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* $OpenXM: OpenXM_contrib2/asir2018/lib/primdec_lex,v 1.1 2018/09/19 05:45:08 noro Exp $
*/
/* Primary decomposition & Radical decomposition program */
/* written by T.Shimoyama, Fujitsu Lab. Date: 1995.10.12 */
/* comments about flags *
PRIMEORD term order of Groebner basis in primedec
PRIMAORD term order of Groebner basis in primadec
PRINTLOG print out log (1 (simple) -- 5 (pricise))
SHOWTIME if 1 : print out timings and data
ISOLATED if 1 : compute only isolated primary components
NOEMBEDDED if 1 : compute only pseudo-primary components
NOINITGB if 1 : no initial G-base computation
REDUNDANT if 1 : no redundancy check
COMPLETE if 1 : use complete criterion of redundancy
COMMONCHECK if 1 : redundancy check by intersection (in gr_fctr_sub)
SELECTFLAG selection strategy of separators (0 -- 3)
*/
if (vtype(minipoly) != 3) load("gr")$$
#define GR(R,F,V,O) T2=newvect(4,time());R=dp_gr_main(F,V,0,0,O);GRTIME+=newvect(4,time())-T2;
#define HGRM(R,F,V,O) T2=newvect(4,time());R=dp_gr_main(F,V,1,1,O);GRTIME+=newvect(4,time())-T2;
#define NF(R,IN,F,G,O) T2=newvect(4,time());R=dp_nf(IN,F,G,O);NFTIME+=newvect(4,time())-T2;
/* optional flags */
extern PRIMAORD,PRIMEORD,PRINTLOG,SHOWTIME,NOINITGB$
extern COMMONCHECK,ISOLATED,NOEMBEDDED,REDUNDANT,SELECTFLAG,COMPLETE$
extern EXTENDED,CONTINUE,BSAVE,MAXALGIND,NOSPECIALDEC$
def primflags() {
print("PRIMAORD,PRIMEORD,PRINTLOG,SHOWTIME,NOINITGB,ISOLATED,NOEMBEDDED,COMMONCHECK");
print("REDUNDANT,SELECTFLAG,COMPLETE,EXTENDED,CONTINUE,BSAVE,MAXALGIND,NOSPECIALDEC");}
PRIMAORD=0$ PRIMEORD=2$
/* global variables */
extern DIRECTRY,COMMONIDEAL,NOMRADDEC,NOMISOLATE,RADDECTIME$
extern MISTIME,ISORADDEC,GRTIME,NFTIME$
/* primary ideal decomposition of ideal(F) */
/* return the list of [P,Q] where Q is P-primary component of ideal(F) */
def primadec(F,VL)
{
if ( !VL ) {
print("invalid variables"); return 0; }
if ( !F ) {
print("invalid argument"); return 0; }
if ( F == [] )
return [];
if ( length(F) == 1 && type(F[0]) == 1 )
return [[1],[1]];
NOMRADDEC = NOMISOLATE = 0; RADDECTIME = newvect(4); T0 = newvect(4,time());
GRTIME = newvect(4); NFTIME = newvect(4); MISTIME = newvect(4);
R = primadec_main(F,[["begin",F,F,[1],[]]],[],VL);
if ( PRINTLOG ) {
print(""); print("primary decomposition done.");
}
if ( PRINTLOG || SHOWTIME ) {
print("number of radical decompositions = ",0); print(NOMRADDEC);
print("number of primary components = ",0); print(length(R),0);
print(" ( isolated = ",0); print(NOMISOLATE,0); print(" )");
print("total time of m.i.s. computation = ",0);
print(MISTIME[0],0); GT = MISTIME[1];
if ( GT ) { print(" + gc ",0);print(GT); } else print("");
print("total time of n-form computation = ",0);
print(NFTIME[0],0); GT = NFTIME[1];
if ( GT ) { print(" + gc ",0);print(GT); } else print("");
print("total time of G-base computation = ",0);
print(GRTIME[0],0); GT = GRTIME[1];
if ( GT ) { print(" + gc ",0);print(GT); } else print("");
print("total time of radical decomposition = ",0);
print(RADDECTIME[0],0); GT = RADDECTIME[1];
if ( GT ) { print(" + gc ",0);print(GT,0); }
print(" (iso ",0); print(ISORADDEC[0],0); GT = ISORADDEC[1];
if ( GT ) { print(" +gc ",0);print(GT,0); } print(")");
print("total time of primary decomposition = ",0);
TT = newvect(4,time())-T0; print(TT[0],0);
if ( TT[1] ) { print(" + gc ",0);print(TT[1]); } else print("");
}
return R;
}
/* prime ideal decomposition of radical(F) */
/* return the list of prime components of radical(F) */
def primedec(F,VL)
{
if ( !VL ) {
print("invalid variables"); return 0; }
if ( !F ) {
print("invalid argument"); return 0; }
if ( F == [] )
return [];
GRTIME = newvect(4);
T0 = newvect(4,time());
if ( !NOINITGB ) {
if ( PRINTLOG ) {
print("G-base computation w.r.t ordering = ",0);
print(PRIMEORD);
}
T1 = newvect(4,time());
HGRM(F,F,VL,PRIMEORD);
Tg = newvect(4,time())-T1;
if ( PRINTLOG > 0 ) {
print(" G-base time = ",0); print(Tg[0],0);
if ( Tg[1] ) { print(" + gc : ",0); print(Tg[1]); }
else print("");
}
}
R = primedec_main([F],VL);
Ta = newvect(4,time())-T0;
if ( PRINTLOG || SHOWTIME ) {
print("number of prime components = ",0); print(length(R));
print("G-base time = ",0); print(GRTIME[0],0);
if ( GRTIME[1] ) { print(" + gc : ",0); print(GRTIME[1]); }
else print("");
