===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2018/engine/nd.c,v
retrieving revision 1.20
retrieving revision 1.37
diff -u -p -r1.20 -r1.37
--- OpenXM_contrib2/asir2018/engine/nd.c	2019/09/15 08:46:12	1.20
+++ OpenXM_contrib2/asir2018/engine/nd.c	2020/10/06 06:31:19	1.37
@@ -1,4 +1,4 @@
-/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.19 2019/09/04 05:32:10 noro Exp $ */
+/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.36 2020/09/27 04:35:04 noro Exp $ */
 
 #include "nd.h"
 
@@ -8,14 +8,17 @@ struct oEGT eg_search,f4_symb,f4_conv,f4_elim1,f4_elim
 int diag_period = 6;
 int weight_check = 1;
 int (*ndl_compare_function)(UINT *a1,UINT *a2);
-/* for schreyer order */
+/* for general module order */
 int (*ndl_base_compare_function)(UINT *a1,UINT *a2);
+int (*dl_base_compare_function)(int nv,DL a,DL b);
+int nd_base_ordtype;
 int nd_dcomp;
 int nd_rref2;
 NM _nm_free_list;
 ND _nd_free_list;
 ND_pairs _ndp_free_list;
 NODE nd_hcf;
+int Nsyz,Nsamesig;
 
 Obj nd_top_weight;
 
@@ -47,7 +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;
@@ -57,7 +60,7 @@ static int nd_worb_len;
 static int nd_found,nd_create,nd_notfirst;
 static int nmv_adv;
 static int nd_demand;
-static int nd_module,nd_ispot,nd_mpos,nd_pot_nelim;
+static int nd_module,nd_module_ordtype,nd_mpos,nd_pot_nelim;
 static int nd_module_rank,nd_poly_weight_len;
 static int *nd_poly_weight,*nd_module_weight;
 static NODE nd_tracelist;
@@ -68,6 +71,8 @@ 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);
@@ -526,6 +531,13 @@ void ndl_weight_mask(UINT *d)
     }
 }
 
+int ndl_glex_compare(UINT *d1,UINT *d2)
+{
+  if ( TD(d1) > TD(d2) ) return 1;
+  else if ( TD(d1) < TD(d2) ) return -1;
+  else return ndl_lex_compare(d1,d2);
+}
+
 int ndl_lex_compare(UINT *d1,UINT *d2)
 {
     int i;
@@ -695,135 +707,147 @@ int ndl_ww_lex_compare(UINT *d1,UINT *d2)
     return ndl_lex_compare(d1,d2);
 }
 
-int ndl_module_weight_compare(UINT *d1,UINT *d2)
+// common function for module glex and grlex comparison
+int ndl_module_glex_compare(UINT *d1,UINT *d2)
 {
-  int s,j;
+  int c;
 
-  if ( nd_nvar != nd_poly_weight_len )
-    error("invalid module weight : the length of polynomial weight != the number of variables");
-  s = 0;
-  for ( j = 0; j < nd_nvar; j++ )
-     s += (GET_EXP(d1,j)-GET_EXP(d2,j))*nd_poly_weight[j];
-  if ( MPOS(d1) >= 1 && MPOS(d2) >= 1 ) {
-    s += nd_module_weight[MPOS(d1)-1]-nd_module_weight[MPOS(d2)-1];
-  }
-  if ( s > 0 ) return 1;
-  else if ( s < 0 ) return -1;
-  else return 0;
-}
+  switch ( nd_module_ordtype ) {
+    case 0:
+      if ( TD(d1) > TD(d2) ) return 1;
+      else if ( TD(d1) < TD(d2) ) return -1;
+      else if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c;
+      else if ( MPOS(d1) < MPOS(d2) ) return 1;
+      else if ( MPOS(d1) > MPOS(d2) ) return -1;
+      else return 0;
+      break;
 
-int ndl_module_grlex_compare(UINT *d1,UINT *d2)
-{
-    int i,c;
-
-//    if ( nd_module_rank && (c = ndl_module_weight_compare(d1,d2)) ) return c;
-    if ( nd_ispot ) {
+    case 1:
       if ( nd_pot_nelim && MPOS(d1)>=nd_pot_nelim+1 && MPOS(d2) >= nd_pot_nelim+1 ) {
          if ( TD(d1) > TD(d2) ) return 1;
          else if ( TD(d1) < TD(d2) ) return -1;
          if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c;
          if ( MPOS(d1) < MPOS(d2) ) return 1;
          else if ( MPOS(d1) > MPOS(d2) ) return -1;
-         return 0;
       }
       if ( MPOS(d1) < MPOS(d2) ) return 1;
       else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    if ( TD(d1) > TD(d2) ) return 1;
-    else if ( TD(d1) < TD(d2) ) return -1;
-    if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c;
-    if ( !nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    return 0;
-}
+      else if ( TD(d1) > TD(d2) ) return 1;
+      else if ( TD(d1) < TD(d2) ) return -1;
+      else return ndl_lex_compare(d1,d2);
+      break;
 
-int ndl_module_glex_compare(UINT *d1,UINT *d2)
-{
-    int i,c;
+    case 2: // weight -> POT
+      if ( TD(d1) > TD(d2) ) return 1;
+      else if ( TD(d1) < TD(d2) ) return -1;
+      else if ( MPOS(d1) < MPOS(d2) ) return 1;
+      else if ( MPOS(d1) > MPOS(d2) ) return -1;
+      else return ndl_lex_compare(d1,d2);
+      break;
 
