===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2018/engine/nd.c,v
retrieving revision 1.11
retrieving revision 1.41
diff -u -p -r1.11 -r1.41
--- OpenXM_contrib2/asir2018/engine/nd.c	2018/10/23 04:53:37	1.11
+++ OpenXM_contrib2/asir2018/engine/nd.c	2020/11/26 03:55:23	1.41
@@ -1,19 +1,24 @@
-/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.10 2018/10/19 23:27:38 noro Exp $ */
+/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.40 2020/11/02 08:30:55 noro Exp $ */
 
 #include "nd.h"
 
-int Nnd_add,Nf4_red;
-struct oEGT eg_search;
+int Nnd_add,Nf4_red,NcriB,NcriMF,Ncri2,Npairs;
+struct oEGT eg_search,f4_symb,f4_conv,f4_elim1,f4_elim2;
 
 int diag_period = 6;
 int weight_check = 1;
 int (*ndl_compare_function)(UINT *a1,UINT *a2);
+/* 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;
 
@@ -45,7 +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;
@@ -55,17 +60,21 @@ 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;
 static NODE nd_alltracelist;
-static int nd_gentrace,nd_gensyz,nd_nora,nd_newelim,nd_intersect,nd_lf;
+static int nd_gentrace,nd_gensyz,nd_nora,nd_newelim,nd_intersect,nd_lf,nd_norb;
+static int nd_f4_td,nd_sba_f4step,nd_sba_pot,nd_sba_largelcm,nd_sba_dontsort,nd_sba_redundant_check;
+static int nd_top;
 static int *nd_gbblock;
 static NODE nd_nzlist,nd_check_splist;
 static int nd_splist;
 static int *nd_sugarweight;
 static int nd_f4red,nd_rank0,nd_last_nonzero;
+static DL *nd_sba_hm;
+static NODE *nd_sba_pos;
 
 NumberField get_numberfield();
 UINT *nd_det_compute_bound(NDV **dm,int n,int j);
@@ -78,6 +87,7 @@ NDV pltondv(VL vl,VL dvl,LIST p);
 void pltozpl(LIST l,Q *cont,LIST *pp);
 void ndl_max(UINT *d1,unsigned *d2,UINT *d);
 void nmtodp(int mod,NM m,DP *r);
+void ndltodp(UINT *d,DP *r);
 NODE reverse_node(NODE n);
 P ndc_div(int mod,union oNDC a,union oNDC b);
 P ndctop(int mod,union oNDC c);
@@ -87,6 +97,11 @@ void parse_nd_option(NODE opt);
 void dltondl(int n,DL dl,UINT *r);
 DP ndvtodp(int mod,NDV p);
 DP ndtodp(int mod,ND p);
+DPM ndvtodpm(int mod,NDV p);
+NDV dpmtondv(int mod,DPM p);
+int dpm_getdeg(DPM p,int *rank);
+void dpm_ptozp(DPM p,Z *cont,DPM *r);
+int compdmm(int nv,DMM a,DMM b);
 
 void Pdp_set_weight(NODE,VECT *);
 void Pox_cmo_rpc(NODE,Obj *);
@@ -101,6 +116,7 @@ NODE nd_f4_red_mod64_main(int m,ND_pairs sp0,int nsp,U
 NODE nd_f4_red_lf_main(int m,ND_pairs sp0,int nsp,int trace,UINT *s0vect,int col,
         NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred);
 int nd_gauss_elim_lf(mpz_t **mat0,int *sugar,int row,int col,int *colstat);
+int nd_gauss_elim_mod_s(UINT **mat,int *sugar,ND_pairs *spactive,int row,int col,int md,int *colstat,SIG *sig);
 NODE nd_f4_lf_trace_main(int m,int **indp);
 void nd_f4_lf_trace(LIST f,LIST v,int trace,int homo,struct order_spec *ord,LIST *rp);
 
@@ -470,8 +486,11 @@ int ndl_weight(UINT *d)
             for ( j = 0; j < nd_epw; j++, u>>=nd_bpe )
                 t += (u&nd_mask0); 
         }
-    if ( nd_module && current_module_weight_vector && MPOS(d) )
-        t += current_module_weight_vector[MPOS(d)];
+    if ( nd_module && nd_module_rank && MPOS(d) )
+        t += nd_module_weight[MPOS(d)-1];
+    for ( i = nd_exporigin; i < nd_wpd; i++ )
+      if ( d[i] && !t ) 
+        printf("afo\n");
     return t;
 }
 
