===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2018/engine/nd.c,v
retrieving revision 1.25
retrieving revision 1.41
diff -u -p -r1.25 -r1.41
--- OpenXM_contrib2/asir2018/engine/nd.c	2020/06/19 22:58:48	1.25
+++ OpenXM_contrib2/asir2018/engine/nd.c	2020/11/26 03:55:23	1.41
@@ -1,8 +1,8 @@
-/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.24 2020/06/19 10:18:13 noro Exp $ */
+/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.40 2020/11/02 08:30:55 noro Exp $ */
 
 #include "nd.h"
 
-int Nnd_add,Nf4_red;
+int Nnd_add,Nf4_red,NcriB,NcriMF,Ncri2,Npairs;
 struct oEGT eg_search,f4_symb,f4_conv,f4_elim1,f4_elim2;
 
 int diag_period = 6;
@@ -18,6 +18,7 @@ NM _nm_free_list;
 ND _nd_free_list;
 ND_pairs _ndp_free_list;
 NODE nd_hcf;
+int Nsyz,Nsamesig;
 
 Obj nd_top_weight;
 
@@ -49,7 +50,7 @@ static NDV *nd_ps_trace;
 static NDV *nd_ps_sym;
 static NDV *nd_ps_trace_sym;
 static RHist *nd_psh;
-static int nd_psn,nd_pslen;
+static int nd_psn,nd_pslen,nd_nbase;
 static RHist *nd_red;
 static int *nd_work_vector;
 static int **nd_matrix;
@@ -64,12 +65,16 @@ 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;
 static int *nd_gbblock;
 static NODE nd_nzlist,nd_check_splist;
 static int nd_splist;
 static int *nd_sugarweight;
 static int nd_f4red,nd_rank0,nd_last_nonzero;
+static DL *nd_sba_hm;
+static NODE *nd_sba_pos;
 
 NumberField get_numberfield();
 UINT *nd_det_compute_bound(NDV **dm,int n,int j);
@@ -111,6 +116,7 @@ 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);
 
@@ -291,106 +297,6 @@ INLINE int ndl_reducible(UINT *d1,UINT *d2)
 #endif
 }
 
-int ndl_reducible_s(UINT *d1,UINT *d2,UINT *quo)
-{
-    UINT u1,u2;
-    int i,j;
-
-    if ( nd_module && (MPOS(d1) != MPOS(d2)) ) return 0;
-
-    if ( !dp_negative_weight && TD(d1) < TD(d2) ) return 0;
-#if USE_UNROLL
-    switch ( nd_bpe ) {
-        case 3:
-            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
-                u1 = d1[i]; u2 = d2[i];
-                if ( (u1&0x38000000) < (u2&0x38000000) ) return 0;
-                if ( (u1& 0x7000000) < (u2& 0x7000000) ) return 0;
-                if ( (u1&  0xe00000) < (u2&  0xe00000) ) return 0;
-                if ( (u1&  0x1c0000) < (u2&  0x1c0000) ) return 0;
-                if ( (u1&   0x38000) < (u2&   0x38000) ) return 0;
-                if ( (u1&    0x7000) < (u2&    0x7000) ) return 0;
-                if ( (u1&     0xe00) < (u2&     0xe00) ) return 0;
-                if ( (u1&     0x1c0) < (u2&     0x1c0) ) return 0;
-                if ( (u1&      0x38) < (u2&      0x38) ) return 0;
-                if ( (u1&       0x7) < (u2&       0x7) ) return 0;
-            }
-            for ( i = 0; i < nd_wpd; i++ ) d1[i] -= d2[i];
-            return 1;
-            break;
-        case 4:
-            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
-                u1 = d1[i]; u2 = d2[i];
-                if ( (u1&0xf0000000) < (u2&0xf0000000) ) return 0;
-                if ( (u1& 0xf000000) < (u2& 0xf000000) ) return 0;
-                if ( (u1&  0xf00000) < (u2&  0xf00000) ) return 0;
-                if ( (u1&   0xf0000) < (u2&   0xf0000) ) return 0;
-                if ( (u1&    0xf000) < (u2&    0xf000) ) return 0;
-                if ( (u1&     0xf00) < (u2&     0xf00) ) return 0;
-                if ( (u1&      0xf0) < (u2&      0xf0) ) return 0;
-                if ( (u1&       0xf) < (u2&       0xf) ) return 0;
-            }
-            for ( i = 0; i < nd_wpd; i++ ) d1[i] -= d2[i];
-            return 1;
-            break;
-        case 6:
-            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
-                u1 = d1[i]; u2 = d2[i];
-                if ( (u1&0x3f000000) < (u2&0x3f000000) ) return 0;
-                if ( (u1&  0xfc0000) < (u2&  0xfc0000) ) return 0;
-                if ( (u1&   0x3f000) < (u2&   0x3f000) ) return 0;
-                if ( (u1&     0xfc0) < (u2&     0xfc0) ) return 0;
-                if ( (u1&      0x3f) < (u2&      0x3f) ) return 0;
-            }
-            for ( i = 0; i < nd_wpd; i++ ) d1[i] -= d2[i];
-            return 1;
-            break;
-        case 8:
-            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
-                u1 = d1[i]; u2 = d2[i];
-                if ( (u1&0xff000000) < (u2&0xff000000) ) return 0;
-                if ( (u1&  0xff0000) < (u2&  0xff0000) ) return 0;
-                if ( (u1&    0xff00) < (u2&    0xff00) ) return 0;
-                if ( (u1&      0xff) < (u2&      0xff) ) return 0;
-            }
-            for ( i = 0; i < nd_wpd; i++ ) d1[i] -= d2[i];
-            return 1;
-            break;
-        case 16:
-            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
-                u1 = d1[i]; u2 = d2[i];
-                if ( (u1&0xffff0000) < (u2&0xffff0000) ) return 0;
-                if ( (u1&    0xffff) < (u2&    0xffff) ) return 0;
-            }
-            for ( i = 0; i < nd_wpd; i++ ) d1[i] -= d2[i];
-            return 1;
-            break;
-        case 32:
-            for ( i = nd_exporigin; i < nd_wpd; i++ )
-                if ( d1[i] < d2[i] ) return 0;
-            for ( i = 0; i < nd_wpd; i++ ) d1[i] -= d2[i];
-            return 1;
-            break;
-        default:
-            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
-                u1 = d1[i]; u2 = d2[i];
-                for ( j = 0; j < nd_epw; j++ )
-                    if ( (u1&nd_mask[j]) < (u2&nd_mask[j]) ) return 0;
-            }
-            for ( i = 0; i < nd_wpd; i++ ) d1[i] -= d2[i];
-            return 1;
-    }
-#else
-    for ( i = nd_exporigin; i < nd_wpd; i++ ) {
-        u1 = d1[i]; u2 = d2[i];
-        for ( j = 0; j < nd_epw; j++ )
-            if ( (u1&nd_mask[j]) < (u2&nd_mask[j]) ) return 0;
-    }
-    for ( i = 0; i < nd_wpd; i++ ) d1[i] -= d2[i];
-    return 1;
-#endif
-}
-
 /*
  * If the current order is a block order,
  * then the last block is length 1 and contains
@@ -844,6 +750,7 @@ int ndl_module_glex_compare(UINT *d1,UINT *d2)
 
