===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2018/engine/nd.c,v
retrieving revision 1.32
retrieving revision 1.53
diff -u -p -r1.32 -r1.53
--- OpenXM_contrib2/asir2018/engine/nd.c	2020/07/07 08:08:26	1.32
+++ OpenXM_contrib2/asir2018/engine/nd.c	2021/03/12 01:18:33	1.53
@@ -1,8 +1,11 @@
-/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.31 2020/07/07 08:04:30 noro Exp $ */
+/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.52 2021/03/09 08:48:50 noro Exp $ */
 
 #include "nd.h"
 
-int Nnd_add,Nf4_red;
+void print_siglist(NODE l);
+
+NODE nd_hpdata;
+int Nnd_add,Nf4_red,NcriB,NcriMF,Ncri2,Npairs,Nnewpair;
 struct oEGT eg_search,f4_symb,f4_conv,f4_elim1,f4_elim2;
 
 int diag_period = 6;
@@ -18,7 +21,7 @@ NM _nm_free_list;
 ND _nd_free_list;
 ND_pairs _ndp_free_list;
 NODE nd_hcf;
-int Nsyz;
+int Nsyz,Nsamesig;
 
 Obj nd_top_weight;
 
@@ -65,7 +68,9 @@ static int nd_module_rank,nd_poly_weight_len;
 static int *nd_poly_weight,*nd_module_weight;
 static NODE nd_tracelist;
 static NODE nd_alltracelist;
-static int nd_gentrace,nd_gensyz,nd_nora,nd_newelim,nd_intersect,nd_lf;
+static int nd_gentrace,nd_gensyz,nd_nora,nd_newelim,nd_intersect,nd_lf,nd_norb;
+static int nd_f4_td,nd_sba_f4step,nd_sba_pot,nd_sba_largelcm,nd_sba_dontsort,nd_sba_redundant_check;
+static int nd_top,nd_sba_syz,nd_sba_inputisgb;
 static int *nd_gbblock;
 static NODE nd_nzlist,nd_check_splist;
 static int nd_splist;
@@ -74,6 +79,21 @@ static int nd_f4red,nd_rank0,nd_last_nonzero;
 static DL *nd_sba_hm;
 static NODE *nd_sba_pos;
 
+struct comp_sig_spec {
+  int n;
+  // current_i <-> oldv[i]
+  int *oldv;
+  int *weight;
+  struct order_pair *order_pair;
+  int block_length;
+  int **matrix;
+  int row;
+  int (*cmpdl)(int n,DL d1,DL d2);
+};
+
+struct comp_sig_spec *nd_sba_modord;
+
+DL ndltodl(int n,UINT *ndl);
 NumberField get_numberfield();
 UINT *nd_det_compute_bound(NDV **dm,int n,int j);
 void nd_det_reconstruct(NDV **dm,int n,int j,NDV d);
@@ -91,15 +111,19 @@ P ndc_div(int mod,union oNDC a,union oNDC b);
 P ndctop(int mod,union oNDC c);
 void finalize_tracelist(int i,P cont);
 void conv_ilist(int demand,int trace,NODE g,int **indp);
-void parse_nd_option(NODE opt);
+void parse_nd_option(VL vl,NODE opt);
 void dltondl(int n,DL dl,UINT *r);
 DP ndvtodp(int mod,NDV p);
 DP ndtodp(int mod,ND p);
 DPM ndvtodpm(int mod,NDV p);
+NDV dptondv(int mod,DP p);
 NDV dpmtondv(int mod,DPM p);
+int dp_getdeg(DP p);
 int dpm_getdeg(DPM p,int *rank);
 void dpm_ptozp(DPM p,Z *cont,DPM *r);
 int compdmm(int nv,DMM a,DMM b);
+DPM sigtodpm(SIG s);
+SIG dup_sig(SIG sig);
 
 void Pdp_set_weight(NODE,VECT *);
 void Pox_cmo_rpc(NODE,Obj *);
@@ -114,6 +138,7 @@ NODE nd_f4_red_mod64_main(int m,ND_pairs sp0,int nsp,U
 NODE nd_f4_red_lf_main(int m,ND_pairs sp0,int nsp,int trace,UINT *s0vect,int col,
         NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred);
 int nd_gauss_elim_lf(mpz_t **mat0,int *sugar,int row,int col,int *colstat);
+int nd_gauss_elim_mod_s(UINT **mat,int *sugar,ND_pairs *spactive,int row,int col,int md,int *colstat,SIG *sig);
 NODE nd_f4_lf_trace_main(int m,int **indp);
 void nd_f4_lf_trace(LIST f,LIST v,int trace,int homo,struct order_spec *ord,LIST *rp);
 
@@ -791,13 +816,16 @@ int _eqdl(int n,DL d1,DL d2);
 
 int ndl_module_schreyer_compare(UINT *m1,UINT *m2)
 {
-  int pos1,pos2,t,j;
+  int pos1,pos2,t,j,retpot;
   DMM *in;
   DMMstack s;
   static DL d1=0;
   static DL d2=0;
   static int dlen=0;
+  extern int ReversePOT;
 
+  if ( ReversePOT ) retpot = -1;
+  else retpot = 1;
   pos1 = MPOS(m1); pos2 = MPOS(m2);
   if ( pos1 == pos2 ) return (*ndl_base_compare_function)(m1,m2);
   if ( nd_nvar > dlen ) {
@@ -814,8 +842,8 @@ int ndl_module_schreyer_compare(UINT *m1,UINT *m2)
     _addtodl(nd_nvar,in[pos1]->dl,d1);
     _addtodl(nd_nvar,in[pos2]->dl,d2);
     if ( in[pos1]->pos == in[pos2]->pos && _eqdl(nd_nvar,d1,d2)) {
-      if ( pos1 < pos2 ) return 1;
-      else if ( pos1 > pos2 ) return -1;
+      if ( pos1 < pos2 ) return retpot;
+      else if ( pos1 > pos2 ) return -retpot;
       else return 0;
     }
     pos1 = in[pos1]->pos;
@@ -828,20 +856,20 @@ LAST:
     case 0:
       t = (*dl_base_compare_function)(nd_nvar,d1,d2);
       if ( t ) return t;
-      else if ( pos1 < pos2 ) return 1;
-      else if ( pos1 > pos2 ) return -1;
+      else if ( pos1 < pos2 ) return retpot;
+      else if ( pos1 > pos2 ) return -retpot;
       else return 0;
       break;
     case 1:
-      if ( pos1 < pos2 ) return 1;
-      else if ( pos1 > pos2 ) return -1;
+      if ( pos1 < pos2 ) return retpot;
+      else if ( pos1 > pos2 ) return -retpot;
       else return (*dl_base_compare_function)(nd_nvar,d1,d2);
       break;
     case 2:
       if ( d1->td > d2->td  ) return 1;
       else if ( d1->td < d2->td ) return -1;
-      else if ( pos1 < pos2 ) return 1;
-      else if ( pos1 > pos2 ) return -1;
+      else if ( pos1 < pos2 ) return retpot;
+      else if ( pos1 > pos2 ) return -retpot;
       else return (*dl_base_compare_function)(nd_nvar,d1,d2);
       break;
     default:
@@ -1204,6 +1232,18 @@ INLINE int ndl_find_reducer(UINT *dg)
     return -1;
 }
 
+INLINE int ndl_find_reducer_nonsig(UINT *dg)
+{
+    RHist r;
+    int i;
+
+    for ( i = 0; i < nd_psn; i++ ) {
+      r = nd_psh[i];
+      if ( ndl_reducible(dg,DL(r)) ) return i;
+    }
+    return -1;
+}
+
 // ret=0,...,nd_psn-1 => reducer found
 // ret=nd_psn => reducer not found
 // ret=-1 => singular top reducible
@@ -1223,6 +1263,15 @@ void print_sig(SIG s)
   fprintf(asir_out,">>*e%d",s->pos);
 }
 
+void print_siglist(NODE l)
+{
+  for ( ; l; l = NEXT(l) )
+   print_sig((SIG)l->body);
+}
+
+
+// assuming increasing order wrt signature 
+
 INLINE int ndl_find_reducer_s(UINT *dg,SIG sig)
 {
   RHist r;
@@ -1237,11 +1286,13 @@ INLINE int ndl_find_reducer_s(UINT *dg,SIG sig)
     tmp = (UINT *)MALLOC(wpd*sizeof(UINT));
   }
   d = ndl_hash_value(dg);
+#if 1
   for ( r = nd_red[d], k = 0; r; r = NEXT(r), k++ ) {
     if ( ndl_equal(dg,DL(r)) ) {
       return r->index;
     }
   }
+#endif
   singular = 0;
   for ( i = 0; i < nd_psn; i++ ) {
     r = nd_psh[i];
@@ -1252,7 +1303,7 @@ INLINE int ndl_find_reducer_s(UINT *dg,SIG sig)
       quo->pos = nd_psh[i]->sig->pos;
       ret = comp_sig(sig,quo);
       if ( ret > 0 ) { singular = 0; break; }
-      if ( ret == 0 ) { fprintf(asir_out,"s"); fflush(asir_out); singular = 1; }
+      if ( ret == 0 ) { /* fprintf(asir_out,"s"); fflush(asir_out); */ singular = 1; }
     }
   }
   if ( singular ) return -1;
@@ -2024,6 +2075,7 @@ void free_pbucket(PGeoBucket b) {
     GCFREE(b);
 }
 
+#if 0
 void add_pbucket_symbolic(PGeoBucket g,ND d)
 {
     int l,i,k,m;
@@ -2041,7 +2093,32 @@ void add_pbucket_symbolic(PGeoBucket g,ND d)
     g->body[k] = d;
     g->m = MAX(g->m,k);
 }
+#else
+void add_pbucket_symbolic(PGeoBucket g,ND d)
+{
+  int l,i,k,m,m0;
 
+  if ( !d )
+    return;
+  m0 = g->m;
+  while ( 1 ) {
+    l = LEN(d);
+    for ( k = 0, m = 1; l > m; k++, m <<= 1 );
+    /* 2^(k-1) < l <= 2^k (=m) */
+    if ( g->body[k] == 0 ) {
+      g->body[k] = d;
+      m0 = MAX(k,m0);
+      break;
+    } else { 
+      d = nd_merge(g->body[k],d);
+      g->body[k] = 0; 
+    }
+  }
+  g->m = m0;
+}
+#endif
+
+#if 0
 void add_pbucket(int mod,PGeoBucket g,ND d)
 {
     int l,i,k,m;
@@ -2059,7 +2136,29 @@ void add_pbucket(int mod,PGeoBucket g,ND d)
     g->body[k] = d;
     g->m = MAX(g->m,k);
 }
+#else
+void add_pbucket(int mod,PGeoBucket g,ND d)
+{
+  int l,i,k,m,m0;
 
+  m0 = g->m;
+  while ( d != 0 ) {
+    l = LEN(d);
+    for ( k = 0, m = 1; l > m; k++, m <<= 1 );
+    /* 2^(k-1) < l <= 2^k (=m) */
+    if ( g->body[k] == 0 ) {
+      g->body[k] = d;
+      m0 = MAX(k,m0);
+      break;
+    } else { 
+      d = nd_add(mod,g->body[k],d);
+      g->body[k] = 0; 
+    }
+  }
+  g->m = m0;
+}
+#endif
+
 void mulq_pbucket(PGeoBucket g,Z c)
 {
     int k;
@@ -2370,6 +2469,130 @@ LIST compute_splist()
   return l0;
 }
 
