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Diff for /OpenXM/src/asir-contrib/testing/noro/ndbf.rr between version 1.1 and 1.20

version 1.1, 2009/10/09 07:15:44

version 1.20, 2014/09/05 11:55:19

Line 1

/* $OpenXM: OpenXM/src/asir-contrib/testing/noro/ndbf.rr,v 1.19 2011/03/30 05:07:01 noro Exp $ */

/* requires 'primdec' */

#define TMP_H hhhhhhhh

#define TMP_S ssssssss

#define TMP_DS dssssssss

#define TMP_T t

#define TMP_T tttttttt

#define TMP_DT dt

#define TMP_DT dtttttttt

#define TMP_Y1 yyyyyyyy1

#define TMP_DY1 dyyyyyyyy1

#define TMP_Y2 yyyyyyyy2

Line 12

Line 13

if (!module_definedp("gr")) load("gr")$ else{ }$

if (!module_definedp("primdec")) load("primdec")$ else{ }$

if (!module_definedp("newsyz")) load("noro_module_syz.rr")$ else{ }$

/* Empty for now. It will be used in a future. */

/* toplevel */

Line 21 module ndbf$

Line 23 module ndbf$

/* bfunction */

localf bfunction, in_ww, in_ww_main, ann, ann_n$

localf ann0, psi, ww_weight, compare_first, generic_bfct$

localf ann0, ann_fa, psi, ww_weight, compare_first, generic_bfct$

localf generic_bfct_1, initial_part, bfct, indicial1, bfct_via_gbfct$

localf bfct_via_gbfct_weight, bfct_via_gbfct_weight_1, bfct_via_gbfct_weight_2$

localf weyl_minipolym, weyl_minipoly, weyl_nf, weyl_nf_quo_check$

localf weyl_nf_quo, weyl_nf_mod, b_subst, v_factorial, w_tdeg$

localf replace_vars_f, replace_vars_v, replace_var$

localf action_on_gfs, action_on_gfs_1$

localf nd_gb_candidate$

localf in_gb_oaku, homogenize_oaku$

/* stratification */

Line 41 localf ideal_intersection$

Line 45 localf ideal_intersection$

def bfunction(F)

{

if ( member(s,vars(F)) )

error("ann : the variable 's' is reserved.");

/* F -> F/Fcont */

F1 = ptozp(F); Fcont = sdiv(F,F1); F = F1;

if ( type(Heu=getopt(heuristic)) == -1 ) Heu = 0;

if ( type(Vord=getopt(vord)) == -1 || type(Vord) != 4 ) Vord = 0;

if ( type(Wt=getopt(weight)) == -1 ) Wt = 0;

if ( type(Op=getopt(op)) == -1 ) Op = 0;

L = in_ww(F|weight=Wt,heuristic=Heu,vord=Vord);

Indata = L[0]; AllData = L[1]; VData = L[2];

GIN = Indata[0]; VDV = Indata[1]; WVDV = AllData[4];

Line 51 def bfunction(F)

Line 61 def bfunction(F)

dp_set_weight(W);

B = weyl_minipoly(GIN,VDV,0,WVDV);

dp_set_weight(0);

return subst(B,s,-s-1);

if ( !Op ) return subst(B,s,-s-1);

V0 = VData[0]; DV0 = VData[1]; T = VData[2]; DT = VData[3];

BPT = weyl_subst(B,T*DT,VDV);

/* computation using G0,GIN0,VDV0 */

G0 = AllData[0]; GIN0 = AllData[1]; VDV0 = AllData[2]; WtV0 = AllData[5];

dp_set_weight(WtV0); dp_ord(0);

PS = map(dp_ptod,GIN0,VDV0); Len = length(PS);

for ( I = Len-1, Ind = []; I >= 0; I-- ) Ind = cons(I,Ind);

/* QR = [D,M,Coef] */

Ax = 1;

AxBPT = dp_ptod(Ax*BPT,VDV0);