@@ -486,8 +505,8 @@ int ndl_weight2(UINT *d)
         u = GET_EXP(d,i);
         t += nd_sugarweight[i]*u;
     }
-    if ( nd_module && current_module_weight_vector && MPOS(d) )
-        t += current_module_weight_vector[MPOS(d)];
+    if ( nd_module && nd_module_rank && MPOS(d) )
+        t += nd_module_weight[MPOS(d)-1];
     return t;
 }
 
@@ -515,6 +534,13 @@ 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;
@@ -684,135 +710,147 @@ 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;
+    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;
+      }
+      if ( MPOS(d1) < MPOS(d2) ) return 1;
+      else if ( MPOS(d1) > MPOS(d2) ) return -1;
+      else if ( TD(d1) > TD(d2) ) return 1;
+      else if ( TD(d1) < TD(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 ( 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;
-}
+    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;
 
-int ndl_module_glex_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 ( 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)
@@ -1130,7 +1168,7 @@ INLINE int ndl_hash_value(UINT *d)
 
     r = 0;
     for ( i = 0; i < nd_wpd; i++ )    
-        r = (r*10007+d[i]);
+        r = (r*1511+d[i]);
     r %= REDTAB_LEN;
     return r;
 }
@@ -1169,6 +1207,79 @@ INLINE int ndl_find_reducer(UINT *dg)
     return -1;
 }
 
+INLINE int ndl_find_reducer_nonsig(UINT *dg)
+{
+    RHist r;
+    int i;
+
+    for ( i = 0; i < nd_psn; i++ ) {
+      r = nd_psh[i];
+      if ( ndl_reducible(dg,DL(r)) ) return i;
+    }
+    return -1;
+}
+
+// ret=0,...,nd_psn-1 => reducer found
+// ret=nd_psn => reducer not found
+// ret=-1 => singular top reducible
+
+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;
@@ -1511,6 +1622,90 @@ 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;
@@ -1623,6 +1818,132 @@ 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)
@@ -1635,7 +1956,7 @@ 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; }
@@ -1722,6 +2043,7 @@ void free_pbucket(PGeoBucket b) {
     GCFREE(b);
 }
 
+#if 0
 void add_pbucket_symbolic(PGeoBucket g,ND d)
 {
     int l,i,k,m;
@@ -1739,7 +2061,32 @@ void add_pbucket_symbolic(PGeoBucket g,ND d)
     g->body[k] = d;
     g->m = MAX(g->m,k);
 }
+#else
+void add_pbucket_symbolic(PGeoBucket g,ND d)
+{
+  int l,i,k,m,m0;
 
+  if ( !d )
+    return;
+  m0 = g->m;
+  while ( 1 ) {
+    l = LEN(d);
+    for ( k = 0, m = 1; l > m; k++, m <<= 1 );
+    /* 2^(k-1) < l <= 2^k (=m) */
+    if ( g->body[k] == 0 ) {
+      g->body[k] = d;
+      m0 = MAX(k,m0);
+      break;
+    } else { 
+      d = nd_merge(g->body[k],d);
+      g->body[k] = 0; 
+    }
+  }
+  g->m = m0;
+}
+#endif
+
+#if 0
 void add_pbucket(int mod,PGeoBucket g,ND d)
 {
     int l,i,k,m;
@@ -1757,7 +2104,29 @@ void add_pbucket(int mod,PGeoBucket g,ND d)
     g->body[k] = d;
     g->m = MAX(g->m,k);
 }
+#else
+void add_pbucket(int mod,PGeoBucket g,ND d)
+{
+  int l,i,k,m,m0;
 
+  m0 = g->m;
+  while ( d != 0 ) {
+    l = LEN(d);
+    for ( k = 0, m = 1; l > m; k++, m <<= 1 );
+    /* 2^(k-1) < l <= 2^k (=m) */
+    if ( g->body[k] == 0 ) {
+      g->body[k] = d;
+      m0 = MAX(k,m0);
+      break;
+    } else { 
+      d = nd_add(mod,g->body[k],d);
+      g->body[k] = 0; 
+    }
+  }
+  g->m = m0;
+}
+#endif
+
 void mulq_pbucket(PGeoBucket g,Z c)
 {
     int k;
@@ -2081,9 +2450,12 @@ NODE nd_gb(int m,int ishomo,int checkonly,int gensyz,i
   Z q;
   union oNDC dn,hc;
   int diag_count = 0;
+  int Nnfnz = 0,Nnfz = 0;
   P cont;
   LIST list;
+struct oEGT eg1,eg2,eg_update;
 