     default:    
       error("ndl_module_glex_compare : invalid module_ordtype");
+      return 0;
   }
 }
 
@@ -876,11 +783,13 @@ int ndl_module_compare(UINT *d1,UINT *d2)
 
     default:    
       error("ndl_module_compare : invalid module_ordtype");
+      return 0;
   }
 }
 
 extern DMMstack dmm_stack;
 void _addtodl(int n,DL d1,DL d2);
+void _adddl(int n,DL d1,DL d2,DL d3);
 int _eqdl(int n,DL d1,DL d2);
 
 int ndl_module_schreyer_compare(UINT *m1,UINT *m2)
@@ -940,6 +849,7 @@ LAST:
       break;
     default:
       error("ndl_schreyer_compare : invalid base ordtype");
+      return 0;
   }
 }
 
@@ -1051,35 +961,6 @@ INLINE void ndl_addto(UINT *d1,UINT *d2)
 #endif
 }
 
-/* d1 -= d2 */
-INLINE void ndl_subfrom(UINT *d1,UINT *d2)
-{
-    int i;
-
-    if ( nd_module ) {
-        if ( MPOS(d1) && MPOS(d2) && (MPOS(d1) != MPOS(d2)) ) 
-            error("ndl_addto : invalid operation");
-    }
-#if 1
-    switch ( nd_wpd ) {
-        case 2:
-            TD(d1) -= TD(d2);
-            d1[1] -= d2[1];
-            break;
-        case 3:
-            TD(d1) -= TD(d2);
-            d1[1] -= d2[1];
-            d1[2] -= d2[2];
-            break;
-        default:
-            for ( i = 0; i < nd_wpd; i++ ) d1[i] -= d2[i];
-            break;
-    }
-#else
-    for ( i = 0; i < nd_wpd; i++ ) d1[i] -= d2[i];
-#endif
-}
-
 INLINE void ndl_sub(UINT *d1,UINT *d2,UINT *d)
 {
     int i;
@@ -1326,6 +1207,18 @@ 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
@@ -1345,35 +1238,46 @@ void print_sig(SIG s)
   fprintf(asir_out,">>*e%d",s->pos);
 }
 
+// assuming increasing order wrt signature 
+
 INLINE int ndl_find_reducer_s(UINT *dg,SIG sig)
 {
   RHist r;
-  int i,singular,ret;
-  static int wpd;
+  int i,singular,ret,d,k;
+  static int wpd,nvar;
   static SIG quo;
   static UINT *tmp;
 
-  if ( wpd < nd_wpd ) {
+  if ( !quo || nvar != nd_nvar ) NEWSIG(quo);
+  if ( wpd != nd_wpd ) {
     wpd = nd_wpd;
-    NEWSIG(quo);
     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];
     if ( ndl_reducible(dg,DL(r)) ) {
-      ndl_copy(dg,tmp);
-      ndl_subfrom(tmp,DL(r));
+      ndl_sub(dg,DL(r),tmp);
       _ndltodl(tmp,DL(quo));
       _addtodl(nd_nvar,DL(nd_psh[i]->sig),DL(quo));
       quo->pos = nd_psh[i]->sig->pos;
       ret = comp_sig(sig,quo);
       if ( ret > 0 ) { singular = 0; break; }
-      if ( ret == 0 ) { singular = 1; }
+      if ( ret == 0 ) { /* fprintf(asir_out,"s"); fflush(asir_out); */ singular = 1; }
     }
   }
   if ( singular ) return -1;
-  else return i;
+  else if ( i < nd_psn )
+    nd_append_red(dg,i);
+  return i;
 }
 
 ND nd_merge(ND p1,ND p2)
@@ -2139,6 +2043,7 @@ void free_pbucket(PGeoBucket b) {
     GCFREE(b);
 }
 
+#if 0
 void add_pbucket_symbolic(PGeoBucket g,ND d)
 {
     int l,i,k,m;
@@ -2156,7 +2061,32 @@ 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;
@@ -2174,7 +2104,29 @@ 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;
@@ -2498,9 +2450,12 @@ 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 oEGT eg1,eg2,eg_update;
 
+init_eg(&eg_update);
   Nnd_add = 0;
   g = 0; d = 0;
   for ( i = 0; i < nd_psn; i++ ) {
@@ -2532,16 +2487,17 @@ 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 ) {
@@ -2575,28 +2531,38 @@ again:
           goto again;
         }
       }
+get_eg(&eg1);
       d = update_pairs(d,g,nh,0);
+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); }
-    return g;
+    } 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,NODE g,int t,NODE syz);
-ND_pairs nd_newpairs_s( NODE g, int t ,NODE syz);
+ND_pairs update_pairs_s(ND_pairs d,int t,NODE *syz);
+ND_pairs nd_newpairs_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);
@@ -2626,9 +2592,12 @@ NODE insert_sig(NODE l,SIG s)
     } else
       prev = p;
   }
-  NEWNODE(r); r->body = (pointer)s;
-  r->next = root.next;
-  return r;
+  NEWNODE(r); r->body = (pointer)s; r->next = 0;
+  for ( p = &root; p->next; p = p->next );
+  p->next = r;
+//  r->next = root.next;
+//  return r;
+  return root.next;
 }
 