QR = weyl_nf_quo(Ind,AxBPT,1,PS);

if ( !weyl_nf_quo_check(AxBPT,PS,QR) )

error("bfunction : invalid quotient");

if ( QR[0] ) error("bfunction : invalid quotient");

Den = QR[1]; Coef = QR[2];

for ( I = 0, R = Den*AxBPT; I < Len; I++ )

R -= dp_weyl_mul(Coef[I],dp_ptod(G0[I],VDV0));

R = dp_dtop(R,VDV0);

CR = conv_tdt(R,F,V0,DV0,T,DT);

dp_set_weight(0);

Cont = cont(CR); CR /= Cont;

Cont *= dn(Fcont); Den *= nm(Fcont);

Gcd = igcd(Den,Cont);

return [subst(B,s,-s-1),(Cont*CR)/(Den*Ax)];

}

Line 65 def bfunction(F)

Line 102 def bfunction(F)

def in_ww(F)

{

F = ptozp(F);

V = vars(F);

N = length(V);

D = newvect(N);

Line 74 def in_ww(F)

Line 112 def in_ww(F)

if ( type(Vord) != 4 ) {

for ( I = 0; I < N; I++ )

D[I] = [deg(F,V[I]),V[I]];

qsort(D,compare_first);

qsort(D,ndbf.compare_first);

for ( V = [], I = 0; I < N; I++ )

V = cons(D[I][1],V);

V = reverse(V);

Line 93 def in_ww(F)

Line 131 def in_ww(F)

}

for ( I = 0; I < N; I++ )

D[I] = [deg(F1,V[I]),V[I]];

qsort(D,compare_first);

qsort(D,ndbf.compare_first);

for ( V = [], I = 0; I < N; I++ )

V = cons(D[I][1],V);

V = reverse(V);

Line 203 def in_ww_main(F,VW1,VW2)

Line 241 def in_ww_main(F,VW1,VW2)

VDVH = append(VDV,[TMP_H]);

FH = map(dp_dtop,map(dp_homo,map(dp_ptod,F,VDV)),VDVH);

/* compute a groebner basis of FH w.r.t. MWH */

* FH is a GB w.r.t. any term order s.t. LT(FH)=[t,dx1,...,dxn]

* Compute a groebner basis of FH w.r.t. MWH by modular change of

* ordering.

* Since F is Z-coef, LC(FH)=[1,...,1] and we can use any prime p

* for trace algorithm.

/* dp_gr_flags(["Top",1,"NoRA",1]); */

#if 0

for ( I = 0, HC=[]; I <= N; I++ ) HC = cons(1,HC);

GH = dp_weyl_gr_main(FH,VDVH,0,0,11);

GH = nd_gb_candidate(FH,VDVH,11,0,HC,1);

#else

#if 0

GH = dp_weyl_gr_main(FH,VDVH,0,-1,11);

#else

GH = nd_weyl_gr_trace(FH,VDVH,0,-1,11);

#endif

/* dp_gr_flags(["Top",0,"NoRA",0]); */

/* dehomigenize GH */

Line 232 def in_ww_main(F,VW1,VW2)

Line 269 def in_ww_main(F,VW1,VW2)

AllData = [G,GIN,VDV,W,T,WtV];

if ( VW2 ) {

/* take LC(GIN) w.r.t. DRL */

dp_set_weight(WtV); dp_ord(0);

HC = map(dp_hc,map(dp_ptod,GIN,VDV));

V2 = VW2[0]; DV2 = VW2[1]; WtV2 = VW2[2];

VDV2 = append(V2,DV2);

dp_set_weight(WtV2);

GIN2 = nd_weyl_gr_trace(GIN,VDV2,0,-1,0);

GIN2 = nd_gb_candidate(GIN,VDV2,0,0,HC,1);

InData = [GIN2,VDV2,V2,DV2,WtV2];

} else {

if ( 0 ) {

Line 259 def ann(F)

Line 299 def ann(F)

{

if ( member(s,vars(F)) )

error("ann : the variable 's' is reserved.");

if ( type(Vord=getopt(vord)) == -1 ) Vord = 0;

F = ptozp(F);