print("total time = ",0); print(Ta[0],0);
if ( Ta[1] ) { print(" + gc : ",0); print(Ta[1]); } else print("");
}
return R;
}
/* main procedure for primary decomposition. */
/* F : ideal, VL : variable list, REMS : remaining components */
def primadec_main(F,REMS,H,VL)
{
DEC = RES = [];
for (D = [], I = 0; I < length(REMS); I++) {
MARK = REMS[I][0]; WF = REMS[I][1]; WP = REMS[I][2]; SC = REMS[I][3];
if ( !NOINITGB || MARK != "begin" ) {
ORD = PRIMAORD;
if ( PRINTLOG > 1 ) {
if ( MARK != "begin" ) print("");
print("G-base computation w.r.t ordering = ",0);
print(ORD);
}
T1 = newvect(4,time());
/* G-base of ideal */
GR(GF,WF,VL,ORD);
if ( MARK != "begin" && ( COMPLETE || EXTENDED ) ) {
if ( SC!=[1] && SC!=[-1] ) {
LG = localize(WF,SC,VL,ORD); /* VR_s\cap R */
if ( EXTENDED ) { GF = LG; }
} else
LG = GF;
if ( idealinc(H,LG,VL,ORD) ) {
if ( PRINTLOG ) {
print("eliminate the remaining component ",0);
print("by complete criterion");
}
continue; /* complete criterion */
}
}
/* G-base of radical */
if ( MARK == "begin" ) {
RA = ["begin",GF];
} else if ( MARK == "ext" ) {
if ( WF==WP || idealinc(WP,GF,VL,ORD) )
RA = ["ext",GF];
else {
if ( EXTENDED ) {
GA = localize(WP,SC,VL,PRIMEORD);
} else {
GR(GA,WP,VL,PRIMEORD);
}
RA = ["ext",GA];
}
} else if ( MARK == "sep" ) {
for (U=[], T=WP,J=length(T)-1;J>=0;J--) {
if ( EXTENDED ) {
GA = localize(T[J],SC,VL,PRIMEORD);
} else {
GR(GA,T[J],VL,PRIMEORD);
}
if (GA != [1] && GA != [-1])
U = cons(GA,U);
}
RA = ["sep",U];
} else debug;
Tg = newvect(4,time())-T1;
if ( PRINTLOG > 1 ) {
print(" G-base time = ",0); print(Tg[0],0);
if ( Tg[1] ) { print(" + gc : ",0); print(Tg[1]); }
else print("");
}
} else {
GF = F; /* NOINITGB = 1 */
RA = ["begin",GF];
}
if ( PRINTLOG ) {
if ( MARK == "begin" ) {
print("primary decomposition of the ideal");
} else { /* at the begining */
print("");
print("primary decomposition of the remaining component");
}
if ( MARK == "begin" && PRINTLOG > 1 ) { /* at the begining */
print(" ideal = ",0);
print(WF);
} else if ( PRINTLOG >= 4 ) {
print(" remaining component = ",0);
print(GF);
}
}
/* input: init, generator, G-base, radical, intersection, sep.cond.*/
/* output: primary comp. remaining comp. */
Y = isolated(F,WF,GF,RA,REMS[I][4],SC,VL);
D = append(D,Y[0]);
if ( MARK == "begin" )
NOMISOLATE = length(Y[0]);
RES = append(RES,Y[1]);
}
if ( MARK == "begin" ) {
F = GF; /* input polynomial -> G-base of it */
}
DEC = append(DEC,D);
if ( PRINTLOG ) {
print("");
print("# number of remainig components = ",0); print(length(RES));
}
if ( !length(RES) )
return DEC;
if ( !REDUNDANT ) { /* check whether Id(F,RES) is redundant or not */
for(L = [H],I = length(D)-1; I>=0; I--)
L=append(L,[D[I][0]]);
H = idealsetcap(L,VL,ORD); /* new intersection H */
if ( idealinc(H,F,VL,ORD) ) {
if ( PRINTLOG ) {
print("");
print("all primary components are found!");
}
return DEC;
}
REMS = mksepext(RES,H,VL); /* new remainig comps. */
} else {
REMS = mksepext(RES,H,VL); /* new rmaining comps. */
}
D = primadec_main(F,REMS,H,VL);
return append(DEC,D);
}
/* isolated components and embedded components */
/* GF is the G-base of F, RA is the radical of F */
def isolated(IP,F,GF,RA,H,SC,VL)
{
T0 = newvect(4,time());
if ( RA[0] == "begin" ) {
PD = primedec_main([RA[1]],VL);
PD = map(dp_gr_main,PD,VL,0,1,PRIMEORD); /* XXX */
} else if ( RA[0] == "ext" || RA[0] == "sep" ) {
if ( RA[0] == "sep" )
T = prime_irred(idealsav(RA[1]),VL);
else
T = [RA[1]];
if ( !NOSPECIALDEC )
PD = primedec_special(T,VL);
else
PD = primedec_main(T,VL);
} else debug;
T1 = newvect(4,time())-T0;
if ( RA[0] == "begin" ) ISORADDEC = T1;
NOMRADDEC++; RADDECTIME += T1;
if ( PRINTLOG ) {
print("number of prime components = ",0); print(length(PD),0);
print(", time = ",0); print(T1[0],0);
if ( T1[1] ) { print(" + gc : ",0); print(T1[1]); } else print("");
if ( PRINTLOG > 0 ) {
print("dimensions of primes = ",0);
for (I = 0; I < length(PD); I++) {
print(length(VL)-length(minalgdep(PD[I],VL,PRIMEORD)),0);
print(", ",0);
}
print("");
}
}
if ( RA[0] == "begin" ) { /* isolated part of initial ideal */
if ( PRINTLOG ) {
print("check 'prime decomposition = primary decomposition?'");
}
CP = idealsetcap(PD,VL,PRIMAORD);
if ( idealinc(CP,GF,VL,PRIMAORD) ) {
if ( PRINTLOG ) {
print("lucky!");
}
for (L = [],I = length(PD)-1; I >= 0; I--)
L = cons([PD[I],PD[I]],L);
