D*1;
D1[I] = M;
Gelim = elim_gb(G,V,PV,Mod,Ord);
D1[N] = LD = ldim(Gelim,V);
GD1 = [Gelim,D1];
for ( J = 0; J < N; J++ )
if ( D1[J] && deg(D1[J],V[J]) == LD )
return [[GD1],[]];
return [[],[GD1]];
}
P = []; NP = [];
GI = elim_gb(G,V,PV,Mod,Ord);
for ( T = cdr(MF); T != []; T = cdr(T) ) {
Mt = car(car(T));
D1 = D*1;
D1[I] = Mt;
GIt = map(gen_nf,GI,[Mt],V,Ord,Mod);
G1 = cons(Mt,GIt);
Gelim = elim_gb(G1,V,PV,Mod,Ord);
D1[N] = LD = ldim(Gelim,V);
for ( J = 0; J < N; J++ )
if ( D1[J] && deg(D1[J],V[J]) == LD ) break;
if ( J < N )
P = cons([Gelim,D1],P);
else
NP = cons([Gelim,D1],NP);
}
return [P,NP];
}
def zprimecomp(G,V,Indep) {
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
W = maxindep(G,V,0|mod=Mod);
V0 = setminus(V,W);
V1 = append(V0,W);
#if 0
O1 = [[0,length(V0)],[0,length(W)]];
G1 = fast_gb(G,V1,Mod,O1);
dp_ord(0);
#else
G1 = G;
#endif
PD = zprimedec(G1,V0,Mod);
dp_ord(0);
R = [];
for ( T = PD; T != []; T = cdr(T) ) {
U = contraction(car(T),V0|mod=Mod);
U = nd_gr(U,V,Mod,0);
R = cons(Indep?[U,W]:U,R);
}
return R;
}
def fast_gb(B,V,Mod,Ord)
{
if ( type(Block=getopt(gbblock)) == -1 ) Block = [];
if ( type(NoRA=getopt(nora)) == -1 ) NoRA = 0;
if ( Mod )
G = nd_f4(B,V,Mod,Ord|nora=NoRA);
else if ( Chrem )
G = map(ptozp,noro_grcrt.f4_chr(B,V,Ord));
else if ( GBTrace ) {
if ( GBF4 )
G = nd_f4_trace(B,V,1,GBCheck,Ord|nora=NoRA,gbblock=Block);
else
G = nd_gr_trace(B,V,1,GBCheck,Ord|nora=NoRA,gbblock=Block);
} else {
if ( GBF4 )
G = nd_f4(B,V,0,Ord|nora=NoRA,gbblock=Block);
else
G = nd_gr(B,V,0,Ord|nora=NoRA,gbblock=Block);
}
return G;
}
def incremental_gb(A,V,Ord)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(Block=getopt(gbblock)) == -1 ) Block = [];
if ( Mod ) {
G = fast_gb(A,V,Mod,Ord|gbblock=Block);
} else if ( Competitive && Procs ) {
Arg0 = ["nd_f4",A,V,0,Ord];
Arg1 = ["nd_f4_trace",A,V,1,GBCheck,Ord];
G = competitive_exec("incremental_gb",Procs,[Arg0,Arg1]);
} else
G = fast_gb(A,V,0,Ord|gbblock=Block);
return G;
}
def elim_gb(G,V,PV,Mod,Ord)
{
N = length(V); PN = length(PV);
O1 = [[0,N],[0,PN]];
if ( Ord == O1 )
Ord = Ord[0][0];
if ( Mod ) /* XXX */ {
for ( T = G, H = []; T != []; T = cdr(T) )
if ( car(T) ) H = cons(car(T),H);
G = reverse(H);
if ( PV == [] )
G = nd_f4(G,V,Mod,Ord);
else
G = dp_gr_mod_main(G,V,0,Mod,Ord);
} else if ( Competitive && Procs ) {
Arg0 = ["nd_gr",G,V,0,Ord];
Arg1 = ["noro_pd.nd_gr_elim",G,V,PV,O1,Ord];
Arg2 = ["noro_pd.nd_gr_trace_elim",G,V,PV,O1,Ord];
Arg3 = ["noro_pd.nd_gr_rat",G,V,PV,O1,Ord];
G = competitive_exec("elim_gb",Procs,[Arg0,Arg1,Arg2,Arg3]);
} else
G = nd_gr_rat(G,V,PV,O1,Ord);
return G;
}
def nd_gr_rat(B,V,PV,Ord1,Ord)
{
if ( subset(vars(B),V) )
G = nd_f4_trace(B,V,1,1,Ord);
else
G = nd_gr_trace(B,V,1,1,Ord);
return G;
}
def nd_gr_elim(B,V,PV,Ord1,Ord)
{
G = nd_gr(B,append(V,PV),0,Ord1|homo=1);
G1 = nd_gr_postproc(G,V,0,Ord,0);
return G1;
}
def nd_gr_trace_elim(B,V,PV,Ord1,Ord)
{
G = nd_gr_trace(B,append(V,PV),1,1,Ord);
G = nd_gr_trace(G,append(V,PV),1,-1,Ord1);
G1 = nd_gr_postproc(G,V,0,Ord,0);
return G1;
}
def ldim(G,V)
{
O0 = dp_ord(); dp_ord(0);
D = length(dp_mbase(map(dp_ptod,G,V)));
dp_ord(O0);
return D;
}
/* over Q only */
def make_mod_subst(GD,V,PV,HC)
{
N = length(V);
PN = length(PV);
G = GD[0]; D = GD[1];
for ( I = 0; ; I = (I+1)%100 ) {
Mod = lprime(I);
S = [];
for ( J = PN-1; J >= 0; J-- )
S = append([PV[J],random()%Mod],S);
for ( T = HC; T != []; T = cdr(T) )
if ( !(subst(car(T),S)%Mod) ) break;
if ( T != [] ) continue;
for ( J = 0; J < N; J++ ) {
M = subst(D[J],S);
F = modsqfr(M,Mod);
if ( length(F) != 2 || F[1][1] != 1 ) break;
}
if ( J < N ) continue;
G0 = map(subst,G,S);
return [G0,Mod];
}
}
def rsgn()
{
return random()%2 ? 1 : -1;
}
def find_npos(GD,V,PV,Mod)
{
N = length(V); PN = length(PV);