 ND_pairs remove_spair_s(ND_pairs d,SIG sig)
@@ -2641,22 +2610,149 @@ ND_pairs remove_spair_s(ND_pairs d,SIG sig)
   prev = &root; p = d;
   while ( p ) {
     spsig = p->sig;
-    if ( sig->pos == spsig->pos && _dl_redble(DL(sig),DL(spsig),nd_nvar) ) 
+    if ( sig->pos == spsig->pos && _dl_redble(DL(sig),DL(spsig),nd_nvar) ) {
       // remove p
       prev->next = p->next;
-    else
+      Nsyz++;
+    } else
       prev = p;
     p = p->next;
   }
   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;
+
+  if ( nd_sba_largelcm ) return 0;
+  if ( nvar < nd_nvar ) {
+    nvar = nd_nvar; NEWDL(lcm,nvar); NEWDL(quo,nvar); NEWDL(mul,nvar);
+  }
+  sig = l->sig;
+  _ndltodl(l->lcm,lcm);
+#if 0
+  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),quo,nd_nvar) ) {
+      _ndltodl(DL(nd_psh[i]),mul);
+      _addtodl(nd_nvar,quo,mul);
+      if ( (*cmpdl)(nd_nvar,lcm,mul) > 0 )
+        break;
+    }
+  }
+  if ( i < nd_psn ) return 1;
+  else return 0;
+#else
+  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,lcm,mul) > 0 )
+        break;
+    }
+  }
+  if ( t ) return 1;
+  else return 0;
+#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;
+
+  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;
+        _copydl(nd_nvar,mul,minlm);
+      }
+    }
+  }
+  // l->lcm is minimal; return l itself
+  if ( minindex < 0 ) return l;
+  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;
+  ND_pairs prev,p;
+
+  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;
+  }
+  return (ND_pairs)root.next;
+}
+
+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)
 {
-  int i,nh,sugar,stat;
-  NODE r,g,t;
+  int i,j,nh,sugar,stat,pos;
+  NODE r,t,g;
   ND_pairs d;
-  ND_pairs l;
+  ND_pairs l,l1;
   ND h,nf,s,head,nf1;
   NDV nfv;
   Z q;
@@ -2664,85 +2760,153 @@ NODE nd_sba_buch(int m,int ishomo,int **indp)
   P cont;
   LIST list;
   SIG sig;
-  NODE syzlist;
-  static int wpd;
-  static SIG quo,mul;
-  static DL lcm;
+  NODE *syzlist;
+  int Nnominimal,Nredundant;
+  DL lcm,quo,mul;
+  struct oEGT eg1,eg2,eg_update,eg_remove,eg_large,eg_nf,eg_nfzero;
+  int Nnfs=0,Nnfz=0,Nnfnz=0;
 
-  syzlist = 0;
+init_eg(&eg_remove);
+  syzlist = (NODE *)MALLOC(nd_psn*sizeof(NODE));
+  Nsyz = 0;
   Nnd_add = 0;
-  g = 0; d = 0;
+  Nnominimal = 0;
+  Nredundant = 0;
+  d = 0;
+  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);
+    }
   for ( i = 0; i < nd_psn; i++ ) {
-    d = update_pairs_s(d,g,i,0);
-    g = append_one(g,i);
+    d = update_pairs_s(d,i,syzlist);
   }
   sugar = 0;
+  pos = 0;
+  NEWDL(lcm,nd_nvar); NEWDL(quo,nd_nvar); NEWDL(mul,nd_nvar);
+init_eg(&eg_create);
+init_eg(&eg_merge);
+init_eg(&eg_large);
+init_eg(&eg_nf);
+init_eg(&eg_nfzero);
   while ( d ) {
 again:
-    l = d; d = d->next;
-    sig = l->sig;
-    if ( wpd < nd_wpd ) {
-      wpd = nd_wpd;
-      NEWSIG(quo);
-      NEWSIG(mul);
-      NEWDL(lcm,nd_nvar);
-    }
-    _ndltodl(l->lcm,lcm);
-    for ( i = 0; i < nd_psn; i++ ) {
-      if ( sig->pos == nd_psh[i]->sig->pos &&
-        _dl_redble(DL(nd_psh[i]->sig),DL(sig),nd_nvar) ) {
-        _copydl(nd_nvar,DL(sig),DL(quo));
-        _subfromdl(nd_nvar,DL(nd_psh[i]->sig),DL(quo));
-        _ndltodl(DL(nd_psh[i]),DL(mul));
-        _addtodl(nd_nvar,DL(quo),DL(mul));
-        if ( (*cmpdl)(nd_nvar,lcm,DL(mul)) > 0 )
-          break;
+    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);
       }
-    }
-    if ( i < nd_psn ) {
+    l = d; d = d->next;
+#if 0
+    if ( small_lcm(l) ) {
       if ( DP_Print ) fprintf(asir_out,"M");
+      Nnominimal++;
       continue;
     }
     if ( SG(l) != sugar ) {
       sugar = SG(l);
       if ( DP_Print ) fprintf(asir_out,"%d",sugar);
     }
+    sig = l->sig;
+    if ( DP_Print && nd_sba_pot ) {
+      if ( sig->pos != pos ) {
+        fprintf(asir_out,"[%d]",sig->pos);
+        pos = sig->pos;
+      }
+    }
     stat = nd_sp(m,0,l,&h);
+#else
+    l1 = find_smallest_lcm(l);
+    if ( l1 == 0 ) {
+      if ( DP_Print ) fprintf(asir_out,"M");
+      Nnominimal++;
+      continue;
+    }
+    if ( SG(l1) != sugar ) {
+      sugar = SG(l1);
+      if ( DP_Print ) fprintf(asir_out,"%d",sugar);
+    }
+    sig = l1->sig;
+    if ( DP_Print && nd_sba_pot ) {
+      if ( sig->pos != pos ) {
+        fprintf(asir_out,"[%d]",sig->pos);
+        pos = sig->pos;
+      }
+    }
+    stat = nd_sp(m,0,l1,&h);
+#endif
     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,!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);
       goto again;
     } else if ( stat == -1 ) {
+      Nnfs++;
       if ( DP_Print ) { printf("S"); fflush(stdout); }
+      FREENDP(l);
     } else if ( nf ) {
-      if ( DP_Print ) { printf("+"); fflush(stdout); }
+      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);
       nd_removecont(m,nf);
       nfv = ndtondv(m,nf); nd_free(nf);
       nh = ndv_newps(m,nfv,0);
-      d = update_pairs_s(d,g,nh,syzlist);
-      g = append_one(g,nh);
+
+      d = update_pairs_s(d,nh,syzlist);
+      nd_sba_pos[sig->pos] = append_one(nd_sba_pos[sig->pos],nh);
       FREENDP(l);
    } else {
+      Nnfz++;
+      add_eg(&eg_nfzero,&eg1,&eg2);
      // syzygy
+get_eg(&eg1);
      d = remove_spair_s(d,sig);
-     syzlist = insert_sig(syzlist,sig);
+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);
    }
  }
- conv_ilist(nd_demand,0,g,indp);
- if ( DP_Print ) { printf("nd_sba done. Number of nd_add=%d\n",Nnd_add); fflush(stdout); }
+ g = conv_ilist_s(nd_demand,0,indp);
+ if ( DP_Print ) { 
+   printf("\nnd_sba done. nd_add=%d,Nsyz=%d,Nsamesig=%d,Nnominimal=%d\n",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("create",&eg_create);
+   print_eg("merge",&eg_merge);
+   print_eg("remove",&eg_remove);
+   print_eg("nf",&eg_nf);
+   print_eg("nfzero",&eg_nfzero);
+   printf("\n");
+ }
  return g;
 }
 