+init_eg(&eg_update);
   Nnd_add = 0;
   g = 0; d = 0;
   for ( i = 0; i < nd_psn; i++ ) {
@@ -2115,16 +2487,17 @@ again:
       goto again;
     }
 #if USE_GEOBUCKET
-    stat = (m&&!nd_gentrace)?nd_nf_pbucket(m,h,nd_ps,!Top,&nf)
-      :nd_nf(m,0,h,nd_ps,!Top,&nf);
+    stat = (m&&!nd_gentrace)?nd_nf_pbucket(m,h,nd_ps,!nd_top&&!Top,&nf)
+      :nd_nf(m,0,h,nd_ps,!nd_top&&!Top,&nf);
 #else
-    stat = nd_nf(m,0,h,nd_ps,!Top,&nf);
+    stat = nd_nf(m,0,h,nd_ps,!nd_top&&!Top,&nf);
 #endif
     if ( !stat ) {
       NEXT(l) = d; d = l;
       d = nd_reconstruct(0,d);
       goto again;
     } else if ( nf ) {
+      Nnfnz++;
       if ( checkonly || gensyz ) return 0;
       if ( nd_newelim ) {
         if ( nd_module ) {
@@ -2148,7 +2521,7 @@ 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);
@@ -2158,24 +2531,383 @@ 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 {
+      Nnfz++;
+      if ( nd_gentrace && gensyz ) {
+        nd_tracelist = reverse_node(nd_tracelist); 
+        MKLIST(list,nd_tracelist);
+        STOZ(-1,q); t = mknode(2,q,list); MKLIST(list,t);
+        MKNODE(t,list,nd_alltracelist); 
+        nd_alltracelist = t; nd_tracelist = 0;
+      }
+      if ( DP_Print ) { printf("."); fflush(stdout); }
+        FREENDP(l);
+    }
+  }
+  conv_ilist(nd_demand,0,g,indp);
+  if ( !checkonly && DP_Print ) { 
+    printf("\nnd_gb done. Nnd_add=%d,Npairs=%d, Nnfnz=%d,Nnfz=%d,",Nnd_add,Npairs,Nnfnz,Nnfz);
+    printf("Nremoved=%d\n",NcriB+NcriMF+Ncri2);
+    fflush(asir_out);
+  }
+  if ( DP_Print ) {
+    print_eg("update",&eg_update); fprintf(asir_out,"\n");
+  }
+  return g;
+}
+
+ND_pairs update_pairs_s(ND_pairs d,int t,NODE *syz);
+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 ( nd_sba_largelcm ) return 0;
+  if ( nvar < nd_nvar ) {
+    nvar = nd_nvar; NEWDL(lcm,nvar); NEWDL(quo,nvar); NEWDL(mul,nvar);
+  }
+  sig = l->sig;
+  _ndltodl(l->lcm,lcm);
+#if 0
+  for ( i = 0; i < nd_psn; i++ ) {
+    if ( sig->pos == nd_psh[i]->sig->pos &&
+      _dl_redble_ext(DL(nd_psh[i]->sig),DL(sig),quo,nd_nvar) ) {
+      _ndltodl(DL(nd_psh[i]),mul);
+      _addtodl(nd_nvar,quo,mul);
+      if ( (*cmpdl)(nd_nvar,lcm,mul) > 0 )
+        break;
+    }
+  }
+  if ( i < nd_psn ) return 1;
+  else return 0;
+#else
+  for ( t = nd_sba_pos[sig->pos]; t; t = t->next ) {
+    i = (long)BDY(t);
+    if ( _dl_redble_ext(DL(nd_psh[i]->sig),DL(sig),quo,nd_nvar) ) {
+      _ndltodl(DL(nd_psh[i]),mul);
+      _addtodl(nd_nvar,quo,mul);
+      if ( (*cmpdl)(nd_nvar,lcm,mul) > 0 )
+        break;
+    }
+  }
+  if ( t ) return 1;
+  else return 0;
+#endif
+}
+
+ND_pairs find_smallest_lcm(ND_pairs l)
+{
+  SIG sig;
+  int i,minindex;
+  NODE t;
+  ND_pairs r;
+  struct oSIG sig1;
+  static DL mul,quo,minlm;
+  static int nvar;
+
+  if ( nvar < nd_nvar ) {
+    nvar = nd_nvar; 
+    NEWDL(quo,nvar); NEWDL(mul,nvar);
+    NEWDL(minlm,nvar);
+  }
+  sig = l->sig;
+  // find mg s.t. m*s(g)=sig and m*lm(g) is minimal
+  _ndltodl(l->lcm,minlm); minindex = -1;
+  for ( t = nd_sba_pos[sig->pos]; t; t = t->next ) {
+    i = (long)BDY(t);
+    if ( _dl_redble_ext(DL(nd_psh[i]->sig),DL(sig),quo,nd_nvar) ) {
+      _ndltodl(DL(nd_psh[i]),mul);
+      _addtodl(nd_nvar,quo,mul);
+      if ( (*cmpdl)(nd_nvar,minlm,mul) > 0 ) {
+        minindex = i;
+        _copydl(nd_nvar,mul,minlm);
+      }
+    }
+  }
+  // l->lcm is minimal; return l itself
+  if ( minindex < 0 ) return l;
+  for ( i = 0; i < nd_psn; i++ ) {
+    if ( i == minindex ) continue;
+    _ndltodl(DL(nd_psh[i]),mul);
+    if ( _dl_redble_ext(mul,minlm,quo,nd_nvar) ) {
+      _addtodl(nd_nvar,nd_ps[i]->sig->dl,quo);
+      sig1.pos = nd_ps[i]->sig->pos;
+      sig1.dl = quo;
+      if ( comp_sig(sig,&sig1) > 0 ) {
+//        printf("X");
+        NEWND_pairs(r);
+        r->sig = sig;
+        r->i1 = minindex;
+        r->i2 = i;
+        dltondl(nd_nvar,minlm,r->lcm);
+        r->next = 0;
+        return r;
+      }
+    }
+  }
+  // there is no suitable spair 
+  return 0;
+}
+
+ND_pairs remove_large_lcm(ND_pairs d)
+{
+  struct oND_pairs root;
+  ND_pairs prev,p;
+
+  root.next = d;
+  prev = &root; p = d;
+  while ( p ) {
+#if 0
+    if ( small_lcm(p) ) {
+      // remove p
+      prev->next = p->next;
+    } else
+#else
+    if ( find_smallest_lcm(p) == 0 ) {
+      // remove p