return [L,[]];
}
if ( PRINTLOG ) {
print("done.");
}
}
R = pseudo_extract(IP,F,GF,PD,H,SC,VL);
return R;
}
def pseudo_extract(IP,F,GF,PD,H,SC,VL)
{
REMS = DEC = PDEC = SEL = RES = [];
ZERODIM = 1; CAP = H;
for (I = 0; I < length(PD); I++) {
P = PD[I];
if ( length(minalgdep(P,VL,PRIMEORD)) != length(VL) )
ZERODIM=0;
if ( length(PD) == 1 ) { /* pseudo primary ideal case */
if ( PRINTLOG >= 1 ) { print(""); print("pseudo primary ideal"); }
DD = GF; SEL = [SC];
} else {
T0 = time();
Y = pseudodec_main(F,P,PD,VL);
T1 = time();
DD = Y[0]; SS = Y[1]; SEL = append(SEL,[SS]);
PDEC = append(PDEC,[[DD,P]]);
if ( PRINTLOG >= 1 ) {
print(""); print("pseudo primary component of ",0);
print(I,0); print(", time = ",0); print(T1[0]-T0[0]);
if ( PRINTLOG >= 4 ) { print(" = ",0); print(DD); }
}
if ( NOEMBEDDED )
continue;
}
if ( !REDUNDANT && H != [] ) { /* elim. pseu-comp. */
if ( !sepcond_ps(P,SC,VL) )
continue;
LG = localize(DD,SC,VL,PRIMAORD);
if ( idealinc(H,LG,VL,PRIMAORD)) {
if ( PRINTLOG ) {
print("eliminate the pseudo primary component ",0);
print(I);
}
continue;
}
}
if ( PRINTLOG ) {
print("extraction of the pseudo primary component ",0);
print(I);
if ( PRINTLOG > 2 ) {
print(" associated prime of pseudo primary ideal = ",0);
print(P);
}
}
U = extraction(DD,P,VL);
if ( !REDUNDANT && H != [] && idealinc(H,U[0][0],VL,PRIMAORD) ) {
if ( PRINTLOG )
print("redundant primary component!");
} else {
DEC = append(DEC,[U[0]]);
H = idealcap(H,U[0][0],VL,PRIMAORD);
if ( idealeq(IP,H) ) {
if ( PRINTLOG ) {
print("");
print("all primary components are found!");
}
return [DEC,[]];
}
}
if ( !ISOLATED && U[1] != [] )
if ( sepcond_re(U[1],SC,VL) ) {
NSC = setunion([SS,SC]); /* new separating condition */
REM = cons(DD,append(U[1],[NSC,H]));
REMS = append(REMS,[REM]);
}
}
if ( NOEMBEDDED )
DEC = PDEC;
if ( length(PD) != 1 && !NOEMBEDDED && !ISOLATED && !ZERODIM ) {
for (QD=[],I=length(PDEC)-1;I>=0;I--)
QD = cons(PDEC[I][0],QD);
RES = ["sep",PD,QD,GF];
if ( sepcond_re(append(RES,[SEL]),SC,VL) ) {
REM = cons(F,append(RES,[SC,H]));
REMS = append(REMS,[REM]);
}
}
return [DEC,REMS];
}
/* F:input set, PD:primes of radical, E:higher dimensional ideal */
/* length(PD) > 1 */
/* output : pseudo primary comp., remaining comp., selectors */
def pseudodec_main(F,P,PD,VL)
{
ZERODIM = 1;
S = selects(P,PD,VL,SELECTFLAG);
R = localize(F,S,VL,PRIMAORD);
if ( R[0] == 1 || R[0] == -1 ) {
print("error, R = ",0); print(R);
debug;
}
R = idealnormal(R);
return [R,S];
}
/* Id(GF) is a pseudo primary ideal. (GF must be the G-base.) */
def extraction(GF,Pr,VL)
{
TMPORD1=TMPORD2=0;
V = minalgdep(Pr,VL,PRIMEORD);
U = listminus(VL,V);
V0 = append(V,U);
#if 0
/* This may be a bug. GF is not a GB w.r.t the elimination order */
if ( V0 != VL ) {
ORD = [[TMPORD1,length(V)],[TMPORD2,length(U)]];
GR(G,GF,V0,ORD);
} else
G = GF;
#else
ORD = [[TMPORD1,length(V)],[TMPORD2,length(U)]];
GR(G,GF,V0,ORD);
#endif
dp_ord(TMPORD1);
for (LL = [],HC = 1,I = 0; I < length(G); I++)
LL = append(LL,cdr(fctr(dp_hc(dp_ptod(G[I],V)))));
for (L=[],I=0;I<length(LL);I++)
L = cons(LL[I][0],L);
L = setunion([L]);
for (S=1,SL=[],I=0;I<length(L);I++) {
S *= L[I];
if ( SELECTFLAG )
SL = cons(L[I],SL);
}
if ( !SELECTFLAG )
SL= [S];
if ( PRINTLOG > 1 ) {
print("extractor = ",0);
print(S);
}
T0 = time()[0];
Q = localize(GF,SL,VL,PRIMAORD);
Q = idealnormal(Q);
DEC = [Q,Pr];
if ( PRINTLOG ) {
print("find a primary component! time = ",0);
print(time()[0]-T0);
if (PRINTLOG >= 3){
print(" associated prime of primary component = ",0);
print(DEC[1]);
}
if (PRINTLOG >= 4){print(" primary component = ",0); print(Q);}
}
if ( !ISOLATED && !NOEMBEDDED && SL != [1]
&& length(V) != length(VL) /* nonzerodim */
&& (REDUNDANT || !idealinc(Q,GF,VL,PRIMAORD)) ) {
REM = ["ext",[Q,Pr],GF,S];
if ( PRINTLOG ) {
print("find the remaining component of the extraction");
}
} else {
REM = [];
if ( PRINTLOG ) {
print("eliminate the remaining component of the extraction");
}
}
return [DEC,REM];
}
/* sep. cond. for pseudo-primary components */
def sepcond_ps(P,SC,VL)
{
for (J = 0; J < length(SC); J++) {
if ( idealinc([SC[J]],P,VL,PRIMEORD) )
break; /* separating condition */
}
if ( J != length(SC) ) {
if ( PRINTLOG ) {
print("");
print("elim. the pseudo primary comp. by separating cond.");
}
return 0;
}
return 1;
}
/* sep. cond. for rem. components. */