G = GD[0]; D = GD[1]; LD = D[N];
DH = map(dp_dtop,map(dp_ht,map(dp_ptod,D,V)),V);
Ord0 = dp_ord(); dp_ord(0);
HC = map(dp_hc,map(dp_ptod,G,V));
dp_ord(Ord0);
if ( !Mod ) {
W = append(V,PV);
G1 = nd_gr_trace(G,W,1,GBCheck,[[0,N],[0,PN]]);
L = make_mod_subst([G1,D],V,PV,HC);
return find_npos([L[0],D],V,[],L[1]);
}
N = length(V);
NV = ttttt;
for ( B = 2; ; B++ ) {
for ( J = N-2; J >= 0; J-- ) {
for ( U = 0, K = J; K < N; K++ ) {
if ( DH[K] == V[K] ) continue;
U += rsgn()*((random()%B+1))*V[K];
}
#if 0
M = minipolym(G,V,0,U,NV,Mod);
#else
M = gen_minipoly(cons(NV-U,G),cons(NV,V),PV,0,NV,Mod);
#endif
if ( deg(M,NV) == LD ) return U;
}
}
}
def gen_minipoly(G,V,PV,Ord,VI,Mod)
{
if ( PV == [] ) {
O0 = dp_ord();
NV = sssss;
if ( Mod )
M = minipolym(G,V,Ord,VI,NV,Mod);
else
M = minipoly(G,V,Ord,VI,NV);
dp_ord(O0);
return subst(M,NV,VI);
}
if ( Mod ) {
W = setminus(V,[VI]);
PV1 = cons(VI,PV);
V1 = append(W,PV1);
G = nd_f4(G,V1,Mod,[[0,length(W)],[0,length(PV1)]]|homo=1);
G = elimination(G,PV1);
G = nd_gr(G,PV1,Mod,[[0,1],[0,length(PV)]]|nora=1);
for ( M = car(G), T = cdr(G); T != []; T = cdr(T) )
if ( deg(car(T),VI) < deg(M,VI) ) M = car(T);
dp_ord(O0);
return M;
}
if ( Competitive && Procs ) {
Arg0 = ["noro_pd.gen_minipoly_rat1",G,V,PV,Ord,VI,GBCheck];
Arg1 = ["noro_pd.gen_minipoly_rat",G,V,PV,Ord,VI,GBCheck];
Arg2 = ["noro_pd.gen_minipoly_elim",G,V,PV,Ord,VI,GBCheck];
Arg3 = ["noro_pd.gen_minipoly_chr",G,V,PV,Ord,VI,GBCheck];
Arg4 = ["noro_pd.gen_minipoly_leq",G,V,PV,Ord,VI,GBCheck];
M = competitive_exec("gen_minipoly",Procs,[Arg0,Arg1,Arg2,Arg3,Arg4]);
bsave([Arg0,Arg1,Arg2,Arg3,Arg4],"mp"+rtostr(MP_Serial++));
} else
M = gen_minipoly_rat(G,V,PV,Ord,VI,GBCheck);
return M;
}
static MP_Var$
def comp_by_deg(A,B)
{
DA = deg(A,MP_Var);
DB = deg(B,MP_Var);
if ( DA > DB ) return 1;
else if ( DA < DB ) return -1;
else return 0;
}
def gen_minipoly_rat1(B,V,PV,Ord,VI,Check) {
PV1 = cons(VI,PV);
PV2 = setminus(PV1,[PV1[length(PV1)-1]]);
W = setminus(V,[VI]);
V2 = append(W,PV2);
G = nd_gr_trace(B,V2,1,Check,[[0,length(W)],[0,length(PV2)]]|nora=1);
G = elimination(G,PV1);
G = nd_gr_trace(G,PV1,1,-1,[[0,1],[0,length(PV)]]|nora=1);
for ( M = car(G), T = cdr(G); T != []; T = cdr(T) )
if ( deg(car(T),VI) < deg(M,VI) ) M = car(T);
return sdiv(M,cont(M,VI));
}
def gen_minipoly_rat(B,V,PV,Ord,VI,Check)
{
PV1 = cons(VI,PV);
V1 = append(setminus(V,[VI]),[VI]);
G = nd_gr(B,V1,0,[[0,length(V1)-1],[0,1]]|nora=1);
G = elimination(G,PV1);
M = G[0];
return sdiv(M,cont(M,VI));
}
def gen_minipoly_elim(B,V,PV,Ord,VI,Check) {
PV1 = cons(VI,PV);
W = setminus(V,[VI]);
V1 = append(W,PV1);
G = nd_gr_trace(B,V1,1,Check,[[0,length(W)],[0,length(PV1)]]|nora=1);
G = elimination(G,PV1);
G = nd_gr_trace(G,PV1,1,Check,[[0,1],[0,length(PV)]]|nora=1);
for ( M = car(G), T = cdr(G); T != []; T = cdr(T) )
if ( deg(car(T),VI) < deg(M,VI) ) M = car(T);
return sdiv(M,cont(M,VI));
}
def gen_minipoly_chr(B,V,PV,Ord,VI,Check)
{
N =length(V); PN = length(PV);
W2 = cons(VI,PV);
if ( N >= 2 ) {
V2 = append(setminus(V,[VI]),[VI]);
W = append(V2,PV);
#if 1
VPV = append(V,PV);
G = nd_f4_trace(B,VPV,1,Check,0);
G2 = noro_grcrt.f4_chr(G,W,[[0,N-1],[0,PN+1]]|homo=1,elim=N-2);
for ( T = G2; T != []; T = cdr(T) )
if ( nd_nf(car(T),reverse(G),VPV,0,0) )
#else
G2 = noro_grcrt.f4_chr(B,W,[[0,N-1],[0,PN+1]]|homo=1,elim=N-2);
#endif
return gen_minipoly_rat(B,V,PV,Ord,VI,Check);
} else {
G2 = nd_f4_trace(B,W2,1,Check,0);
}
G3 = nd_f4_trace(G2,W2,1,-1,[[0,1],[0,PN]]);
for ( M = car(G3), T = cdr(G3); T != []; T = cdr(T) )
if ( deg(car(T),VI) < deg(M,VI) ) M = car(T);
return sdiv(M,cont(M,VI));
}
def gen_minipoly_leq(B,V,PV,Ord,VI,Check)
{
W = setminus(V,[VI]);
PV1 = cons(VI,PV);
VV = append(W,PV1);
VPV = append(V,PV);
GG = nd_f4_trace(B,VPV,1,Check,Ord);