+typedef struct oHPDATA {
+  P hn; // HP(t)=hn(t)/(1-t)^n
+  int len;
+  P *head; // hp(i)=head[i] (i=0,...,len-1)
+  P hp; // dim Hm(i)=hp(i) (i >= len)
+  VECT x; // BDY(x)[i] = <<0,...,1,...,0>>
+  P *plist; // plist[i]=(1-t)^i
+} *HPDATA;
+
+void make_reduced(VECT b,int nv);
+void mhp_rec(VECT b,VECT x,P t,P *r);
+P mhp_ctop(P *r,P *plist,int n);
+void mhp_to_hf(VL vl,P hp,int n,P *plist,VECT *head,P *hf);
+DL monomial_colon(DL a,DL b,int n);
+LIST dp_monomial_hilbert_poincare(VECT b,VECT x,P *plist);
+
+int hpvalue(HPDATA data,int d)
+{
+  P *head;
+  int len;
+  P hp,val;
+  Z dz;
+
+  head = data->head;
+  len = data->len;
+  hp = data->hp;
+  if ( d < len )
+    return ZTOS((Z)head[d]);
+  else {
+    STOZ(d,dz);
+    substp(CO,hp,hp->v,(P)dz,&val);
+    return ZTOS((Z)val);
+  }
+}
+
+void setup_hpdata(HPDATA final,HPDATA current)
+{
+  int n,i;
+  P *r;
+  DL *p;
+  P tv;
+  VECT b,x,head;
+  DL dl;
+
+  n = nd_nvar;
+  final->hn = (P)ARG0(nd_hpdata);
+  head = (VECT)ARG2(nd_hpdata);
+  final->len = head->len;
+  final->head = (P *)BDY(head);
+  final->hp = (P)ARG3(nd_hpdata);
+  final->plist = (P *)BDY((VECT)ARG4(nd_hpdata));
+  MKVECT(x,n);
+  for ( i = 0; i < n; i++ ) {
+    NEWDL(dl,n); dl->d[i] = 1; dl->td = 1; BDY(x)[i] = dl;
+  }
+  final->x = x;
+
+  r = (P *)CALLOC(n+1,sizeof(P));
+  MKVECT(b,nd_psn); p = (DL *)BDY(b);
+  for ( i = 0; i < nd_psn; i++ ) {
+    p[i] = ndltodl(n,nd_psh[i]->dl);
+  }
+  make_reduced(b,n);
+  makevar("t",&tv);
+  mhp_rec(b,x,tv,r);
+  current->hn = mhp_ctop(r,final->plist,n);
+  mhp_to_hf(CO,current->hn,n,final->plist,&head,&current->hp);
+  current->head = (P *)BDY(head);
+  current->len = head->len;
+  current->x = x;
+  current->plist = final->plist;
+}
+
+void update_hpdata(HPDATA current,int nh,int do_hf)
+{
+  NODE data1,nd,t;
+  DL new,dl;
+  int len,i,n;
+  Z dz;
+  DL *p;
+  VECT b,head;
+  P tv,td,s,hn,hpoly;
+  LIST list1;
+
+  n = nd_nvar;
+  new = ndltodl(n,nd_psh[nh]->dl);
+  MKVECT(b,nh); p = (DL *)BDY(b);
+  for ( i = 0; i < nh; i++ ) {
+    p[i] = monomial_colon(ndltodl(n,nd_psh[i]->dl),new,n);
+  }
+  // compute HP(I:new)
+  list1 = dp_monomial_hilbert_poincare(b,current->x,current->plist);
+  data1 = BDY((LIST)list1);
+  // HP(I+<new>) = H(I)-t^d*H(I:new), d=tdeg(new)
+  makevar("t",&tv); UTOZ(new->td,dz);
+  pwrp(CO,tv,dz,&td);
+  mulp(CO,(P)ARG0(data1),td,&s);
+  subp(CO,current->hn,s,&hn);
+  current->hn = hn;
+  if ( do_hf ) {
+    mhp_to_hf(CO,hn,n,current->plist,&head,&hpoly);
+    current->head = (P *)BDY(head);
+    current->len = head->len;
+    current->hp = hpoly;
+  }
+}
+
+ND_pairs nd_remove_same_sugar( ND_pairs d, int sugar)
+{
+  struct oND_pairs root;
+  ND_pairs prev,cur;
+
+  root.next = d;
+  prev = &root; cur = d;
+  while ( cur ) {
+    if ( SG(cur) == sugar )
+      prev->next = cur->next;
+    else
+      prev = cur;
+    cur = cur->next;
+  }
+  return root.next;
+}
+
 /* return value = 0 => input is not a GB */
 
 NODE nd_gb(int m,int ishomo,int checkonly,int gensyz,int **indp)
@@ -2383,8 +2606,12 @@ NODE nd_gb(int m,int ishomo,int checkonly,int gensyz,i
   Z q;
   union oNDC dn,hc;
   int diag_count = 0;
+  int Nnfnz = 0,Nnfz = 0;
   P cont;
   LIST list;
+  struct oHPDATA current_hpdata,final_hpdata;
+  int final_hpvalue;
+
 struct oEGT eg1,eg2,eg_update;
 
 init_eg(&eg_update);
@@ -2395,6 +2622,10 @@ init_eg(&eg_update);
     g = update_base(g,i);
   }
   sugar = 0;
+  if ( nd_hpdata ) {
+    if ( DP_Print ) fprintf(asir_out,"Hilbert driven algorithm.\n");
+    setup_hpdata(&final_hpdata,&current_hpdata);
+  }
   while ( d ) {
 again:
     l = nd_minp(d,&d);
@@ -2411,6 +2642,18 @@ again:
       }
       sugar = SG(l);
       if ( DP_Print ) fprintf(asir_out,"%d",sugar);
+      if ( nd_hpdata ) {
+        if ( !compp(CO,final_hpdata.hn,current_hpdata.hn) )
+          break;
+        else {
+          final_hpvalue = hpvalue(&final_hpdata,sugar);
+          if ( final_hpvalue == hpvalue(&current_hpdata,sugar) ) {
+//            if ( DP_Print ) fprintf(asir_out,"done.\n",sugar);
+            d = nd_remove_same_sugar(d,sugar);
+            continue;
+          }
+        }
+      }
     }
     stat = nd_sp(m,0,l,&h);
     if ( !stat ) {
@@ -2419,16 +2662,17 @@ again:
       goto again;
     }
 #if USE_GEOBUCKET
-    stat = (m&&!nd_gentrace)?nd_nf_pbucket(m,h,nd_ps,!Top,&nf)
-      :nd_nf(m,0,h,nd_ps,!Top,&nf);
+    stat = (m&&!nd_gentrace)?nd_nf_pbucket(m,h,nd_ps,!nd_top&&!Top,&nf)
+      :nd_nf(m,0,h,nd_ps,!nd_top&&!Top,&nf);
 #else
-    stat = nd_nf(m,0,h,nd_ps,!Top,&nf);
+    stat = nd_nf(m,0,h,nd_ps,!nd_top&&!Top,&nf);
 #endif
     if ( !stat ) {
       NEXT(l) = d; d = l;
       d = nd_reconstruct(0,d);
       goto again;
     } else if ( nf ) {
+      Nnfnz++;
       if ( checkonly || gensyz ) return 0;
       if ( nd_newelim ) {
         if ( nd_module ) {
@@ -2467,26 +2711,42 @@ get_eg(&eg1);
 get_eg(&eg2); add_eg(&eg_update,&eg1,&eg2);
       g = update_base(g,nh);
       FREENDP(l);
-   } else {
-     if ( nd_gentrace && gensyz ) {
-       nd_tracelist = reverse_node(nd_tracelist); 
-       MKLIST(list,nd_tracelist);
-       STOZ(-1,q); t = mknode(2,q,list); MKLIST(list,t);
-       MKNODE(t,list,nd_alltracelist); 
-       nd_alltracelist = t; nd_tracelist = 0;
-     }
-     if ( DP_Print ) { printf("."); fflush(stdout); }
-       FREENDP(l);
-   }
- }
- conv_ilist(nd_demand,0,g,indp);
-    if ( !checkonly && DP_Print ) { printf("nd_gb done. Number of nd_add=%d\n",Nnd_add); fflush(stdout); }
-print_eg("update",&eg_update);
-    return g;
+      if ( nd_hpdata ) {
+        update_hpdata(&current_hpdata,nh,1);
+        if ( final_hpvalue == hpvalue(&current_hpdata,sugar) ) {
+//          if ( DP_Print ) fprintf(asir_out,"sugar=%d done.\n",sugar);
+          d = nd_remove_same_sugar(d,sugar);
+        }
+      }
+    } else {
+      Nnfz++;
+      if ( nd_gentrace && gensyz ) {
+        nd_tracelist = reverse_node(nd_tracelist); 
+        MKLIST(list,nd_tracelist);
+        STOZ(-1,q); t = mknode(2,q,list); MKLIST(list,t);
+        MKNODE(t,list,nd_alltracelist); 
+        nd_alltracelist = t; nd_tracelist = 0;
+      }
+      if ( DP_Print ) { printf("."); fflush(stdout); }
+        FREENDP(l);
+    }
+  }
+  conv_ilist(nd_demand,0,g,indp);
+  if ( !checkonly && DP_Print ) { 
+    printf("\nnd_gb done. Nnd_add=%d,Npairs=%d, Nnfnz=%d,Nnfz=%d,",Nnd_add,Npairs,Nnfnz,Nnfz);
+    printf("Nremoved=%d\n",NcriB+NcriMF+Ncri2);
+    fflush(asir_out);
+  }
+  if ( DP_Print ) {
+    print_eg("update",&eg_update); fprintf(asir_out,"\n");
+  }
+  return g;
 }
 
 ND_pairs update_pairs_s(ND_pairs d,int t,NODE *syz);
+int update_pairs_array_s(ND_pairs *d,int t,NODE *syz);
 ND_pairs nd_newpairs_s(int t ,NODE *syz);
+ND_pairs *nd_newpairs_array_s(int t ,NODE *syz);
 
 int nd_nf_pbucket_s(int mod,ND g,NDV *ps,int full,ND *nf);
 int nd_nf_s(int mod,ND d,ND g,NDV *ps,int full,ND *nf);
@@ -2494,7 +2754,38 @@ int nd_nf_s(int mod,ND d,ND g,NDV *ps,int full,ND *nf)
 void _copydl(int n,DL d1,DL d2);
 void _subfromdl(int n,DL d1,DL d2);
 extern int (*cmpdl)(int n,DL d1,DL d2);
+int _dl_redble_ext(DL,DL,DL,int);
 
+int primitive_irred(ND p,SIG sig)
+{
+  static int wpd=0,dlen=0;
+  static DL dquo,squo;
+  static UINT *quo;
+  int i;
+
+  if ( dlen < nd_nvar ) {
+    NEWDL(dquo,nd_nvar);
+    NEWDL(squo,nd_nvar);
+    dlen = nd_nvar;
+  }
+  if ( wpd != nd_wpd ) {
+    wpd = nd_wpd;
+    quo = (UINT *)MALLOC(wpd*sizeof(UINT));
+  }
+  for ( i = 0; i < nd_psn; i++ ) {
+    if ( sig->pos == nd_psh[i]->sig->pos &&
+      _dl_redble_ext(DL(nd_psh[i]->sig),DL(sig),squo,nd_nvar) )
+      if ( ndl_reducible(HDL(p),DL(nd_psh[i])) ) {
+        if ( DP_Print ) fprintf(asir_out,"D");
+        ndl_sub(HDL(p),DL(nd_psh[i]),quo);
+        _ndltodl(quo,dquo);
+        if ( _eqdl(nd_nvar,squo,dquo) ) 
+          return 0;
+      }
+  }
+  return 1;
+}
+
 NODE insert_sig(NODE l,SIG s)
 {
   int pos;
@@ -2513,6 +2804,8 @@ NODE insert_sig(NODE l,SIG s)
       else if ( _dl_redble(sig,DL(t),nd_nvar) )
         // remove p
         prev->next = p->next;
+      else
+        prev = p;
     } else
       prev = p;
   }
@@ -2545,16 +2838,15 @@ ND_pairs remove_spair_s(ND_pairs d,SIG sig)
   return (ND_pairs)root.next;
 }
 
-int _dl_redble_ext(DL,DL,DL,int);
-
 int small_lcm(ND_pairs l)
 {
   SIG sig;
   int i;
   NODE t;
   static DL lcm,mul,quo;
-  static int nvar;
+  static int nvar = 0;
 
+  if ( nd_sba_largelcm ) return 0;
   if ( nvar < nd_nvar ) {
     nvar = nd_nvar; NEWDL(lcm,nvar); NEWDL(quo,nvar); NEWDL(mul,nvar);
   }
@@ -2587,6 +2879,62 @@ int small_lcm(ND_pairs l)
 #endif
 }
 
+ND_pairs find_smallest_lcm(ND_pairs l)
+{
+  SIG sig;
+  int i,minindex;
+  NODE t;
+  ND_pairs r;
+  struct oSIG sig1;
+  static DL mul,quo,minlm;
+  static int nvar = 0;
+
+  if ( nvar < nd_nvar ) {
+    nvar = nd_nvar; 
+    NEWDL(quo,nvar); NEWDL(mul,nvar);
+    NEWDL(minlm,nvar);
+  }
+  sig = l->sig;
+  // find mg s.t. m*s(g)=sig and m*lm(g) is minimal
+  _ndltodl(l->lcm,minlm); minindex = -1;
+  for ( t = nd_sba_pos[sig->pos]; t; t = t->next ) {
+    i = (long)BDY(t);
+    if ( _dl_redble_ext(DL(nd_psh[i]->sig),DL(sig),quo,nd_nvar) ) {
+      _ndltodl(DL(nd_psh[i]),mul);
+      _addtodl(nd_nvar,quo,mul);
+      if ( (*cmpdl)(nd_nvar,minlm,mul) > 0 ) {
+        minindex = i;
+        break;
+        _copydl(nd_nvar,mul,minlm);
+      }
+    }
+  }
+  // l->lcm is minimal; return l itself
+  if ( minindex < 0 ) return l;
+  else return 0;
+  for ( i = 0; i < nd_psn; i++ ) {
+    if ( i == minindex ) continue;
+    _ndltodl(DL(nd_psh[i]),mul);
+    if ( _dl_redble_ext(mul,minlm,quo,nd_nvar) ) {
+      _addtodl(nd_nvar,nd_ps[i]->sig->dl,quo);
+      sig1.pos = nd_ps[i]->sig->pos;
+      sig1.dl = quo;
+      if ( comp_sig(sig,&sig1) > 0 ) {
+//        printf("X");
+        NEWND_pairs(r);
+        r->sig = sig;
+        r->i1 = minindex;
+        r->i2 = i;
+        dltondl(nd_nvar,minlm,r->lcm);
+        r->next = 0;
+        return r;
+      }
+    }
+  }
+  // there is no suitable spair 
+  return 0;
+}
+
 ND_pairs remove_large_lcm(ND_pairs d)
 {
   struct oND_pairs root;
@@ -2595,10 +2943,17 @@ ND_pairs remove_large_lcm(ND_pairs d)
   root.next = d;
   prev = &root; p = d;
   while ( p ) {
+#if 0
     if ( small_lcm(p) ) {
       // remove p
       prev->next = p->next;
     } else
+#else
+    if ( find_smallest_lcm(p) == 0 ) {
+      // remove p
+      prev->next = p->next;
+    } else
+#endif
       prev = p;
     p = p->next;
   }
@@ -2609,12 +2964,65 @@ struct oEGT eg_create,eg_newpairs,eg_merge;
 