/* REM = ["ext",[Q,Pr],GF,S] or ["sep",PD,QD,GF,SEL], SC : sep.cond. */
def sepcond_re(REM,SC,VL)
{
for (S=1,I=0;I<length(SC);I++)
S *= SC[I];
if (REM[0] == "ext") {
F = cons(REM[3],REM[1][1]);
L = localize(F,[S],VL,PRIMAORD);
if ( L != [1] )
return 1;
else
return 0;
} else if (REM[0] == "sep") {
PL = REM[1]; SEL = REM[4];
for (I=0;I<length(PL);I++) {
F = append(SEL[I],PL[I]);
L = localize(F,[S],VL,PRIMAORD);
if ( L != [1] )
return 1;
}
return 0;
}
}
def minalgdep(Pr,VL,ORD)
{
T0=newvect(4,time());
if (MAXALGIND)
R = minalgdep1(Pr,VL,ORD); /* M.I.S. */
else
R = minalgdep0(Pr,VL,ORD); /* M.S.I.S. */
T1=newvect(4,time())-T0; MISTIME += T1;
if ( PRINTLOG >= 6 ) {
if (MAXALGIND) print("M.I.S. time = ",0);
else print("M.S.I.S. time = ",0);
print(T1[0]);
}
return R;
}
def minalgdep0(Pr,VL,ORD)
{
dp_ord(ORD); N = length(Pr);
for (HD = [],I = N-1; I >= 0; I--)
HD = cons(vars(dp_dtop(dp_ht(dp_ptod(Pr[I],VL)),VL)),HD);
for (R = X = [], I = length(VL)-1; I >= 0; I--) {
V = VL[I];
TX = cons(V,X);
for (J = 0; J < N; J++) {
if ( varinc(HD[J],TX) )
break;
}
if ( J == N )
X = TX;
else
R = cons(V,R);
}
return R;
}
def minalgdep1(Pr,VL,ORD)
{
R = all_msis(Pr,VL,ORD);
for (E=I=0,D=length(R[0]);I<length(R);I++) {
if ( length(R[I])>=D ) {
D=length(R[I]); E=I;
}
}
S = listminus(VL,R[E]);
return S;
}
def all_msis(Pr,VL,ORD)
{
dp_ord(ORD); N = length(Pr);
for (HD = [],I = N-1; I >= 0; I--)
HD = cons(vars(dp_dtop(dp_ht(dp_ptod(Pr[I],VL)),VL)),HD);
R = dimrec(HD,0,[],[],VL);
return R;
}
def dimrec(S,K,U,M,X)
{
MM = M;
for (I=K;I<length(X);I++) {
TX = append(U,[X[I]]);
for (J = 0; J < length(S); J++) {
if ( varinc(S[J],TX) )
break;
}
if ( J == length(S) )
MM = dimrec(S,I+1,TX,MM,X);
}
for (J = 0; J < length(MM); J++) {
if ( varinc(U,MM[J]) )
break;
}
if ( J == length(MM) )
MM = append(MM,[U]);
return MM;
}
/* if V is min.alg.dep. return 1 */
def ismad(Pr,V,VL,ORD)
{
dp_ord(ORD); N = length(Pr);
for (HD = [],I = N-1; I >= 0; I--)
HD = cons(vars(dp_dtop(dp_ht(dp_ptod(Pr[I],VL)),VL)),HD);
W = listminus(VL,V); L = append(W,V);
for (R = TX = [],I = 0; I < length(L); I++) {
TX = cons(L[I],TX);
for (J = 0; J < N; J++) {
if ( varinc(HD[J],TX) )
break;
}
if ((I<length(W)&&J!=N) || (I>=length(W)&&J==N))
return 0;
}
return 1;
}
/* output:list of [flag, generator, primes, sep.cond., intersection] */
def mksepext(RES,H,VL)
{
for (R = [],I=length(RES)-1;I>=0;I--) {
W = RES[I];
if ( COMPLETE || EXTENDED )
HI = idealcap(H,W[6],VL,PRIMAORD);
else
HI = H;
if (W[1] == "sep") {
E = mksep(W[2],W[3],W[4],VL);
F = append(E[0],W[0]);
if ( ( COMPLETE || EXTENDED ) && !REDUNDANT )
HI = idealsetcap(cons(HI,W[3]),VL,PRIMAORD);
R = cons(["sep",F,E[1],W[5],HI],R);
} else if (W[1] == "ext") {
E = mkext(W[2][0],W[3],W[4],VL);
F = cons(E[0],W[0]);
P = cons(E[1],W[2][1]); /* prime component of rem. comp. */
R = cons(["ext",F,P,W[5],HI],R);
} else debug;
}
return R;
}
/* make extractor with exponents ; F must be G-Base */
/* output : extractor, max.sqfr.of extractor */
def mkext(Q,F,S,VL)
{
if ( PRINTLOG > 1 ) {
print("make extractor = ",0);
}
if ( S == 1 || S == -1 ) {
print(1); return [1,1];
}
DD=dp_mkdist([Q],F,VL,PRIMAORD);
DQ=DD[0][0]; DF=DD[1];
for (L=fctr(S),SL=[],J=length(L)-1;J>0;J--)
SL=cons(dp_ptod(L[J][0],VL),SL);
K = dp_fexponent(dp_ptod(S,VL),DF,DQ);
E = dp_vectexp(SL,EX=dp_minexp(K,SL,DF,DQ));
if ( E != 1 ) E = dp_dtop(E,VL);
for (U=1, I=0;I<size(EX)[0];I++)
if ( EX[I] )
U *= L[I+1][0];
/* for (L=sqfr(E),U=1,J=length(L)-1;J>0;J--)
U *= L[J][0]; */
if ( PRINTLOG > 1 ) {
print(E);
}
return [E,U];
}
/* make separators with exponents ; F must be G-Base */
/* output [separator, list of components of radical] */
def mksep(PP,QQ,F,VL)
{
if ( PRINTLOG > 1 ) {
print("make separators, ",0); print(length(PP));
}
DD=dp_mkdist(QQ,F,VL,PRIMAORD);
DQ=DD[0]; DF=DD[1];
E = dp_mksep(PP,DQ,DF,VL,PRIMAORD);
for (RA=[],I=length(E)-1;I>=0;I--) {
for (L=fctr(E[I]),J=length(L)-1;J>0;J--) {
ES=cons(L[J][0],PP[I]);
RA = cons(ES,RA); /* radical of remaining comp. */
}
}
return [E,RA];
}
def dp_mksep(PP,DQ,DF,VL,ORD)
{
dp_ord(ORD);
for (E=[],I=0;I<length(PP);I++) {
T0=time()[0];
if ( CONTINUE ) {
E = bload("sepa");
I = length(E);
CONTINUE = 0;
}
S = selects(PP[I],PP,VL,0)[0];
for (L=fctr(S),SL=[],J=length(L)-1;J>0;J--)
SL=cons(dp_ptod(L[J][0],VL),SL);
K = dp_fexponent(dp_ptod(S,VL),DF,DQ[I]);