-//    if ( nd_module_rank && (c = ndl_module_weight_compare(d1,d2)) ) return c;
-    if ( nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    if ( TD(d1) > TD(d2) ) return 1;
-    else if ( TD(d1) < TD(d2) ) return -1;
-    if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c;
-    if ( !nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    return 0;
+    default:    
+      error("ndl_module_glex_compare : invalid module_ordtype");
+      return 0;
+  }
 }
 
-int ndl_module_lex_compare(UINT *d1,UINT *d2)
+// common  for module comparison
+int ndl_module_compare(UINT *d1,UINT *d2)
 {
-    int i,c;
+  int c;
 
-//    if ( nd_module_rank && (c = ndl_module_weight_compare(d1,d2)) ) return c;
-    if ( nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c;
-    if ( !nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    return 0;
-}
+  switch ( nd_module_ordtype ) {
+    case 0:
+      if ( (c = (*ndl_base_compare_function)(d1,d2)) != 0 ) return c;
+      else if ( MPOS(d1) > MPOS(d2) ) return -1;
+      else if ( MPOS(d1) < MPOS(d2) ) return 1;
+      else return 0;
+      break;
 
-int ndl_module_block_compare(UINT *d1,UINT *d2)
-{
-    int i,c;
+    case 1:
+      if ( MPOS(d1) < MPOS(d2) ) return 1;
+      else if ( MPOS(d1) > MPOS(d2) ) return -1;
+      else return (*ndl_base_compare_function)(d1,d2); 
+      break;
 
-//    if ( nd_module_rank && (c = ndl_module_weight_compare(d1,d2)) ) return c;
-    if ( nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    if ( (c = ndl_block_compare(d1,d2)) != 0 ) return c;
-    if ( !nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    return 0;
-}
+    case 2: // weight -> POT
+      if ( TD(d1) > TD(d2) ) return 1;
+      else if ( TD(d1) < TD(d2) ) return -1;
+      else if ( MPOS(d1) < MPOS(d2) ) return 1;
+      else if ( MPOS(d1) > MPOS(d2) ) return -1;
+      else return (*ndl_base_compare_function)(d1,d2); 
+      break;
 
-int ndl_module_matrix_compare(UINT *d1,UINT *d2)
-{
-    int i,c;
-
-//    if ( nd_module_rank && (c = ndl_module_weight_compare(d1,d2)) ) return c;
-    if ( nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    if ( (c = ndl_matrix_compare(d1,d2)) != 0 ) return c;
-    if ( !nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    return 0;
+    default:    
+      error("ndl_module_compare : invalid module_ordtype");
+      return 0;
+  }
 }
 
-int ndl_module_composite_compare(UINT *d1,UINT *d2)
+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)
 {
-    int i,c;
+  int pos1,pos2,t,j;
+  DMM *in;
+  DMMstack s;
+  static DL d1=0;
+  static DL d2=0;
+  static int dlen=0;
 
-//    if ( nd_module_rank && (c = ndl_module_weight_compare(d1,d2)) ) return c;
-    if ( nd_ispot ) {
-        if ( MPOS(d1) > MPOS(d2) ) return 1;
-        else if ( MPOS(d1) < MPOS(d2) ) return -1;
+  pos1 = MPOS(m1); pos2 = MPOS(m2);
+  if ( pos1 == pos2 ) return (*ndl_base_compare_function)(m1,m2);
+  if ( nd_nvar > dlen ) {
+    NEWDL(d1,nd_nvar);
+    NEWDL(d2,nd_nvar);
+    dlen = nd_nvar;
+  }
+  d1->td = TD(m1);
+  for ( j = 0; j < nd_nvar; j++ ) d1->d[j] = GET_EXP(m1,j);
+  d2->td = TD(m2);
+  for ( j = 0; j < nd_nvar; j++ ) d2->d[j] = GET_EXP(m2,j);
+  for ( s = dmm_stack; s; s = NEXT(s) ) {
+    in = s->in;
+    _addtodl(nd_nvar,in[pos1]->dl,d1);
+    _addtodl(nd_nvar,in[pos2]->dl,d2);
+    if ( in[pos1]->pos == in[pos2]->pos && _eqdl(nd_nvar,d1,d2)) {
+      if ( pos1 < pos2 ) return 1;
+      else if ( pos1 > pos2 ) return -1;
+      else return 0;
     }
-    if ( (c = ndl_composite_compare(d1,d2)) != 0 ) return c;
-    if ( !nd_ispot ) {
-        if ( MPOS(d1) > MPOS(d2) ) return 1;
-        else if ( MPOS(d1) < MPOS(d2) ) return -1;
-    }
-    return 0;
+    pos1 = in[pos1]->pos;
+    pos2 = in[pos2]->pos;
+    if ( pos1 == pos2 ) return (*dl_base_compare_function)(nd_nvar,d1,d2);
+  }
+  // comparison by the bottom order
+LAST:
+  switch ( nd_base_ordtype ) {
+    case 0:
+      t = (*dl_base_compare_function)(nd_nvar,d1,d2);
+      if ( t ) return t;
+      else if ( pos1 < pos2 ) return 1;
+      else if ( pos1 > pos2 ) return -1;
+      else return 0;
+      break;
+    case 1:
+      if ( pos1 < pos2 ) return 1;
+      else if ( pos1 > pos2 ) return -1;
+      else return (*dl_base_compare_function)(nd_nvar,d1,d2);
+      break;
+    case 2:
+      if ( d1->td > d2->td  ) return 1;
+      else if ( d1->td < d2->td ) return -1;
+      else if ( pos1 < pos2 ) return 1;
+      else if ( pos1 > pos2 ) return -1;
+      else return (*dl_base_compare_function)(nd_nvar,d1,d2);
+      break;
+    default:
+      error("ndl_schreyer_compare : invalid base ordtype");
+      return 0;
+  }
 }
 