+      prev->next = p->next;
+    } else
+#endif
+      prev = p;
+    p = p->next;
+  }
+  return (ND_pairs)root.next;
+}
+
+struct oEGT eg_create,eg_newpairs,eg_merge;
+
+NODE conv_ilist_s(int demand,int trace,int **indp);
+
+NODE nd_sba_buch(int m,int ishomo,int **indp)
+{
+  int i,j,nh,sugar,stat,pos;
+  NODE r,t,g;
+  ND_pairs d;
+  ND_pairs l,l1;
+  ND h,nf,s,head,nf1;
+  NDV nfv;
+  Z q;
+  union oNDC dn,hc;
+  P cont;
+  LIST list;
+  SIG sig;
+  NODE *syzlist;
+  int Nnominimal,Nredundant;
+  DL lcm,quo,mul;
+  struct oEGT eg1,eg2,eg_update,eg_remove,eg_large,eg_nf,eg_nfzero;
+  int Nnfs=0,Nnfz=0,Nnfnz=0;
+
+init_eg(&eg_remove);
+  syzlist = (NODE *)MALLOC(nd_psn*sizeof(NODE));
+  Nsyz = 0;
+  Nnd_add = 0;
+  Nnominimal = 0;
+  Nredundant = 0;
+  d = 0;
+  for ( i = 0; i < nd_psn; i++ )
+    for ( j = i+1; j < nd_psn; j++ ) {
+      NEWSIG(sig); sig->pos = j;
+      _copydl(nd_nvar,nd_sba_hm[i],sig->dl);
+      syzlist[sig->pos] = insert_sig(syzlist[sig->pos],sig);
+    }
+  for ( i = 0; i < nd_psn; i++ ) {
+    d = update_pairs_s(d,i,syzlist);
+  }
+  sugar = 0;
+  pos = 0;
+  NEWDL(lcm,nd_nvar); NEWDL(quo,nd_nvar); NEWDL(mul,nd_nvar);
+init_eg(&eg_create);
+init_eg(&eg_merge);
+init_eg(&eg_large);
+init_eg(&eg_nf);
+init_eg(&eg_nfzero);
+  while ( d ) {
+again:
+    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 0
+    if ( small_lcm(l) ) {
+      if ( DP_Print ) fprintf(asir_out,"M");
+      Nnominimal++;
+      continue;
+    }
+    if ( SG(l) != sugar ) {
+      sugar = SG(l);
+      if ( DP_Print ) fprintf(asir_out,"%d",sugar);
+    }
+    sig = l->sig;
+    if ( DP_Print && nd_sba_pot ) {
+      if ( sig->pos != pos ) {
+        fprintf(asir_out,"[%d]",sig->pos);
+        pos = sig->pos;
+      }
+    }
+    stat = nd_sp(m,0,l,&h);
+#else
+    l1 = find_smallest_lcm(l);
+    if ( l1 == 0 ) {
+      if ( DP_Print ) fprintf(asir_out,"M");
+      Nnominimal++;
+      continue;
+    }
+    if ( SG(l1) != sugar ) {
+      sugar = SG(l1);
+      if ( DP_Print ) fprintf(asir_out,"%d",sugar);
+    }
+    sig = l1->sig;
+    if ( DP_Print && nd_sba_pot ) {
+      if ( sig->pos != pos ) {
+        fprintf(asir_out,"[%d]",sig->pos);
+        pos = sig->pos;
+      }
+    }
+    stat = nd_sp(m,0,l1,&h);
+#endif
+    if ( !stat ) {
+      NEXT(l) = d; d = l;
+      d = nd_reconstruct(0,d);
+      goto again;
+    }
+get_eg(&eg1);
+#if USE_GEOBUCKET
+    stat = m?nd_nf_pbucket_s(m,h,nd_ps,!nd_top&&!Top,&nf):nd_nf_s(m,0,h,nd_ps,!nd_top&&!Top,&nf);
+#else
+    stat = nd_nf_s(m,0,h,nd_ps,!nd_top&&!Top,&nf);
+#endif
+get_eg(&eg2); 
+    if ( !stat ) {
+      NEXT(l) = d; d = l;
+      d = nd_reconstruct(0,d);
+      goto again;
+    } else if ( stat == -1 ) {
+      Nnfs++;
+      if ( DP_Print ) { printf("S"); fflush(stdout); }
+      FREENDP(l);
+    } else if ( nf ) {
+      Nnfnz++;
+      if ( DP_Print ) { 
+        if ( nd_sba_redundant_check ) {
+          if ( ndl_find_reducer_nonsig(HDL(nf)) >= 0 ) {
+            Nredundant++;
+            printf("R"); 
+          } else 
+            printf("+"); 
+        } else
+          printf("+"); 
+        fflush(stdout); 
+      }
+      add_eg(&eg_nf,&eg1,&eg2);
+      hc = HCU(nf);
+      nd_removecont(m,nf);
+      nfv = ndtondv(m,nf); nd_free(nf);
+      nh = ndv_newps(m,nfv,0);
+
+      d = update_pairs_s(d,nh,syzlist);
+      nd_sba_pos[sig->pos] = append_one(nd_sba_pos[sig->pos],nh);
+      FREENDP(l);
    } else {
-     if ( nd_gentrace && gensyz ) {
-       nd_tracelist = reverse_node(nd_tracelist); 
-       MKLIST(list,nd_tracelist);
-       STOZ(-1,q); t = mknode(2,q,list); MKLIST(list,t);
-       MKNODE(t,list,nd_alltracelist); 
-       nd_alltracelist = t; nd_tracelist = 0;
-     }
+      Nnfz++;
+      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);
+     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,Nnominimal=%d\n",Nnd_add,Nsyz,Nsamesig,Nnominimal);
+   printf("Nnfnz=%d,Nnfz=%d,Nnfsingular=%d\n",Nnfnz,Nnfz,Nnfs);
+   fflush(stdout); 
+   if ( nd_sba_redundant_check )
+   printf("Nredundant=%d\n",Nredundant);
+   fflush(stdout); 
+   print_eg("create",&eg_create);
+   print_eg("merge",&eg_merge);
+   print_eg("remove",&eg_remove);
+   print_eg("nf",&eg_nf);
+   print_eg("nfzero",&eg_nfzero);
+   printf("\n");
+ }
+ return g;
 }
 