M = dp_vectexp(SL,dp_minexp(K,SL,DF,DQ[I]));
if (M != 1) M = dp_dtop(M,VL);
E = append(E,[M]);
if ( PRINTLOG > 1 ) {
print("separator of ",0); print(I,0);
print(" in ",0); print(length(PP),0);
print(", time = ",0); print(time()[0]-T0,0); print(", ",0);
printsep(cdr(fctr(M))); print("");
}
if (BSAVE) {
bsave(E,"sepa");
print("bsave to sepa");
}
}
return E;
}
extern AFO$
/* F,Id,Q is given by distributed polynomials. Id is a G-Base.*/
/* get the exponent K s.t. (Id : F^K) = Q, Id is a G-Basis */
def dp_fexponent(F,Id,Q)
{
if (!AFO)
for (IN=[],I=size(Id)[0]-1;I>=0;I--) IN = cons(I,IN);
else
for (IN=[],I=0;I<size(Id)[0];I++) IN = cons(I,IN);
NF(G,IN,F,Id,0);
if ( F != G ) { F = G; }
N=size(Q)[0]; U = newvect(N);
for (I=0;I<N;I++)
U[I]=Q[I];
for (K = 1;; K++) { /* U[I] = Q[I]*F^K mod Id */
for (FLAG = I = 0; I < N; I++) {
NF(U[I],IN,U[I]*F,Id,1);
if ( U[I] ) FLAG = 1;
}
if ( !FLAG )
return K;
}
}
/* F must be a G-Base. SL is a set of factors of S.*/
def dp_minexp(K,SL,F,Q)
{
if (!AFO)
for (IN=[],I=size(F)[0]-1;I>=0;I--) IN = cons(I,IN);
else
for (IN=[],I=0;I<size(F)[0];I++) IN = cons(I,IN);
N = length(SL); M = size(Q)[0];
EX = newvect(N); U = newvect(M); T = newvect(M);
for (I=0;I<N;I++)
EX[I]=K;
for (I=0;I<M;I++) {
NF(Q[I],IN,Q[I],F,1);
}
for (I=0;I<N;I++) {
EX[I] = 0;
for (FF=1,II=0;II<N;II++)
for (J = 0; J < EX[II]; J++) {
NF(FF,IN,FF*SL[II],F,1);
}
for (J = 0; J < M; J++)
U[J] = Q[J]*FF;
for (; EX[I] < K; EX[I]++) {
FLAG = 0;
for (J = 0; J < M; J++) {
NF(U[J],IN,U[J],F,1);
if ( U[J] ) FLAG = 1;
}
if ( !FLAG )
break;
if ( EX[I] < K-1 )
for (J = 0; J < M; J++) U[J] = U[J]*SL[I];
}
}
return EX;
}
def dp_vectexp(SS,EE)
{
N = length(SS);
for (A=1,I=0;I<N;I++)
for (J = 0; J < EE[I]; J++)
A *= SS[I];
return A;
}
def dp_mkdist(QQ,F,VL,ORD)
{
dp_ord(ORD);
for (DQ=[],I=length(QQ)-1;I>=0;I--) {
for (T=[],J=length(QQ[I])-1;J>=0;J--)
T = cons(dp_ptod(QQ[I][J],VL),T);
DQ=cons(newvect(length(T),T),DQ);
}
for (T=[],J=length(F)-1;J>=0;J--)
T = cons(dp_ptod(F[J],VL),T);
DF = newvect(length(T),T);
return [DQ,DF]$
}
/* if FLAG == 0 return singltonset */
def selects(P,PD,VL,FLAG)
{
PP=dp_mkdist([],P,VL,PRIMEORD)[1];
for (M=[],I=length(P)-1;I>=0;I--)
M = cons(I,M);
for (SL = [],I = length(PD)-1; I >= 0; I--) {
B = PD[I];
if (B == P) continue;
for (L = [],J = 0; J < length(B); J++) {
A = B[J];
NF(E,M,dp_ptod(A,VL),PP,0);
if ( E ) {
L = append(L,[A]); /* A \notin Id(P) */
}
}
SL = cons(L,SL); /* candidate of separators */
}
for (S=[],I=length(SL)-1;I>=0;I--) {/* choose an element from L */
if ( FLAG >= 2 ) {
S = append(SL[I],S);
continue;
}
C = minselect(SL[I],VL,PRIMAORD);
S = cons(C,S);
}
S = setunion([S]);
if ( FLAG == 3 || length(S) == 1 )
return S;
if ( FLAG == 2 ) {
for (R=1,I=0;I<length(S);I++)
R *= S[I];
return [R];
}
/* FLAG == 0 || FLAG == 1 */
for (T=[]; S!=[];S = cdr(S)) { /* FLAG <= 1 and length(S) != 1 */
A = car(S);
U = append(T,cdr(S));
for (R=1,I=0;I<length(U);I++)
R *= U[I];
for (I=0;I<length(PD);I++) {
if ( PD[I] != P && !idealinc([R],PD[I],VL,PRIMAORD) )
break;
}
if ( I != length(PD) )
T = append(T,[A]);
}
if ( FLAG )
return T;
for (R=1,I=0;I<length(T);I++)
R *= T[I];
return [R]; /* if FLAG == 0 */
}
def minselect(L,VL,ORD)
{
dp_ord(ORD);
F = dp_ptod(L[0],VL); MAG=dp_mag(F); DEG=dp_td(F);
for (J = 0, I = 1; I < length(L); I++) {
A = dp_ptod(L[I],VL); M=dp_mag(A); D=dp_td(A);
if ( dp_ht(A) > dp_ht(F) )
continue;
else if ( dp_ht(A) == dp_ht(F) && (D > DEG || (D == DEG && M > MAG)))
continue;
F = A; J = I; MAG = M; DEG=D;
}
return L[J];
}
/* localization Id(F)_MI \cap Q[VL] */
/* output is the G-base w.r.t ordering O */
def localize(F,MI,VL,O)
{
if ( MI == [1] || MI == [-1] )
return F;
for (SVL = [],R = [],I = 0; I < length(MI); I++) {
V = strtov("zz"+rtostr(I));
R = append(R,[V*MI[I]-1]);
SVL = append(SVL,[V]);
}
if ( O == 0 ) {
dp_nelim(length(SVL)); ORD = 6;
} else if ( O == 1 || O == 2 ) {
ORD = [[0,length(SVL)],[O,length(VL)]];
} else if ( O == 3 || O == 4 || O == 5 )
ORD = [[0,length(SVL)],[O-3,length(VL)-1],[2,1]];
else
error("invarid ordering");
GR(G,append(F,R),append(SVL,VL),ORD);
S = varminus(G,SVL);
return S;
}
def varminus(G,VL)
{
for (S = [],I = 0; I < length(G); I++) {
V = vars(G[I]);
if (listminus(V,VL) == V)
S = append(S,[G[I]]);
}
return S;
}
def idealnormal(L)
{
R=[];
for (I=length(L)-1;I>=0;I--) {