 NODE conv_ilist_s(int demand,int trace,int **indp);
 
-NODE nd_sba_buch(int m,int ishomo,int **indp)
+// S(fj*ei-fi*ej) 
+
+void _subdl(int,DL,DL,DL);
+
+SIG trivial_sig(int i,int j)
 {
-  int i,j,nh,sugar,stat;
+  static DL lcm;
+  static struct oSIG sigi,sigj;
+  static int nvar = 0;
+  SIG sig;
+
+  if ( nvar != nd_nvar ) {
+    nvar = nd_nvar; NEWDL(lcm,nvar); NEWDL(sigi.dl,nvar); NEWDL(sigj.dl,nvar);
+  }
+  if ( nd_sba_inputisgb != 0 ) {
+    lcm_of_DL(nd_nvar,nd_sba_hm[i],nd_sba_hm[j],lcm);
+    sigi.pos = i; _subdl(nd_nvar,lcm,nd_sba_hm[i],sigi.dl);
+    sigj.pos = j; _subdl(nd_nvar,lcm,nd_sba_hm[j],sigj.dl);
+    if ( comp_sig(&sigi,&sigj) > 0 ) sig = dup_sig(&sigi);
+    else sig = dup_sig(&sigj);
+  } else {
+    sigi.pos = i; _copydl(nd_nvar,nd_sba_hm[j],sigi.dl);
+    sigj.pos = j; _copydl(nd_nvar,nd_sba_hm[i],sigj.dl);
+    if ( comp_sig(&sigi,&sigj) > 0 ) sig = dup_sig(&sigi);
+    else sig = dup_sig(&sigj);
+  }
+  return sig;
+}
+
+int nd_minsig(ND_pairs *d) 
+{
+  int min,i,ret;
+
+  min = -1;
+  for ( i = 0; i < nd_nbase; i++ ) {
+    if ( d[i] != 0 ) {
+      if ( min < 0 ) min = i;
+      else {
+        ret = comp_sig(d[i]->sig,d[min]->sig);
+        if ( ret < 0 ) min = i;
+      }
+    }
+  }
+  return min;
+}
+
+int dlength(ND_pairs d)
+{
+  int i;
+  for ( i = 0; d; d = d->next, i++ );
+  return i;
+}
+
+NODE nd_sba_buch(int m,int ishomo,int **indp,NODE *syzp)
+{
+  int i,j,nh,sugar,stat,pos;
   NODE r,t,g;
-  ND_pairs d;
-  ND_pairs l;
+  ND_pairs *d;
+  ND_pairs l,l1;
   ND h,nf,s,head,nf1;
   NDV nfv;
   Z q;
@@ -2623,105 +3031,196 @@ NODE nd_sba_buch(int m,int ishomo,int **indp)
   LIST list;
   SIG sig;
   NODE *syzlist;
-  int Nredundant;
+  int ngen,ind;
+  int Nnominimal,Nredundant;
   DL lcm,quo,mul;
-  struct oEGT eg1,eg2,eg_update,eg_remove,eg_large,eg_nf,eg_nfzero;
+  struct oHPDATA final_hpdata,current_hpdata;
+  struct oEGT eg1,eg2,eg3,eg4,eg_update,eg_remove,eg_large,eg_nf,eg_nfzero;
+  struct oEGT eg_minsig,eg_smallest,eg_removecont,eg_hpdata,eg_updatepairs,eg_sbabuch,eg_sp;
+  int Nnfs=0,Nnfz=0,Nnfnz=0,dlen,nsyz;
 
 init_eg(&eg_remove);
   syzlist = (NODE *)MALLOC(nd_psn*sizeof(NODE));
+  d = (ND_pairs *)MALLOC(nd_psn*sizeof(ND_pairs));
+  nd_nbase = nd_psn;
   Nsyz = 0;
   Nnd_add = 0;
+  Nnominimal = 0;
   Nredundant = 0;
-  d = 0;
+  ngen = nd_psn;
+  if ( !do_weyl ) {
+    for ( i = 0; i < nd_psn; i++ )
+      for ( j = i+1; j < nd_psn; j++ ) {
+        sig = trivial_sig(i,j);
+        syzlist[sig->pos] = insert_sig(syzlist[sig->pos],sig);
+      }
+    }
+  dlen = 0;
   for ( i = 0; i < nd_psn; i++ ) {
-    d = update_pairs_s(d,i,syzlist);
+    dlen += update_pairs_array_s(d,i,syzlist);
   }
-  for ( i = 0; i < nd_psn; i++ )
-    for ( j = i+1; j < nd_psn; j++ ) {
-      NEWSIG(sig); sig->pos = j;
-      _copydl(nd_nvar,nd_sba_hm[i],sig->dl);
-      syzlist[sig->pos] = insert_sig(syzlist[sig->pos],sig);
-    }
   sugar = 0;
+  pos = 0;
+  if ( nd_hpdata ) {
+    setup_hpdata(&final_hpdata,&current_hpdata);
+  }
   NEWDL(lcm,nd_nvar); NEWDL(quo,nd_nvar); NEWDL(mul,nd_nvar);
+init_eg(&eg_sp);
 init_eg(&eg_create);
 init_eg(&eg_merge);
+init_eg(&eg_minsig);
+init_eg(&eg_smallest);
 init_eg(&eg_large);
 init_eg(&eg_nf);
 init_eg(&eg_nfzero);
-  while ( d ) {
-again:
-    if ( DP_Print ) {
-      int len;
-      ND_pairs td;
-      for ( td = d, len=0; td; td = td->next, len++)
-        ;
-       if ( !(len%100) ) fprintf(asir_out,"(%d)",len);
-      }
-    l = d; d = d->next;
-    if ( small_lcm(l) ) {
-      if ( DP_Print ) fprintf(asir_out,"M");
-      Nredundant++;
+init_eg(&eg_removecont);
+init_eg(&eg_updatepairs);
+init_eg(&eg_hpdata);
+init_eg(&eg_sbabuch);
+get_eg(&eg3);
+  while ( 1 ) {
+    if ( DP_Print && !nd_hpdata && dlen%1000 == 0 ) fprintf(asir_out,"(%d)",dlen);
+again :
+get_eg(&eg1);
+    ind = nd_minsig(d); 
+get_eg(&eg2); add_eg(&eg_minsig,&eg1,&eg2);
+    if ( ind < 0 ) break;
+    l = d[ind];
+//    printf("(%d,%d)",l->i1,l->i2); print_sig(l->sig); printf("\n");
+get_eg(&eg1);
+    l1 = find_smallest_lcm(l);
+get_eg(&eg2); add_eg(&eg_smallest,&eg1,&eg2);
+    if ( l1 == 0 ) {
+      d[ind] = d[ind]->next; dlen--;
+//      if ( DP_Print && !nd_hpdata ) fprintf(asir_out,"M");
+      Nnominimal++;
       continue;
     }
-    if ( SG(l) != sugar ) {
-      sugar = SG(l);
+    if ( SG(l1) != sugar ) {
+      sugar = SG(l1);
       if ( DP_Print ) fprintf(asir_out,"%d",sugar);
     }
-    sig = l->sig;
-    stat = nd_sp(m,0,l,&h);
+    sig = l1->sig;
+    if ( DP_Print && nd_sba_pot ) {
+      if ( sig->pos != pos ) {
+        fprintf(asir_out,"[%d]",sig->pos);
+        pos = sig->pos;
+      }
+    }
+get_eg(&eg1);
+    stat = nd_sp(m,0,l1,&h);
+get_eg(&eg2); add_eg(&eg_sp,&eg1,&eg2);
     if ( !stat ) {
-      NEXT(l) = d; d = l;
-      d = nd_reconstruct(0,d);
+      nd_reconstruct_s(0,d);
       goto again;
     }
 get_eg(&eg1);
 #if USE_GEOBUCKET
-    stat = m?nd_nf_pbucket_s(m,h,nd_ps,!Top,&nf):nd_nf_s(m,0,h,nd_ps,!Top,&nf);
+    stat = m?nd_nf_pbucket_s(m,h,nd_ps,!nd_top&&!Top,&nf):nd_nf_s(m,0,h,nd_ps,!nd_top&&!Top,&nf);
 #else
-    stat = nd_nf_s(m,0,h,nd_ps,!Top,&nf);
+    stat = nd_nf_s(m,0,h,nd_ps,!nd_top&&!Top,&nf);
 #endif
 get_eg(&eg2); 
     if ( !stat ) {
-      NEXT(l) = d; d = l;
-      d = nd_reconstruct(0,d);
+      nd_reconstruct_s(0,d);
       goto again;
     } else if ( stat == -1 ) {
+      d[ind] = d[ind]->next; dlen--;
+      Nnfs++;
       if ( DP_Print ) { printf("S"); fflush(stdout); }
-      FREENDP(l);
     } else if ( nf ) {
-      if ( DP_Print ) { printf("+"); fflush(stdout); }
+      d[ind] = d[ind]->next; dlen--;
+      Nnfnz++;
+      if ( DP_Print ) { 
+        if ( nd_sba_redundant_check ) {
+          if ( ndl_find_reducer_nonsig(HDL(nf)) >= 0 ) {
+            Nredundant++;
+            printf("R"); 
+          } else 
+            printf("+"); 
+        } else
+          printf("+"); 
+        fflush(stdout); 
+      }
       add_eg(&eg_nf,&eg1,&eg2);
       hc = HCU(nf);
+      get_eg(&eg1);
       nd_removecont(m,nf);
+      get_eg(&eg2); add_eg(&eg_removecont,&eg1,&eg2);
       nfv = ndtondv(m,nf); nd_free(nf);
       nh = ndv_newps(m,nfv,0);
-
-      d = update_pairs_s(d,nh,syzlist);
+ 
+      get_eg(&eg1);
+      dlen += update_pairs_array_s(d,nh,syzlist);
+      get_eg(&eg2); add_eg(&eg_updatepairs,&eg1,&eg2);
       nd_sba_pos[sig->pos] = append_one(nd_sba_pos[sig->pos],nh);
-      FREENDP(l);
+      if ( nd_hpdata ) {
+        get_eg(&eg1);
+        update_hpdata(&current_hpdata,nh,0);
+        get_eg(&eg2); add_eg(&eg_hpdata,&eg1,&eg2);
+        if ( !compp(CO,final_hpdata.hn,current_hpdata.hn) ) {
+          if ( DP_Print ) { printf("\nWe found a gb.\n"); }
+            break;
+        }
+      }
    } else {
+      d[ind] = d[ind]->next; dlen--;
+      Nnfz++;
       add_eg(&eg_nfzero,&eg1,&eg2);
      // syzygy
 get_eg(&eg1);
-     d = remove_spair_s(d,sig);
+     nsyz = Nsyz;
+     d[sig->pos] = remove_spair_s(d[sig->pos],sig);
+     dlen -= Nsyz-nsyz;
 get_eg(&eg2); add_eg(&eg_remove,&eg1,&eg2);
      syzlist[sig->pos] = insert_sig(syzlist[sig->pos],sig);
      if ( DP_Print ) { printf("."); fflush(stdout); }
-     FREENDP(l);
    }
  }
+ get_eg(&eg4); add_eg(&eg_sbabuch,&eg3,&eg4);
  g = conv_ilist_s(nd_demand,0,indp);
  if ( DP_Print ) { 
-   printf("\nnd_sba done. nd_add=%d,Nsyz=%d,Nredundant=%d\n",Nnd_add,Nsyz,Nredundant);
-   fflush(stdout); 
+   printf("\ndlen=%d,nd_sba done. nd_add=%d,Nsyz=%d,Nsamesig=%d,Nnominimal=%d\n",dlen,Nnd_add,Nsyz,Nsamesig,Nnominimal);
+   printf("Nnfnz=%d,Nnfz=%d,Nnfsingular=%d\n",Nnfnz,Nnfz,Nnfs);
+   fflush(stdout);
+   if ( nd_sba_redundant_check )
+   printf("Nredundant=%d\n",Nredundant);
+   fflush(stdout);
+   print_eg("sp",&eg_sp);
    print_eg("create",&eg_create);
    print_eg("merge",&eg_merge);
+   print_eg("minsig",&eg_minsig);
+   print_eg("smallest",&eg_smallest);
    print_eg("remove",&eg_remove);
+   printf("\n");
    print_eg("nf",&eg_nf);
    print_eg("nfzero",&eg_nfzero);
+   print_eg("removecont",&eg_removecont);
+   print_eg("updatepairs",&eg_updatepairs);
+   print_eg("hpdata",&eg_hpdata);
+   print_eg("total",&eg_sbabuch);
    printf("\n");
  }
+ if ( nd_sba_syz ) {
+   print_eg("remove",&eg_remove);
+   print_eg("nf",&eg_nf);
+   print_eg("nfzero",&eg_nfzero);
+   printf("\n");
+ }
+ if ( nd_sba_syz ) {
+   NODE hsyz,tsyz,prev;
+
+   hsyz = 0;
+   for ( i = 0; i < ngen; i++ ) {
+     tsyz = syzlist[i];
+     for ( prev = 0; tsyz != 0; prev = tsyz, tsyz = NEXT(tsyz))
+       BDY(tsyz) = (pointer)sigtodpm((SIG)BDY(tsyz));
+     if ( prev != 0 ) {
+       prev->next = hsyz; hsyz = syzlist[i];
+     }
+   }
+   *syzp = hsyz;
+ } else *syzp = 0;
  return g;
 }
 