V = vars(F);

if ( Vord ) {

Param = setminus(V,Vord);

V = Vord;

}

N = length(V);

D = newvect(N);

if ( type(Wt=getopt(weight)) == -1 )

for ( I = N-1, Wt = []; I >= 0; I-- ) Wt = append([V[I],1],Wt);

for ( I = 0; I < N; I++ )

Wt1 = vector(N);

D[I] = [deg(F,V[I]),V[I]];

for ( I = 0, F1 =F; I < N; I++ ) {

qsort(D,compare_first);

VI = Wt[2*I]; WI = Wt[2*I+1];

for ( V = [], I = N-1; I >= 0; I-- )

for ( J = 0; J < N; J++ )

V = cons(D[I][1],V);

if ( VI == V[J] ) break;

F1 = subst(F1,VI,VI^WI);

}

for ( I = 0; I < N; I++ ) D[I] = [deg(F1,V[I]),V[I]];

qsort(D,ndbf.compare_first);

for ( V = [], I = 0; I < N; I++ ) V = cons(D[I][1],V);

V = reverse(V);

for ( I = 0; I < N; I++ ) {

VI = Wt[2*I]; WI = Wt[2*I+1];

for ( J = 0; J < N; J++ ) if ( VI == V[J] ) break;

Wt1[J] = WI;

}

Wt = vtol(Wt1);

for ( I = N-1, DV = []; I >= 0; I-- )

DV = cons(strtov("d"+rtostr(V[I])),DV);

Line 280 def ann(F)

Line 340 def ann(F)

B = cons(DV[I]+TMP_Y1*diff(F,V[I])*TMP_DT,B);

}

/* homogenized (heuristics) */

Tdeg = w_tdeg(F,V,Wt);

dp_nelim(2);

/* y1*y2-1, t-y1*f, dx1+y1*df/dx1*dt ... */

G0 = nd_weyl_gr(B,append(W,DW),0,[[0,2],[0,length(W)*2-2]]);

/* weight for [y1,y2,t, x1,...,xn, dy1,dy2, dt,dx1,...,dxn, h] */

/* 0 1 2 3 N3-1 N3 N3+1 N3+2 2*N3 */

/* 1 1 D+1 w1 wn 1 1 1 D D 1 */

N3 = N+3;

WtV = newvect(2*N3+1);

WtV[0] = WtV[1] = 1; WtV[2] = Tdeg+1;

for ( I = 3; I < N3; I++ ) WtV[I] = Wt[I-3];

for ( ; I <= N3+2; I++ ) WtV[I] = 1;

for ( ; I < 2*N3; I++ ) WtV[I] = Tdeg;

WtV[2*N3] = 1;

/* B is already a GB => modular change of ordering can be applied */

/* any prime is available => HC=[1] */

dp_set_weight(WtV);

G0 = nd_gb_candidate(B,append(W,DW),[[0,2],[0,length(W)*2-2]],0,[1],1);

dp_set_weight(0);

G1 = [];

for ( T = G0; T != []; T = cdr(T) ) {

E = car(T); VL = vars(E);

Line 294 def ann(F)

Line 369 def ann(F)

return G3;

}

def in_gb_oaku(F)

{

if ( member(s,vars(F)) )

error("ann : the variable 's' is reserved.");

F = ptozp(F);

V = vars(F);

N = length(V);

D = newvect(N);

if ( type(Wt=getopt(weight)) == -1 )

for ( I = N-1, Wt = []; I >= 0; I-- ) Wt = append([V[I],1],Wt);

Wt1 = vector(N);

for ( I = 0, F1 =F; I < N; I++ ) {

VI = Wt[2*I]; WI = Wt[2*I+1];

for ( J = 0; J < N; J++ )

if ( VI == V[J] ) break;

F1 = subst(F1,VI,VI^WI);

}

for ( I = 0; I < N; I++ ) D[I] = [deg(F1,V[I]),V[I]];

qsort(D,ndbf.compare_first);

for ( V = [], I = 0; I < N; I++ ) V = cons(D[I][1],V);