@@ -2773,7 +2937,7 @@ 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);
@@ -2948,9 +3112,9 @@ 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;
@@ -2963,7 +3127,7 @@ 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;
@@ -3029,7 +3193,7 @@ 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;
 }
 
@@ -3117,9 +3281,17 @@ 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 */
@@ -3136,8 +3308,10 @@ 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 {
@@ -3147,7 +3321,7 @@ 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);
       }
@@ -3165,13 +3339,17 @@ ND_pairs update_pairs( ND_pairs d, NODE /* of index */
 
 ND_pairs merge_pairs_s(ND_pairs d,ND_pairs d1);
 
-ND_pairs update_pairs_s( ND_pairs d, NODE /* of index */ g, int t,NODE syz)
+ND_pairs update_pairs_s( ND_pairs d, int t,NODE *syz)
 {
   ND_pairs d1;
+  struct oEGT eg1,eg2,eg3;
 
-  if ( !g ) return d;
-  d1 = nd_newpairs_s(g,t,syz);
+  if ( !t ) return d;
+get_eg(&eg1);
+  d1 = nd_newpairs_s(t,syz);
+get_eg(&eg2); add_eg(&eg_create,&eg1,&eg2);
   d = merge_pairs_s(d,d1);
+get_eg(&eg3); add_eg(&eg_merge,&eg2,&eg3);
   return d;
 }
 
@@ -3198,7 +3376,7 @@ 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);
@@ -3212,33 +3390,28 @@ ND_pairs nd_newpairs( NODE g, int t )
   return r0;
 }
 
-
 int comp_sig(SIG s1,SIG s2)
 {
-#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
-  static DL m1,m2;
-  static int nvar;
-  int ret;
-
-  if ( nvar < nd_nvar ) {
-    nvar = nd_nvar;
-    NEWDL(m1,nvar);
-    NEWDL(m2,nvar);
+  if ( nd_sba_pot ) {
+    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 {
+    static DL m1,m2;
+    static int nvar;
+    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);
+    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;
   }
-  _ndltodl(DL(nd_psh[s1->pos]),m1);
-  _ndltodl(DL(nd_psh[s2->pos]),m2);
-  _addtodl(nd_nvar,s1->dl,m1);
-  _addtodl(nd_nvar,s2->dl,m2);
-  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)
@@ -3257,15 +3430,14 @@ int _create_spair_s(int i1,int i2,ND_pairs sp,SIG sig1
   s2 = SG(p2)-TD(DL(p2));
   SG(sp) = MAX(s1,s2) + TD(sp->lcm);
 
-  if ( wpd < nd_wpd ) {
+  if ( wpd != nd_wpd ) {
     wpd = nd_wpd;
     lcm = (UINT *)MALLOC(wpd*sizeof(UINT));
   }
   // DL(sig1) <- sp->lcm
   // DL(sig1) -= DL(p1)
   // DL(sig1) += DL(p1->sig)
-  ndl_copy(sp->lcm,lcm);
-  ndl_subfrom(lcm,DL(p1));
+  ndl_sub(sp->lcm,DL(p1),lcm);
   _ndltodl(lcm,DL(sig1));
   _addtodl(nd_nvar,DL(p1->sig),DL(sig1));
   sig1->pos = p1->sig->pos;
@@ -3273,8 +3445,7 @@ int _create_spair_s(int i1,int i2,ND_pairs sp,SIG sig1
   // DL(sig2) <- sp->lcm
   // DL(sig2) -= DL(p2)
   // DL(sig2) += DL(p2->sig)
-  ndl_copy(sp->lcm,lcm);
-  ndl_subfrom(lcm,DL(p2));
+  ndl_sub(sp->lcm,DL(p2),lcm);
   _ndltodl(lcm,DL(sig2));
   _addtodl(nd_nvar,DL(p2->sig),DL(sig2));
   sig2->pos = p2->sig->pos;
@@ -3324,6 +3495,7 @@ ND_pairs merge_pairs_s(ND_pairs p1,ND_pairs p2)
       r->next = q2; r = q2; q2 = q2->next;
     } else {
       ret = DL_COMPARE(q1->lcm,q2->lcm);
+      Nsamesig++;
       if ( ret < 0 ) {
         r->next = q1; r = q1; q1 = q1->next;
         q2 = q2->next;
@@ -3375,33 +3547,52 @@ ND_pairs insert_pair_s(ND_pairs l,ND_pairs s)
   }
 }
 
-ND_pairs nd_newpairs_s( NODE g, int t, NODE syz)
+INLINE int __dl_redble(DL d1,DL d2,int nvar)
 {
+  int i;
+
+  if ( d1->td > d2->td )
+    return 0;
+  for ( i = nvar-1; i >= 0; i-- )
+    if ( d1->d[i] > d2->d[i] )
+      break;
+  if ( i >= 0 )
+    return 0;
+  else
+    return 1;
+}
+
+ND_pairs nd_newpairs_s(int t, NODE *syz)
+{
   NODE h,s;
   UINT *dl;
-  int ts,ret;
+  int ts,ret,i;
   ND_pairs r,r0,_sp,sp;
-  SIG _sig1,_sig2,spsig,tsig;
+  SIG spsig,tsig;
+  static int nvar;
+  static SIG _sig1,_sig2;
+  struct oEGT eg1,eg2,eg3,eg4;
 