@@ -2752,7 +3251,7 @@ again:
       d = nd_reconstruct(0,d);
       goto again;
     }
-    stat = nd_nf(m,0,h,nd_ps,!Top,&nf);
+    stat = nd_nf(m,0,h,nd_ps,!nd_top&&!Top,&nf);
     if ( !stat ) {
       NEXT(l) = d; d = l;
       d = nd_reconstruct(0,d);
@@ -2889,6 +3388,8 @@ NODE nd_gb_trace(int m,int ishomo,int **indp)
   int diag_count = 0;
   P cont;
   LIST list;
+  struct oHPDATA current_hpdata,final_hpdata;
+  int final_hpvalue;
 
   init_eg(&eg_monic);
   init_eg(&eg_invdalg);
@@ -2899,6 +3400,11 @@ NODE nd_gb_trace(int m,int ishomo,int **indp)
     g = update_base(g,i);
   }
   sugar = 0;
+  if ( nd_hpdata ) {
+    if ( DP_Print ) fprintf(asir_out,"Hilbert driven algorithm.\n");
+    setup_hpdata(&final_hpdata,&current_hpdata);
+  }
+
   while ( d ) {
 again:
     l = nd_minp(d,&d);
@@ -2919,6 +3425,18 @@ again:
 #endif
       sugar = SG(l);
       if ( DP_Print ) fprintf(asir_out,"%d",sugar);
+      if ( nd_hpdata ) {
+        if ( !compp(CO,final_hpdata.hn,current_hpdata.hn) )
+          break;
+        else {
+          final_hpvalue = hpvalue(&final_hpdata,sugar);
+          if ( final_hpvalue == hpvalue(&current_hpdata,sugar) ) {
+//            if ( DP_Print ) fprintf(asir_out,"sugar=%d done.\n",sugar);
+            d = nd_remove_same_sugar(d,sugar);
+            continue;
+          }
+        }
+      }
     }
     stat = nd_sp(m,0,l,&h);
     if ( !stat ) {
@@ -2927,9 +3445,9 @@ again:
       goto again;
     }
 #if USE_GEOBUCKET
-    stat = nd_nf_pbucket(m,h,nd_ps,!Top,&nf);
+    stat = nd_nf_pbucket(m,h,nd_ps,!nd_top&&!Top,&nf);
 #else
-    stat = nd_nf(m,0,h,nd_ps,!Top,&nf);
+    stat = nd_nf(m,0,h,nd_ps,!nd_top&&!Top,&nf);
 #endif
     if ( !stat ) {
       NEXT(l) = d; d = l;
@@ -2942,7 +3460,7 @@ again:
       } else
         nfq = 0;
       if ( !nfq ) {
-        if ( !nd_sp(0,1,l,&h) || !nd_nf(0,0,h,nd_ps_trace,!Top,&nfq) ) {
+        if ( !nd_sp(0,1,l,&h) || !nd_nf(0,0,h,nd_ps_trace,!nd_top&&!Top,&nfq) ) {
           NEXT(l) = d; d = l;
           d = nd_reconstruct(1,d);
           goto again;
@@ -2992,6 +3510,13 @@ again:
         }
         d = update_pairs(d,g,nh,0);
         g = update_base(g,nh);
+        if ( nd_hpdata ) {
+          update_hpdata(&current_hpdata,nh,1);
+          if ( final_hpvalue == hpvalue(&current_hpdata,sugar) ) {
+//            if ( DP_Print ) fprintf(asir_out,"sugar=%d done.\n",sugar);
+            d = nd_remove_same_sugar(d,sugar);
+          }
+        }
       } else {
         if ( DP_Print ) { printf("*"); fflush(stdout); }
       }
@@ -3008,7 +3533,7 @@ again:
     }
   }
   conv_ilist(nd_demand,1,g,indp);
-  if ( DP_Print ) { printf("nd_gb_trace done.\n"); fflush(stdout); }
+  if ( DP_Print ) { printf("\nnd_gb_trace done.\n"); fflush(stdout); }
   return g;
 }
 
@@ -3096,9 +3621,17 @@ NODE ndv_reduceall(int m,NODE f)
   return a0;
 }
 
+int ndplength(ND_pairs d)
+{
+  int i;
+  for ( i = 0; d; i++ ) d = NEXT(d);
+  return i;
+}
+
 ND_pairs update_pairs( ND_pairs d, NODE /* of index */ g, int t, int gensyz)
 {
   ND_pairs d1,nd,cur,head,prev,remove;
+  int len0;
 
   if ( !g ) return d;
   /* for testing */
@@ -3115,8 +3648,10 @@ ND_pairs update_pairs( ND_pairs d, NODE /* of index */
   }
   d = crit_B(d,t);
   d1 = nd_newpairs(g,t);
+  len0 = ndplength(d1); 
   d1 = crit_M(d1);
   d1 = crit_F(d1);
+  NcriMF += len0-ndplength(d1); 
   if ( gensyz || do_weyl )
     head = d1;
   else {
@@ -3126,7 +3661,7 @@ ND_pairs update_pairs( ND_pairs d, NODE /* of index */
         remove = cur;
         if ( !prev ) head = cur = NEXT(cur);
         else cur = NEXT(prev) = NEXT(cur);
-        FREENDP(remove);
+        FREENDP(remove); Ncri2++;
       } else {
         prev = cur; cur = NEXT(cur);
       }
@@ -3158,6 +3693,23 @@ get_eg(&eg3); add_eg(&eg_merge,&eg2,&eg3);
   return d;
 }
 
+int update_pairs_array_s( ND_pairs *d, int t,NODE *syz)
+{
+  ND_pairs *d1;
+  struct oEGT eg1,eg2,eg3;
+  int i;
+
+  if ( !t ) return 0;
+get_eg(&eg1);
+  Nnewpair = 0;
+  d1 = nd_newpairs_array_s(t,syz);
+get_eg(&eg2); add_eg(&eg_create,&eg1,&eg2);
+  for ( i = 0; i < nd_nbase; i++ )
+    d[i] = merge_pairs_s(d[i],d1[i]);
+get_eg(&eg3); add_eg(&eg_merge,&eg2,&eg3);
+  return Nnewpair;
+}
+
 ND_pairs nd_newpairs( NODE g, int t )
 {
   NODE h;
@@ -3181,7 +3733,7 @@ ND_pairs nd_newpairs( NODE g, int t )
       if ( nd_gbblock[i] >= 0 )
         continue;
     }
-    NEXTND_pairs(r0,r);
+    NEXTND_pairs(r0,r); Npairs++;
     r->i1 = (long)BDY(h);
     r->i2 = t;
     ndl_lcm(DL(nd_psh[r->i1]),dl,r->lcm);
@@ -3195,35 +3747,224 @@ ND_pairs nd_newpairs( NODE g, int t )
   return r0;
 }
 
-int comp_sig(SIG s1,SIG s2)
+int sig_cmpdl_op(int n,DL d1,DL d2)
 {
-#if 0
-  if ( s1->pos > s2->pos ) return 1;
-  else if ( s1->pos < s2->pos ) return -1;
-  else return (*cmpdl)(nd_nvar,s1->dl,s2->dl);
-#else
+  int e1,e2,i,j,l;
+  int *t1,*t2;
+  int len,head;
+  struct order_pair *pair;
+
+  len = nd_sba_modord->block_length;
+  pair = nd_sba_modord->order_pair;
+
+  head = 0;
+  for ( i = 0, t1 = d1->d, t2 = d2->d; i < len; i++ ) {
+    l = pair[i].length;
+    switch ( pair[i].order ) {
+      case 0:
+        for ( j = 0, e1 = e2 = 0; j < l; j++ ) {
+          e1 += t1[j];
+          e2 += t2[j];
+        }
+        if ( e1 > e2 )
+          return 1;
+        else if ( e1 < e2 )
+          return -1;
+        else {
+          for ( j = l - 1; j >= 0 && t1[j] == t2[j]; j-- );
+          if ( j >= 0 )
+            return t1[j] < t2[j] ? 1 : -1;
+        }
+        break;
+      case 1:
+        for ( j = 0, e1 = e2 = 0; j < l; j++ ) {
+          e1 += t1[j];
+          e2 += t2[j];
+        }
+        if ( e1 > e2 )
+          return 1;
+        else if ( e1 < e2 )
+          return -1;
+        else {
+          for ( j = 0; j < l && t1[j] == t2[j]; j++ );
+          if ( j < l )
+            return t1[j] > t2[j] ? 1 : -1;
+        }
+        break;
+      case 2:
+        for ( j = 0; j < l && t1[j] == t2[j]; j++ );
+        if ( j < l )
+          return t1[j] > t2[j] ? 1 : -1;
+        break;
+      default:
+        error("sig_cmpdl_op : invalid order"); break;
+    }
+    t1 += l; t2 += l; head += l;
+  }
+  return 0;
+}
+
+int sig_cmpdl_mat(int n,DL d1,DL d2)
+{
+  int *v,*t1,*t2;
+  int s,i,j,len;
+  int **matrix;
+  static int *w;
+  static int nvar = 0;
+
+  if ( nvar != n ) {
+    nvar = n; w = (int *)MALLOC(n*sizeof(int));
+  }
+  for ( i = 0, t1 = d1->d, t2 = d2->d; i < n; i++ )
+    w[i] = t1[i]-t2[i];
+  len = nd_sba_modord->row;
+  matrix = nd_sba_modord->matrix;
+  for ( j = 0; j < len; j++ ) {
+    v = matrix[j];
+    for ( i = 0, s = 0; i < n; i++ )
+      s += v[i]*w[i];
+    if ( s > 0 )
+      return 1;
+    else if ( s < 0 )
+      return -1;
+  }
+  return 0;
+}
+
+struct comp_sig_spec *create_comp_sig_spec(VL current_vl,VL old_vl,Obj ord,Obj weight)
+{
+  struct comp_sig_spec *spec;
+  VL ovl,vl;
+  V ov;
+  int i,j,n,nvar,s;
+  NODE node,t,tn;
+  struct order_pair *l;
+  MAT m;
+  Obj **b;
+  int **w;
+  int *a;
+
+  spec = (struct comp_sig_spec *)MALLOC(sizeof(struct comp_sig_spec));
+  for ( i = 0, vl = current_vl; vl; vl = NEXT(vl), i++ );
+  spec->n = nvar = i;
+  if ( old_vl != 0 ) {
+    spec->oldv = (int *)MALLOC(nvar*sizeof(int));
+    for ( i = 0, ovl = old_vl; i < nvar; ovl = NEXT(ovl), i++ ) {
+      ov = ovl->v;
+      for ( j = 0, vl = current_vl; vl; vl = NEXT(vl), j++ )
+        if ( ov == vl->v ) break;
+      spec->oldv[i] = j;
+    }
+  } else
+    spec->oldv = 0;
+  if ( !ord || NUM(ord) ) {
+    switch ( ZTOS((Z)ord) ) {
+      case 0:
+        spec->cmpdl = cmpdl_revgradlex; break;
+      case 1:
+        spec->cmpdl = cmpdl_gradlex; break;
+      case 2:
+        spec->cmpdl = cmpdl_lex; break;
+      default:
+        error("create_comp_sig_spec : invalid spec"); break;
+    }
+  } else if ( OID(ord) == O_LIST ) {
+    node = BDY((LIST)ord);
+    for ( n = 0, t = node; t; t = NEXT(t), n++ );
+    l = (struct order_pair *)MALLOC_ATOMIC(n*sizeof(struct order_pair));
+    for ( i = 0, t = node, s = 0; i < n; t = NEXT(t), i++ ) {
+      tn = BDY((LIST)BDY(t)); l[i].order = ZTOS((Q)BDY(tn));
+      tn = NEXT(tn); l[i].length = ZTOS((Q)BDY(tn));
+      s += l[i].length;
+    }
+    if ( s != nvar )
+      error("create_comp_sig_spec : invalid spec");
+    spec->order_pair = l;
+    spec->block_length = n;
+    spec->cmpdl = sig_cmpdl_op;
+  } else if ( OID(ord) == O_MAT ) {
+    m = (MAT)ord; b = (Obj **)BDY(m);
+    if ( m->col != nvar )
+      error("create_comp_sig_spec : invalid spec");
+    w = almat(m->row,m->col);
+    for ( i = 0; i < m->row; i++ )
+      for ( j = 0; j < m->col; j++ )
+        w[i][j] = ZTOS((Q)b[i][j]);
+    spec->row = m->row;
+    spec->matrix = w;
+    spec->cmpdl = sig_cmpdl_mat;
+  } else
+    error("create_comp_sig_spec : invalid spec");
+  if ( weight != 0 ) {
+    node = BDY((LIST)weight);
+    a = (int *)MALLOC(nvar*sizeof(int));
+    for ( i = 0; i < nvar; i++, node = NEXT(node) )
+      a[i] = ZTOS((Z)BDY(node));
+    spec->weight = a;
+  }
+  return spec;
+}
+
+#define SIG_MUL_WEIGHT(a,i) (weight?(a)*weight[i]:(a))
+  
+int comp_sig_monomial(int n,DL d1,DL d2)
+{
   static DL m1,m2;
-  static int nvar;
-  int ret;
+  static int nvar = 0;
+  int *oldv,*weight;
+  int i,w1,w2;
+ 
+  if ( nvar != n ) {
+    nvar = n; NEWDL(m1,nvar); NEWDL(m2,nvar);
+  }
+  if ( !nd_sba_modord )
+    return (*cmpdl)(n,d1,d2);
+  else {
+    weight = nd_sba_modord->weight;
+    oldv = nd_sba_modord->oldv;
+    if ( oldv ) {
+      for ( i = 0; i < n; i++ ) {
+        m1->d[i] = d1->d[oldv[i]]; m2->d[i] = d2->d[oldv[i]];
+      }
+    } else {
+      for ( i = 0; i < n; i++ ) {
+        m1->d[i] = d1->d[i]; m2->d[i] = d2->d[i];
+      }
+    }
+    for ( i = 0, w1 = w2 = 0; i < n; i++ ) {
+      w1 += SIG_MUL_WEIGHT(m1->d[i],i); 
+      w2 += SIG_MUL_WEIGHT(m2->d[i],i);
+    }
+    m1->td = w1; m2->td = w2;
+    return (*nd_sba_modord->cmpdl)(n,m1,m2);
+  }
+}
 