V = reverse(V);

for ( I = 0; I < N; I++ ) {

VI = Wt[2*I]; WI = Wt[2*I+1];

for ( J = 0; J < N; J++ ) if ( VI == V[J] ) break;

Wt1[J] = WI;

}

Wt = vtol(Wt1);

for ( I = N-1, DV = []; I >= 0; I-- )

DV = cons(strtov("d"+rtostr(V[I])),DV);

W = append([TMP_Y1,TMP_Y2,TMP_T],V);

DW = append([TMP_DY1,TMP_DY2,TMP_DT],DV);

B = [TMP_T-TMP_Y1*F];

for ( I = 0; I < N; I++ ) {

B = cons(DV[I]+TMP_Y1*diff(F,V[I])*TMP_DT,B);

}

Tdeg = w_tdeg(F,V,Wt);

/* y1*y2-1, t-y1*f, dx1+y1*df/dx1*dt ... */

/* weight for [y1,y2,t, x1,...,xn, dy1,dy2, dt,dx1,...,dxn, h] */

/* 0 1 2 3 N3-1 N3 N3+1 N3+2 2*N3 */

/* 1 1 D+1 1 1 1 1 1 D D 1 */

N3 = N+3;

WtV = newvect(2*N3+1);

WtV[0] = WtV[1] = 1; WtV[2] = Tdeg+1;

for ( I = 3; I <= N3+2; I++ ) WtV[I] = 1;

for ( ; I < 2*N3; I++ ) WtV[I] = Tdeg;

WtV[2*N3] = 1;

/* B is already a GB => modular change of ordering can be applied */

/* any prime is available => HC=[1] */

dp_set_weight(WtV);

G0 = nd_gb_candidate(B,append(W,DW),[[0,2],[0,length(W)*2-2]],0,[1],1);

dp_set_weight(0);

G1 = map(subst,G0,TMP_Y1,1);

return [G1,append(V,DV)];

}

/* homogenization w.r.t. (-W,W)-weight */

/* VDV = [x1,...,xn,dx1,...,dxn] */

/* homogenize F w.r.t. (W,-W,1) for (x,dx,y) */

def homogenize_oaku(F,VDV,W,Y)

{

N = length(VDV);

if ( N%2 ) error("invalid variable list");

N2 = N/2;

if ( length(W) != N2 ) error("inconsistent weight vector");

W0 = dp_set_weight();

Wt = append(W,append(vtol(-ltov(W)),[1]));

dp_set_weight(Wt);

H = homogenize(F,VDV,Y);

dp_set_weight(W0);

if ( type(Vars=getopt(vars)) != -1 && Vars ) {

DY = strtov("d"+rtostr(Y));

for ( I = 0, T = VDV, V = []; I < N2; I++, T = cdr(T) )

V = cons(car(T),V);

T = cons(Y,append(T,[DY]));

for ( ; V != []; V = cdr(V) ) T = cons(car(V),T);

return [H,T];

} else return H;

}

/* F = [F0,F1,...] */

def ann_n(F)

Line 331 def ann_n(F)

Line 492 def ann_n(F)

VA = append(U,append(W,V));

DVA = append(DU,append(DW,DV));

VDV = append(VA,DVA);

#if 0

G0 = nd_weyl_gr(B,VDV,0,[[0,2*L],[0,length(VDV)-2*L]]);

#else

G0 = nd_gb_candidate(B,VDV,[[0,2*L],[0,length(VDV)-2*L]],0,[1],1);

#endif

G1 = [];

for ( T = G0; T != []; T = cdr(T) ) {

E = car(T); VL = vars(E);

Line 369 def ann0(F)

Line 534 def ann0(F)

return [Min,map(subst,Ann,s,Min,TMP_S,s,TMP_DS,ds)];

}

* For a polynomial F and a scalar A,

* compute generators of Ann(F^A).

def ann_fa(F,A)

{

if ( type(Syz=getopt(syz)) == -1 ) Syz = 0;

F = subst(F,s,TMP_S);

Ann = ann(F);

Bf = bfunction(F);