for ( I = 0; ; I++ ) {
Mod = lprime(I);
M0 = gen_minipoly(GG,V,PV,Ord,VI,Mod);
M = find_member_with_support(M0,GG,VPV,PV1,Ord);
if ( M )
return sdiv(M,cont(M,VI));
}
}
def comp_by_tdeg(A,B)
{
if ( dp_td(A) > dp_td(B) ) return 1;
else if ( dp_td(A) < dp_td(B) ) return -1;
else return 0;
}
def redcont(NF)
{
Nm = NF[1]; Dn = NF[2];
if ( !Nm ) return [NF[0],0,1];
C = dp_cont(Nm);
Gcd = igcd(C,Dn);
return [NF[0],Nm/Gcd,Dn/Gcd];
}
def nf_mlist(M,G,V,Ord)
{
dp_ord(Ord);
PS = ltov(map(dp_ptod,G,V));
Len = length(G);
for ( I = Len-1, Ind = []; I >= 0; I-- ) Ind = cons(I,Ind);
W=dp_set_weight();
dp_set_weight(0);
M = map(dp_dtop,qsort(map(dp_ptod,M,V),noro_pd.comp_by_tdeg),V);
dp_set_weight(W);
NF = [];
for ( T = M; T != []; T = cdr(T) ) {
T0 = car(T);
for ( S = NF; S != []; S = cdr(S) )
if ( tdiv(T0,car(S)[0]) ) break;
if ( S != [] ) {
S0 = car(S);
U = dp_ptod(sdiv(T0,S0[0]),V);
L = dp_true_nf(Ind,U*S0[1],PS,1);
NF0 = [T0,L[0],L[1]*S0[2]];
} else {
L = dp_true_nf(Ind,dp_ptod(T0,V),PS,1);
NF0 = [T0,L[0],L[1]];
}
NF0 = redcont(NF0);
NF = cons(NF0,NF);
}
}
def find_member_with_support(F,G,V,V0,Ord)
{
G = map(dp_dtop,qsort(map(dp_ptod,G,V0),noro_pd.comp_by_tdeg),V0);
M = p_terms(F,V,Ord);
NF = nf_mlist(M,G,V,Ord);
Len = length(NF);
S = NF[0][0];
R = NF[0][1]/NF[0][2];
TT = [];
for ( I = 1; I < Len; I++ ) {
TI = strtov("tttt"+rtostr(I));
R += TI*(NF[I][1]/NF[I][2]);
S += TI*NF[I][0];
TT = cons(TI,TT);
}
TT = reverse(TT);
for ( L = [], T = R; T; T = dp_rest(T) ) L = cons(dp_hc(T),L);
W=dp_set_weight(); dp_set_weight(0);
Sol = nd_f4(L,TT,0,0);
dp_set_weight(W);
if ( length(Sol) == 1 && type(Sol[0])==1 ) return 0;
U = p_nf(S,Sol,TT,0);
return U;
}
def indepset(V,H)
{
if ( H == [] ) return V;
N = -1;
for ( T = V; T != []; T = cdr(T) ) {
VI = car(T);
HI = [];
for ( S = H; S != []; S = cdr(S) )
if ( !tdiv(car(S),VI) ) HI = cons(car(S),HI);
RI = indepset(setminus(V,[VI]),HI);
if ( length(RI) > N ) {
R = RI; N = length(RI);
}
}
return R;
}
def maxindep(B,V,O)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
G = fast_gb(B,V,Mod,O);
Old = dp_ord();
dp_ord(O);
H = map(dp_dtop,map(dp_ht,map(dp_ptod,G,V)),V);
H = map(sq,H,0);
H = nd_gr(H,V,0,0);
H = monodec0(H,V);
N = length(V);
Dep = [];
for ( T = H, Len = N+1; T != []; T = cdr(T) ) {
M = length(car(T));
if ( M < Len ) {
Dep = [car(T)];
Len = M;
} else if ( M == Len )
Dep = cons(car(T),Dep);
}
R = setminus(V,Dep[0]);
dp_ord(Old);
return R;
}
def maxindep2(B,V,O)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
G = fast_gb(B,V,Mod,O);
Old = dp_ord();
dp_ord(O);
H = map(dp_dtop,map(dp_ht,map(dp_ptod,G,V)),V);
H = map(sq,H,0);
H = nd_gr(H,V,0,0);
H = monodec0(H,V);
N = length(V);
Dep = [];
for ( T = H, Len = N+1; T != []; T = cdr(T) ) {
M = length(car(T));
if ( M < Len ) {
Dep = [car(T)];
Len = M;
} else if ( M == Len )
Dep = cons(car(T),Dep);
}
R = [];
for ( T = Dep; T != []; T = cdr(T) )
R = cons(setminus(V,car(T)),R);
dp_ord(Old);
return reverse(R);
}
/* ideal operations */
def contraction(G,V)
{
if ( type(AllV=getopt(allv)) == -1 ) AllV = 0;
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
C = [];
for ( T = G; T != []; T = cdr(T) ) {
C1 = dp_hc(dp_ptod(car(T),V));
S = gen_fctr(C1,Mod);
for ( S = cdr(S); S != []; S = cdr(S) )
if ( !member(S[0][0],C) ) C = cons(S[0][0],C);
}
W = vars(G);
PV = setminus(W,V);
if ( AllV ) W = AllV;
else W = append(V,PV);
if ( ContAlg == 0 )
contraction_onetime(G,C,W,Mod);
else if ( ContAlg == 1 )
contraction_succ(G,C,W,Mod);
else if ( ContAlg == 2 )
contraction_m(G,C,W,Mod);
else
error("contraction : invalid algorithm selection");
}
def contraction_onetime(G,C,W,Mod)
{
for ( T = C, S = 1; T != []; T = cdr(T) )
S *= car(T);
G = sat(G,S,W|mod=Mod);
return G;
}
def contraction_succ(G,C,W,Mod)