-  dl = DL(nd_psh[t]);
-  ts = SG(nd_psh[t]) - TD(dl);
   NEWND_pairs(_sp);
-  NEWSIG(_sig1); NEWSIG(_sig2);
+  if ( !_sig1 || nvar != nd_nvar ) {
+    nvar = nd_nvar; NEWSIG(_sig1); NEWSIG(_sig2);
+  }
   r0 = 0;
-  for ( h = g; h; h = NEXT(h) ) {
-    ret = _create_spair_s((long)BDY(h),t,_sp,_sig1,_sig2);
+  for ( i = 0; i < t; i++ ) {
+    ret = _create_spair_s(i,t,_sp,_sig1,_sig2);
     if ( ret ) {
       spsig = _sp->sig;
-      for ( s = syz; s; s = s->next ) {
+      for ( s = syz[spsig->pos]; s; s = s->next ) {
         tsig = (SIG)s->body;
-        if ( tsig->pos == spsig->pos && _dl_redble(DL(tsig),DL(spsig),nd_nvar) )
+        if ( _dl_redble(DL(tsig),DL(spsig),nd_nvar) )
           break;
       }
       if ( s == 0 ) {
         NEWND_pairs(sp);
         dup_ND_pairs(sp,_sp);
         r0 = insert_pair_s(r0,sp);
-      }
+      } else
+        Nsyz++;
     }
   }
   return r0;
@@ -3457,7 +3648,7 @@ 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);
         }
@@ -3684,6 +3875,18 @@ ND_pairs nd_minsugarp( ND_pairs d, ND_pairs *prest )
     return dm0;
 }
 
+ND_pairs nd_minsugarp_s( ND_pairs d, ND_pairs *prest )
+{
+  int msugar;
+  ND_pairs t,last;
+
+  for ( msugar = SG(d), t = d; t; t = NEXT(t) )
+    if ( SG(t) == msugar ) last = t;
+  *prest = last->next;
+  last->next = 0;
+  return d;
+}
+
 int nd_tdeg(NDV c)
 {
   int wmax = 0;
@@ -3792,7 +3995,7 @@ int ndv_setup(int mod,int trace,NODE f,int dont_sort,i
     if ( BDY(s) ) { w[i].p = BDY(s); w[i].i = j; i++; }
   if ( !dont_sort ) {
     /* XXX heuristic */
-    if ( !nd_ord->id && (nd_ord->ord.simple<2) )
+    if ( !sba && !nd_ord->id && (nd_ord->ord.simple<2) )
       qsort(w,nd_psn,sizeof(struct oNDVI),
         (int (*)(const void *,const void *))ndvi_compare_rev);
     else
@@ -3869,19 +4072,27 @@ int ndv_setup(int mod,int trace,NODE f,int dont_sort,i
     }
   }
   if ( sba ) {
+    nd_sba_hm = (DL *)MALLOC(nd_psn*sizeof(DL));
    // setup signatures
-   for ( i = 0; i < nd_psn; i++ ) {
-     SIG sig;
+    for ( i = 0; i < nd_psn; i++ ) {
+      SIG sig;
 
-     NEWSIG(sig); sig->pos = i;
-     nd_ps[i]->sig = sig;
-     if ( nd_demand ) nd_ps_sym[i]->sig = sig;
-      nd_psh[i]->sig = sig;
-     if ( trace ) { 
-       nd_ps_trace[i]->sig = sig;
-       if ( nd_demand ) nd_ps_trace_sym[i]->sig = sig;
-     }
-   }
+      NEWSIG(sig); sig->pos = i;
+      nd_ps[i]->sig = sig;
+      if ( nd_demand ) nd_ps_sym[i]->sig = sig;
+        nd_psh[i]->sig = sig;
+      if ( trace ) { 
+        nd_ps_trace[i]->sig = sig;
+        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]);
+    }
+    nd_sba_pos = (NODE *)MALLOC(nd_psn*sizeof(NODE));
+    for ( i = 0; i < nd_psn; i++ ) {
+      j = nd_psh[i]->sig->pos;
+      nd_sba_pos[j] = append_one(nd_sba_pos[j],i);
+    }
   }
   if ( nd_gentrace && nd_tracelist ) NEXT(tn) = 0;
   return 1;
@@ -4017,6 +4228,7 @@ 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;
@@ -4222,7 +4434,9 @@ FINAL:
 #endif
 }
 
-void nd_sba(LIST f,LIST v,int m,int homo,int retdp,struct order_spec *ord,LIST *rp)
+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;
@@ -4237,11 +4451,12 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,str
   int *perm;
   EPOS oepos;
   int obpe,oadv,ompos,cbpe;
+  struct oEGT eg0,eg1,egconv;
 
   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);
@@ -4293,8 +4508,8 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,str
         ndv_homogenize((NDV)BDY(t),obpe,oadv,oepos,ompos);
   }
 
-  ndv_setup(m,0,fd0,0,0,1);
-  x = 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);
   if ( !x ) {
     *rp = 0; return;
   }
@@ -4308,13 +4523,16 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,str
   x = ndv_reducebase(x,perm);
   x = ndv_reduceall(m,x);
   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);
+  get_eg(&eg1); init_eg(&egconv); add_eg(&egconv,&eg0,&eg1);
+  print_eg("conv",&egconv); fprintf(asir_out,"\n");
 }
 
 void nd_gr_postproc(LIST f,LIST v,int m,struct order_spec *ord,int do_check,LIST *rp)
@@ -4578,6 +4796,7 @@ 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);
@@ -4830,7 +5049,7 @@ 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 ) {
@@ -4924,7 +5143,7 @@ void nd_print(ND p)
     else {
         for ( m = BDY(p); m; m = NEXT(m) ) {
             if ( CM(m) & 0x80000000 ) printf("+@_%d*",IFTOF(CM(m)));
-            else printf("+%d*",CM(m));
+            else printf("+%ld*",CM(m));
             ndl_print(DL(m));
         }
         printf("\n");
@@ -5557,6 +5776,91 @@ ND_pairs nd_reconstruct(int trace,ND_pairs d)
     return s0;
 }
 