 /* splist = [[i1,i2],...] */
@@ -2205,7 +2937,7 @@ again:
       d = nd_reconstruct(0,d);
       goto again;
     }
-    stat = nd_nf(m,0,h,nd_ps,!Top,&nf);
+    stat = nd_nf(m,0,h,nd_ps,!nd_top&&!Top,&nf);
     if ( !stat ) {
       NEXT(l) = d; d = l;
       d = nd_reconstruct(0,d);
@@ -2380,9 +3112,9 @@ again:
       goto again;
     }
 #if USE_GEOBUCKET
-    stat = nd_nf_pbucket(m,h,nd_ps,!Top,&nf);
+    stat = nd_nf_pbucket(m,h,nd_ps,!nd_top&&!Top,&nf);
 #else
-    stat = nd_nf(m,0,h,nd_ps,!Top,&nf);
+    stat = nd_nf(m,0,h,nd_ps,!nd_top&&!Top,&nf);
 #endif
     if ( !stat ) {
       NEXT(l) = d; d = l;
@@ -2395,7 +3127,7 @@ again:
       } else
         nfq = 0;
       if ( !nfq ) {
-        if ( !nd_sp(0,1,l,&h) || !nd_nf(0,0,h,nd_ps_trace,!Top,&nfq) ) {
+        if ( !nd_sp(0,1,l,&h) || !nd_nf(0,0,h,nd_ps_trace,!nd_top&&!Top,&nfq) ) {
           NEXT(l) = d; d = l;
           d = nd_reconstruct(1,d);
           goto again;
@@ -2431,7 +3163,7 @@ 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,"|");
@@ -2461,7 +3193,7 @@ again:
     }
   }
   conv_ilist(nd_demand,1,g,indp);
-  if ( DP_Print ) { printf("nd_gb_trace done.\n"); fflush(stdout); }
+  if ( DP_Print ) { printf("\nnd_gb_trace done.\n"); fflush(stdout); }
   return g;
 }
 