{
if ( C != [] ) {
G = sat(G,car(C),W|mod=Mod);
for ( T = cdr(C); T != []; T = cdr(T) )
G = sat(G,car(T),W|isgb=1,mod=Mod);
}
return G;
}
def contraction_m(G,C,W,Mod)
{
H = H0 = G;
while ( 1 ) {
for ( T = C; T != []; T = cdr(T) )
H = map(sdiv,ideal_intersection_m([car(T)],H,W,0|mod=Mod),car(T));
H = nd_gr(H,W,Mod,0);
if ( gen_gb_comp(H0,H,Mod) ) break;
else H0 = H;
}
return H;
}
def ideal_list_intersection(L,V,Ord)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
N = length(L);
if ( N == 0 ) return [1];
if ( N == 1 )
return IsGB ? L[0] : fast_gb(L[0],V,Mod,Ord);
else {
for ( I = 0, T = [1]; I < N; I++ )
T = ideal_intersection_m(T,L[I],V,Ord|mod=Mod);
if ( !Mod )
T = nd_f4_trace(T,V,1,1,Ord);
else
T = nd_gr(T,V,Mod,Ord);
return T;
}
}
def call_ideal_list_intersection(L,V,Mod,Ord,IsGB)
{
return ideal_list_intersection(L,V,Ord|mod=Mod,isgb=IsGB);
}
def ideal_intersection(A,B,V,Ord)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(Block=getopt(gbblock)) == -1 ) Block = [];
T = ttttt;
if ( Mod ) {
G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
cons(T,V),Mod,[[0,1],[Ord,length(V)]]|gbblock=Block);
} else
if ( Competitive && Procs ) {
Arg0 = ["nd_gr",
append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
cons(T,V),0,[[0,1],[Ord,length(V)]]];
Arg1 = ["nd_gr_trace",
append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
cons(T,V),1,GBCheck,[[0,1],[Ord,length(V)]]];
G = competitive_exec("ideal_intersection",Procs,[Arg0,Arg1]);
} else {
if ( GBF4 ) {
G = nd_f4_trace(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
cons(T,V),1,1,[[0,1],[Ord,length(V)]]|gbblock=Block);
} else {
G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
cons(T,V),0,[[0,1],[Ord,length(V)]]|gbblock=Block);
}
}
G0 = elimination(G,V);
return G0;
}
def aa(A) { return [A,A]; }
def ideal_intersection_m(A,B,V,Ord)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
dp_ord(Ord);
if ( UsualInt )
return ideal_intersection(A,B,V,Ord|mod=Mod);
DA = map(dp_ptod,A,V); DB = ltov(map(dp_ptod,B,V));
if ( Mod ) {
DA = map(dp_mod,DA,Mod,[]); DB = map(dp_mod,DB,Mod,[]);
setmod(Mod);
}
N = length(B);
for ( Ind = [], I = N-1; I >= 0; I-- ) Ind = cons(I,Ind);
for ( T = DA, C = []; T != []; T = cdr(T) ) {
R = Mod?dp_nf_mod(Ind,car(T),DB,1,Mod):dp_nf(Ind,car(T),DB,1);
if ( !R )
C = cons([0,dp_dtop(car(T),V)],C);
else
C = cons([dp_dtop(car(T),V),0],C);
}
if ( IntGB ) {
if ( Mod )
G = nd_gr(append(C,map(aa,B)),V,Mod,[1,Ord]);
else
G = nd_gr_trace(append(C,map(aa,B)),V,0,1,[1,Ord]);
for ( T = G, G1 = []; T != []; T = cdr(T) )
if ( !car(T)[0] ) G1 = cons(car(T)[1],G1);
G = reverse(G1);
} else {
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;
if ( type(L=getopt(dg)) == -1 ) L = 0;
if ( type(Sat=getopt(sat)) == -1 ) Sat = 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
|gbblock=[[0,length(G)]]);
else
T = nd_gr(append(G,[NV*F-1]),cons(NV,V),Mod,0);
if ( type(car(T)) == 1 ) return 0;
else if ( Sat ) {
G1 = fast_gb(T,cons(NV,V),Mod,[[0,1],[0,length(V)]]);
G0 = elimination(G1,V);
return G0;
} else return [T,NV];
}
def radical_membership_sat(F,G,V) {
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 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,[[0,1],[0,length(V)]]
|gbblock=[[0,length(G)]]);
else
T = nd_gr(append(G,[NV*F-1]),cons(NV,V),Mod,[[0,1],[0,length(V)]]);
if ( type(car(T)) == 1 ) return 0;
G0 = elimination(T,V);
return G0;
}
def modular_radical_membership(F,G,V) {
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( Mod )
return radical_membership(F,G,V|mod=Mod);
F = gen_nf(F,G,V,0,0);
if ( !F ) return 0;
NV = ttttt;
for ( J = 0; ; J++ ) {
Mod = lprime(J);
H = map(dp_hc,map(dp_ptod,G,V));
for ( ; H != []; H = cdr(H) ) if ( !(car(H)%Mod) ) break;
if ( H != [] ) continue;
