===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2018/engine/nd.c,v
retrieving revision 1.24
retrieving revision 1.28
diff -u -p -r1.24 -r1.28
--- OpenXM_contrib2/asir2018/engine/nd.c	2020/06/19 10:18:13	1.24
+++ OpenXM_contrib2/asir2018/engine/nd.c	2020/06/30 01:52:17	1.28
@@ -1,4 +1,4 @@
-/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.23 2020/02/05 04:56:10 noro Exp $ */
+/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.27 2020/06/25 02:53:31 noro Exp $ */
 
 #include "nd.h"
 
@@ -18,6 +18,7 @@ NM _nm_free_list;
 ND _nd_free_list;
 ND_pairs _ndp_free_list;
 NODE nd_hcf;
+int Nsyz;
 
 Obj nd_top_weight;
 
@@ -70,6 +71,7 @@ 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;
 
 NumberField get_numberfield();
 UINT *nd_det_compute_bound(NDV **dm,int n,int j);
@@ -291,106 +293,6 @@ 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 +746,7 @@ int ndl_module_glex_compare(UINT *d1,UINT *d2)
 
     default:    
       error("ndl_module_glex_compare : invalid module_ordtype");
+      return 0;
   }
 }
 
@@ -876,6 +779,7 @@ int ndl_module_compare(UINT *d1,UINT *d2)
 
     default:    
       error("ndl_module_compare : invalid module_ordtype");
+      return 0;
   }
 }
 
@@ -940,6 +844,7 @@ LAST:
       break;
     default:
       error("ndl_schreyer_compare : invalid base ordtype");
+      return 0;
   }
 }
 
@@ -1051,35 +956,6 @@ 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;
@@ -1348,22 +1224,27 @@ void print_sig(SIG s)
 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);
+  for ( r = nd_red[d], k = 0; r; r = NEXT(r), k++ ) {
+    if ( ndl_equal(dg,DL(r)) ) {
+      return r->index;
+    }
+  }
   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;
@@ -1373,7 +1254,9 @@ INLINE int ndl_find_reducer_s(UINT *dg,SIG sig)
     }
   }
   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)
@@ -1914,6 +1797,132 @@ int nd_nf_pbucket(int mod,ND g,NDV *ps,int full,ND *rp
     }
 }
 