 INLINE int ndl_equal(UINT *d1,UINT *d2)
@@ -1180,6 +1204,67 @@ INLINE int ndl_find_reducer(UINT *dg)
     return -1;
 }
 
+// ret=0,...,nd_psn-1 => reducer found
+// ret=nd_psn => reducer not found
+// ret=-1 => singular top reducible
+
+int comp_sig(SIG s1,SIG s2);
+void _ndltodl(UINT *ndl,DL dl);
+
+void print_sig(SIG s)
+{
+  int i;
+
+  fprintf(asir_out,"<<");
+  for ( i = 0; i < nd_nvar; i++ ) {
+    fprintf(asir_out,"%d",s->dl->d[i]);
+    if ( i != nd_nvar-1 ) fprintf(asir_out,",");
+  }
+  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,d,k;
+  static int wpd,nvar;
+  static SIG quo;
+  static UINT *tmp;
+
+  if ( !quo || nvar != nd_nvar ) NEWSIG(quo);
+  if ( wpd != nd_wpd ) {
+    wpd = nd_wpd;
+    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_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 ) { fprintf(asir_out,"s"); fflush(asir_out); singular = 1; }
+    }
+  }
+  if ( singular ) return -1;
+  else if ( i < nd_psn )
+    nd_append_red(dg,i);
+  return i;
+}
+
 ND nd_merge(ND p1,ND p2)
 {
     int n,c;
@@ -1522,6 +1607,90 @@ int nd_nf(int mod,ND d,ND g,NDV *ps,int full,ND *rp)
     return 1;
 }
 
+// ret=1 => success
+// ret=0 => overflow
+// ret=-1 => singular top reducible
+
+int nd_nf_s(int mod,ND d,ND g,NDV *ps,int full,ND *rp)
+{
+    NM m,mrd,tail;
+    NM mul;
+    int n,sugar,psugar,sugar0,stat,index;
+    int c,c1,c2,dummy;
+    RHist h;
+    NDV p,red;
+    Q cg,cred,gcd,tq,qq;
+    Z iq;
+    DP dmul;
+    NODE node;
+    LIST hist;
+    double hmag;
+    P tp,tp1;
+    Obj tr,tr1,div;
+    union oNDC hg;
+    P cont;
+    SIG sig;
+
+    if ( !g ) {
+        *rp = d;
+        return 1;
+    }
+    if ( !mod ) hmag = ((double)p_mag(HCP(g)))*nd_scale;
+
+    sugar0 = sugar = SG(g);
+    n = NV(g);
+    mul = (NM)MALLOC(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT));
+    if ( d )
+        for ( tail = BDY(d); NEXT(tail); tail = NEXT(tail) );
+    sig = g->sig;
+    for ( ; g; ) {
+        index = ndl_find_reducer_s(HDL(g),sig);
+        if ( index >= 0 && index < nd_psn ) {
+            // reducer found
+            h = nd_psh[index];
+            ndl_sub(HDL(g),DL(h),DL(mul));
+            if ( ndl_check_bound2(index,DL(mul)) ) {
+                nd_free(g); nd_free(d);
+                return 0;
+            }
+            p = ps[index];
+            /* d+g -> div*(d+g)+mul*p */
+            g = nd_reduce2(mod,d,g,p,mul,0,&div);
+            sugar = MAX(sugar,SG(p)+TD(DL(mul)));
+            if ( !mod && g && ((double)(p_mag(HCP(g))) > hmag) ) {
+                hg = HCU(g);
+                nd_removecont2(d,g);
+                hmag = ((double)p_mag(HCP(g)))*nd_scale;
+            }
+        } else if ( index == -1 ) {
+          // singular top reducible
+          return -1;
+        } else if ( !full ) {
+            *rp = g;
+            g->sig = sig;
+            return 1;
+        } else {
+            m = BDY(g); 
+            if ( NEXT(m) ) {
+                BDY(g) = NEXT(m); NEXT(m) = 0; LEN(g)--;
+            } else {
+                FREEND(g); g = 0;
+            }
+            if ( d ) {
+                NEXT(tail)=m; tail=m; LEN(d)++;
+            } else {
+                MKND(n,m,1,d); tail = BDY(d);
+            }
+        }
+    }
+    if ( d ) {
+      SG(d) = sugar;
+      d->sig = sig;
+    }
+    *rp = d;
+    return 1;
+}
+
 int nd_nf_pbucket(int mod,ND g,NDV *ps,int full,ND *rp)
 {
     int hindex,index;
@@ -1634,6 +1803,132 @@ 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)
@@ -1646,7 +1941,7 @@ int ndv_check_membership(int m,NODE input,int obpe,int
     Z q;
     LIST list;
 
-    ndv_setup(m,0,cand,nd_gentrace?1:0,1);
+    ndv_setup(m,0,cand,nd_gentrace?1:0,1,0);
     n = length(cand);
 