T = nd_f4(cons(NV*F-1,G),cons(NV,V),Mod,0);
if ( type(car(T)) == 1 ) {
I = radical_membership_rep(F,G,V,-1,0,Mod);
I1 = radical_membership_rep(F,G,V,I,0,0);
if ( I1 > 0 ) return 0;
}
return radical_membership(F,G,V);
}
}
def radical_membership_rep(F,G,V,Max,Ord,Mod) {
Ft = F;
I = 1;
while ( Max < 0 || I <= Max ) {
Ft = gen_nf(Ft,G,V,Ord,Mod);
if ( !Ft ) return I;
Ft *= F;
I++;
}
return -1;
}
def ideal_product(A,B,V)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
dp_ord(0);
DA = map(dp_ptod,A,V);
DB = map(dp_ptod,B,V);
DegA = map(dp_td,DA);
DegB = map(dp_td,DB);
for ( PA = [], T = A, DT = DegA; T != []; T = cdr(T), DT = cdr(DT) )
PA = cons([car(T),car(DT)],PA);
PA = reverse(PA);
for ( PB = [], T = B, DT = DegB; T != []; T = cdr(T), DT = cdr(DT) )
PB = cons([car(T),car(DT)],PB);
PB = reverse(PB);
R = [];
for ( T = PA; T != []; T = cdr(T) )
for ( S = PB; S != []; S = cdr(S) )
R = cons([car(T)[0]*car(S)[0],car(T)[1]+car(S)[1]],R);
T = qsort(R,noro_pd.comp_by_second);
T = map(first,T);
Len = length(A)>length(B)?length(A):length(B);
Len *= 2;
L = sep_list(T,Len); B0 = L[0]; B1 = L[1];
R = fast_gb(B0,V,Mod,0);
while ( B1 != [] ) {
print(length(B1));
L = sep_list(B1,Len);
B0 = L[0]; B1 = L[1];
R = fast_gb(append(R,B0),V,Mod,0|gbblock=[[0,length(R)]],nora=1);
}
return R;
}
def sat(G,F,V)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
NV = ttttt;
if ( Mod )
G1 = fast_gb(cons(NV*F-1,G),cons(NV,V),Mod,[[0,1],[0,length(V)]]);
#if 0
else if ( Competitive && Procs ) {
Arg0 = ["nd_f4_trace",
cons(NV*F-1,G),cons(NV,V),0,GBCheck,[[0,1],[0,length(V)]]];
Arg1 = ["nd_f4_trace",
cons(NV*F-1,G),cons(NV,V),1,GBCheck,[[0,1],[0,length(V)]]];
G1 = competitive_exec("sat",Procs,[Arg0,Arg1]);
}
#endif
else {
B1 = append(G,[NV*F-1]);
V1 = cons(NV,V);
Ord1 = [[0,1],[0,length(V)]];
if ( IsGB )
G1 = fast_gb(B1,V1,0,Ord1|gbblock=[[0,length(G)]]);
else
G1 = fast_gb(B1,V1,0,Ord1);
}
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;
}
/* homogeneous case only */
def sat_ind_var(G,F,V)
{
if ( type(Ord=getopt(ord)) == -1 ) Ord = 0;
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
V0 = append(setminus(V,[F]),[F]);
G0 = nd_gr(G,V0,Mod,0);
M = 0;
for ( G1 = [], T = G0; T != []; T = cdr(T) ) {
S = car(T);
M1 = mindeg(S,F);
S = sdiv(S,F^M1);
G1 = cons(S,G1);
if ( M1 > M ) M = M1;
}
G1 = nd_gr(G1,V,Mod,Ord);
return [G1,M];
}
def sat_ind(G,F,V)
{
if ( type(Ord=getopt(ord)) == -1 ) Ord = 0;
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
NV = ttttt;
F = gen_nf(F,G,V,Ord,Mod);
for ( I = 0, GI = G; ; I++ ) {
G1 = colon(GI,F,V|mod=Mod,ord=Ord);
if ( ideal_inclusion(G1,GI,V,Ord|mod=Mod) ) {
return [GI,I];
}
else GI = G1;
}
}
def colon(G,F,V)
{
if ( type(Ord=getopt(ord)) == -1 ) Ord = 0;
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
F = gen_nf(F,G,V,Ord,Mod);
if ( !F ) return [1];
if ( IsGB )
T = ideal_intersection(G,[F],V,Ord|gbblock=[[0,length(G)]],mod=Mod);
else
T = ideal_intersection(G,[F],V,Ord|mod=Mod);
Gen = Mod?map(sdivm,T,F,Mod):map(ptozp,map(sdiv,T,F));
return nd_gr(Gen,V,Mod,Ord);
}
#if 1
def ideal_colon(G,F,V)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
G = nd_gr(G,V,Mod,0);
C = [1];
TV = ttttt;
F = qsort(F,noro_pd.comp_tdeg);
for ( T = F; T != []; T = cdr(T) ) {
S = colon(G,car(T),V|isgb=1,mod=Mod);
if ( type(S[0])!= 1 ) {
C = nd_gr(append(vtol(ltov(C)*TV),vtol(ltov(S)*(1-TV))),
cons(TV,V),Mod,[[0,1],[Ord,length(V)]]|gbblock=[[0,length(C)]]);
C = elimination(C,V);
}
}
return C;
}
#else
def ideal_colon(G,F,V)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
G = nd_gr(G,V,Mod,0);
for ( T = F, L = []; T != []; T = cdr(T) ) {
C = colon(G,car(T),V|isgb=1,mod=Mod);
if ( type(C[0]) != 1 ) L = cons(C,L);
}
L = reverse(L);
return ideal_list_intersection(L,V,0|mod=Mod);