+int nd_nf_pbucket_s(int mod,ND g,NDV *ps,int full,ND *rp)
+{
+  int hindex,index;
+  NDV p;
+  ND u,d,red;
+  NODE l;
+  NM mul,m,mrd,tail;
+  int sugar,psugar,n,h_reducible;
+  PGeoBucket bucket;
+  int c,c1,c2;
+  Z cg,cred,gcd,zzz;
+  RHist h;
+  double hmag,gmag;
+  int count = 0;
+  int hcount = 0;
+  SIG sig;
+
+  if ( !g ) {
+    *rp = 0;
+    return 1;
+  }
+  sugar = SG(g);
+  n = NV(g);
+  if ( !mod ) hmag = ((double)p_mag((P)HCZ(g)))*nd_scale;
+  bucket = create_pbucket();
+  add_pbucket(mod,bucket,g);
+  d = 0;
+  mul = (NM)MALLOC(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT));
+  sig = g->sig;
+  while ( 1 ) {
+    if ( mod > 0 || mod == -1 )
+      hindex = head_pbucket(mod,bucket);
+    else if ( mod == -2 )
+      hindex = head_pbucket_lf(bucket);
+    else
+      hindex = head_pbucket_q(bucket);
+    if ( hindex < 0 ) {
+      if ( DP_Print > 3 ) printf("(%d %d)",count,hcount);
+      if ( d ) {
+        SG(d) = sugar;
+        d->sig = sig;
+      }
+      *rp = d;
+      return 1;
+    }
+    g = bucket->body[hindex];
+    index = ndl_find_reducer_s(HDL(g),sig);
+    if ( index >= 0 && index < nd_psn ) {
+      count++;
+      if ( !d ) hcount++;
+      h = nd_psh[index];
+      ndl_sub(HDL(g),DL(h),DL(mul));
+      if ( ndl_check_bound2(index,DL(mul)) ) {
+        nd_free(d);
+        free_pbucket(bucket);
+        *rp = 0;
+        return 0;
+      }
+      p = ps[index];
+      if ( mod == -1 )
+        CM(mul) = _mulsf(_invsf(HCM(p)),_chsgnsf(HCM(g)));
+      else if ( mod == -2 ) { 
+        Z inv,t;
+        divlf(ONE,HCZ(p),&inv);
+        chsgnlf(HCZ(g),&t);
+        mullf(inv,t,&CZ(mul));
+      } else if ( mod ) {
+        c1 = invm(HCM(p),mod); c2 = mod-HCM(g);
+        DMAR(c1,c2,0,mod,c); CM(mul) = c;
+      } else {
+        igcd_cofactor(HCZ(g),HCZ(p),&gcd,&cg,&cred);
+        chsgnz(cg,&CZ(mul));
+        nd_mul_c_q(d,(P)cred);
+        mulq_pbucket(bucket,cred);
+        g = bucket->body[hindex];
+        gmag = (double)p_mag((P)HCZ(g));
+      }
+      red = ndv_mul_nm(mod,mul,p);
+      bucket->body[hindex] = nd_remove_head(g);
+      red = nd_remove_head(red);
+      add_pbucket(mod,bucket,red);
+      psugar = SG(p)+TD(DL(mul));
+      sugar = MAX(sugar,psugar);
+      if ( !mod && hmag && (gmag > hmag) ) {
+         g = normalize_pbucket(mod,bucket);
+         if ( !g ) {
+           if ( d ) {
+             SG(d) = sugar;
+             d->sig = sig;
+           }
+           *rp = d;
+           return 1;
+         }
+         nd_removecont2(d,g);
+         hmag = ((double)p_mag((P)HCZ(g)))*nd_scale;
+         add_pbucket(mod,bucket,g);
+      }
+    } else if ( index == -1 ) {
+      // singular top reducible
+      return -1;
+    } else if ( !full ) {
+      g = normalize_pbucket(mod,bucket);
+      if ( g ) {
+        SG(g) = sugar;
+        g->sig = sig;
+      }
+      *rp = g;
+      return 1;
+    } else {
+      m = BDY(g); 
+      if ( NEXT(m) ) {
+        BDY(g) = NEXT(m); NEXT(m) = 0; LEN(g)--;
+      } else {
+        FREEND(g); g = 0;
+      }
+      bucket->body[hindex] = g;
+      NEXT(m) = 0;
+      if ( d ) {
+        NEXT(tail)=m; tail=m; LEN(d)++;
+      } else {
+        MKND(n,m,1,d); tail = BDY(d);
+      }
+    }
+  }
+}
+
 /* input : list of NDV, cand : list of NDV */
 
 int ndv_check_membership(int m,NODE input,int obpe,int oadv,EPOS oepos,NODE cand)
@@ -2374,7 +2383,9 @@ NODE nd_gb(int m,int ishomo,int checkonly,int gensyz,i
   int diag_count = 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++ ) {
@@ -2449,7 +2460,9 @@ 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 {
@@ -2466,6 +2479,7 @@ again:
  }
  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;
 }
 