-  if ( nvar != nd_nvar ) {
-    nvar = nd_nvar; NEWDL(m1,nvar); NEWDL(m2,nvar);
+int comp_sig(SIG s1,SIG s2)
+{
+  if ( nd_sba_pot ) {
+    if ( s1->pos > s2->pos ) return 1;
+    else if ( s1->pos < s2->pos ) return -1;
+    else return comp_sig_monomial(nd_nvar,s1->dl,s2->dl);
+  } else {
+    static DL m1,m2;
+    static int nvar = 0;
+    int ret;
+  
+    if ( nvar != nd_nvar ) {
+      nvar = nd_nvar; NEWDL(m1,nvar); NEWDL(m2,nvar);
+    }
+    _adddl(nd_nvar,s1->dl,nd_sba_hm[s1->pos],m1);
+    _adddl(nd_nvar,s2->dl,nd_sba_hm[s2->pos],m2);
+    if ( !nd_sba_modord )
+      ret = (*cmpdl)(nd_nvar,m1,m2);
+    else
+      ret = comp_sig_monomial(nd_nvar,m1,m2);
+    if ( ret != 0 ) return ret;
+    else if ( s1->pos > s2->pos ) return 1;
+    else if ( s1->pos < s2->pos ) return -1;
+    else return 0;
   }
-#if 0
-  _copydl(nd_nvar,nd_sba_hm[s1->pos],m1);
-  _copydl(nd_nvar,nd_sba_hm[s2->pos],m2);
-  _addtodl(nd_nvar,s1->dl,m1);
-  _addtodl(nd_nvar,s2->dl,m2);
-#else
-  _adddl(nd_nvar,s1->dl,nd_sba_hm[s1->pos],m1);
-  _adddl(nd_nvar,s2->dl,nd_sba_hm[s2->pos],m2);
-#endif
-  ret = (*cmpdl)(nd_nvar,m1,m2);
-  if ( ret != 0 ) return ret;
-  else if ( s1->pos > s2->pos ) return 1;
-  else if ( s1->pos < s2->pos ) return -1;
-  else return 0;
-#endif
 }
 
 int _create_spair_s(int i1,int i2,ND_pairs sp,SIG sig1,SIG sig2)
@@ -3238,9 +3979,11 @@ int _create_spair_s(int i1,int i2,ND_pairs sp,SIG sig1
   p1 = nd_psh[i1];
   p2 = nd_psh[i2];
   ndl_lcm(DL(p1),DL(p2),sp->lcm);
+#if 0
   s1 = SG(p1)-TD(DL(p1));
   s2 = SG(p2)-TD(DL(p2));
   SG(sp) = MAX(s1,s2) + TD(sp->lcm);
+#endif
 
   if ( wpd != nd_wpd ) {
     wpd = nd_wpd;
@@ -3266,6 +4009,11 @@ int _create_spair_s(int i1,int i2,ND_pairs sp,SIG sig1
   if ( ret == 0 ) return 0;
   else if ( ret > 0 ) sp->sig = sig1;
   else sp->sig = sig2;
+
+  s1 = DL(sig1)->td+nd_sba_hm[p1->sig->pos]->td;
+  s2 = DL(sig2)->td+nd_sba_hm[p2->sig->pos]->td;
+  SG(sp) = MAX(s1,s2);
+
   return 1;
 }
 
@@ -3306,7 +4054,9 @@ ND_pairs merge_pairs_s(ND_pairs p1,ND_pairs p2)
     } else if ( ret > 0 ) {
       r->next = q2; r = q2; q2 = q2->next;
     } else {
+      Nnewpair--;
       ret = DL_COMPARE(q1->lcm,q2->lcm);
+      Nsamesig++;
       if ( ret < 0 ) {
         r->next = q1; r = q1; q1 = q1->next;
         q2 = q2->next;
@@ -3327,7 +4077,7 @@ ND_pairs merge_pairs_s(ND_pairs p1,ND_pairs p2)
 ND_pairs insert_pair_s(ND_pairs l,ND_pairs s)
 {
   ND_pairs p,prev;
-  int ret;
+  int ret=1;
 
   for ( p = l, prev = 0; p != 0; prev = p, p = p->next ) {
     if ( (ret = comp_sig(s->sig,p->sig)) <= 0 )
@@ -3348,6 +4098,7 @@ ND_pairs insert_pair_s(ND_pairs l,ND_pairs s)
       return l;
   } else {
     // insert s between prev and p
+    Nnewpair++;
     s->next = p;
     if ( prev == 0 ) {
       return s;
@@ -3380,7 +4131,7 @@ ND_pairs nd_newpairs_s(int t, NODE *syz)
   int ts,ret,i;
   ND_pairs r,r0,_sp,sp;
   SIG spsig,tsig;
-  static int nvar;
+  static int nvar = 0;
   static SIG _sig1,_sig2;
   struct oEGT eg1,eg2,eg3,eg4;
 
@@ -3409,6 +4160,44 @@ ND_pairs nd_newpairs_s(int t, NODE *syz)
   return r0;
 }
 
+ND_pairs *nd_newpairs_array_s(int t, NODE *syz)
+{
+  NODE h,s;
+  UINT *dl;
+  int ts,ret,i;
+  ND_pairs r,r0,_sp,sp;
+  ND_pairs *d;
+  SIG spsig,tsig;
+  static int nvar = 0;
+  static SIG _sig1,_sig2;
+  struct oEGT eg1,eg2,eg3,eg4;
+
+  NEWND_pairs(_sp);
+  if ( !_sig1 || nvar != nd_nvar ) {
+    nvar = nd_nvar; NEWSIG(_sig1); NEWSIG(_sig2);
+  }
+  d = (ND_pairs *)MALLOC(nd_nbase*sizeof(ND_pairs));
+  Nnewpair = 0;
+  for ( i = 0; i < t; i++ ) {
+    ret = _create_spair_s(i,t,_sp,_sig1,_sig2);
+    if ( ret ) {
+      spsig = _sp->sig;
+      for ( s = syz[spsig->pos]; s; s = s->next ) {
+        tsig = (SIG)s->body;
+        if ( _dl_redble(DL(tsig),DL(spsig),nd_nvar) )
+          break;
+      }
+      if ( s == 0 ) {
+        NEWND_pairs(sp);
+        dup_ND_pairs(sp,_sp);
+        d[spsig->pos] = insert_pair_s(d[spsig->pos],sp);
+      } else
+        Nsyz++;
+    }
+  }
+  return d;
+}
+
 /* ipair = [i1,i2],[i1,i2],... */
 ND_pairs nd_ipairtospair(NODE ipair)
 {
@@ -3459,7 +4248,7 @@ ND_pairs crit_B( ND_pairs d, int s )
           } else {
             cur = NEXT(prev) = NEXT(cur);
           }
-          FREENDP(remove);
+          FREENDP(remove); NcriB++;
         } else {
           prev = cur; cur = NEXT(cur);
         }
@@ -3691,14 +4480,8 @@ ND_pairs nd_minsugarp_s( ND_pairs d, ND_pairs *prest )
   int msugar;
   ND_pairs t,last;
 
-#if 1
   for ( msugar = SG(d), t = d; t; t = NEXT(t) )
     if ( SG(t) == msugar ) last = t;
-#else
-  msugar = (d->sig->dl->td)+nd_sba_hm[d->sig->pos]->td;
-  for ( t = d; t; t = NEXT(t) )
-    if ( ((t->sig->dl->td)+nd_sba_hm[t->sig->pos]->td) == msugar ) last = t;
-#endif
   *prest = last->next;
   last->next = 0;
   return d;
@@ -3785,6 +4568,24 @@ int ndv_newps(int m,NDV a,NDV aq)
     return nd_psn++;
 }
 
+// find LM wrt the specified modord
+void ndv_lm_modord(NDV p,DL d)
+{
+  NMV m;
+  DL tmp;
+  int len,i,ret;
+
+  NEWDL(tmp,nd_nvar);
+  m = BDY(p); len = LEN(p);
+  _ndltodl(DL(m),d); // printdl(d); printf("->");
+  for ( i = 1, NMV_ADV(m); i < len; i++, NMV_ADV(m) ) {
+    _ndltodl(DL(m),tmp);
+    ret = comp_sig_monomial(nd_nvar,tmp,d);
+    if ( ret > 0 ) _copydl(nd_nvar,tmp,d);
+  }
+//   printdl(d); printf("\n");
+}
+
 /* nd_tracelist = [[0,index,div],...,[nd_psn-1,index,div]] */
 /* return 1 if success, 0 if failure (HC(a mod p)) */
 
@@ -3903,7 +4704,10 @@ int ndv_setup(int mod,int trace,NODE f,int dont_sort,i
         if ( nd_demand ) nd_ps_trace_sym[i]->sig = sig;
       }
       NEWDL(nd_sba_hm[i],nd_nvar);
-      _ndltodl(DL(nd_psh[i]),nd_sba_hm[i]);
+      if ( nd_sba_modord )
+        ndv_lm_modord(nd_ps[i],nd_sba_hm[i]);
+      else
+        _ndltodl(DL(nd_psh[i]),nd_sba_hm[i]);
     }
     nd_sba_pos = (NODE *)MALLOC(nd_psn*sizeof(NODE));
     for ( i = 0; i < nd_psn; i++ ) {
@@ -4045,10 +4849,10 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     int obpe,oadv,ompos,cbpe;
     VECT hvect;
 
+    NcriB = NcriMF = Ncri2 = 0;
     nd_module = 0;
     if ( !m && Demand ) nd_demand = 1;
     else nd_demand = 0;
-    parse_nd_option(current_option);
 
     if ( DP_Multiple )
         nd_scale = ((double)DP_Multiple)/(double)(Denominator?Denominator:1);
@@ -4056,6 +4860,7 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     ndv_alloc = 0;
 #endif
     get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+    parse_nd_option(vv,current_option);
     if ( m && nd_vc )
        error("nd_{gr,f4} : computation over Fp(X) is unsupported. Use dp_gr_mod_main().");
     for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
@@ -4101,8 +4906,13 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
                   }
                 }
             } else {
-                e = getdeg(tv->v,(P)BDY(t));
-                max = MAX(e,max);
+                if ( OID(BDY(t)) == O_DP ) {
+                  e = dp_getdeg((DP)BDY(t));
+                  max = MAX(e,max);
+                } else {
+                  e = getdeg(tv->v,(P)BDY(t));
+                  max = MAX(e,max);
+                }
             }
         }
     nd_setup_parameters(nvar,nd_nzlist?0:max);
@@ -4123,9 +4933,17 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
           b = (pointer)pltondv(CO,vv,zpl);
         }
       } else {
-        if ( !m && !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp);
-        else zp = (P)BDY(t);
-        b = (pointer)ptondv(CO,vv,zp);
+        if ( OID(BDY(t)) == O_DP ) {
+          DP zdp;
+
+          if ( !m && !nd_gentrace ) dp_ptozp((DP)BDY(t),&zdp);
+          else zdp = (DP)BDY(t);
+          b = (pointer)dptondv(m,zdp);
+        } else {
+          if ( !m && !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp);
+          else zp = (P)BDY(t);
+          b = (pointer)ptondv(CO,vv,zp);
+        }
       }
       if ( ishomo )
         ishomo = ishomo && ndv_ishomo(b);
@@ -4255,7 +5073,7 @@ NODE nd_sba_f4(int m,int **indp);
 void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int f4,struct order_spec *ord,LIST *rp)
 {
   VL tv,fv,vv,vc,av;
-  NODE fd,fd0,r,r0,t,x,s,xx;
+  NODE fd,fd0,r,r0,t,x,s,xx,nd,syz;
   int e,max,nvar,i;
   NDV b;
   int ishomo,nalg,wmax,len;
@@ -4267,15 +5085,15 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int
   int *perm;
   EPOS oepos;
   int obpe,oadv,ompos,cbpe;
-  struct oEGT eg0,eg1,egconv;
+  struct oEGT eg0,eg1,egconv,egintred;
 
   nd_module = 0;
   nd_demand = 0;
-  parse_nd_option(current_option);
-
+  Nsamesig = 0;
   if ( DP_Multiple )
     nd_scale = ((double)DP_Multiple)/(double)(Denominator?Denominator:1);
   get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+  parse_nd_option(vv,current_option);
   if ( m && nd_vc )
     error("nd_sba : computation over Fp(X) is unsupported. Use dp_gr_mod_main().");
   for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
@@ -4293,17 +5111,30 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int
   initd(ord);
   for ( t = BDY(f), max = 1; t; t = NEXT(t) ) {
     for ( tv = vv; tv; tv = NEXT(tv) ) {
-      e = getdeg(tv->v,(P)BDY(t));
-      max = MAX(e,max);
+      if ( OID(BDY(t)) == O_DP ) {
+        e = dp_getdeg((DP)BDY(t));
+        max = MAX(e,max);
+      } else {
+        e = getdeg(tv->v,(P)BDY(t));
+        max = MAX(e,max);
+      }
     }
   }
   nd_setup_parameters(nvar,max);
   obpe = nd_bpe; oadv = nmv_adv; oepos = nd_epos; ompos = nd_mpos;
   ishomo = 1;
   for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
-    if ( !m ) ptozp((P)BDY(t),1,&dmy,&zp);
-    else zp = (P)BDY(t);
-    b = (pointer)ptondv(CO,vv,zp);
+    if ( OID(BDY(t)) == O_DP ) {
+      DP zdp;
+
+      if ( !m ) dp_ptozp((DP)BDY(t),&zdp);
+      else zdp = (DP)BDY(t);
+      b = (pointer)dptondv(m,zdp);
+    } else {
+      if ( !m ) ptozp((P)BDY(t),1,&dmy,&zp);
+      else zp = (P)BDY(t);
+      b = (pointer)ptondv(CO,vv,zp);
+    }
     if ( ishomo )
       ishomo = ishomo && ndv_ishomo(b);
     if ( m ) ndv_mod(m,b);
@@ -4319,13 +5150,15 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int
       }
       homogenize_order(ord,nvar,&ord1);
       nd_init_ord(ord1);
+      // for SIG comparison
+      initd(ord1);
       nd_setup_parameters(nvar+1,nd_nzlist?0:wmax);
       for ( t = fd0; t; t = NEXT(t) )
         ndv_homogenize((NDV)BDY(t),obpe,oadv,oepos,ompos);
   }
 