}
#endif
def member(A,L)
{
for ( ; L != []; L = cdr(L) )
if ( car(L) == A ) return 1;
return 0;
}
/* return 1 of A is a subset of B */
def subset(A,B)
{
for ( ; A != []; A = cdr(A) )
if ( !member(car(A),B) ) return 0;
return 1;
}
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]; STrace = Data[6];
N = length(G);
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(N,V,Trace,Mod)
{
P = vector(N);
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_trace(Ti[1],P,V,Mod);
U = cons(R,U);
}
return reverse(U);
}
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 = 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]);
Den *= Cj;
}
return Num;
}
def ideal_sat(G,F,V)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
G = nd_gr(G,V,Mod,0);
for ( T = F, L = []; T != []; T = cdr(T) )
L = cons(sat(G,car(T),V|mod=Mod),L);
L = reverse(L);
return ideal_list_intersection(L,V,0|mod=Mod);
}
def ideal_inclusion(F,G,V,O)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
for ( T = F; T != []; T = cdr(T) )
if ( gen_nf(car(T),G,V,O,Mod) ) return 0;
return 1;
}
/* remove redundant components */
def qd_simp_comp(QP,V)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
R = ltov(QP);
N = length(R);
for ( I = 0; I < N; I++ ) {
if ( R[I] ) {
QI = R[I][0]; PI = R[I][1];
for ( J = I+1; J < N; J++ )
if ( R[J] && gen_gb_comp(PI,R[J][1],Mod) ) {
QI = ideal_intersection(QI,R[J][0],V,0|mod=Mod);
R[J] = 0;
}
R[I] = [QI,PI];
}
}
for ( I = N-1, S = []; I >= 0; I-- )
if ( R[I] ) S = cons(R[I],S);
return S;
}
def qd_remove_redundant_comp(G,Iso,Emb,V,Ord)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
IsoInt = ideal_list_intersection(map(first,Iso),V,Ord|mod=Mod);
Emb = qd_simp_comp(Emb,V|mod=Mod);
Emb = reverse(qsort(Emb));
A = ltov(Emb); N = length(A);
Pre = IsoInt; Post = vector(N+1);
for ( Post[N] = IsoInt, I = N-1; I >= 1; I-- )
Post[I] = ideal_intersection(Post[I+1],A[I][0],V,Ord|mod=Mod);
for ( I = 0; I < N; I++ ) {
print(".",2);
Int = ideal_intersection(Pre,Post[I+1],V,Ord|mod=Mod);
if ( gen_gb_comp(Int,G,Mod) ) A[I] = 0;
else
Pre = ideal_intersection(Pre,A[I][0],V,Ord|mod=Mod);
}
for ( T = [], I = 0; I < N; I++ )
if ( A[I] ) T = cons(A[I],T);
return reverse(T);
}
def pd_simp_comp(PL,V)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(First=getopt(first)) == -1 ) First = 0;
A = ltov(PL); N = length(A);
if ( N == 1 ) return PL;
for ( I = 0; I < N; I++ ) {
if ( !A[I] ) continue;
AI = First?A[I][0]:A[I];
for ( J = 0; J < N; J++ ) {
if ( J == I || !A[J] ) continue;
AJ = First?A[J][0]:A[J];
if ( gen_gb_comp(AI,AJ,Mod) || ideal_inclusion(AI,AJ,V,Ord|mod=Mod) )
A[J] = 0;
}
}
for ( I = 0, T = []; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
return reverse(T);
}
def pd_remove_redundant_comp(G,P,V,Ord)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( type(First=getopt(first)) == -1 ) First = 0;
if ( length(P) == 1 ) return P;
A = ltov(P); N = length(A);
for ( I = 0; I < N; I++ ) {
if ( !A[I] ) continue;
for ( J = I+1; J < N; J++ )
if ( A[J] &&
gen_gb_comp(First?A[I][0]:A[I],First?A[J][0]:A[J],Mod) ) A[J] = 0;
}
for ( I = 0, T = []; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
A = ltov(reverse(T)); N = length(A);
Pre = [1]; Post = vector(N+1);
for ( Post[N] = [1], I = N-1; I >= 1; I-- )
Post[I] = ideal_intersection(Post[I+1],First?A[I][0]:A[I],V,Ord|mod=Mod);
for ( I = 0; I < N; I++ ) {
Int = ideal_intersection(Pre,Post[I+1],V,Ord|mod=Mod);
if ( gen_gb_comp(Int,G,Mod) ) A[I] = 0;
else
Pre = ideal_intersection(Pre,First?A[I][0]:A[I],V,Ord|mod=Mod);
}
for ( T = [], I = 0; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
return reverse(T);
}
def remove_identical_comp(L)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
if ( length(L) == 1 ) return L;