@@ -2500,9 +2514,12 @@ 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)
@@ -2515,16 +2532,64 @@ 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 small_lcm(ND_pairs l)
+{
+  SIG sig;
+  int i;
+  static DL lcm,mul,quo;
+  static int nvar;
+
+  if ( nvar < nd_nvar ) {
+    nvar = nd_nvar; NEWDL(lcm,nvar); NEWDL(quo,nvar); NEWDL(mul,nvar);
+  }
+  sig = l->sig;
+  _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),quo);
+      _subfromdl(nd_nvar,DL(nd_psh[i]->sig),quo);
+      _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;
+}
+
+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 ( small_lcm(p) ) {
+      // remove p
+      prev->next = p->next;
+    } else
+      prev = p;
+    p = p->next;
+  }
+  return (ND_pairs)root.next;
+}
+
+struct oEGT eg_create,eg_newpairs,eg_merge;
+
 NODE nd_sba_buch(int m,int ishomo,int **indp)
 {
   int i,nh,sugar,stat;
@@ -2539,55 +2604,51 @@ NODE nd_sba_buch(int m,int ishomo,int **indp)
   LIST list;
   SIG sig;
   NODE syzlist;
-  static int wpd;
-  static SIG quo,mul;
-  static DL lcm;
+  int Nredundant;
+  DL lcm,quo,mul;
+  struct oEGT eg1,eg2,eg_update,eg_remove;
 
+init_eg(&eg_remove);
   syzlist = 0;
+  Nsyz = 0;
   Nnd_add = 0;
+  Nredundant = 0;
   g = 0; d = 0;
   for ( i = 0; i < nd_psn; i++ ) {
     d = update_pairs_s(d,g,i,0);
     g = append_one(g,i);
   }
   sugar = 0;
+  NEWDL(lcm,nd_nvar); NEWDL(quo,nd_nvar); NEWDL(mul,nd_nvar);
+init_eg(&eg_create);
+init_eg(&eg_merge);
   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 ( small_lcm(l) ) {
       if ( DP_Print ) fprintf(asir_out,"M");
+      Nredundant++;
       continue;
     }
     if ( SG(l) != sugar ) {
       sugar = SG(l);
       if ( DP_Print ) fprintf(asir_out,"%d",sugar);
     }
+    sig = l->sig;
     stat = nd_sp(m,0,l,&h);
     if ( !stat ) {
       NEXT(l) = d; d = l;
       d = nd_reconstruct(0,d);
       goto again;
     }
-#if 0 && USE_GEOBUCKET
+#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);
 #else
     stat = nd_nf_s(m,0,h,nd_ps,!Top,&nf);
@@ -2598,25 +2659,36 @@ again:
       goto again;
     } else if ( stat == -1 ) {
       if ( DP_Print ) { printf("S"); fflush(stdout); }
+      FREENDP(l);
     } else if ( nf ) {
       if ( DP_Print ) { printf("+"); fflush(stdout); }
       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);
       FREENDP(l);
    } else {
      // syzygy
+get_eg(&eg1);
      d = remove_spair_s(d,sig);
+get_eg(&eg2); add_eg(&eg_remove,&eg1,&eg2);
      syzlist = insert_sig(syzlist,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); }
+ if ( DP_Print ) { 
+   printf("\nnd_sba done. nd_add=%d,Nsyz=%d,Nredundant=%d\n",Nnd_add,Nsyz,Nredundant);
+   fflush(stdout); 
+   print_eg("create",&eg_create);
+   print_eg("merge",&eg_merge);
+   print_eg("remove",&eg_remove);
+   printf("\n");
+ }
  return g;
 }
 
@@ -3042,10 +3114,14 @@ 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 d1;
+  struct oEGT eg1,eg2,eg3;
 
   if ( !g ) return d;
+get_eg(&eg1);
   d1 = nd_newpairs_s(g,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;
 }
 
@@ -3098,13 +3174,13 @@ int comp_sig(SIG s1,SIG s2)
   static int nvar;
   int ret;
 