A = ptozp(L[I]);
V = vars(A);
for (B = A,J = 0;J < length(V);J++)
B = coef(B,deg(B,V[J]),V[J]);
R = cons((B>0?A:-A),R);
}
return R;
}
def idealsav(L) /* sub procedure of welldec and normposdec */
{
if ( PRINTLOG >= 4 )
print("multiple check ",2);
for (R = [],I = 0,N=length(L); I < N; I++) {
if ( PRINTLOG >= 4 && !irem(I,10) )
print(".",2);
if ( R == [] )
R = append(R,[L[I]]);
else {
for (J = 0; J < length(R); J++)
if ( idealeq(L[I],R[J]) )
break;
if ( J == length(R) )
R = append(R,[L[I]]);
}
}
if ( PRINTLOG >= 4 )
print("done.");
return R;
}
/* intersection of ideals in PL, PL : list of ideals */
/* VL : variable list, O : output the G-base w.r.t order O */
def idealsetcap(PL,VL,O)
{
for (U = [], I = 0; I < length(PL); I++)
if ( PL[I] != [] )
U = append(U,[PL[I]]);
if ( U == [] )
return [];
if ( PRINTLOG >= 4 ) {print("intersection of ideal ",0); print(length(U),0);}
for (L = U[0],I=1;I<length(U);I++) {
if ( PRINTLOG >=4 ) print(".",2);
L = idealcap(L,U[I],VL,O);
}
if ( PRINTLOG >=4 ) print("");
return L;
}
/* return intersection set of ideals P and Q */
def idealcap(P,Q,VL,O)
{
if ( P == [] )
if ( VL )
return Q;
else
return [];
if ( Q == [] )
return P;
T = tmp;
for (PP = [],I = 0; I < length(P); I++)
PP = append(PP,[P[I]*T]);
for (QQ = [],I = 0; I < length(Q); I++)
QQ = append(QQ,[Q[I]*(T-1)]);
if ( O == 0 ) {
dp_nelim(1); ORD = 6;
} else if ( O == 1 || O == 2 )
ORD = [[2,1],[O,length(VL)]];
else if ( O == 3 || O == 4 || O == 5 )
ORD = [[2,1],[O-3,length(VL)-1],[2,1]];
else
error("invarid ordering");
GR(G,append(PP,QQ),append([T],VL),ORD);
S = varminus(G,[T]);
return S;
}
/* return ideal P : Q */
def idealquo(P,Q,VL,O)
{
for (R = [], I = 0; I < length(Q); I++) {
F = car(Q);
G = idealcap(P,[F],VL,O);
for (H = [],J = 0; J < length(G); J++) {
H = append(H,[sdiv(G[J],F)]);
}
R = idealcap(R,H,VL,O);
}
}
/* if ideal Q includes P then return 1 else return 0 */
/* Q must be a Groebner Basis w.r.t ordering ORD */
def idealinc(P,Q,VL,ORD)
{
dp_ord(ORD);
for (T=IN=[],I=length(Q)-1;I>=0;I--) {
T=cons(dp_ptod(Q[I],VL),T);
IN=cons(I,IN);
}
DQ = newvect(length(Q),T);
for (I = 0; I < length(P); I++) {
NF(E,IN,dp_ptod(P[I],VL),DQ,0);
if ( E )
return 0;
}
return 1;
}
/* FL : list of polynomial set */
def primedec_main(FL,VL)
{
if ( PRINTLOG ) {
print("prime decomposition of the radical");
}
if ( PRINTLOG >= 2 )
print("G-base factorization");
PP = gr_fctr(FL,VL);
if ( PRINTLOG >= 2 )
print("irreducible variety decomposition");
RP = welldec(PP,VL);
SP = normposdec(RP,VL);
for (L=[],I=length(SP)-1;I>=0;I--) {
L=cons(idealnormal(SP[I]),L); /* head coef. > 0 */
}
SP = L;
return SP;
}
def gr_fctr(FL,VL)
{
for (TP = [],I = 0; I<length(FL); I++ ) {
F = FL[I];
SF = idealsqfr(F);
if ( !idealeq(F,SF) ) { GR(F,SF,VL,PRIMEORD); }
DIRECTRY = []; COMMONIDEAL=[1];
SP = gr_fctr_sub(F,VL);
TP = append(TP,SP);
}
TP = idealsav(TP);
TP = prime_irred(TP,VL);
return TP;
}
def gr_fctr_sub(G,VL)
{
CONTINUE;
if ( length(G) == 1 && type(G[0]) == 1 )
return [G];
RL = [];
for (I = 0; I < length(G); I++) {
FL = fctr(G[I]); L = length(FL); N = FL[1][1];
if (L > 2 || N > 1) {
TLL = [];
for (J = 1; J < L; J++) {
if ( CONTINUE ) {
JCOPP=bload("jcopp");
J = JCOPP[0]+1;
COMMONIDEAL = JCOPP[1];
RL = JCOPP[2];
CONTINUE = 0;
}
if ( PRINTLOG >= 5 ) {
for (D = length(DIRECTRY)-1; D >= 0; D--)
print(DIRECTRY[D],0);
print([L-1,J,length(RL)]);
/*
L-1:a number of factors of polynomial
J:a factor executed now [0,...L-1]
length(RL):a number of prime components
*/
}
W = cons(FL[J][0],G);
GR(NG,W,VL,PRIMEORD);
TNG = idealsqfr(NG);
if ( NG != TNG ) { GR(NG,TNG,VL,PRIMEORD); }
if ( idealinc(COMMONIDEAL,NG,VL,PRIMEORD) )
continue;
else {
DIRECTRY=cons(L-J-1,DIRECTRY);
DG = gr_fctr_sub(NG,VL);
DIRECTRY=cdr(DIRECTRY);
RL = append(RL,DG);
if ( J <= L-2 && !idealinc(COMMONIDEAL,NG,VL,PRIMEORD)
&& COMMONCHECK ) {
if ( PRINTLOG >= 5 ) {
for (D = 0; D < length(DIRECTRY); D++) print(" ",2);
print("intersection ideal");
}
COMMONIDEAL=idealcap(COMMONIDEAL,NG,VL,PRIMEORD);
}
}
if ( BSAVE && !length(DIRECTRY) ) {
bsave([J,COMMONIDEAL,RL],"jcopp");
if ( PRINTLOG >= 2 )
print("bsave j, intersection ideal and primes to icopp ");
}
}
break;
}
}
if (I == length(G)) {
RL = append([G],RL);
if ( PRINTLOG >= 5 ) {
for (D = 0; D < length(DIRECTRY)-1; D++) print(" ",0);
print("prime G-base ",0);
if ( PRINTLOG >= 6 )