   if ( nd_gentrace ) { nd_alltracelist = 0; nd_tracelist = 0; }
@@ -2094,7 +2389,9 @@ 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++ ) {
@@ -2159,7 +2456,7 @@ again:
         }
       }
       nfv = ndtondv(m,nf); nd_free(nf);
-      nh = ndv_newps(m,nfv,0,0);
+      nh = ndv_newps(m,nfv,0);
       if ( !m && (ishomo && ++diag_count == diag_period) ) {
         diag_count = 0;
         stat = do_diagonalize(sugar,m);
@@ -2169,7 +2466,9 @@ 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 {
@@ -2182,11 +2481,254 @@ again:
      }
      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); }
+ 
+  if ( DP_Print )
+    print_eg("update",&eg_update);
+  return g;
+}
+
+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);
+
+void _copydl(int n,DL d1,DL d2);
+void _subfromdl(int n,DL d1,DL d2);
+extern int (*cmpdl)(int n,DL d1,DL d2);
+
+NODE insert_sig(NODE l,SIG s)
+{
+  int pos;
+  DL sig;
+  struct oNODE root;
+  NODE p,prev,r;
+  SIG t;
+
+  pos = s->pos; sig = DL(s);
+  root.next = l; prev = &root;
+  for ( p = l; p; p = p->next ) {
+    t = (SIG)p->body;
+    if ( t->pos == pos ) {
+      if ( _dl_redble(DL(t),sig,nd_nvar) )
+        return root.next;
+      else if ( _dl_redble(sig,DL(t),nd_nvar) )
+        // remove p
+        prev->next = p->next;
+    } else
+      prev = p;
+  }
+  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)
+{
+  struct oND_pairs root;
+  ND_pairs prev,p;
+  SIG spsig;
+
+  root.next = d;
+  prev = &root; p = d;
+  while ( p ) {
+    spsig = p->sig;
+    if ( sig->pos == spsig->pos && _dl_redble(DL(sig),DL(spsig),nd_nvar) ) {
+      // remove p
+      prev->next = p->next;
+      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 ( 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 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 conv_ilist_s(int demand,int trace,int **indp);
+
+NODE nd_sba_buch(int m,int ishomo,int **indp)
+{
+  int i,j,nh,sugar,stat;
+  NODE r,t,g;
+  ND_pairs d;
+  ND_pairs l;
+  ND h,nf,s,head,nf1;
+  NDV nfv;
+  Z q;
+  union oNDC dn,hc;
+  P cont;
+  LIST list;
+  SIG sig;
+  NODE *syzlist;
+  int Nredundant;
+  DL lcm,quo,mul;
+  struct oEGT eg1,eg2,eg_update,eg_remove,eg_large,eg_nf,eg_nfzero;
+
+init_eg(&eg_remove);
+  syzlist = (NODE *)MALLOC(nd_psn*sizeof(NODE));
+  Nsyz = 0;
+  Nnd_add = 0;
+  Nredundant = 0;
+  d = 0;
+  for ( i = 0; i < nd_psn; i++ ) {
+    d = update_pairs_s(d,i,syzlist);
+  }
+  for ( i = 0; i < nd_psn; i++ )
+    for ( j = i+1; j < nd_psn; j++ ) {
+      NEWSIG(sig); sig->pos = j;
+      _copydl(nd_nvar,nd_sba_hm[i],sig->dl);
+      syzlist[sig->pos] = insert_sig(syzlist[sig->pos],sig);
+    }
+  sugar = 0;
+  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:
+    if ( DP_Print ) {
+      int len;
+      ND_pairs td;
+      for ( td = d, len=0; td; td = td->next, len++)
+        ;
+       if ( !(len%100) ) fprintf(asir_out,"(%d)",len);
+      }
+    l = d; d = d->next;
+    if ( small_lcm(l) ) {
+      if ( DP_Print ) fprintf(asir_out,"M");
+      Nredundant++;
+      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;
+    }
+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);
+#else
+    stat = nd_nf_s(m,0,h,nd_ps,!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);
    }
  }
- 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;
+ g = conv_ilist_s(nd_demand,0,indp);
+ if ( DP_Print ) { 
+   printf("\nnd_sba done. nd_add=%d,Nsyz=%d,Nsamesig=%d,Nredundant=%d\n",Nnd_add,Nsyz,Nsamesig,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;
 }
 
 /* splist = [[i1,i2],...] */
@@ -2442,7 +2984,7 @@ again:
             nd_tracelist = t;
           }
         }
-        nh = ndv_newps(0,nfv,nfqv,0);
+        nh = ndv_newps(0,nfv,nfqv);
         if ( ishomo && ++diag_count == diag_period ) {
           diag_count = 0;
           if ( DP_Print > 2 ) fprintf(asir_out,"|");
@@ -2512,7 +3054,7 @@ NODE ndv_reduceall(int m,NODE f)
 