@@ -2501,7 +3233,7 @@ 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) )
@@ -2549,9 +3281,17 @@ NODE ndv_reduceall(int m,NODE f)
   return a0;
 }
 
+int ndplength(ND_pairs d)
+{
+  int i;
+  for ( i = 0; d; i++ ) d = NEXT(d);
+  return i;
+}
+
 ND_pairs update_pairs( ND_pairs d, NODE /* of index */ g, int t, int gensyz)
 {
   ND_pairs d1,nd,cur,head,prev,remove;
+  int len0;
 
   if ( !g ) return d;
   /* for testing */
@@ -2568,8 +3308,10 @@ ND_pairs update_pairs( ND_pairs d, NODE /* of index */
   }
   d = crit_B(d,t);
   d1 = nd_newpairs(g,t);
+  len0 = ndplength(d1); 
   d1 = crit_M(d1);
   d1 = crit_F(d1);
+  NcriMF += len0-ndplength(d1); 
   if ( gensyz || do_weyl )
     head = d1;
   else {
@@ -2579,7 +3321,7 @@ ND_pairs update_pairs( ND_pairs d, NODE /* of index */
         remove = cur;
         if ( !prev ) head = cur = NEXT(cur);
         else cur = NEXT(prev) = NEXT(cur);
-        FREENDP(remove);
+        FREENDP(remove); Ncri2++;
       } else {
         prev = cur; cur = NEXT(cur);
       }
@@ -2595,7 +3337,22 @@ 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;
@@ -2605,7 +3362,7 @@ ND_pairs nd_newpairs( NODE g, int t )
 
   dl = DL(nd_psh[t]);
   ts = SG(nd_psh[t]) - TD(dl);
-  if ( nd_module && nd_intersect && (MPOS(dl) > 1) ) return 0;
+  if ( nd_module && nd_intersect && (MPOS(dl) > nd_intersect) ) return 0;
   for ( r0 = 0, h = g; h; h = NEXT(h) ) {
     if ( nd_module && (MPOS(DL(nd_psh[(long)BDY(h)])) != MPOS(dl)) )
       continue;
@@ -2619,7 +3376,7 @@ ND_pairs nd_newpairs( NODE g, int t )
       if ( nd_gbblock[i] >= 0 )
         continue;
     }
-    NEXTND_pairs(r0,r);
+    NEXTND_pairs(r0,r); Npairs++;
     r->i1 = (long)BDY(h);
     r->i2 = t;
     ndl_lcm(DL(nd_psh[r->i1]),dl,r->lcm);
@@ -2633,6 +3390,214 @@ ND_pairs nd_newpairs( NODE g, int t )
   return r0;
 }
 
+int comp_sig(SIG s1,SIG s2)
+{
+  if ( nd_sba_pot ) {
+    if ( s1->pos > s2->pos ) return 1;
+    else if ( s1->pos < s2->pos ) return -1;
+    else return (*cmpdl)(nd_nvar,s1->dl,s2->dl);
+  } else {
+    static DL m1,m2;
+    static int nvar;
+    int ret;
+  
+    if ( nvar != nd_nvar ) {
+      nvar = nd_nvar; NEWDL(m1,nvar); NEWDL(m2,nvar);
+    }
+    _adddl(nd_nvar,s1->dl,nd_sba_hm[s1->pos],m1);
+    _adddl(nd_nvar,s2->dl,nd_sba_hm[s2->pos],m2);
+    ret = (*cmpdl)(nd_nvar,m1,m2);
+    if ( ret != 0 ) return ret;
+    else if ( s1->pos > s2->pos ) return 1;
+    else if ( s1->pos < s2->pos ) return -1;
+    else return 0;
+  }
+}
+
+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)
 {
@@ -2683,7 +3648,7 @@ ND_pairs crit_B( ND_pairs d, int s )
           } else {
             cur = NEXT(prev) = NEXT(cur);
           }
-          FREENDP(remove);
+          FREENDP(remove); NcriB++;
         } else {
           prev = cur; cur = NEXT(cur);
         }
@@ -2910,6 +3875,18 @@ ND_pairs nd_minsugarp( ND_pairs d, ND_pairs *prest )
     return dm0;
 }
 