-  ndv_setup(m,0,fd0,0,0,1);
-  x = f4 ? nd_sba_f4(m,&perm) : nd_sba_buch(m,ishomo || homo,&perm);
+  ndv_setup(m,0,fd0,nd_sba_dontsort,0,1);
+  x = f4 ? nd_sba_f4(m,&perm) : nd_sba_buch(m,ishomo || homo,&perm,&syz);
   if ( !x ) {
     *rp = 0; return;
   }
@@ -4333,21 +5166,35 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int
        /* dehomogenization */
     for ( t = x; t; t = NEXT(t) ) ndv_dehomogenize((NDV)BDY(t),ord);
     nd_init_ord(ord);
+    // for SIG comparison
+    initd(ord);
     nd_setup_parameters(nvar,0);
   }
   nd_demand = 0;
+  get_eg(&eg0);
   x = ndv_reducebase(x,perm);
   x = ndv_reduceall(m,x);
+  get_eg(&eg1); init_eg(&egintred); add_eg(&egintred,&eg0,&eg1);
   nd_setup_parameters(nd_nvar,0);
   get_eg(&eg0);
   for ( r0 = 0, t = x; t; t = NEXT(t) ) {
     NEXTNODE(r0,r); 
     if ( retdp ) BDY(r) = ndvtodp(m,BDY(t));
-    BDY(r) = ndvtop(m,CO,vv,BDY(t));
+    else BDY(r) = ndvtop(m,CO,vv,BDY(t));
   }
   if ( r0 ) NEXT(r) = 0;
-  MKLIST(*rp,r0);
+  if ( nd_sba_syz ) {
+    LIST gb,hsyz;
+    NODE nd;
+
+    MKLIST(gb,r0);
+    MKLIST(hsyz,syz);
+    nd = mknode(2,gb,hsyz);
+    MKLIST(*rp,nd);
+  } else
+    MKLIST(*rp,r0);
   get_eg(&eg1); init_eg(&egconv); add_eg(&egconv,&eg0,&eg1);
+  print_eg("intred",&egintred); fprintf(asir_out,"\n");
   print_eg("conv",&egconv); fprintf(asir_out,"\n");
 }
 
@@ -4367,8 +5214,8 @@ void nd_gr_postproc(LIST f,LIST v,int m,struct order_s
     struct order_spec *ord1;
     int *perm;
 
-    parse_nd_option(current_option);
     get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+    parse_nd_option(vv,current_option);
     for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
     switch ( ord->id ) {
         case 1:
@@ -4515,8 +5362,8 @@ void nd_gr_recompute_trace(LIST f,LIST v,int m,struct 
   int len,n,j;
   NDV *db,*pb;
 
-    parse_nd_option(current_option);
     get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+    parse_nd_option(vv,current_option);
     for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
     switch ( ord->id ) {
         case 1:
@@ -4612,9 +5459,11 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     Z jq,bpe;
     VECT hvect;
 
+    NcriB = NcriMF = Ncri2 = 0;
     nd_module = 0;
     nd_lf = 0;
-    parse_nd_option(current_option);
+    get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+    parse_nd_option(vv,current_option);
     if ( nd_lf ) {
       if ( f4 )
         nd_f4_lf_trace(f,v,trace,homo,ord,rp);
@@ -4625,7 +5474,6 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     if ( DP_Multiple )
         nd_scale = ((double)DP_Multiple)/(double)(Denominator?Denominator:1);
 
-    get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
     for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
     switch ( ord->id ) {
         case 1:
@@ -4679,8 +5527,13 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
                 }
               }
             } else {
+              if ( OID(BDY(t)) == O_DP ) {
+                e = dp_getdeg((DP)BDY(t));
+                max = MAX(e,max);
+              } else {
                 e = getdeg(tv->v,(P)BDY(t));
                 max = MAX(e,max);
+              }
             }
         }
     nd_setup_parameters(nvar,max);
@@ -4701,9 +5554,17 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
             c = (pointer)pltondv(CO,vv,zpl);
           }
         } else {
-          if ( !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp);
-          else zp = (P)BDY(t);
-          c = (pointer)ptondv(CO,vv,zp);
+          if ( OID(BDY(t)) == O_DP ) {
+            DP zdp;
+
+            if ( !nd_gentrace ) dp_ptozp((DP)BDY(t),&zdp);
+            else zdp = (DP)BDY(t);
+            c = (pointer)dptondv(m,zdp);
+          } else {
+            if ( !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp);
+            else zp = (P)BDY(t);
+            c = (pointer)ptondv(CO,vv,zp);
+          }
         }
         if ( ishomo )
             ishomo = ishomo && ndv_ishomo(c);
@@ -4864,7 +5725,7 @@ DL ndltodl(int n,UINT *ndl)
     int i,j,l,s,ord_l;
     struct order_pair *op;
 
-    NEWDL(dl,n);
+    NEWDL_NOINIT(dl,n);
     dl->td = TD(ndl);
     d = dl->d;
     if ( nd_blockmask ) {
@@ -5439,8 +6300,10 @@ int nd_get_exporigin(struct order_spec *ord)
 void nd_setup_parameters(int nvar,int max) {
     int i,j,n,elen,ord_o,ord_l,l,s,wpd;
     struct order_pair *op;
+    extern int CNVars;
 
     nd_nvar = nvar;
+    CNVars = nvar;
     if ( max ) {
         /* XXX */
         if ( do_weyl ) nd_bpe = 32;
@@ -5641,6 +6504,7 @@ void nd_reconstruct_s(int trace,ND_pairs *d)
           SG(s) = SG(t);
           ndl_reconstruct(LCM(t),LCM(s),obpe,oepos);
       }
+      if ( s0 ) NEXT(s) = 0;
       d[i] = s0;
     }
     
@@ -6356,7 +7220,7 @@ ND ptond(VL vl,VL dvl,P p)
     else if ( NUM(p) ) {
         NEWNM(m);
         ndl_zero(DL(m));
-        if ( !INT((Q)p) )
+        if ( RATN(p) && !INT((Q)p) )
           error("ptond : input must be integer-coefficient");
         CZ(m) = (Z)p;
         NEXT(m) = 0;
@@ -6570,6 +7434,32 @@ int nmv_comp(NMV a,NMV b)
   return -t;
 }
 
+NDV dptondv(int mod,DP p)
+{
+  NDV d;
+  NMV m,m0;
+  MP t;
+  MP *a;
+  int i,len,n;
+
+  if ( !p ) return 0;
+  for ( t = BDY(p), len = 0; t; t = NEXT(t), len++ );
+  n = p->nv;
+  if ( mod > 0 || mod == -1 )
+    m0 = m = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(len*nmv_adv);
+  else
+    m0 = m = MALLOC(len*nmv_adv);
+  for ( i = 0, t = BDY(p); i < len; i++, NMV_ADV(m), t = NEXT(t) ) {
+    dltondl(n,t->dl,DL(m));
+    TD(DL(m)) = ndl_weight(DL(m));
+    CZ(m) = (Z)t->c;
+  }
+  qsort(m0,len,nmv_adv,(int (*)(const void *,const void *))nmv_comp);
+  MKNDV(NV(p),m0,len,d);
+  SG(d) = SG(p);
+  return d;
+}
+
 NDV dpmtondv(int mod,DPM p)
 {
   NDV d;
@@ -6646,6 +7536,21 @@ DP ndvtodp(int mod,NDV p)
     return d;
 }
 
+DPM sigtodpm(SIG s)
+{
+  DMM m;
+  DPM d;
+
+  NEWDMM(m); 
+  m->c = (Obj)ONE;
+  m->dl = s->dl;
+  m->pos = s->pos+1;
+  m->next = 0;
+  MKDPM(nd_nvar,m,d);
+  SG(d) = s->dl->td;
+  return d;
+}
+
 DPM ndvtodpm(int mod,NDV p)
 {
   DMM m,m0;
@@ -6731,6 +7636,7 @@ NODE ndv_reducebase(NODE x,int *perm)
     NDVI w;
     NODE t,t0;
 
+    if ( nd_norb ) return x;
     len = length(x);
     w = (NDVI)MALLOC(len*sizeof(struct oNDVI));
     for ( i = 0, t = x; i < len; i++, t = NEXT(t) ) {
@@ -7406,7 +8312,7 @@ int ndv_reduce_vect_q(Z *svect0,int trace,int col,IndA
 }
 #endif
 
-int ndv_reduce_vect(int m,UINT *svect,int col,IndArray *imat,NM_ind_pair *rp0,int nred)
+int ndv_reduce_vect(int m,UINT *svect,int col,IndArray *imat,NM_ind_pair *rp0,int nred,SIG sig)
 {
     int i,j,k,len,pos,prev;
     UINT c,c1,c2,c3,up,lo,dmy;
@@ -7423,7 +8329,7 @@ int ndv_reduce_vect(int m,UINT *svect,int col,IndArray
     for ( i = 0; i < nred; i++ ) {
         ivect = imat[i];
         k = ivect->head; svect[k] %= m;
-        if ( (c = svect[k]) != 0 ) {
+        if ( (c = svect[k]) != 0 && (sig == 0 || comp_sig(sig,rp0[i]->sig) > 0 ) ) {
             maxrs = MAX(maxrs,rp0[i]->sugar);
             c = m-c; redv = nd_ps[rp0[i]->index];
             len = LEN(redv); mr = BDY(redv);
@@ -7433,12 +8339,12 @@ int ndv_reduce_vect(int m,UINT *svect,int col,IndArray
                     ivc = ivect->index.c;
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivc[j]; c1 = CM(mr); prev = pos;
-            if ( c1 ) {
-              c2 = svect[pos];
+                        if ( c1 ) {
+                          c2 = svect[pos];
                           DMA(c1,c,c2,up,lo);
                           if ( up ) { DSAB(m,up,lo,dmy,c3); svect[pos] = c3;
                           } else svect[pos] = lo;
-            }
+                        }
                     }
                     break;
                 case 2:
@@ -7446,12 +8352,12 @@ int ndv_reduce_vect(int m,UINT *svect,int col,IndArray
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivs[j]; c1 = CM(mr);
                         prev = pos;
-            if ( c1 ) {
-              c2 = svect[pos];
+                        if ( c1 ) {
+                          c2 = svect[pos];
                           DMA(c1,c,c2,up,lo);
                           if ( up ) { DSAB(m,up,lo,dmy,c3); svect[pos] = c3;
                           } else svect[pos] = lo;
-            }
+                        }
                     }
                     break;
                 case 4:
@@ -7459,12 +8365,12 @@ int ndv_reduce_vect(int m,UINT *svect,int col,IndArray
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivi[j]; c1 = CM(mr);
                         prev = pos;
-            if ( c1 ) {
-              c2 = svect[pos];
+                        if ( c1 ) {
+                          c2 = svect[pos];
                           DMA(c1,c,c2,up,lo);
                           if ( up ) { DSAB(m,up,lo,dmy,c3); svect[pos] = c3;
                           } else svect[pos] = lo;
-            }
+                        }
                     }
                     break;
             }
@@ -7732,6 +8638,29 @@ NDV vect_to_ndv(UINT *vect,int spcol,int col,int *rhea
     }
 }
 