   if ( nd_nora ) return f;
   n = length(f);
-  ndv_setup(m,0,f,0,1);
+  ndv_setup(m,0,f,0,1,0);
   perm = (int *)MALLOC(n*sizeof(int));
   if ( nd_gentrace ) {
     for ( t = nd_tracelist, i = 0; i < n; i++, t = NEXT(t) )
@@ -2606,7 +3148,22 @@ 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, int t,NODE *syz)
+{
+  ND_pairs d1;
+  struct oEGT eg1,eg2,eg3;
+
+  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;
+}
+
 ND_pairs nd_newpairs( NODE g, int t )
 {
   NODE h;
@@ -2644,6 +3201,221 @@ 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 0
+  _copydl(nd_nvar,nd_sba_hm[s1->pos],m1);
+  _copydl(nd_nvar,nd_sba_hm[s2->pos],m2);
+  _addtodl(nd_nvar,s1->dl,m1);
+  _addtodl(nd_nvar,s2->dl,m2);
+#else
+  _adddl(nd_nvar,s1->dl,nd_sba_hm[s1->pos],m1);
+  _adddl(nd_nvar,s2->dl,nd_sba_hm[s2->pos],m2);
+#endif
+  ret = (*cmpdl)(nd_nvar,m1,m2);
+  if ( ret != 0 ) return ret;
+  else if ( s1->pos > s2->pos ) return 1;
+  else if ( s1->pos < s2->pos ) return -1;
+  else return 0;
+#endif
+}
+
+int _create_spair_s(int i1,int i2,ND_pairs sp,SIG sig1,SIG sig2)
+{
+  int ret,s1,s2;
+  RHist p1,p2;
+  static int wpd;
+  static UINT *lcm;
+
+  sp->i1 = i1;
+  sp->i2 = i2;
+  p1 = nd_psh[i1];
+  p2 = nd_psh[i2];
+  ndl_lcm(DL(p1),DL(p2),sp->lcm);
+  s1 = SG(p1)-TD(DL(p1));
+  s2 = SG(p2)-TD(DL(p2));
+  SG(sp) = MAX(s1,s2) + TD(sp->lcm);
+
+  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_sub(sp->lcm,DL(p1),lcm);
+  _ndltodl(lcm,DL(sig1));
+  _addtodl(nd_nvar,DL(p1->sig),DL(sig1));
+  sig1->pos = p1->sig->pos;
+
+  // DL(sig2) <- sp->lcm
+  // DL(sig2) -= DL(p2)
+  // DL(sig2) += DL(p2->sig)
+  ndl_sub(sp->lcm,DL(p2),lcm);
+  _ndltodl(lcm,DL(sig2));
+  _addtodl(nd_nvar,DL(p2->sig),DL(sig2));
+  sig2->pos = p2->sig->pos;
+
+  ret = comp_sig(sig1,sig2);
+  if ( ret == 0 ) return 0;
+  else if ( ret > 0 ) sp->sig = sig1;
+  else sp->sig = sig2;
+  return 1;
+}
+
+SIG dup_sig(SIG sig)
+{
+  SIG r;
+
+  if ( !sig ) return 0;
+  else {
+    NEWSIG(r);
+    _copydl(nd_nvar,DL(sig),DL(r));
+    r->pos = sig->pos;
+    return r;
+  }
+}
+
+void dup_ND_pairs(ND_pairs to,ND_pairs from)
+{
+  to->i1 = from->i1; 
+  to->i2 = from->i2; 
+  to->sugar = from->sugar;
+  to->sugar2 = from->sugar2;
+  ndl_copy(from->lcm,to->lcm);
+  to->sig = dup_sig(from->sig);
+}
+
+ND_pairs merge_pairs_s(ND_pairs p1,ND_pairs p2)
+{
+  struct oND_pairs root;
+  ND_pairs q1,q2,r0,r;
+  int ret;
+
+  r = &root;
+  for ( q1 = p1, q2 = p2; q1 != 0 && q2 != 0; ) {
+    ret = comp_sig(q1->sig,q2->sig);
+    if ( ret < 0 ) {
+      r->next = q1; r = q1; q1 = q1->next;
+    } else if ( ret > 0 ) {
+      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;
+      } else {
+        r->next = q2; r = q2; q2 = q2->next;
+        q1 = q1->next;
+      }
+    }
+  }
+  if ( q1 ) {
+    r->next = q1;
+  } else {
+    r->next = q2;
+  }
+  return root.next;
+}
+
+ND_pairs insert_pair_s(ND_pairs l,ND_pairs s)
+{
+  ND_pairs p,prev;
+  int ret;
+
+  for ( p = l, prev = 0; p != 0; prev = p, p = p->next ) {
+    if ( (ret = comp_sig(s->sig,p->sig)) <= 0 )
+      break;
+  }
+  if ( ret == 0 ) {
+    ret = DL_COMPARE(s->lcm,p->lcm);
+    if ( ret < 0 ) {
+      // replace p with s
+      s->next = p->next;
+      if ( prev == 0 ) {
+        return s;
+      } else {
+        prev->next = s;
+        return l;
+      }
+    } else
+      return l;
+  } else {
+    // insert s between prev and p
+    s->next = p;
+    if ( prev == 0 ) {
+      return s;
+    } else {
+      prev->next = s;
+      return l;
+    }
+  }
+}
+
+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,i;
+  ND_pairs r,r0,_sp,sp;
+  SIG spsig,tsig;
+  static int nvar;
+  static SIG _sig1,_sig2;
+  struct oEGT eg1,eg2,eg3,eg4;
+
+  NEWND_pairs(_sp);
+  if ( !_sig1 || nvar != nd_nvar ) {
+    nvar = nd_nvar; NEWSIG(_sig1); NEWSIG(_sig2);
+  }
+  r0 = 0;
+  for ( i = 0; i < t; i++ ) {
+    ret = _create_spair_s(i,t,_sp,_sig1,_sig2);
+    if ( ret ) {
+      spsig = _sp->sig;
+      for ( s = syz[spsig->pos]; s; s = s->next ) {
+        tsig = (SIG)s->body;
+        if ( _dl_redble(DL(tsig),DL(spsig),nd_nvar) )
+          break;
+      }
+      if ( s == 0 ) {
+        NEWND_pairs(sp);
+        dup_ND_pairs(sp,_sp);
+        r0 = insert_pair_s(r0,sp);
+      } else
+        Nsyz++;
+    }
+  }
+  return r0;
+}
+
 /* ipair = [i1,i2],[i1,i2],... */
 ND_pairs nd_ipairtospair(NODE ipair)
 {
@@ -2921,6 +3693,18 @@ 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;
@@ -2933,7 +3717,7 @@ int nd_tdeg(NDV c)
   return wmax;
 }
 