+ND_pairs nd_minsugarp_s( ND_pairs d, ND_pairs *prest )
+{
+  int msugar;
+  ND_pairs t,last;
+
+  for ( msugar = SG(d), t = d; t; t = NEXT(t) )
+    if ( SG(t) == msugar ) last = t;
+  *prest = last->next;
+  last->next = 0;
+  return d;
+}
+
 int nd_tdeg(NDV c)
 {
   int wmax = 0;
@@ -2922,7 +3899,7 @@ 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;
@@ -2958,6 +3935,7 @@ 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);
@@ -2967,6 +3945,7 @@ 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 ) {
@@ -2992,7 +3971,7 @@ 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;
@@ -3016,7 +3995,7 @@ int ndv_setup(int mod,int trace,NODE f,int dont_sort,i
     if ( BDY(s) ) { w[i].p = BDY(s); w[i].i = j; i++; }
   if ( !dont_sort ) {
     /* XXX heuristic */
-    if ( !nd_ord->id && (nd_ord->ord.simple<2) )
+    if ( !sba && !nd_ord->id && (nd_ord->ord.simple<2) )
       qsort(w,nd_psn,sizeof(struct oNDVI),
         (int (*)(const void *,const void *))ndvi_compare_rev);
     else
@@ -3092,6 +4071,29 @@ 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;
 }
@@ -3224,7 +4226,9 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     int *perm;
     EPOS oepos;
     int obpe,oadv,ompos,cbpe;
+    VECT hvect;
 