+void nd_reconstruct_s(int trace,ND_pairs *d)
+{
+    int i,obpe,oadv,h;
+    static NM prev_nm_free_list;
+    static ND_pairs prev_ndp_free_list;
+    RHist mr0,mr;
+    RHist r;
+    RHist *old_red;
+    ND_pairs s0,s,t;
+    EPOS oepos;
+
+    obpe = nd_bpe;
+    oadv = nmv_adv;
+    oepos = nd_epos;
+    if ( obpe < 2 ) nd_bpe = 2;
+    else if ( obpe < 3 ) nd_bpe = 3;
+    else if ( obpe < 4 ) nd_bpe = 4;
+    else if ( obpe < 5 ) nd_bpe = 5;
+    else if ( obpe < 6 ) nd_bpe = 6;
+    else if ( obpe < 8 ) nd_bpe = 8;
+    else if ( obpe < 10 ) nd_bpe = 10;
+    else if ( obpe < 16 ) nd_bpe = 16;
+    else if ( obpe < 32 ) nd_bpe = 32;
+    else error("nd_reconstruct_s : exponent too large");
+
+    nd_setup_parameters(nd_nvar,0);
+    prev_nm_free_list = _nm_free_list;
+    prev_ndp_free_list = _ndp_free_list;
+    _nm_free_list = 0;
+    _ndp_free_list = 0;
+    for ( i = nd_psn-1; i >= 0; i-- ) {
+        ndv_realloc(nd_ps[i],obpe,oadv,oepos);
+        ndv_realloc(nd_ps_sym[i],obpe,oadv,oepos);
+    }
+    if ( trace )
+        for ( i = nd_psn-1; i >= 0; i-- ) {
+            ndv_realloc(nd_ps_trace[i],obpe,oadv,oepos);
+            ndv_realloc(nd_ps_trace_sym[i],obpe,oadv,oepos);
+        }
+
+    for ( i = 0; i < nd_nbase; i++ ) {
+      s0 = 0;
+      for ( t = d[i]; t; t = NEXT(t) ) {
+          NEXTND_pairs(s0,s);
+          s->i1 = t->i1;
+          s->i2 = t->i2;
+          s->sig = t->sig;
+          SG(s) = SG(t);
+          ndl_reconstruct(LCM(t),LCM(s),obpe,oepos);
+      }
+      d[i] = s0;
+    }
+    
+    old_red = (RHist *)MALLOC(REDTAB_LEN*sizeof(RHist));
+    for ( i = 0; i < REDTAB_LEN; i++ ) {
+        old_red[i] = nd_red[i];
+        nd_red[i] = 0;
+    }
+    for ( i = 0; i < REDTAB_LEN; i++ )
+        for ( r = old_red[i]; r; r = NEXT(r) ) {
+            NEWRHist(mr);
+            mr->index = r->index;
+            SG(mr) = SG(r);
+            ndl_reconstruct(DL(r),DL(mr),obpe,oepos);
+            h = ndl_hash_value(DL(mr));
+            NEXT(mr) = nd_red[h];
+            nd_red[h] = mr;
+            mr->sig = r->sig;
+        }
+    for ( i = 0; i < REDTAB_LEN; i++ ) old_red[i] = 0;
+    old_red = 0;
+    for ( i = 0; i < nd_psn; i++ ) {
+        NEWRHist(r); SG(r) = SG(nd_psh[i]);
+        ndl_reconstruct(DL(nd_psh[i]),DL(r),obpe,oepos);
+        r->sig = nd_psh[i]->sig;
+        nd_psh[i] = r;
+    }
+    if ( s0 ) NEXT(s) = 0;
+    prev_nm_free_list = 0;
+    prev_ndp_free_list = 0;
+#if 0
+    GC_gcollect();
+#endif
+}
+
 void ndl_reconstruct(UINT *d,UINT *r,int obpe,EPOS oepos)
 {
     int n,i,ei,oepw,omask0,j,s,ord_l,l;
@@ -6502,6 +6806,7 @@ ND ndvtond(int mod,NDV p)
     NEXT(m) = 0;
     MKND(NV(p),m0,len,d);
     SG(d) = SG(p);
+    d->sig = p->sig;
     return d;
 }
 
@@ -6580,7 +6885,7 @@ void ndv_print(NDV p)
         len = LEN(p);
         for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
             if ( CM(m) & 0x80000000 ) printf("+@_%d*",IFTOF(CM(m)));
-            else printf("+%d*",CM(m));
+            else printf("+%ld*",CM(m));
             ndl_print(DL(m));
         }
         printf("\n");
@@ -6611,6 +6916,7 @@ 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) ) {
@@ -7286,7 +7592,7 @@ 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;
@@ -7303,7 +7609,7 @@ 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);
@@ -7313,12 +7619,12 @@ 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:
@@ -7326,12 +7632,12 @@ 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:
@@ -7339,12 +7645,12 @@ 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;
             }
@@ -7612,6 +7918,29 @@ 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;
@@ -7773,7 +8102,7 @@ int nd_symbolic_preproc(PGeoBucket bucket,int trace,UI
             if ( ndl_check_bound2(index,DL(mul)) ) 
                 return 0;
             sugar = TD(DL(mul))+SG(ps[index]);
-            MKNM_ind_pair(pair,mul,index,sugar);
+            MKNM_ind_pair(pair,mul,index,sugar,0);
             red = ndv_mul_nm_symbolic(mul,ps[index]);
             add_pbucket_symbolic(bucket,nd_remove_head(red));
             NEXTNODE(rp0,rp); BDY(rp) = (pointer)pair;
@@ -7878,6 +8207,7 @@ 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;
@@ -7921,6 +8251,7 @@ 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;
@@ -8282,7 +8613,7 @@ 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));
@@ -8338,7 +8669,84 @@ 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,
@@ -8750,7 +9158,57 @@ 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;
@@ -9426,41 +9884,63 @@ void conv_ilist(int demand,int trace,NODE g,int **indp
   if ( indp ) *indp = ind;
 }
 
+NODE conv_ilist_s(int demand,int trace,int **indp)
+{
+  int n,i,j;
+  int *ind;
+  NODE g0,g;
+
+  n = nd_psn;
+  ind = (int *)MALLOC(n*sizeof(int));
+  g0 = 0;
+  for ( i = 0; i < n; i++ ) {
+    ind[i] = i;
+    NEXTNODE(g0,g);
+    BDY(g) = (pointer)(demand?ndv_load(i):(trace?nd_ps_trace[i]:nd_ps[i]));
+  }
+  if ( g0 ) NEXT(g) = 0;
+  if ( indp ) *indp = ind;
+  return g0;
+}
+
 void parse_nd_option(NODE opt)
 {
-    NODE t,p,u;
+  NODE t,p,u;
   int i,s,n;
-    char *key;
-    Obj value;
+  char *key;
+  Obj value;
 