A = ltov(L); N = length(A);
for ( I = 0; I < N; I++ ) {
if ( !A[I] ) continue;
for ( J = I+1; J < N; J++ )
if ( A[J] &&
gen_gb_comp(A[I],A[J],Mod) ) A[J] = 0;
}
for ( I = 0, T = []; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
return reverse(T);
}
/* polynomial operations */
def ppart(F,V,Mod)
{
if ( !Mod )
G = nd_gr([F],[V],0,0);
else
G = dp_gr_mod_main([F],[V],0,Mod,0);
return G[0];
}
def sq(F,Mod)
{
if ( !F ) return 0;
A = cdr(gen_fctr(F,Mod));
for ( R = 1; A != []; A = cdr(A) )
R *= car(car(A));
return R;
}
def lcfactor(G,V,O,Mod)
{
O0 = dp_ord(); dp_ord(O);
C = [];
for ( T = G; T != []; T = cdr(T) ) {
C1 = dp_hc(dp_ptod(car(T),V));
S = gen_fctr(C1,Mod);
for ( S = cdr(S); S != []; S = cdr(S) )
if ( !member(S[0][0],C) ) C = cons(S[0][0],C);
}
dp_ord(O0);
return C;
}
def gen_fctr(F,Mod)
{
if ( Mod ) return modfctr(F,Mod);
else return fctr(F);
}
def gen_mptop(F)
{
if ( !F ) return F;
else if ( type(F)==1 )
if ( ntype(F)==5 ) return mptop(F);
else return F;
else {
V = var(F);
D = deg(F,V);
for ( R = 0, I = 0; I <= D; I++ )
if ( C = coef(F,I,V) ) R += gen_mptop(C)*V^I;
return R;
}
}
def gen_nf(F,G,V,Ord,Mod)
{
if ( !Mod ) return p_nf(F,G,V,Ord);
setmod(Mod);
dp_ord(Ord); DF = dp_mod(dp_ptod(F,V),Mod,[]);
N = length(G); DG = newvect(N);
for ( I = N-1, IL = []; I >= 0; I-- ) {
DG[I] = dp_mod(dp_ptod(G[I],V),Mod,[]);
IL = cons(I,IL);
}
T = dp_nf_mod(IL,DF,DG,1,Mod);
for ( R = 0; T; T = dp_rest(T) )
R += gen_mptop(dp_hc(T))*dp_dtop(dp_ht(T),V);
return R;
}
/* Ti = [D,I,M,C] */
def compute_deg0(Ti,P,V,TV)
{
N = length(P[0]);
Num = vector(N);
for ( I = 0; I < N; I++ ) Num[I] = -1;
for ( ; Ti != []; Ti = cdr(Ti) ) {
Sj = car(Ti);
Dj = Sj[0];
Ij =Sj[1];
Mj = deg(type(Sj[2])==9?dp_dtop(Sj[2],V):Sj[2],TV);
Pj = P[Ij];
if ( Dj )
for ( I = 0; I < N; I++ )
if ( Pj[I] >= 0 ) {
T = Mj+Pj[I];
Num[I] = MAX(Num[I],T);
}
}
return Num;
}
def compute_deg(B,V,TV,Data)
{
GB = Data[0];
Homo = Data[1];
Trace = Data[2];
IntRed = Data[3];
Ind = Data[4];
DB = map(dp_ptod,B,V);
if ( Homo ) {
DB = map(dp_homo,DB);
V0 = append(V,[hhh]);
} else
V0 = V;
Perm = Trace[0]; Trace = cdr(Trace);
for ( I = length(Perm)-1, T = Trace; T != []; T = cdr(T) )
if ( (J=car(T)[0]) > I ) I = J;
N = I+1;
N0 = length(B);
P = vector(N);
for ( T = Perm, I = 0; T != []; T = cdr(T), I++ ) {
Pi = car(T);
C = vector(N0);
for ( J = 0; J < N0; J++ ) C[J] = -1;
C[Pi[1]] = 0;
P[Pi[0]] = C;
}
for ( T = Trace; T != []; T = cdr(T) ) {
Ti = car(T); P[Ti[0]] = compute_deg0(Ti[1],P,V0,TV);
}
M = length(Ind);
for ( T = IntRed; T != []; T = cdr(T) ) {
Ti = car(T); P[Ti[0]] = compute_deg0(Ti[1],P,V,TV);
}
R = [];
for ( J = 0; J < M; J++ ) {
U = P[Ind[J]];
R = cons(U,R);
}
return reverse(R);
}
/* set theoretic functions */
def member(A,S)
{
for ( ; S != []; S = cdr(S) )
if ( car(S) == A ) return 1;
return 0;
}
def elimination(G,V) {
for ( R = [], T = G; T != []; T = cdr(T) )
if ( setminus(vars(car(T)),V) == [] ) R =cons(car(T),R);
return R;
}
def setintersection(A,B)
{
for ( L = []; A != []; A = cdr(A) )
if ( member(car(A),B) )
L = cons(car(A),L);
return L;
}
def setminus(A,B) {
for ( T = reverse(A), R = []; T != []; T = cdr(T) ) {
for ( S = B, M = car(T); S != []; S = cdr(S) )
if ( car(S) == M ) break;
if ( S == [] ) R = cons(M,R);
}
return R;
}
def sep_list(L,N)
{
if ( length(L) <= N ) return [L,[]];
R = [];
for ( T = L, I = 0; I < N; I++, T = cdr(T) )
R = cons(car(T),R);
return [reverse(R),T];
}
def first(L)
{
return L[0];
}
def second(L)
{
return L[1];
}
def third(L)
{
return L[2];
}
def first_second(L)
{
return [L[0],L[1]];
}
def comp_tord(A,B)
{
DA = dp_ht(A);
DB = dp_ht(B);
if ( DA > DB ) return 1;
else if ( DA < DB ) return -1;
else return 0;
}
def comp_tdeg(A,B)
{
DA = tdeg(A);
DB = tdeg(B);
if ( DA > DB ) return 1;