-int ndv_newps(int m,NDV a,NDV aq,int f4)
+int ndv_newps(int m,NDV a,NDV aq)
 {
     int len;
     RHist r;
@@ -2969,6 +3753,7 @@ int ndv_newps(int m,NDV a,NDV aq,int f4)
         SG(r) = nd_tdeg(aq);
 #endif
         ndl_copy(HDL(aq),DL(r));
+        r->sig = dup_sig(aq->sig);
     } else {
         if ( !m ) register_hcf(a);
         nd_bound[nd_psn] = ndv_compute_bound(a);
@@ -2978,6 +3763,7 @@ int ndv_newps(int m,NDV a,NDV aq,int f4)
         SG(r) = nd_tdeg(a);
 #endif
         ndl_copy(HDL(a),DL(r));
+        r->sig = dup_sig(a->sig);
     }
     if ( nd_demand ) {
         if ( aq ) {
@@ -3003,7 +3789,7 @@ int ndv_newps(int m,NDV a,NDV aq,int f4)
 /* nd_tracelist = [[0,index,div],...,[nd_psn-1,index,div]] */
 /* return 1 if success, 0 if failure (HC(a mod p)) */
 
-int ndv_setup(int mod,int trace,NODE f,int dont_sort,int dont_removecont)
+int ndv_setup(int mod,int trace,NODE f,int dont_sort,int dont_removecont,int sba)
 {
   int i,j,td,len,max;
   NODE s,s0,f0,tn;
@@ -3027,7 +3813,7 @@ 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
@@ -3103,6 +3889,29 @@ 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;
+
+      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;
 }
@@ -3339,7 +4148,7 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
             ndv_homogenize((NDV)BDY(t),obpe,oadv,oepos,ompos);
     }
 
-    ndv_setup(m,0,fd0,(nd_gbblock||nd_splist||nd_check_splist)?1:0,0);
+    ndv_setup(m,0,fd0,(nd_gbblock||nd_splist||nd_check_splist)?1:0,0,0);
     if ( nd_gentrace ) {
         MKLIST(l1,nd_tracelist); MKNODE(nd_alltracelist,l1,0);
     }
@@ -3442,6 +4251,107 @@ FINAL:
 #endif
 }
 
+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;
+  int e,max,nvar,i;
+  NDV b;
+  int ishomo,nalg,wmax,len;
+  NMV a;
+  P p,zp;
+  Q dmy;
+  struct order_spec *ord1;
+  int j;
+  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);
+  if ( m && nd_vc )
+    error("nd_sba : computation over Fp(X) is unsupported. Use dp_gr_mod_main().");
+  for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
+  switch ( ord->id ) {
+    case 1:
+      if ( ord->nv != nvar )
+        error("nd_sba : invalid order specification");
+        break;
+      default:
+        break;
+  }
+  nd_nalg = 0;
+  nd_init_ord(ord);
+  // for SIG comparison
+  initd(ord);
+  for ( t = BDY(f), max = 1; t; t = NEXT(t) ) {
+    for ( tv = vv; tv; tv = NEXT(tv) ) {
+      e = getdeg(tv->v,(P)BDY(t));
+      max = MAX(e,max);
+    }
+  }
+  nd_setup_parameters(nvar,max);
+  obpe = nd_bpe; oadv = nmv_adv; oepos = nd_epos; ompos = nd_mpos;
+  ishomo = 1;
+  for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
+    if ( !m ) ptozp((P)BDY(t),1,&dmy,&zp);
+    else zp = (P)BDY(t);
+    b = (pointer)ptondv(CO,vv,zp);
+    if ( ishomo )
+      ishomo = ishomo && ndv_ishomo(b);
+    if ( m ) ndv_mod(m,b);
+    if ( b ) { NEXTNODE(fd0,fd); BDY(fd) = (pointer)b; }
+  }
+  if ( fd0 ) NEXT(fd) = 0;
+
+  if ( !ishomo && homo ) {
+    for ( t = fd0, wmax = max; t; t = NEXT(t) ) {
+      b = (NDV)BDY(t); len = LEN(b);
+      for ( a = BDY(b), i = 0; i < len; i++, NMV_ADV(a) )
+        wmax = MAX(TD(DL(a)),wmax);
+      }
+      homogenize_order(ord,nvar,&ord1);
+      nd_init_ord(ord1);
+      nd_setup_parameters(nvar+1,nd_nzlist?0:wmax);
+      for ( t = fd0; t; t = NEXT(t) )
+        ndv_homogenize((NDV)BDY(t),obpe,oadv,oepos,ompos);
+  }
+
+  ndv_setup(m,0,fd0,0,0,1);
+  x = f4 ? nd_sba_f4(m,&perm) : nd_sba_buch(m,ishomo || homo,&perm);
+  if ( !x ) {
+    *rp = 0; return;
+  }
+  if ( !ishomo && homo ) {
+       /* dehomogenization */
+    for ( t = x; t; t = NEXT(t) ) ndv_dehomogenize((NDV)BDY(t),ord);
+    nd_init_ord(ord);
+    nd_setup_parameters(nvar,0);
+  }
+  nd_demand = 0;
+  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));
+    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)
 {
     VL tv,fv,vv,vc,av;
@@ -3501,7 +4411,7 @@ void nd_gr_postproc(LIST f,LIST v,int m,struct order_s
         if ( b ) { NEXTNODE(fd0,fd); BDY(fd) = (pointer)b; }
     }
     if ( fd0 ) NEXT(fd) = 0;
-    ndv_setup(m,0,fd0,0,1);
+    ndv_setup(m,0,fd0,0,1,0);
     for ( x = 0, i = 0; i < nd_psn; i++ )
         x = update_base(x,i);
     if ( do_check ) {
@@ -3822,7 +4732,7 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     tl1 = tl2 = tl3 = tl4 = 0;
         if ( Demand )
             nd_demand = 1;
-        ret = ndv_setup(m,1,fd0,nd_gbblock?1:0,0);
+        ret = ndv_setup(m,1,fd0,nd_gbblock?1:0,0,0);
         if ( nd_gentrace ) {
             MKLIST(l1,nd_tracelist); MKNODE(nd_alltracelist,l1,0);
         }
@@ -3955,7 +4865,7 @@ 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 ) {
@@ -3971,6 +4881,27 @@ DL ndltodl(int n,UINT *ndl)
     return dl;
 }
 