-    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;
+
+  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") )
@@ -9470,27 +9950,41 @@ 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,"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 = value?1:0;
+    } 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_redundant_check") ) {
+      nd_sba_redundant_check = value?1:0;
+    } else if ( !strcmp(key,"top") ) {
+      nd_top = value?1:0;
     }
-    }
+  }
 }
 
 ND mdptond(DP d);
@@ -10178,6 +10672,29 @@ NDV vect64_to_ndv(mp_limb_t *vect,int spcol,int col,in
     }
 }
 
+NDV vect64_to_ndv_s(mp_limb_t *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 = (UINT)vect[k++]) != 0 ) {
+            ndl_copy(p,DL(mr)); CM(mr) = c; NMV_ADV(mr);
+          }
+        MKNDV(nd_nvar,mr0,len,r);
+        return r;
+    }
+}
+
 int nd_to_vect64(int mod,UINT *s0,int n,ND d,mp_limb_t *r)
 {
     NM m;
@@ -10207,7 +10724,7 @@ int nd_to_vect64(int mod,UINT *s0,int n,ND d,mp_limb_t
 
 #define MOD128(a,c,m) ((a)=(((c)!=0||((a)>=(m)))?(((((U128)(c))<<64)+(a))%(m)):(a)))
 
-int ndv_reduce_vect64(int m,mp_limb_t *svect,mp_limb_t *cvect,int col,IndArray *imat,NM_ind_pair *rp0,int nred)
+int ndv_reduce_vect64(int m,mp_limb_t *svect,mp_limb_t *cvect,int col,IndArray *imat,NM_ind_pair *rp0,int nred,SIG sig)
 {
     int i,j,k,len,pos,prev;
     mp_limb_t a,c,c1,c2;
@@ -10228,7 +10745,7 @@ int ndv_reduce_vect64(int m,mp_limb_t *svect,mp_limb_t
         a = svect[k]; c = cvect[k];
         MOD128(a,c,m);
         svect[k] = a; cvect[k] = 0;
-        if ( (c = svect[k]) != 0 ) {
+        if ( (c = svect[k]) != 0 && (sig == 0 || comp_sig(sig,rp0[i]->sig) > 0 ) ) {
             Nf4_red++;
             maxrs = MAX(maxrs,rp0[i]->sugar);
             c = m-c; redv = nd_ps[rp0[i]->index];
@@ -10302,7 +10819,7 @@ NODE nd_f4_red_mod64_main(int m,ND_pairs sp0,int nsp,U
         nd_sp(m,0,sp,&spol);
         if ( !spol ) continue;
         nd_to_vect64(m,s0vect,col,spol,svect);
-        maxrs = ndv_reduce_vect64(m,svect,cvect,col,imat,rvect,nred);
+        maxrs = ndv_reduce_vect64(m,svect,cvect,col,imat,rvect,nred,0);
         for ( i = 0; i < col; i++ ) if ( svect[i] ) break;
         if ( i < col ) {
             spmat[sprow] = v = (mp_limb_t *)MALLOC_ATOMIC(spcol*sizeof(mp_limb_t));
@@ -10432,5 +10949,432 @@ int nd_gauss_elim_mod64(mp_limb_t **mat,int *sugar,ND_
   GCFREE(cmat);
   return rank;
 }
+
+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)
+{
+  int i,j,k,l,rank,s,imin;
+  mp_limb_t inv;
+  mp_limb_t a;
+  UINT c;
+  mp_limb_t *t,*pivot,*pk;
+  UINT *ck;
+  UINT **cmat;
+  UINT *ct;
+  ND_pairs pair;
+  SIG sg;
+  int *used;
+
+  used = (int *)MALLOC(row*sizeof(int));
+  cmat = (UINT **)MALLOC(row*sizeof(UINT *));
+  for ( i = 0; i < row; i++ ) {
+    cmat[i] = MALLOC_ATOMIC(col*sizeof(UINT));
+    bzero(cmat[i],col*sizeof(UINT));
+  }
+
+  for ( j = 0; j < col; j++ ) {
+    for ( i = 0; i < row; i++ ) {
+      a = mat[i][j]; c = cmat[i][j];
+      MOD128(a,c,md);
+      mat[i][j] = a; cmat[i][j] = 0;
+    }
+    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((UINT)mat[i][j],md);
+    /* normalize pivot row */
+    for ( k = j, pk = mat[i]+j, ck = cmat[i]+j; k < col; k++, pk++, ck++ ) {
+      a = *pk; c = *ck; MOD128(a,c,md); *pk = (a*inv)%md; *ck = 0;
+    }
+    for ( k = i+1; k < row; k++ ) {
+      if ( (a = mat[k][j]) != 0 ) {
+        sugar[k] = MAX(sugar[k],s);
+        red_by_vect64(md,mat[k]+j,cmat[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++;
+  }
+  for ( i = 0; i < row; i++ ) GCFREE(cmat[i]);
+  GCFREE(cmat);
+  return rank;
+}
+
+NODE nd_f4_red_mod64_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;
+    mp_limb_t **spmat;
+    mp_limb_t *svect,*cvect;
+    mp_limb_t *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 = (mp_limb_t **)MALLOC(nsp*sizeof(mp_limb_t *));
+    cvect = (mp_limb_t *)MALLOC(col*sizeof(mp_limb_t));
+    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 = (mp_limb_t *)MALLOC(col*sizeof(mp_limb_t));
+        nd_to_vect64(m,s0vect,col,spol,svect);
+        maxrs = ndv_reduce_vect64(m,svect,cvect,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_mod64_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) = vect64_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;
+}
 #endif
 