print(G);
else
print("");
}
}
return RL;
}
def prime_irred(TP,VL)
{
if ( PRINTLOG >= 4 )
print("irredundancy check for prime ideal");
N = length(TP);
for (P = [], I = 0; I < N; I++) {
if ( PRINTLOG >= 4 )
print(".",2);
for (J = 0; J < N; J++)
if ( I != J && idealinc(TP[J],TP[I],VL,PRIMEORD) )
break;
if (J == N)
P = append(P,[TP[I]]);
}
if ( PRINTLOG >= 4 )
print("done.");
return P;
}
/* if V1 \subset V2 then return 1 else return 0 */
def varinc(V1,V2)
{
N1=length(V1); N2=length(V2);
for (I=N1-1;I>=0;I--) {
for (J=N2-1;J>=0;J--)
if (V1[I]==V2[J])
break;
if (J==-1)
return 0;
}
return 1;
}
def setunion(PS)
{
for (R=C=[]; PS != [] && car(PS); PS=cdr(PS)) {
for (L = car(PS); L != []; L = cdr(L)) {
A = car(L);
for (G = C; G != []; G = cdr(G)) {
if ( A == car(G) || -A == car(G) )
break;
}
if ( G == [] ) {
R = append(R,[A]);
C = cons(A,C);
}
}
}
return R;
}
def idealeq(L,M)
{
if ((N1=length(L)) != (N2=length(M)))
return 0;
for (I = 0; I < length(L); I++) {
for (J = 0; J < length(M); J++)
if (L[I] == M[J] || L[I] == - M[J])
break;
if (J == length(M))
return 0;
}
return 1;
}
def listminus(L,M)
{
for (R = []; L != []; L = cdr(L) ) {
A = car(L);
for (G = M; G != []; G = cdr(G)) {
if ( A == car(G) )
break;
}
if ( G == [] ) {
R = append(R,[A]);
M = cons(A,M);
}
}
return R;
}
def idealsqfr(G)
{
for(Flag=0,LL=[],I=length(G)-1;I>=0;I--) {
for(A=1,L=sqfr(G[I]),J=1;J<length(L);J++)
A*=L[J][0];
LL=cons(A,LL);
}
return LL;
}
def welldec(PRIME,VL)
{
PP = PRIME; NP = [];
while ( !Flag ) {
LP = [];
Flag = 1;
for (I=0;I<length(PP);I++) {
U = welldec_sub(PP[I],VL);
if (length(U) >= 2) {
Flag = 0;
if ( PRINTLOG >= 3 ) {
print("now decomposing to irreducible varieties ",0);
print(I,0); print(" ",0); print(length(PP));
}
DIRECTRY = []; COMMONIDEAL=[1];
PL1 = gr_fctr([U[0]],VL);
DIRECTRY = []; COMMONIDEAL=[1];
PL2 = gr_fctr([U[1]],VL);
LP = append(LP,append(PL1,PL2));
}
else
NP = append(NP,U);
}
PP = LP;
if ( PRINTLOG > 3 ) {
print("prime length and non-prime length = ",0);
print(length(NP),0); print(" ",0); print(length(PP));
}
}
if ( length(PRIME) != length(NP) ) {
NP = idealsav(NP);
NP = prime_irred(NP,VL);
}
return NP;
for (I = 0; I<length(PP);I++) {
}
}
def welldec_sub(PP,VL)
{
VV = minalgdep(PP,VL,PRIMEORD);
S = wellsep(PP,VV,VL);
if ( S == 1 )
return [PP];
P1 = localize(PP,[S],VL,PRIMEORD);
if ( idealeq(P1,PP) )
return([PP]);
GR(P2,cons(S,PP),VL,PRIMEORD);
return [P1,P2];
}
def wellsep(PP,VV,VL)
{
TMPORD = 0;
V0 = listminus(VL,VV);
V1 = append(VV,V0);
/* ORD = [[TMPORD,length(VV)],[0,length(V0)]]; */
dp_nelim(length(VV)); ORD = 6;
GR(PP,PP,V1,ORD);
dp_ord(TMPORD);
for (E=1,I=0;I<length(PP);I++)
E = lcm(E,dp_hc(dp_ptod(PP[I],VV)));
for (F=1,L=sqfr(E),K=1;K<length(L);K++)
F *= L[K][0];
return F;
}
/* prime decomposition by using primitive element method */
def normposdec(NP,VL)
{
if ( PRINTLOG >= 3 )
print("radical decomposition by using normal position.");
for (R=MP=[],I=0;I<length(NP);I++) {
V=minalgdep(NP[I],VL,PRIMEORD);
L=raddec(NP[I],V,VL,1);
if ( PRINTLOG >= 3 )
if ( length(L) == 1 ) {
print(".",2);
} else {
print(" ",2); print(length(L),2); print(" ",2);
}
/* if (length(L)==1) {
MP=append(MP,[NP[I]]);
continue;
} */
R=append(R,L);
}
if ( PRINTLOG >= 3 )
print("done");
if ( length(R) )
MP = idealsav(append(R,MP));
LP = prime_irred(MP,VL);
return LP;
}
/* radical decomposition program using by Zianni, Trager, Zacharias */
/* R : factorized G-base in K[X], if FLAG then A is well comp. */
def raddec(R,V,X,FLAG)
{
GR(A,R,V,irem(PRIMEORD,3));
ZQ=zraddec(A,V); /* zero dimensional */
/* if ( FLAG && length(ZQ) == 1 )
return [R]; */
if ( length(V) != length(X) )
CQ=radcont(ZQ,V,X); /* contraction */
else {
for (CQ=[],I=length(ZQ)-1;I>=0;I--) {
GR(R,ZQ[I],X,PRIMEORD);
CQ=cons(R,CQ);
}
}
return CQ;
}
/* radical decomposition for zero dimensional ideal */
/* F is G-base w.r.t irem(PRIMEORD,3) */
def zraddec(F,X)
{
if (length(F) == 1)
return [F];
Z=vvv;
C=normposit(F,X,Z);
/* C=[minimal polynomial, adding polynomial] */
T=cdr(fctr(C[0]));
if ( length(T) == 1 && T[0][1] == 1 )
return [F];
for (Q=[],I=0;I<length(T);I++) {
if ( !C[1] ) {
GR(P,cons(T[I][0],F),X,irem(PRIMEORD,3));
} else {
P=idealgrsub(append([T[I][0],C[1]],F),X,Z);
}
Q=cons(P,Q);
}
return Q;
}
/* contraction from V to X */
def radcont(Q,V,X)
{
for (R=[],I=length(Q)-1;I>=0;I--) {