else if ( DA < DB ) return -1;
else return 0;
}
def comp_tdeg_first(A,B)
{
DA = tdeg(A[0]);
DB = tdeg(B[0]);
if ( DA > DB ) return 1;
else if ( DA < DB ) return -1;
else return 0;
}
def comp_third_tdeg(A,B)
{
if ( A[2] > B[2] ) return 1;
if ( A[2] < B[2] ) return -1;
DA = tdeg(A[0]);
DB = tdeg(B[0]);
if ( DA > DB ) return 1;
else if ( DA < DB ) return -1;
else return 0;
}
def tdeg(P)
{
dp_ord(0);
return dp_td(dp_ptod(P,vars(P)));
}
def comp_by_ord(A,B)
{
if ( dp_ht(A) > dp_ht(B) ) return 1;
else if ( dp_ht(A) < dp_ht(B) ) return -1;
else return 0;
}
def comp_by_second(A,B)
{
if ( A[1] > B[1] ) return 1;
else if ( A[1] < B[1] ) return -1;
else return 0;
}
def get_lc(F)
{
if ( type(F)==1 ) return F;
V = var(F);
D = deg(F,V);
return get_lc(coef(F,D,V));
}
def tomonic(F,Mod)
{
C = get_lc(F);
IC = inv(C,Mod);
return (IC*F)%Mod;
}
def gen_gb_comp(A,B,Mod)
{
if ( !Mod ) return gb_comp(A,B);
LA = length(A); LB = length(B);
if ( LA != LB ) return 0;
A = map(tomonic,A,Mod);
B = map(tomonic,B,Mod);
A = qsort(A); B = qsort(B);
if ( A != B ) return 0;
return 1;
}
def prod(L)
{
for ( R = 1; L != []; L = cdr(L) )
R *= car(L);
return R;
}
def monodec0(B,V)
{
M = monodec(B,V);
return map(vars,M);
}
def monodec(B,V)
{
B = map(sq,B,0);
G = nd_gr_postproc(B,V,0,0,0);
V = vars(G);
N = length(V);
if ( N == 0 ) return G == [] ? [[]] : [];
if ( N == 1 ) return G;
if ( N < 20 ) {
T = dp_mono_raddec(G,V);
return map(prod,T);
}
X = car(V); W = cdr(V);
D0 = monodec(map(subst,B,X,0),W);
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);
}
def separator(P,V)
{
if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
N = length(P);
dp_ord(0);
DP = vector(N);
for ( I = 0; I < N; I++ ) DP[I] = qsort(ltov(map(dp_ptod,P[I][0],V)),noro_pd.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++ ) {
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;
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));
}
}
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);
R = vector(N);
Pre[0] = [1];
print("pre ",2);
for ( I = 1; I < N; I++, print(".",2) )
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_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_m(Pre[I],Post[I],V,0|mod=Mod);
print("done");
return R;
}
/* XXX */
def call_func(Arg)
{
F = car(Arg);
return call(strtov(F),cdr(Arg));
}
def call_func_serial(Arg,Serial)
{
F = car(Arg);
return [call(strtov(F),cdr(Arg)),Serial];
}
def competitive_exec(Name,P,Args)
{
print([Name],2);
N = length(Args);
for ( I = 0; I < N; I++ )
ox_cmo_rpc(P[I],"noro_pd.call_func",Args[I]|sync=1);
F = ox_select(P);
P0 = setminus(P,F);
for ( Win = [], T = F; T != []; T = cdr(T) )
Win = cons(Args[car(T)][0],Win);
print(Win);
R = map(ox_get,F);
map(ox_reset,P);
return R[0];
}
/* Task[i] = [fname,[arg0,...,argn]] */
def para_exec(Proc,Task) {
Free = Proc;
N = length(Task);
R = [];
print([N],2); print("->",2);
Serial = 0;
while ( N ) {
while ( Task != [] && Free != [] ) {
T = car(Task); Task = cdr(Task);
ox_rpc(car(Free),"noro_pd.call_func_serial",T,Serial++);
ox_push_cmd(car(Free),258); Free = cdr(Free);
}
Finish0 = Finish = ox_select(Proc);
for ( ; Finish != []; Finish = cdr(Finish) ) {
print(".",2);
L = ox_get(car(Finish));
R = cons(L,R);
N--;
}
print([N],2);
Free = append(Free,Finish0);
}
print("");
R = qsort(R,noro_pd.comp_by_second);
R = map(first,R);
return 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,noro_pd.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);
}
def zero_dim(G,V,O) {
dp_ord(O);
HL = map(dp_dtop,map(dp_ht,map(dp_ptod,G,V)),V);
for ( L = []; HL != []; HL = cdr(HL) )
if ( length(vars(car(HL))) == 1 )
L = cons(car(HL),L);
return length(vars(L)) == length(V) ? 1 : 0;
}
endmodule$
end$
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