FList = cdr(fctr(Bf));

for ( T = FList, Min = 0; T != []; T = cdr(T) ) {

LF = car(car(T));

Root = -coef(LF,0)/coef(LF,1);

if ( dn(Root) == 1 && Root < Min )

Min = Root;

}

D = A-Min;

if ( dn(D) != 1 || D <= 0 )

return map(ptozp,map(subst,Ann,s,A,TMP_S,s,TMP_DS,ds));

V = vars(F);

for ( I = length(V)-1, DV = []; I >= 0; I-- )

DV = cons(strtov("d"+rtostr(V[I])),DV);

VDV = append(V,DV);

R = map(subst,Ann,s,Min,TMP_S,s,TMP_DS,ds);

F = ptozp(F);

if ( Syz ) {

/* syzygy method */

S = newsyz.module_syz(cons(F^D,R),VDV,1,0|weyl=1);

B = car(S);

for ( R = []; B != []; B = cdr(B) )

if ( H = car(car(B)) )

R = cons(ptozp(H),R);

} else {

/* colon method */

for ( I = 0; I < D; I++ )

R = weyl_ideal_quotient(R,F,VDV);

}

return R;

}

def psi0(F,T,DT)

{

D = dp_ptod(F,[T,DT]);

Line 584 def bfct(F)

Line 795 def bfct(F)

for ( I = 0; I < N; I++ )

D[I] = [deg(F,V[I]),V[I]];

qsort(D,compare_first);

qsort(D,ndbf.compare_first);

for ( V = [], I = 0; I < N; I++ )

V = cons(D[I][1],V);

for ( I = N-1, DV = []; I >= 0; I-- )

Line 630 def bfct_via_gbfct(F)

Line 841 def bfct_via_gbfct(F)

for ( I = 0; I < N; I++ )

D[I] = [deg(F,V[I]),V[I]];

qsort(D,compare_first);

qsort(D,ndbf.compare_first);

for ( V = [], I = 0; I < N; I++ )

V = cons(D[I][1],V);

V = reverse(V);

Line 1082 def replace_var(V,X,Y)

Line 1293 def replace_var(V,X,Y)

def action_on_gfs(P,V,GFS)

{

for ( T = V, DV = []; T != []; T = cdr(T) )

DV = cons(strtov("d"+rtostr(car(T))),DV);

V = append(append(V,[s]),reverse(cons(ds,DV)));

DP = dp_ptod(P,V);

N = length(V)/2;

for ( I = N-1, V0 = []; I >= 0; I-- )

Line 1223 def weyl_ideal_quotient(B,F,VDV)

Line 1437 def weyl_ideal_quotient(B,F,VDV)

O1 = [[0,1],[0,N+1]];

GJ = nd_weyl_gr(J,VDV1,0,O1);

R = elimination(GJ,VDV);

return R;

return map(weyl_divide_by_right,R,F,VDV,0);

}

def bf_strat(F)

{

if ( member(s,vars(F)) )

error("ann : the variable 's' is reserved.");

dp_ord(0);

T0 = time();

if ( type(Heu=getopt(heuristic)) == -1 ) Heu = 0;

if ( type(Vord=getopt(vord)) == -1 || type(Vord) != 4 ) Vord = 0;

if ( type(Wt=getopt(weight)) == -1 ) Wt = 0;

if ( type(ElimIdeal=getopt(elimideal)) == -1 ) ElimIdeal = 0;

L = in_ww(F|weight=Wt,heuristic=Heu,vord=Vord);

T1 = time();

print(["in_ww",(T1[0]+T1[1])-(T0[0]+T0[1])]);

Line 1271 def bf_strat(F)

Line 1488 def bf_strat(F)

}

L2 = bf_strat_stage2(L);

if ( ElimIdeal ) return L2;

S = bf_strat_stage3(L2);

R = [];

for ( T = S; T != []; T = cdr(T) ) {

Line 1304 def bf_strat_stage2(L)

Line 1522 def bf_strat_stage2(L)