-  if ( nvar < nd_nvar ) {
-    nvar = nd_nvar;
-    NEWDL(m1,nvar);
-    NEWDL(m2,nvar);
+  if ( nvar != nd_nvar ) {
+    nvar = nd_nvar; NEWDL(m1,nvar); NEWDL(m2,nvar);
   }
-  _ndltodl(DL(nd_psh[s1->pos]),m1);
-  _ndltodl(DL(nd_psh[s2->pos]),m2);
+//  _ndltodl(DL(nd_psh[s1->pos]),m1);
+//  _ndltodl(DL(nd_psh[s2->pos]),m2);
+  _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);
   ret = (*cmpdl)(nd_nvar,m1,m2);
@@ -3131,15 +3207,14 @@ 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;
@@ -3147,8 +3222,7 @@ 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;
@@ -3253,17 +3327,18 @@ ND_pairs nd_newpairs_s( NODE g, 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;
+  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);
   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);
+//  for ( h = g; h; h = NEXT(h) ) {
+//    ret = _create_spair_s((long)BDY(h),t,_sp,_sig1,_sig2);
     if ( ret ) {
       spsig = _sp->sig;
       for ( s = syz; s; s = s->next ) {
@@ -3275,7 +3350,8 @@ ND_pairs nd_newpairs_s( NODE g, int t, NODE syz)
         NEWND_pairs(sp);
         dup_ND_pairs(sp,_sp);
         r0 = insert_pair_s(r0,sp);
-      }
+      } else
+        Nsyz++;
     }
   }
   return r0;
@@ -3558,6 +3634,24 @@ 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;
+
+#if 0
+  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;
+}
+
 int nd_tdeg(NDV c)
 {
   int wmax = 0;
@@ -3666,7 +3760,7 @@ 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
@@ -3743,19 +3837,22 @@ 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]);
+    }
   }
   if ( nd_gentrace && nd_tracelist ) NEXT(tn) = 0;
   return 1;
@@ -4096,7 +4193,9 @@ 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;
@@ -4140,8 +4239,7 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,str
       max = MAX(e,max);
     }
   }
-//  nd_setup_parameters(nvar,max);
-  nd_setup_parameters(nvar,16);
+  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) ) {
@@ -4169,7 +4267,7 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,str
   }
 
   ndv_setup(m,0,fd0,0,0,1);
-  x = nd_sba_buch(m,ishomo || homo,&perm);
+  x = f4 ? nd_sba_f4(m,&perm) : nd_sba_buch(m,ishomo || homo,&perm);
   if ( !x ) {
     *rp = 0; return;
   }
@@ -4799,7 +4897,7 @@ 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");
@@ -6377,6 +6475,7 @@ 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;
 }
 