+void _ndltodl(UINT *ndl,DL dl)
+{
+    int *d;
+    int i,j,l,s,ord_l,n;
+    struct order_pair *op;
+
+    n = nd_nvar;
+    dl->td = TD(ndl);
+    d = dl->d;
+    if ( nd_blockmask ) {
+        l = nd_blockmask->n;
+        op = nd_blockmask->order_pair;
+        for ( j = 0, s = 0; j < l; j++ ) {
+            ord_l = op[j].length;
+            for ( i = 0; i < ord_l; i++, s++ ) d[s] = GET_EXP(ndl,s);
+        }
+    } else {
+        for ( i = 0; i < n; i++ ) d[i] = GET_EXP(ndl,i);
+    }
+}
+
 void nmtodp(int mod,NM m,DP *r)
 {
     DP dp;
@@ -4028,7 +4959,7 @@ 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");
@@ -4487,7 +5418,7 @@ UINT *nd_compute_bound(ND p)
 int nd_get_exporigin(struct order_spec *ord)
 {
     switch ( ord->id ) {
-        case 0: case 2: case 256: case 258:
+        case 0: case 2: case 256: case 258: case 300:
             return 1+nd_module;
         case 1: case 257:
             /* block order */
@@ -4623,6 +5554,7 @@ ND_pairs nd_reconstruct(int trace,ND_pairs d)
         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);
     }
@@ -4641,12 +5573,14 @@ ND_pairs nd_reconstruct(int trace,ND_pairs d)
             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;
@@ -4658,6 +5592,91 @@ 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;
@@ -4766,6 +5785,8 @@ int nd_sp(int mod,int trace,ND_pairs p,ND *rp)
         MKLIST(hist,node); MKNODE(node,hist,nd_tracelist);
         nd_tracelist = node;
     }
+    if ( *rp )
+      (*rp)->sig = p->sig;
     FREENM(m1); FREENM(m2);
     return 1;
 }
@@ -5144,6 +6165,7 @@ NDV ndv_dup_realloc(NDV p,int obpe,int oadv,EPOS oepos
     }
     MKNDV(NV(p),mr0,len,r);
     SG(r) = SG(p);
+    r->sig = p->sig;
     return r;
 }
 
@@ -5476,6 +6498,7 @@ NDV ndtondv(int mod,ND p)
     }
     MKNDV(NV(p),m0,len,d);
     SG(d) = SG(p);
+    d->sig = p->sig;
     return d;
 }
 
@@ -5521,7 +6544,7 @@ void dpm_sort(DPM p,DPM *rp)
 
 int dpm_comp(DPM *a,DPM *b)
 {
-  return compdpm(CO,*a,*b);
+  return -compdpm(CO,*a,*b);
 }
 
 NODE dpm_sort_list(NODE l)
@@ -5543,7 +6566,9 @@ NODE dpm_sort_list(NODE l)
 
 int nmv_comp(NMV a,NMV b)
 {
-  return -DL_COMPARE(a->dl,b->dl);
+  int t;
+  t = DL_COMPARE(a->dl,b->dl);
+  return -t;
 }
 
 NDV dpmtondv(int mod,DPM p)
@@ -5597,6 +6622,7 @@ 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;
 }
 
@@ -5675,7 +6701,7 @@ 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");
@@ -5731,20 +6757,20 @@ NODE ndv_reducebase(NODE x,int *perm)
 
 /* XXX incomplete */
 
-extern int dpm_ordtype;
+extern DMMstack dmm_stack;
+int ndl_module_schreyer_compare(UINT *a,UINT *b);
 