M = elim_mat(VDV,DVRV);

for ( K = 0; K < N; K++ )

M[1][K] = W[K];

dp_ord(0); H1 = map(dp_ht,map(dp_ptod,G1,VDV));

dp_ord(0); D1 = map(dp_ptod,G1,VDV);

H1 = map(dp_ht,D1); HC1 = map(dp_hc,D1);

dp_ord(M); H2 = map(dp_ht,map(dp_ptod,G1,VDV));

if ( H1 == H2 )

G2 = G1;

else

G2 = nd_weyl_gr_trace(G1,VDV,0,-1,M);

G2 = nd_gb_candidate(G1,VDV,M,0,HC1,1);

G1 = elimination(G2,DVRV);

}

T1 = time();

Line 1332 def bf_strat_stage3(L)

Line 1551 def bf_strat_stage3(L)

QQ = L[0]; V0 = L[2]; B = L[3]; BF = L[4]; W0 = L[5];

NF = length(BF);

Data = vector(NF);

W1 = W0? cons(1,append(W0,[1])) : 0;

for ( I = J = 0; I < NF; I++ ) {

DI = tower_in_p(QQ,B,BF[I],V0,W0);

NDI = length(DI);

dp_set_weight(W1);

for ( K = 0; K < J; K++ ) {

if ( length(DK=Data[K]) == NDI ) {

for ( L = 0; L < NDI; L++ ) {

Line 1345 def bf_strat_stage3(L)

Line 1566 def bf_strat_stage3(L)

if ( L == NDI ) break;

}

dp_set_weight(0);

if ( K < J ) {

for ( L = 0, T = []; L < NDI; L++ )

for ( L = 0, T = []; L < NDI; L++ ) {

#if 0

NewId = DK[L][1];

#else

NewId = ideal_intersection(DK[L][1],DI[L][1],V0,0);

#endif

T = cons([[DK[L][0][0]*DI[L][0][0],DK[L][0][1]],

DK[L][1],DK[L][2]],T);

NewId,DK[L][2]],T);

}

Data[K] = reverse(T);

} else

Data[J++] = DI;

Line 1357 def bf_strat_stage3(L)

Line 1585 def bf_strat_stage3(L)

for ( I = 0; I < J; I++ )

Data1[I] = Data[I];

T1 = time();

Str = stratify_bf(Data1,V0);

Str = stratify_bf(Data1,V0,W0);

T2 = time();

print(["tower",(T1[0]+T1[1])-(T0[0]+T0[1])]);

print(["strat",(T2[0]+T2[1])-(T1[0]+T1[1])]);

Line 1371 def bf_strat_stage3(L)

Line 1599 def bf_strat_stage3(L)

def bf_local(F,P)

{

if ( member(s,vars(F)) )

error("ann : the variable 's' is reserved.");

/* F -> F/Fcont */

F1 = ptozp(F); Fcont = sdiv(F,F1); F = F1;

if ( type(Heu=getopt(heuristic)) == -1 ) Heu = 0;

if ( type(Vord=getopt(vord)) == -1 || type(Vord) != 4 ) Vord = 0;

if ( type(Wt=getopt(weight)) == -1 ) Wt = 0;

if ( type(Op=getopt(op)) == -1 ) Op = 0;

L = in_ww(F|weight=Wt,heuristic=Heu,vord=Vord);

InData = L[0]; AllData = L[1]; VData = L[2];

G = InData[0]; VDV = InData[1];

Line 1407 def bf_local(F,P)

Line 1640 def bf_local(F,P)

break;

if ( List == [] ) error("bf_local : inconsitent intersection");

Ax = car(List);

for ( BPT = 1, List = BP; List != []; List = cdr(List) )

LB = [];

for ( BPT = 1, List = BP; List != []; List = cdr(List) ) {

BPT *= car(List)[0]^car(List)[1];

LB = cons([subst(car(List)[0],s,-s-1),car(List)[1]],LB);

}

LB = reverse(LB);

if ( !Op ) return LB;

BPT = weyl_subst(BPT,T*DT,VDV);