+NDV vect_to_ndv_s(UINT *vect,int col,UINT *s0vect)
+{
+    int j,k,len;
+    UINT *p;
+    UINT c;
+    NDV r;
+    NMV mr0,mr;
+
+    for ( j = 0, len = 0; j < col; j++ ) if ( vect[j] ) len++;
+    if ( !len ) return 0;
+    else {
+        mr0 = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(nmv_adv*len);
+        mr = mr0; 
+        p = s0vect;
+        for ( j = k = 0; j < col; j++, p += nd_wpd )
+          if ( (c = vect[k++]) != 0 ) {
+            ndl_copy(p,DL(mr)); CM(mr) = c; NMV_ADV(mr);
+          }
+        MKNDV(nd_nvar,mr0,len,r);
+        return r;
+    }
+}
+
 NDV vect_to_ndv_2(unsigned long *vect,int col,UINT *s0vect)
 {
     int j,k,len;
@@ -7998,6 +8927,7 @@ NODE nd_f4(int m,int checkonly,int **indp)
         if ( nflist ) nd_last_nonzero = f4red;
         for ( r = nflist; r; r = NEXT(r) ) {
             nf = (NDV)BDY(r);
+            if ( nd_f4_td ) SG(nf) = nd_tdeg(nf);
             ndv_removecont(m,nf);
             if ( !m && nd_nalg ) {
                 ND nf1;
@@ -8041,6 +8971,7 @@ NODE nd_f4(int m,int checkonly,int **indp)
     fprintf(asir_out,"number of red=%d,",Nf4_red);
     fprintf(asir_out,"symb=%.3fsec,conv=%.3fsec,elim1=%.3fsec,elim2=%.3fsec\n",
       f4_symb.exectime,f4_conv.exectime,f4_elim1.exectime,f4_elim2.exectime);
+    fprintf(asir_out,"number of removed pairs=%d\n,",NcriB+NcriMF+Ncri2);
   }
   conv_ilist(nd_demand,0,g,indp);
     return g;
@@ -8402,7 +9333,7 @@ NODE nd_f4_red_main(int m,ND_pairs sp0,int nsp,UINT *s
         if ( m == -1 ) 
             maxrs = ndv_reduce_vect_sf(m,svect,col,imat,rvect,nred);
         else
-            maxrs = ndv_reduce_vect(m,svect,col,imat,rvect,nred);
+            maxrs = ndv_reduce_vect(m,svect,col,imat,rvect,nred,0);
         for ( i = 0; i < col; i++ ) if ( svect[i] ) break;
         if ( i < col ) {
             spmat[sprow] = v = (UINT *)MALLOC_ATOMIC(spcol*sizeof(UINT));
@@ -8458,7 +9389,84 @@ NODE nd_f4_red_main(int m,ND_pairs sp0,int nsp,UINT *s
     return r0;
 }
 
+NODE nd_f4_red_main_s(int m,ND_pairs sp0,int nsp,UINT *s0vect,int col,
+        NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred,NODE *syzlistp)
+{
+    int spcol,sprow,a;
+    int i,j,k,l,rank;
+    NODE r0,r;
+    ND_pairs sp;
+    ND spol;
+    UINT **spmat;
+    UINT *svect,*cvect;
+    UINT *v;
+    int *colstat;
+    struct oEGT eg0,eg1,eg2,eg_f4,eg_f4_1,eg_f4_2;
+    int maxrs;
+    int *spsugar;
+    ND_pairs *spactive;
+    SIG *spsig;
 
+    get_eg(&eg0);
+    /* elimination (1st step) */
+    spmat = (UINT **)MALLOC(nsp*sizeof(UINT *));
+    spsugar = (int *)MALLOC(nsp*sizeof(int));
+    spsig = (SIG *)MALLOC(nsp*sizeof(SIG));
+    for ( a = sprow = 0, sp = sp0; a < nsp; a++, sp = NEXT(sp) ) {
+        nd_sp(m,0,sp,&spol);
+        if ( !spol ) {
+          syzlistp[sp->sig->pos] = insert_sig(syzlistp[sp->sig->pos],sp->sig);
+          continue;
+        }
+        svect = (UINT *)MALLOC(col*sizeof(UINT));
+        nd_to_vect(m,s0vect,col,spol,svect);
+        maxrs = ndv_reduce_vect(m,svect,col,imat,rvect,nred,spol->sig);
+        for ( i = 0; i < col; i++ ) if ( svect[i] ) break;
+        if ( i < col ) {
+            spmat[sprow] = svect;
+            spsugar[sprow] = MAX(maxrs,SG(spol));
+            spsig[sprow] = sp->sig;
+            sprow++;
+        } else {
+          syzlistp[sp->sig->pos] = insert_sig(syzlistp[sp->sig->pos],sp->sig);
+        }
+        nd_free(spol);
+    }
+    get_eg(&eg1); init_eg(&eg_f4_1); add_eg(&eg_f4_1,&eg0,&eg1); add_eg(&f4_elim1,&eg0,&eg1);
+    if ( DP_Print ) {
+        fprintf(asir_out,"elim1=%.3fsec,",eg_f4_1.exectime);
+        fflush(asir_out);
+    }
+    /* free index arrays */
+    for ( i = 0; i < nred; i++ ) GCFREE(imat[i]->index.c);
+
+    /* elimination (2nd step) */
+    colstat = (int *)MALLOC(col*sizeof(int));
+    rank = nd_gauss_elim_mod_s(spmat,spsugar,0,sprow,col,m,colstat,spsig);
+    r0 = 0;
+    for ( i = 0; i < sprow; i++ ) {
+        if ( spsugar[i] >= 0 ) {
+          NEXTNODE(r0,r);
+          BDY(r) = vect_to_ndv_s(spmat[i],col,s0vect);
+          SG((NDV)BDY(r)) = spsugar[i];
+          ((NDV)BDY(r))->sig = spsig[i];
+        } else
+          syzlistp[spsig[i]->pos] = insert_sig(syzlistp[spsig[i]->pos],spsig[i]);
+        GCFREE(spmat[i]);
+    }
+    if ( r0 ) NEXT(r) = 0;
+    get_eg(&eg2); init_eg(&eg_f4_2); add_eg(&eg_f4_2,&eg1,&eg2); add_eg(&f4_elim2,&eg1,&eg2);
+    init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg2);
+    if ( DP_Print ) {
+        fprintf(asir_out,"elim2=%.3fsec,",eg_f4_2.exectime);
+        fprintf(asir_out,"nsp=%d,nred=%d,spmat=(%d,%d),rank=%d ",
+            nsp,nred,sprow,col,rank);
+        fprintf(asir_out,"%.3fsec,",eg_f4.exectime);
+    }
+    return r0;
+}
+
+
 /* for small finite fields */
 
 NODE nd_f4_red_sf_main(int m,ND_pairs sp0,int nsp,UINT *s0vect,int col,
@@ -8870,7 +9878,57 @@ int nd_gauss_elim_mod(UINT **mat0,int *sugar,ND_pairs 
     return rank;
 }
 
+int nd_gauss_elim_mod_s(UINT **mat,int *sugar,ND_pairs *spactive,int row,int col,int md,int *colstat,SIG *sig)
+{
+  int i,j,k,l,rank,s,imin;
+  UINT inv;
+  UINT a;
+  UINT *t,*pivot,*pk;
+  UINT *ck;
+  UINT *ct;
+  ND_pairs pair;
+  SIG sg;
+  int *used;
 
+  used = (int *)MALLOC(row*sizeof(int));
+  for ( j = 0; j < col; j++ ) {
+    for ( i = 0; i < row; i++ )
+      a = mat[i][j] %= md;
+    for ( i = 0; i < row; i++ )
+      if ( !used[i] && mat[i][j] ) break;
+    if ( i == row ) {
+      colstat[j] = 0;
+      continue;
+    } else {
+      colstat[j] = 1;
+      used[i] = 1;
+    }
+    /* column j is normalized */
+    s = sugar[i];
+    inv = invm(mat[i][j],md);
+    /* normalize pivot row */
+    for ( k = j, pk = mat[i]+j; k < col; k++, pk++, ck++ ) {
+      DMAR(*pk,inv,0,md,*pk);
+    }
+    for ( k = i+1; k < row; k++ ) {
+      if ( (a = mat[k][j]) != 0 ) {
+        sugar[k] = MAX(sugar[k],s);
+        red_by_vect(md,mat[k]+j,mat[i]+j,(int)(md-a),col-j);
+        Nf4_red++;
+      }
+    }
+  }
+  rank = 0;
+  for ( i = 0; i < row; i++ ) {
+    for ( j = 0; j < col; j++ )
+      if ( mat[i][j] ) break;
+    if ( j == col ) sugar[i] = -1;
+    else rank++;
+  }
+  return rank;
+}
+
+
 int nd_gauss_elim_sf(UINT **mat0,int *sugar,int row,int col,int md,int *colstat)
 {
     int i,j,k,l,inv,a,rank,s;
@@ -9565,41 +10623,47 @@ NODE conv_ilist_s(int demand,int trace,int **indp)
   return g0;
 }
 
-void parse_nd_option(NODE opt)
+void parse_nd_option(VL vl,NODE opt)
 {
-    NODE t,p,u;
+  NODE t,p,u;
   int i,s,n;
-    char *key;
-    Obj value;
+  char *key;
+  Obj value;
+  VL oldvl;
 
-    nd_gentrace = 0; nd_gensyz = 0; nd_nora = 0; nd_gbblock = 0;
+  nd_gentrace = 0; nd_gensyz = 0; nd_nora = 0; nd_norb = 0; nd_gbblock = 0;
   nd_newelim = 0; nd_intersect = 0; nd_nzlist = 0;
   nd_splist = 0; nd_check_splist = 0;
-    nd_sugarweight = 0;
-    nd_f4red =0;
-    nd_rank0 = 0;
-    for ( t = opt; t; t = NEXT(t) ) {
-        p = BDY((LIST)BDY(t));
-        key = BDY((STRING)BDY(p));
-        value = (Obj)BDY(NEXT(p));
-        if ( !strcmp(key,"gentrace") )
-            nd_gentrace = value?1:0;
-        else if ( !strcmp(key,"gensyz") )
-            nd_gensyz = value?1:0;
-        else if ( !strcmp(key,"nora") )
-            nd_nora = value?1:0;
-        else if ( !strcmp(key,"gbblock") ) {
-            if ( value && OID(value) == O_LIST ) {
+  nd_sugarweight = 0; nd_f4red =0; nd_rank0 = 0;
+  nd_f4_td = 0; nd_sba_f4step = 2; nd_sba_pot = 0; nd_sba_largelcm = 0;
+  nd_sba_dontsort = 0; nd_top = 0; nd_sba_redundant_check = 0;
+  nd_sba_syz = 0; nd_sba_modord = 0; nd_sba_inputisgb = 0;
+  nd_hpdata = 0;
+
+  for ( t = opt; t; t = NEXT(t) ) {
+    p = BDY((LIST)BDY(t));
+    key = BDY((STRING)BDY(p));
+    value = (Obj)BDY(NEXT(p));
+    if ( !strcmp(key,"gentrace") )
+      nd_gentrace = value?1:0;
+    else if ( !strcmp(key,"gensyz") )
+      nd_gensyz = value?1:0;
+    else if ( !strcmp(key,"nora") )
+      nd_nora = value?1:0;
+    else if ( !strcmp(key,"norb") )
+      nd_norb = value?1:0;
+    else if ( !strcmp(key,"gbblock") ) {
+      if ( value && OID(value) == O_LIST ) {
         u = BDY((LIST)value);
-              nd_gbblock = MALLOC((2*length(u)+1)*sizeof(int));
+        nd_gbblock = MALLOC((2*length(u)+1)*sizeof(int));
         for ( i = 0; u; u = NEXT(u) ) {
           p = BDY((LIST)BDY(u));
           s = nd_gbblock[i++] = ZTOS((Q)BDY(p));
           nd_gbblock[i++] = s+ZTOS((Q)BDY(NEXT(p)))-1;
         }
         nd_gbblock[i] = -1;
-            } else
-              nd_gbblock = 0;
+      } else
+        nd_gbblock = 0;
     } else if ( !strcmp(key,"newelim") )
             nd_newelim = value?1:0;
     else if ( !strcmp(key,"intersect") )
@@ -9609,27 +10673,60 @@ void parse_nd_option(NODE opt)
     else if ( !strcmp(key,"lf") )
             nd_lf = value?1:0;
     else if ( !strcmp(key,"trace") ) {
-           if ( value ) {
-               u = BDY((LIST)value);
-           nd_nzlist = BDY((LIST)ARG2(u));
-           nd_bpe = ZTOS((Q)ARG3(u));
-           }
+      if ( value ) {
+        u = BDY((LIST)value);
+        nd_nzlist = BDY((LIST)ARG2(u));
+        nd_bpe = ZTOS((Q)ARG3(u));
+      }
     } else if ( !strcmp(key,"f4red") ) {
-       nd_f4red = ZTOS((Q)value);
+      nd_f4red = ZTOS((Q)value);
     } else if ( !strcmp(key,"rank0") ) {
-            nd_rank0 = value?1:0;
+      nd_rank0 = value?1:0;
     } else if ( !strcmp(key,"splist") ) {
-            nd_splist = value?1:0;
+      nd_splist = value?1:0;
     } else if ( !strcmp(key,"check_splist") ) {
       nd_check_splist = BDY((LIST)value);
+    } else if ( !strcmp(key,"hpdata") ) {
+      if ( value )
+        nd_hpdata = BDY((LIST)value);
     } else if ( !strcmp(key,"sugarweight") ) {
       u = BDY((LIST)value);
-            n = length(u);
-            nd_sugarweight = MALLOC(n*sizeof(int));
+      n = length(u);
+      nd_sugarweight = MALLOC(n*sizeof(int));
       for ( i = 0; i < n; i++, u = NEXT(u) ) 
-                nd_sugarweight[i] = ZTOS((Q)BDY(u));
+        nd_sugarweight[i] = ZTOS((Q)BDY(u));
+    } else if ( !strcmp(key,"f4_td") ) {
+      nd_f4_td = value?1:0;
+    } else if ( !strcmp(key,"sba_f4step") ) {
+      nd_sba_f4step = value?ZTOS((Q)value):0;
+    } else if ( !strcmp(key,"sba_pot") ) {
+      nd_sba_pot = ZTOS((Q)value);
+    } else if ( !strcmp(key,"sba_largelcm") ) {
+      nd_sba_largelcm = value?1:0;
+    } else if ( !strcmp(key,"sba_dontsort") ) {
+      nd_sba_dontsort = value?1:0;
+    } else if ( !strcmp(key,"sba_syz") ) {
+      nd_sba_syz = value?1:0;
+    } else if ( !strcmp(key,"sba_modord") ) {
+      // value=[vlist,ordspec,weight]
+      u = BDY((LIST)value);
+      pltovl((LIST)ARG0(u),&oldvl);
+      nd_sba_modord = create_comp_sig_spec(vl,oldvl,(Obj)ARG1(u),argc(u)==3?ARG2(u):0);
+    } else if ( !strcmp(key,"sba_gbinput") ) {
+      nd_sba_inputisgb = value?1:0;
+      if ( nd_sba_inputisgb != 0 ) {
+        // value=[vlist,ordspec,weight]
+        u = BDY((LIST)value);
+        pltovl((LIST)ARG0(u),&oldvl);
+        nd_sba_modord = create_comp_sig_spec(vl,oldvl,(Obj)ARG1(u),argc(u)==3?ARG2(u):0);
+      }
+    } else if ( !strcmp(key,"sba_redundant_check") ) {
+      nd_sba_redundant_check = value?1:0;
+    } else if ( !strcmp(key,"top") ) {
+      nd_top = value?1:0;
     }
-    }
+  }
+  if ( nd_sba_syz ) nd_sba_dontsort = 1;
 }
 