+NODE nd_f4_red_s(int m,ND_pairs sp0,int trace,UINT *s0vect,int col,NODE rp0,NODE *syzlistp)
+{
+  IndArray *imat;
+  int nsp,nred,i,start;
+  int *rhead;
+  NODE r0,rp;
+  ND_pairs sp;
+  NM_ind_pair *rvect;
+  UINT *s;
+  int *s0hash;
+  struct oEGT eg0,eg1,eg_conv;
+
+  for ( sp = sp0, nsp = 0; sp; sp = NEXT(sp), nsp++ );
+  nred = length(rp0);
+  imat = (IndArray *)MALLOC(nred*sizeof(IndArray));
+  rhead = (int *)MALLOC(col*sizeof(int));
+  for ( i = 0; i < col; i++ ) rhead[i] = 0;
+
+  /* construction of index arrays */
+  get_eg(&eg0);
+  if ( DP_Print ) {
+    fprintf(asir_out,"%dx%d,",nsp+nred,col);
+    fflush(asir_out);
+  }
+  rvect = (NM_ind_pair *)MALLOC(nred*sizeof(NM_ind_pair));
+  for ( start = 0, rp = rp0, i = 0; rp; i++, rp = NEXT(rp) ) {
+    rvect[i] = (NM_ind_pair)BDY(rp);
+    imat[i] = nm_ind_pair_to_vect_compress(trace,s0vect,col,rvect[i],start);
+    rhead[imat[i]->head] = 1;
+    start = imat[i]->head;
+  }
+  get_eg(&eg1); init_eg(&eg_conv); add_eg(&eg_conv,&eg0,&eg1); add_eg(&f4_conv,&eg0,&eg1);
+  if ( DP_Print ) {
+    fprintf(asir_out,"conv=%.3fsec,",eg_conv.exectime);
+    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");
+  return r0;
+}
+
+INLINE int ndl_find_reducer_minsig(UINT *dg)
+{
+  RHist r;
+  int i,singular,ret,d,k,imin;
+  SIG t;
+  static int wpd,nvar;
+  static SIG quo,quomin;
+  static UINT *tmp;
+
+  if ( !quo || nvar != nd_nvar ) { NEWSIG(quo); NEWSIG(quomin); }
+  if ( wpd != nd_wpd ) {
+    wpd = nd_wpd;
+    tmp = (UINT *)MALLOC(wpd*sizeof(UINT));
+  }
+#if 0
+  d = ndl_hash_value(dg);
+  for ( r = nd_red[d], k = 0; r; r = NEXT(r), k++ ) {
+    if ( ndl_equal(dg,DL(r)) ) {
+      return r->index;
+    }
+  }
+#endif
+  imin = -1;
+  for ( i = 0; i < nd_psn; i++ ) {
+    r = nd_psh[i];
+    if ( ndl_reducible(dg,DL(r)) ) {
+      ndl_sub(dg,DL(r),tmp);
+      _ndltodl(tmp,DL(quo));
+      _addtodl(nd_nvar,DL(nd_psh[i]->sig),DL(quo));
+      quo->pos = nd_psh[i]->sig->pos;
+      if ( imin < 0 || comp_sig(quomin,quo) > 0 ) {
+        t = quo; quo = quomin; quomin = t;
+        imin = i;
+      }
+    }
+  }
+  if ( imin == -1 ) return nd_psn;
+  else {
+#if 0
+    nd_append_red(dg,i);
+#endif
+    return imin;
+  }
+}
+
+int nd_symbolic_preproc_s(PGeoBucket bucket,int trace,UINT **s0vect,NODE *r)
+{
+  NODE rp0,rp;
+  NM mul,head,s0,s;
+  int index,col,i,sugar;
+  RHist h;
+  UINT *s0v,*p;
+  NM_ind_pair pair;
+  ND red;
+  NDV *ps;
+  SIG sig;
+
+  s0 = 0; rp0 = 0; col = 0;
+  if ( nd_demand )
+    ps = trace?nd_ps_trace_sym:nd_ps_sym;
+  else
+    ps = trace?nd_ps_trace:nd_ps;
+  while ( 1 ) {
+    head = remove_head_pbucket_symbolic(bucket);
+    if ( !head ) break;
+    if ( !s0 ) s0 = head;
+    else NEXT(s) = head;
+    s = head;
+    index = ndl_find_reducer_minsig(DL(head));
+    if ( index >= 0 && index < nd_psn ) {
+      h = nd_psh[index];
+      NEWNM(mul);
+      ndl_sub(DL(head),DL(h),DL(mul));
+      if ( ndl_check_bound2(index,DL(mul)) ) 
+        return 0;
+      sugar = TD(DL(mul))+SG(ps[index]);
+      NEWSIG(sig);
+      _ndltodl(DL(mul),DL(sig));
+      _addtodl(nd_nvar,DL(nd_psh[index]->sig),DL(sig));
+      sig->pos = nd_psh[index]->sig->pos;
+      MKNM_ind_pair(pair,mul,index,sugar,sig);
+      red = ndv_mul_nm_symbolic(mul,ps[index]);
+      add_pbucket_symbolic(bucket,nd_remove_head(red));
+      NEXTNODE(rp0,rp); BDY(rp) = (pointer)pair;
+    }
+    col++;
+  }
+  if ( rp0 ) NEXT(rp) = 0;
+  NEXT(s) = 0;
+  s0v = (UINT *)MALLOC_ATOMIC(col*nd_wpd*sizeof(UINT));
+  for ( i = 0, p = s0v, s = s0; i < col;
+    i++, p += nd_wpd, s = NEXT(s) ) ndl_copy(DL(s),p);
+  *s0vect = s0v;        
+  *r = rp0;
+
+  return col;
+}
+
+NODE nd_sba_f4(int m,int **indp)
+{
+  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;
+  PGeoBucket bucket;
+  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;
+  syzlist = (NODE *)MALLOC(nd_psn*sizeof(NODE));
+  for ( i = 0; i < nd_psn; i++ ) {
+    d = update_pairs_s(d,i,syzlist);
+  }
+  nd_nbase = nd_psn;
+  f4red = 1;
+  psugar = 0;
+  f4step = 0;
+  while ( d ) {
+    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
+      if ( small_lcm(l) ) {
+        if ( DP_Print ) fprintf(asir_out,"M");
+        continue;
+      }
+      sig = l->sig;
+      stat = nd_sp(m,0,l,&h);
+#else
+      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
+      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);
+        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++;
+    }
+  }
+  if ( DP_Print ) {
+    fprintf(asir_out,"\nnumber of red=%d,",Nf4_red);
+  }
+  g = conv_ilist_s(nd_demand,0,indp);
+  return g;
+}