/* computation using G0,GIN0,VDV0 */

Line 1428 def bf_local(F,P)

Line 1667 def bf_local(F,P)

CR = conv_tdt(R,F,V0,DV0,T,DT);

dp_set_weight(0);

return [BP,Ax,CR];

Cont = cont(CR); CR /= Cont;

Cont *= dn(Fcont); Den *= nm(Fcont);

Gcd = igcd(Den,Cont);

return [LB,(Den/Gcd)*Ax,(Cont/Gcd)*CR];

}

/* t^(l+k)*dt^l (k>l) -> (s-k)(s-k-1)...(s-(k+l-1))t^k */

Line 1453 def conv_tdt(P,F,V0,DV0,T,DT)

Line 1695 def conv_tdt(P,F,V0,DV0,T,DT)

return subst(R,T,s);

}

def merge_tower(Str,Tower,V)

/* W1=[W,1], W2=[1,W,1] */

def merge_tower(Str,Tower,V,W1,W2)

{

Prev = car(Tower); T = cdr(Tower);

Str1 = [];

Line 1468 def merge_tower(Str,Tower,V)

Line 1712 def merge_tower(Str,Tower,V)

U = [];

for ( T = Str; T != []; T = cdr(T) ) {

for ( S = Str1; S != []; S = cdr(S) ) {

Int = int_cons(T[0],S[0],V);

Int = int_cons(T[0],S[0],V,W1,W2);

if ( Int[0] != [1] )

U = cons(append(Int,[append(T[0][2],S[0][2])]),U);

}

Line 1477 def merge_tower(Str,Tower,V)

Line 1721 def merge_tower(Str,Tower,V)

return U;

}

def stratify_bf(Data,V)

def stratify_bf(Data,V,W)

{

N = length(Data);

R = [];

if ( W ) {

W1 = append(W,[1]);

W2 = cons(1,W1);

} else

W1 = W2 = 0;

for ( I = 0; I < N; I++ )

R = merge_tower(R,Data[I],V);

R = merge_tower(R,Data[I],V,W1,W2);

return R;

}

Line 1588 def zero_inclusion(A,B,V)

Line 1837 def zero_inclusion(A,B,V)

NV = ttttt;

for ( T = A; T != []; T = cdr(T) ) {

F = car(T);

G = nd_gr_trace(cons(NV*F-1,B),cons(NV,V),1,-1,0);

G = nd_gr_trace(cons(NV*F-1,B),cons(NV,V),1,1,0);

if ( type(car(G)) != 1 ) return 0;

}

return 1;

Line 1622 def elim_mat(V,W)

Line 1871 def elim_mat(V,W)

=(P cap R)-(Q cup S)

def int_cons(A,B,V)

def int_cons(A,B,V,W1,W2)

{

AZ = A[0]; AN = A[1];

BZ = B[0]; BN = B[1];

if ( W1 ) dp_set_weight(W1);

CZ = nd_gr_trace(append(AZ,BZ),V,1,1,0);

if ( W2 ) dp_set_weight(W2);

CN = ideal_intersection(AN,BN,V,0);

if ( zero_inclusion(CN,CZ,V) )

ZI = zero_inclusion(CN,CZ,V);

dp_set_weight(0);

if ( ZI )

return [[1],[]];

else

return [CZ,CN];

Line 1641 def ideal_intersection(A,B,V,Ord)

Line 1894 def ideal_intersection(A,B,V,Ord)

cons(T,V),1,1,[[0,1],[Ord,length(V)]]);

return elimination(G,V);

}

def nd_gb_candidate(G,V,Ord,Homo,HC,Weyl)

{

Ind = 0;

N = length(HC);

while ( 1 ) {

P = lprime(Ind++);

for ( I = 0; I < N; I++ )

if ( !(HC[I]%P) ) break;

if ( I < N ) continue;

if ( Weyl )

G = nd_weyl_gr_trace(G,V,Homo,-P,Ord);

else

G = nd_gr_trace(G,V,Homo,-P,Ord);

if ( G ) return G;

}

endmodule $

end$

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