dp_ord(irem(PRIMEORD,3));
G=Q[I];
for (E=1,J=0;J<length(G);J++)
E = lcm(E,dp_hc(dp_ptod(G[J],V)));
for (F=1,L=sqfr(E),K=1;K<length(L);K++)
F *= L[K][0];
H=localize(G,[F],X,PRIMEORD);
R=cons(H,R);
}
return R;
}
/* A : polynomials (G-Base) */
/* return [T,Y], T : minimal polynomial of Z, Y : append polynomial */
def normposit(A,X,Z)
{
D = idim(A,X,irem(PRIMEORD,3)); /* dimension of the ideal Id(A) */
for (I = length(A)-1;I>=0;I--) {
for (J = length(X)-1; J>= 0; J--) {
T=deg(A[I],X[J]);
if ( T == D ) /* A[I] is a primitive polynomial of A */
return [A[I],0];
}
}
N=length(X);
for (C = [],I = 0; I < N-1; I++)
C=newvect(N-1);
V=append(X,[Z]);
ZD = (vars(A)==vars(X)); /* A is zero dim. over Q[X] or not */
while( 1 ) {
C = nextweight(C,cdr(X));
for (Y=Z-X[0],I=0;I<N-1;I++) {
Y-=C[I]*X[I+1]; /* new polynomial */
}
if ( !ZD ) {
if ( version() == 940420 ) NOREDUCE = 1;
else dp_gr_flags(["NoRA",1]);
GR(G,cons(Y,A),V,2);
if ( version() == 940420 ) NOREDUCE = 0;
else dp_gr_flags(["NoRA",0]);
for (T=G[length(G)-1],I = length(G)-2;I >= 0; I--)
if ( deg(G[I],Z) > deg(T,Z) )
T = G[I]; /* minimal polynomial */
} else {
T = minipoly(A,X,irem(PRIMEORD,3),Z-Y,Z);
}
if (deg(T,Z)==D)
return [T,Y];
}
}
def nextweight(C,V) /* degrevlex */
{
dp_ord(2);
N = length(V);
for (D=I=0;I<size(C)[0];I++)
D += C[I];
if ( C[N-1] == D ) {
for (L=[],I=0;I<N-1;I++)
L=cons(0,L);
L = cons(D+1,L);
return newvect(N,L);
}
CD=dp_vtoe(C);
for (F=I=0;I<N;I++)
F+=V[I];
for (DF=dp_ptod(F^D,V);dp_ht(DF)!=CD;DF=dp_rest(DF));
MD = dp_ht(dp_rest(DF));
CC = dp_etov(MD);
return CC;
}
def printsep(L)
{
for (I=0;I<length(L);I++) {
if ( nmono(L[I][0]) == 1 )
print(L[I][0],0);
else {
print("(",0); print(L[I][0],0); print(")",0);
}
if (L[I][1] > 1) {
print("^",0); print(L[I][1],0);
}
if (I<length(L)-1)
print("*",0);
}
}
def idealgrsub(A,X,Z)
{
if ( PRIMEORD == 0 ) {
dp_nelim(1); ORD = 8;
} else
ORD = [[2,1],[PRIMERORD,length(X)]];
GR(G,A,cons(Z,X),ORD);
for (R=[],I=length(G)-1;I>=0;I--) {
V=vars(G[I]);
for (J=0;J<length(V);J++)
if (V[J]==Z)
break;
if (J==length(V))
R=cons(G[I],R);
}
return R;
}
/* dimension of ideal */
def idim(F,V,ORD)
{
return length(modbase(F,V,ORD));
}
def modbase(F,V,ORD)
{
dp_ord(ORD);
for(G=[],I=length(F)-1;I>=0;I--)
G = cons(dp_ptod(F[I],V),G);
R = dp_modbase(G,length(V));
for(S=[],I=length(R)-1;I>=0;I--)
S = cons(dp_dtop(R[I],V),S);
return S;
}
def dp_modbase(G,N)
{
E = newvect(N);
R = []; I = 1;
for (L = [];G != []; G = cdr(G))
L = cons(dp_ht(car(G)),L);
while ( I <= N ) {
R = cons(dp_vtoe(E),R);
E[0]++; I = 1;
while( s_redble(dp_vtoe(E),L) ) {
E[I-1] = 0;
if (I < N)
E[I]++;
I++;
}
}
return R;
}
def s_redble(M,L)
{
for (; L != []; L = cdr(L))
if ( dp_redble(M,car(L)) )
return 1;
return 0;
}
/* FL : list of ideal Id(P,s) */
def primedec_special(FL,VL)
{
if ( PRINTLOG ) {
print("prime decomposition of the radical");
}
if ( PRINTLOG >= 2 )
print("G-base factorization");
PP = gr_fctr(FL,VL);
if ( PRINTLOG >= 2 )
print("special decomposition");
SP = yokodec(PP,VL);
for (L=[],I=length(SP)-1;I>=0;I--) {
L=cons(idealnormal(SP[I]),L); /* head coef. > 0 */
}
SP = L;
return SP;
}
/* PL : list of ideal Id(P,s) */
def yokodec(PL,VL)
{
MSISTIME = 0; T = time()[0];
for (R = [],I = 0; I<length(PL);I++) {
PP = PL[I];
if ( PRINTLOG >= 3 ) print(".",2);
V = minalgdep(PP,VL,PRIMEORD);
E = raddec(PP,V,VL,0);
if ( length(E) >= 2 || !idealeq(E[0],PP) ) { /* prime check */
T0 = time()[0];
L=all_msis(PP,VL,PRIMEORD);
MSISTIME += time()[0]-T0;
E = yokodec_main(PP,L,VL);
}
R = append(R,E);
}
R = idealsav(R);
R = prime_irred(R,VL);
if ( PRINTLOG >= 3 ) {
print("special dec time = ",0); print(time()[0]-T0);
/* print(", ",0); print(MSISTIME); */
}
return R;
}
def yokodec_main(PP,L,VL)
{
AL = misset(L,VL); H = [1]; R = [];
for (P=PP,I=0; I<length(AL); I++) {
V = AL[I];
if ( I && !ismad(P,AL[I],VL,PRIMEORD) )
continue;
U = raddec(PP,V,VL,0);
R = append(R,U);
for (I=0;I<length(U);I++)
H = idealcap(H,U[I],VL,PRIMEORD);
if ( idealeq(H,P) )
break;
F = wellsep(P,V,VL);
GR(P,cons(F,P),VL,PRIMEORD);
}
return R;
}
/* output M.A.D. sets. AL : M.S.I.S sets */
def misset(AL,VL)
{
for (L=[],D=0,I=length(AL)-1;I>=0;I--) {
E = length(AL[I]);
C = listminus(VL,AL[I]);
if ( E == D )
L = cons(C,L);
else if ( E > D ) {
L = [C]; D = E;
}
}
return L;
}
end$
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