 ND mdptond(DP d);
@@ -9834,8 +10931,8 @@ MAT nd_btog(LIST f,LIST v,int mod,struct order_spec *o
   if ( mod == -2 )
     return nd_btog_lf(f,v,ord,tlist,rp);
 
-  parse_nd_option(current_option);
   get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+  parse_nd_option(vv,current_option);
   for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
   switch ( ord->id ) {
     case 1:
@@ -9903,8 +11000,8 @@ MAT nd_btog_lf(LIST f,LIST v,struct order_spec *ord,LI
   LM lm;
   Z lf,inv;
 
-  parse_nd_option(current_option);
   get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+  parse_nd_option(vv,current_option);
   for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
   switch ( ord->id ) {
     case 1:
@@ -9974,8 +11071,8 @@ VECT nd_btog_one(LIST f,LIST v,int mod,struct order_sp
   if ( mod == -2 )
     error("nd_btog_one : not implemented yet for a large finite field");
 
-  parse_nd_option(current_option);
   get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+  parse_nd_option(vv,current_option);
   for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
   switch ( ord->id ) {
     case 1:
@@ -10088,8 +11185,8 @@ void nd_f4_lf_trace(LIST f,LIST v,int trace,int homo,s
     Q jq,bpe;
 
     nd_module = 0;
-    parse_nd_option(current_option);
     get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+    parse_nd_option(vv,current_option);
     if ( nd_vc )
       error("nd_f4_lf_trace : computation over a rational function field is not implemented");
     for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
@@ -10594,7 +11691,6 @@ int nd_gauss_elim_mod64(mp_limb_t **mat,int *sugar,ND_
   GCFREE(cmat);
   return rank;
 }
-#endif
 
 int nd_gauss_elim_mod64_s(mp_limb_t **mat,int *sugar,ND_pairs *spactive,int row,int col,int md,int *colstat,SIG *sig)
 {
@@ -10736,6 +11832,7 @@ NODE nd_f4_red_mod64_main_s(int m,ND_pairs sp0,int nsp
     }
     return r0;
 }
+#endif
 
 NODE nd_f4_red_s(int m,ND_pairs sp0,int trace,UINT *s0vect,int col,NODE rp0,NODE *syzlistp)
 {
@@ -10774,7 +11871,11 @@ NODE nd_f4_red_s(int m,ND_pairs sp0,int trace,UINT *s0
     fflush(asir_out);
   }
   if ( m > 0 )
+#if SIZEOF_LONG==8
     r0 = nd_f4_red_mod64_main_s(m,sp0,nsp,s0vect,col,rvect,rhead,imat,nred,syzlistp);
+#else
+    r0 = nd_f4_red_main_s(m,sp0,nsp,s0vect,col,rvect,rhead,imat,nred,syzlistp);
+#endif
   else
 //    r0 = nd_f4_red_q_main_s(sp0,nsp,trace,s0vect,col,rvect,rhead,imat,nred);
     error("nd_f4_red_q_main_s : not implemented yet");
@@ -10881,28 +11982,20 @@ int nd_symbolic_preproc_s(PGeoBucket bucket,int trace,
 
 NODE nd_sba_f4(int m,int **indp)
 {
-  int i,nh,stat,index,f4red;
-  NODE r,g,tn0,tn,node;
-  ND_pairs d,l,t,ll0,ll,lh;
-  LIST l0,l1;
-  ND spol,red;
-  NDV nf,redv;
-  NM s0,s;
-  NODE rp0,srp0,nflist;
-  int nsp,nred,col,rank,len,k,j,a,i1s,i2s;
+  int i,nh,stat,index,f4red,f4step;
+  int col,rank,len,k,j,a,sugar,nbase,psugar,ms;
+  NODE r,g,rp0,nflist;
+  ND_pairs d,l,t,l1;
+  ND h,nf;
+  NDV nfv;
+  union oNDC hc;
+  UINT *s0vect;
   UINT c;
-  UINT **spmat;
-  UINT *s0vect,*svect,*p,*v;
-  int *colstat;
-  IndArray *imat;
-  int *rhead;
-  int spcol,sprow;
-  int sugar,sugarh;
-  int nbase;
   PGeoBucket bucket;
-  struct oEGT eg0,eg1,eg_f4;
-  Z i1,i2,sugarq;
   NODE *syzlist;
+  SIG sig;
+  struct oEGT eg0,eg1,eg_f4;
+  struct oEGT eg2,eg_update,eg_remove,eg_large,eg_nf,eg_nfzero;
 
   Nf4_red=0;
   d = 0;
@@ -10912,76 +12005,117 @@ NODE nd_sba_f4(int m,int **indp)
   }
   nd_nbase = nd_psn;
   f4red = 1;
+  psugar = 0;
+  f4step = 0;
   while ( d ) {
-    l = nd_minsugarp_s(d,&d);
-    if ( !l ) continue;
-    sugar = nd_sugarweight?l->sugar2:SG(l);
-    if ( MaxDeg > 0 && sugar > MaxDeg ) break;
-    bucket = create_pbucket();
-    stat = nd_sp_f4(m,0,l,bucket);
-    if ( !stat ) {
-      for ( t = l; NEXT(t); t = NEXT(t) );
-      NEXT(t) = d; d = l;
-      d = nd_reconstruct(0,d);
-      continue;
-    }
-    if ( bucket->m < 0 ) continue;
-    col = nd_symbolic_preproc_s(bucket,0,&s0vect,&rp0);
-    if ( !col ) {
-      for ( t = l; NEXT(t); t = NEXT(t) );
-      NEXT(t) = d; d = l;
-      d = nd_reconstruct(0,d);
-      continue;
-    }
-    if ( DP_Print ) fprintf(asir_out,"sugar=%d,",sugar);
-    l = remove_large_lcm(l);
-    nflist = nd_f4_red_s(m,l,0,s0vect,col,rp0,syzlist);
-    /* adding new bases */
-    for ( r = nflist; r; r = NEXT(r) ) {
+    for ( t = d, ms = SG(d); t; t = NEXT(t) )
+      if ( SG(t) < ms ) ms = SG(t);
+    if ( ms == psugar && f4step >= nd_sba_f4step ) {
+again:
+      l = d; d = d->next;
 #if 0
-      ND tmp,tmpred;
-      SIG sig;
-
-      nf = (NDV)BDY(r);
-      sig = nf->sig;
-      tmp = ndvtond(m,nf);
-      stat = nd_nf_s(m,0,tmp,nd_ps,!Top,&tmpred);
-#if 0
-      if ( stat < 0 ) {
-        // top reducible
-        if ( DP_Print ) { fprintf(asir_out,"S"); fflush(asir_out); }
-      } else if ( tmpred ) {
+      if ( small_lcm(l) ) {
+        if ( DP_Print ) fprintf(asir_out,"M");
+        continue;
+      }
+      sig = l->sig;
+      stat = nd_sp(m,0,l,&h);
 #else
-      if ( tmpred ) {
+      l1 = find_smallest_lcm(l);
+      if ( l1 == 0 ) {
+        if ( DP_Print ) fprintf(asir_out,"M");
+        continue;
+      }
+      sig = l1->sig;
+      stat = nd_sp(m,0,l1,&h);
 #endif
-        nf = ndtondv(m,tmpred);
-        ndv_removecont(m,nf);
-        nh = ndv_newps(m,nf,0);
+      if ( !stat ) {
+        NEXT(l) = d; d = l;
+        d = nd_reconstruct(0,d);
+        goto again;
+      }
+  get_eg(&eg1);
+  #if USE_GEOBUCKET
+      stat = m?nd_nf_pbucket_s(m,h,nd_ps,!nd_top&&!Top,&nf):nd_nf_s(m,0,h,nd_ps,!nd_top&&!Top,&nf);
+  #else
+      stat = nd_nf_s(m,0,h,nd_ps,!nd_top&&!Top,&nf);
+  #endif
+  get_eg(&eg2); 
+      if ( !stat ) {
+        NEXT(l) = d; d = l;
+        d = nd_reconstruct(0,d);
+        goto again;
+      } else if ( stat == -1 ) {
+        if ( DP_Print ) { printf("S"); fflush(stdout); }
+        FREENDP(l);
+      } else if ( nf ) {
+        if ( DP_Print ) { printf("+"); fflush(stdout); }
+        add_eg(&eg_nf,&eg1,&eg2);
+        hc = HCU(nf);
+        nd_removecont(m,nf);
+        nfv = ndtondv(m,nf); nd_free(nf);
+        nh = ndv_newps(m,nfv,0);
+  
         d = update_pairs_s(d,nh,syzlist);
         nd_sba_pos[sig->pos] = append_one(nd_sba_pos[sig->pos],nh);
+        FREENDP(l);
       } else {
+        add_eg(&eg_nfzero,&eg1,&eg2);
+       // syzygy
+  get_eg(&eg1);
+        d = remove_spair_s(d,sig);
+  get_eg(&eg2); add_eg(&eg_remove,&eg1,&eg2);
         syzlist[sig->pos] = insert_sig(syzlist[sig->pos],sig);
-      } 
-#else
-      nf = (NDV)BDY(r);
-      ndv_removecont(m,nf);
-      nh = ndv_newps(m,nf,0);
-      d = update_pairs_s(d,nh,syzlist);
-      nd_sba_pos[nf->sig->pos] = append_one(nd_sba_pos[nf->sig->pos],nh);
-#endif
+        if ( DP_Print ) { printf("."); fflush(stdout); }
+        FREENDP(l);
+      }
+    } else {
+      if ( ms != psugar ) f4step = 1;
+      else f4step++;
+again2:
+      psugar = ms;
+      l = nd_minsugarp_s(d,&d);
+      sugar = nd_sugarweight?d->sugar2:SG(d);
+      bucket = create_pbucket();
+      stat = nd_sp_f4(m,0,l,bucket);
+      if ( !stat ) {
+        for ( t = l; NEXT(t); t = NEXT(t) );
+        NEXT(t) = d; d = l;
+        d = nd_reconstruct(0,d);
+        goto again2;
+      }
+      if ( bucket->m < 0 ) continue;
+      col = nd_symbolic_preproc_s(bucket,0,&s0vect,&rp0);
+      if ( !col ) {
+        for ( t = l; NEXT(t); t = NEXT(t) )
+          ;
+        NEXT(t) = d; d = l;
+        d = nd_reconstruct(0,d);
+        goto again2;
+      }
+      if ( DP_Print ) fprintf(asir_out,"\nsugar=%d,",psugar);
+      nflist = nd_f4_red_s(m,l,0,s0vect,col,rp0,syzlist);
+      /* adding new bases */
+      for ( r = nflist; r; r = NEXT(r) ) {
+        nfv = (NDV)BDY(r);
+        if ( nd_f4_td ) SG(nfv) = nd_tdeg(nfv);
+        ndv_removecont(m,nfv);
+        nh = ndv_newps(m,nfv,0);
+        d = update_pairs_s(d,nh,syzlist);
+        nd_sba_pos[nfv->sig->pos] = append_one(nd_sba_pos[nfv->sig->pos],nh);
+      }
+      for ( i = 0; i < nd_nbase; i++ )
+        for ( r = syzlist[i]; r; r = NEXT(r) )
+            d = remove_spair_s(d,(SIG)BDY(r));
+      d = remove_large_lcm(d);
+      if ( DP_Print ) { 
+        fprintf(asir_out,"f4red=%d,gblen=%d",f4red,nd_psn); fflush(asir_out);
+      }
+      f4red++;
     }
-    for ( i = 0; i < nd_nbase; i++ )
-      for ( r = syzlist[i]; r; r = NEXT(r) )
-        d = remove_spair_s(d,(SIG)BDY(r));
-    if ( DP_Print ) { 
-      fprintf(asir_out,"f4red=%d,gblen=%d\n",f4red,nd_psn); fflush(asir_out);
-    }
-    f4red++;
-    if ( nd_f4red && f4red > nd_f4red ) break;
-    if ( nd_rank0 && !nflist ) break;
   }
   if ( DP_Print ) {
-    fprintf(asir_out,"number of red=%d,",Nf4_red);
+    fprintf(asir_out,"\nnumber of red=%d,",Nf4_red);
   }
   g = conv_ilist_s(nd_demand,0,indp);
   return g;