 void nd_init_ord(struct order_spec *ord)
 {
   nd_module = (ord->id >= 256);
   if ( nd_module ) {
     nd_dcomp = -1;
-    nd_ispot = ord->ispot;
+    nd_module_ordtype = ord->module_ordtype;
     nd_pot_nelim = ord->pot_nelim;
     nd_poly_weight_len = ord->nv;
     nd_poly_weight = ord->top_weight;
     nd_module_rank = ord->module_rank;
     nd_module_weight = ord->module_top_weight;
-    dpm_ordtype = ord->ispot;
   }
   nd_matrix = 0;
   nd_matrix_len = 0;
@@ -5803,40 +6829,73 @@ void nd_init_ord(struct order_spec *ord)
         case 256:
             switch ( ord->ord.simple ) {
                 case 0:
+                    nd_dcomp = 0;
                     nd_isrlex = 1;
-                    ndl_compare_function = ndl_module_grlex_compare;
+                    ndl_compare_function = ndl_module_glex_compare;
                     break;
                 case 1:
+                    nd_dcomp = 0;
                     nd_isrlex = 0;
                     ndl_compare_function = ndl_module_glex_compare;
                     break;
                 case 2:
+                    nd_dcomp = 0;
                     nd_isrlex = 0;
-                    ndl_compare_function = ndl_module_lex_compare;
+                    ndl_compare_function = ndl_module_compare;
+                    ndl_base_compare_function = ndl_lex_compare;
                     break;
                 default:
-                    error("nd_gr : unsupported order");
+                    error("nd_init_ord : unsupported order");
             }
             break;
         case 257:
             /* block order */
             nd_isrlex = 0;
-            ndl_compare_function = ndl_module_block_compare;
+            ndl_compare_function = ndl_module_compare;
+            ndl_base_compare_function = ndl_block_compare;
             break;
         case 258:
             /* matrix order */
             nd_isrlex = 0;
             nd_matrix_len = ord->ord.matrix.row;
             nd_matrix = ord->ord.matrix.matrix;
-            ndl_compare_function = ndl_module_matrix_compare;
+            ndl_compare_function = ndl_module_compare;
+            ndl_base_compare_function = ndl_matrix_compare;
             break;
         case 259:
             /* composite order */
             nd_isrlex = 0;
             nd_worb_len = ord->ord.composite.length;
             nd_worb = ord->ord.composite.w_or_b;
-            ndl_compare_function = ndl_module_composite_compare;
+            ndl_compare_function = ndl_module_compare;
+            ndl_base_compare_function = ndl_composite_compare;
             break;
+        case 300:
+            /* schreyer order */
+            if ( ord->base->id != 256 )
+               error("nd_init_ord : unsupported base order");
+            ndl_compare_function = ndl_module_schreyer_compare;
+            dmm_stack = ord->dmmstack;
+            switch ( ord->base->ord.simple ) {
+                case 0:
+                    nd_isrlex = 1;
+                    ndl_base_compare_function = ndl_glex_compare;
+                    dl_base_compare_function = cmpdl_revgradlex;
+                    break;
+                case 1:
+                    nd_isrlex = 0;
+                    ndl_base_compare_function = ndl_glex_compare;
+                    dl_base_compare_function = cmpdl_gradlex;
+                    break;
+                case 2:
+                    nd_isrlex = 0;
+                    ndl_base_compare_function = ndl_lex_compare;
+                    dl_base_compare_function = cmpdl_lex;
+                    break;
+                default:
+                    error("nd_init_ord : unsupported order");
+            }
+            break;
     }
     nd_ord = ord;
 }
@@ -5872,7 +6931,7 @@ EPOS nd_create_epos(struct order_spec *ord)
 
     epos = (EPOS)MALLOC_ATOMIC(nd_nvar*sizeof(struct oEPOS));
     switch ( ord->id ) {
-        case 0: case 256:
+        case 0: case 256: case 300:
             if ( nd_isrlex ) {
                 for ( i = 0; i < nd_nvar; i++ ) {
                     epos[i].i = nd_exporigin + (nd_nvar-1-i)/nd_epw;
@@ -5975,7 +7034,7 @@ void nd_nf_p(Obj f,LIST g,LIST v,int m,struct order_sp
     ndf = (pointer)ndvtond(m,ndvf);
 
     /* dont sort, dont removecont */
-    ndv_setup(m,0,in0,1,1);
+    ndv_setup(m,0,in0,1,1,0);
     nd_scale=2;
     stat = nd_nf(m,0,ndf,nd_ps,1,&nf);
     if ( !stat )
@@ -6835,7 +7894,7 @@ 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;
@@ -6949,7 +8008,7 @@ NODE nd_f4(int m,int checkonly,int **indp)
                 nd_removecont(m,nf1);
                 nf = ndtondv(m,nf1);
             }
-            nh = ndv_newps(m,nf,0,1);
+            nh = ndv_newps(m,nf,0);
             d = update_pairs(d,g,nh,0);
             g = update_base(g,nh);
         }
@@ -7077,7 +8136,7 @@ NODE nd_f4_trace(int m,int **indp)
             nfv = ndv_dup(0,nfqv);
             ndv_mod(m,nfv);
             ndv_removecont(m,nfv);
-            nh = ndv_newps(0,nfv,nfqv,1);
+            nh = ndv_newps(0,nfv,nfqv);
             d = update_pairs(d,g,nh,0);
             g = update_base(g,nh);
         }
@@ -8488,6 +9547,25 @@ 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;
@@ -9084,7 +10162,7 @@ void nd_f4_lf_trace(LIST f,LIST v,int trace,int homo,s
             ndv_homogenize((NDV)BDY(t),obpe,oadv,oepos,ompos);
     }
     if ( MaxDeg > 0 ) nocheck = 1;
-    ret = ndv_setup(-2,m,fd0,nd_gbblock?1:0,0);
+    ret = ndv_setup(-2,m,fd0,nd_gbblock?1:0,0,0);
     if ( ret )
       cand = nd_f4_lf_trace_main(m,&perm);
     if ( !ret || !cand ) {
@@ -9200,7 +10278,7 @@ NODE nd_f4_lf_trace_main(int m,int **indp)
             if ( DL_COMPARE(HDL(nfv),HDL(nfqv)) ) return 0;
             ndv_removecont(m,nfv);
             ndv_removecont(-2,nfqv);
-            nh = ndv_newps(-2,nfv,nfqv,1);
+            nh = ndv_newps(-2,nfv,nfqv);
             d = update_pairs(d,g,nh,0);
             g = update_base(g,nh);
         }
@@ -9240,6 +10318,29 @@ 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;
@@ -9269,7 +10370,7 @@ 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;
@@ -9290,7 +10391,7 @@ 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];
@@ -9364,7 +10465,7 @@ 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));
@@ -9496,3 +10597,415 @@ 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;
+  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;
+}
+
+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,f4step;
+  int col,rank,len,k,j,a,sugar,nbase,psugar,ms;
+  NODE r,g,rp0,nflist;
+  ND_pairs d,l,t;
+  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 >= 2 ) {
+again:
+      l = d; d = d->next;
+      if ( small_lcm(l) ) {
+        if ( DP_Print ) fprintf(asir_out,"M");
+        continue;
+      }
+      sig = l->sig;
+      stat = nd_sp(m,0,l,&h);
+      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);
+  #else
+      stat = nd_nf_s(m,0,h,nd_ps,!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);
+        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;
+}