@@ -6455,7 +6554,7 @@ 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");
@@ -7648,7 +7747,7 @@ 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;
@@ -10053,6 +10152,29 @@ 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;
@@ -10082,7 +10204,7 @@ 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;
@@ -10103,7 +10225,7 @@ 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];
@@ -10177,7 +10299,7 @@ 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));
@@ -10309,3 +10431,400 @@ int nd_gauss_elim_mod64(mp_limb_t **mat,int *sugar,ND_
 }
 #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)
+{
+  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;
+
+  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 ( rank = 0, j = 0; j < col; j++ ) {
+    for ( i = rank; i < row; i++ ) {
+      a = mat[i][j]; c = cmat[i][j];
+      MOD128(a,c,md);
+      mat[i][j] = a; cmat[i][j] = 0;
+    }
+    imin = -1;
+    for ( i = rank; i < row; i++ )
+      if ( mat[i][j] && (imin < 0 || comp_sig(sig[imin],sig[i]) > 0) ) imin = i;
+    if ( imin == -1 ) {
+      colstat[j] = 0;
+      continue;
+    } else
+      colstat[j] = 1;
+    if ( imin != rank ) {
+      t = mat[imin]; mat[imin] = mat[rank]; mat[rank] = t;
+      ct = cmat[imin]; cmat[imin] = cmat[rank]; cmat[rank] = ct;
+      s = sugar[imin]; sugar[imin] = sugar[rank]; sugar[rank] = s;
+      sg = sig[imin]; sig[imin] = sig[rank]; sig[rank] = sg;
+      if ( spactive ) {
+        pair = spactive[imin]; spactive[imin] = spactive[rank]; 
+        spactive[rank] = pair;
+      }
+    }
+    /* column j is normalized */
+    s = sugar[rank];
+    inv = invm((UINT)mat[rank][j],md);
+    /* normalize pivot row */
+    for ( k = j, pk = mat[rank]+j, ck = cmat[rank]+j; k < col; k++, pk++, ck++ ) {
+      a = *pk; c = *ck; MOD128(a,c,md); *pk = (a*inv)%md; *ck = 0;
+    }
+    for ( i = rank+1; i < row; i++ ) {
+      if ( (a = mat[i][j]) != 0 ) {
+        sugar[i] = MAX(sugar[i],s);
+        red_by_vect64(md,mat[i]+j,cmat[i]+j,mat[rank]+j,(int)(md-a),col-j);
+        Nf4_red++;
+      }
+    }
+    rank++;
+  }
+#if 1
+  for ( j = col-1, l = rank-1; j >= 0; j-- )
+    if ( colstat[j] ) {
+      for ( k = j, pk = mat[l]+j, ck = cmat[l]+j; k < col; k++, pk++, ck++ ) {
+        a = *pk; c = *ck; MOD128(a,c,md); *pk = a; *ck = 0;
+      }
+      s = sugar[l];
+      for ( i = 0; i < l; i++ ) {
+        a = mat[i][j]; c = cmat[i][j]; MOD128(a,c,md); mat[i][j] = a; cmat[i][j] = 0;
+        if ( a && comp_sig(sig[i],sig[l]) > 0 ) {
+          sugar[i] = MAX(sugar[i],s);
+          red_by_vect64(md,mat[i]+j,cmat[i]+j,mat[l]+j,(int)(md-a),col-j);
+          Nf4_red++;
+        }
+      }
+      l--;
+    }
+#endif
+  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 = insert_sig(*syzlistp,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 = insert_sig(*syzlistp,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 < rank; i++ ) {
+        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];
+        GCFREE(spmat[i]);
+    }
+    if ( r0 ) NEXT(r) = 0;
+
+    for ( ; i < sprow; i++ ) {
+      GCFREE(spmat[i]);
+      *syzlistp = insert_sig(*syzlistp,spsig[i]);
+    }
+    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;
+}
+
+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 )
+    r0 = nd_f4_red_mod64_main_s(m,sp0,nsp,s0vect,col,rvect,rhead,imat,nred,syzlistp);
+  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;
+  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;
+  UINT c;
+  UINT **spmat;
+  UINT *s0vect,*svect,*p,*v;
+  int *colstat;
+  IndArray *imat;
+  int *rhead;
+  int spcol,sprow;
+  int sugar,sugarh;
+  PGeoBucket bucket;
+  struct oEGT eg0,eg1,eg_f4;
+  Z i1,i2,sugarq;
+  NODE syzlist;
+
+  Nf4_red=0;
+  g = 0; d = 0;
+  syzlist = 0;
+  for ( i = 0; i < nd_psn; i++ ) {
+    d = update_pairs_s(d,g,i,syzlist);
+    g = append_one(g,i);
+  }
+  f4red = 1;
+  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) ) {
+      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 ( stat < 0 ) {
+        // top reducible
+        if ( DP_Print ) { fprintf(asir_out,"S"); fflush(asir_out); }
+      } else if ( tmpred ) {
+        nf = ndtondv(m,tmpred);
+        ndv_removecont(m,nf);
+        nh = ndv_newps(m,nf,0);
+        d = update_pairs_s(d,g,nh,syzlist);
+        g = append_one(g,nh);
+      } else {
+        syzlist = insert_sig(syzlist,sig);
+      } 
+    }
+    for ( r = syzlist; r; r = NEXT(r) )
+      d = remove_spair_s(d,(SIG)BDY(r));
+    if ( DP_Print ) { 
+      fprintf(asir_out,"f4red=%d,gblen=%d\n",f4red,length(g)); 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);
+  }
+  conv_ilist(nd_demand,0,g,indp);
+  return g;
+}