+    NcriB = NcriMF = Ncri2 = 0;
     nd_module = 0;
     if ( !m && Demand ) nd_demand = 1;
     else nd_demand = 0;
@@ -3267,12 +4271,18 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     for ( t = BDY(f), max = 1; t; t = NEXT(t) )
         for ( tv = vv; tv; tv = NEXT(tv) ) {
             if ( nd_module ) {
-                s = BDY((LIST)BDY(t));
-                trank = length(s);
-                mrank = MAX(mrank,trank);
-                for ( ; s; s = NEXT(s) ) {
-                    e = getdeg(tv->v,(P)BDY(s));
-                    max = MAX(e,max);
+                if ( OID(BDY(t)) == O_DPM ) {
+                  e = dpm_getdeg((DPM)BDY(t),&trank);
+                  max = MAX(e,max);
+                  mrank = MAX(mrank,trank);
+                } else {
+                  s = BDY((LIST)BDY(t));
+                  trank = length(s);
+                  mrank = MAX(mrank,trank);
+                  for ( ; s; s = NEXT(s) ) {
+                      e = getdeg(tv->v,(P)BDY(s));
+                      max = MAX(e,max);
+                  }
                 }
             } else {
                 e = getdeg(tv->v,(P)BDY(t));
@@ -3284,9 +4294,18 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     ishomo = 1;
     for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
       if ( nd_module ) {
-        if ( !m && !nd_gentrace ) pltozpl((LIST)BDY(t),&dmy,&zpl);
-        else zpl = (LIST)BDY(t);
+        if ( OID(BDY(t)) == O_DPM ) {
+          Z cont;
+          DPM zdpm;
+
+          if ( !m && !nd_gentrace ) dpm_ptozp((DPM)BDY(t),&cont,&zdpm);
+          else zdpm = (DPM)BDY(t);
+          b = (pointer)dpmtondv(m,zdpm);
+        } else {
+          if ( !m && !nd_gentrace ) pltozpl((LIST)BDY(t),&dmy,&zpl);
+          else zpl = (LIST)BDY(t);
           b = (pointer)pltondv(CO,vv,zpl);
+        }
       } else {
         if ( !m && !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp);
         else zp = (P)BDY(t);
@@ -3312,7 +4331,7 @@ 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);
     }
@@ -3334,6 +4353,11 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
   if ( !x ) {
     *rp = 0; return;
   }
+  if ( nd_gentrace ) {
+    MKVECT(hvect,nd_psn);
+    for ( i = 0; i < nd_psn; i++ )
+       ndltodp(nd_psh[i]->dl,(DP *)&BDY(hvect)[i]);
+  }
   if ( !ishomo && homo ) {
        /* dehomogenization */
     for ( t = x; t; t = NEXT(t) ) ndv_dehomogenize((NDV)BDY(t),ord);
@@ -3343,7 +4367,7 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     nd_demand = 0;
   if ( nd_module && nd_intersect ) {
     for ( j = nd_psn-1, x = 0; j >= 0; j-- )
-      if ( MPOS(DL(nd_psh[j])) > 1 ) { 
+      if ( MPOS(DL(nd_psh[j])) > nd_intersect ) { 
         MKNODE(xx,(pointer)((unsigned long)j),x); x = xx; 
       }
     conv_ilist(nd_demand,0,x,0);
@@ -3367,10 +4391,12 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     nd_setup_parameters(nd_nvar,0);
 FINAL:
     for ( r0 = 0, t = x; t; t = NEXT(t) ) {
-        NEXTNODE(r0,r); 
-        if ( nd_module ) BDY(r) = ndvtopl(m,CO,vv,BDY(t),mrank);
-        else if ( retdp ) BDY(r) = ndvtodp(m,BDY(t));
-    else BDY(r) = ndvtop(m,CO,vv,BDY(t));
+      NEXTNODE(r0,r); 
+      if ( nd_module ) {
+        if ( retdp ) BDY(r) = ndvtodpm(m,BDY(t));
+        else BDY(r) = ndvtopl(m,CO,vv,BDY(t),mrank);
+      } else if ( retdp ) BDY(r) = ndvtodp(m,BDY(t));
+      else BDY(r) = ndvtop(m,CO,vv,BDY(t));
     }
     if ( r0 ) NEXT(r) = 0;
     if ( !m && nd_nalg )
@@ -3380,8 +4406,7 @@ FINAL:
   if ( f4 ) {
             STOZ(16,bpe);
             STOZ(nd_last_nonzero,last_nonzero);
-            tr = mknode(5,*rp,(!ishomo&&homo)?ONE:0,BDY(nzlist),bpe,last_nonzero); MKLIST(*rp,tr);
-            
+            tr = mknode(6,*rp,(!ishomo&&homo)?ONE:0,BDY(nzlist),bpe,last_nonzero,hvect); MKLIST(*rp,tr);
         } else {
             tl1 = reverse_node(tl1); tl2 = reverse_node(tl2);
             tl3 = reverse_node(tl3);
@@ -3401,7 +4426,7 @@ FINAL:
             MKLIST(l1,tl1); MKLIST(l2,tl2); MKLIST(l3,t); MKLIST(l4,tl3);
             MKLIST(l5,tl4);
             STOZ(nd_bpe,bpe);
-            tr = mknode(8,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe); MKLIST(*rp,tr);
+            tr = mknode(9,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe,hvect); MKLIST(*rp,tr);
         }
     }
 #if 0
@@ -3409,6 +4434,107 @@ 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,nd_sba_dontsort,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;
@@ -3468,7 +4594,7 @@ 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 ) {
@@ -3645,7 +4771,7 @@ void nd_gr_recompute_trace(LIST f,LIST v,int m,struct 
     if ( DP_Print ) fprintf(asir_out,"\n");
 }
 
-void nd_gr_trace(LIST f,LIST v,int trace,int homo,int f4,struct order_spec *ord,LIST *rp)
+void nd_gr_trace(LIST f,LIST v,int trace,int homo,int retdp,int f4,struct order_spec *ord,LIST *rp)
 {
     VL tv,fv,vv,vc,av;
     NODE fd,fd0,in0,in,r,r0,t,s,cand,alist;
@@ -3668,7 +4794,9 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     int *perm;
     int j,ret;
     Z jq,bpe;
+    VECT hvect;
 
+    NcriB = NcriMF = Ncri2 = 0;
     nd_module = 0;
     nd_lf = 0;
     parse_nd_option(current_option);
@@ -3722,6 +4850,11 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     for ( t = BDY(f), max = 1; t; t = NEXT(t) )
         for ( tv = vv; tv; tv = NEXT(tv) ) {
             if ( nd_module ) {
+              if ( OID(BDY(t)) == O_DPM ) {
+                e = dpm_getdeg((DPM)BDY(t),&trank);
+                max = MAX(e,max);
+                mrank = MAX(mrank,trank);
+              } else {
                 s = BDY((LIST)BDY(t));
                 trank = length(s);
                 mrank = MAX(mrank,trank);
@@ -3729,6 +4862,7 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
                     e = getdeg(tv->v,(P)BDY(s));
                     max = MAX(e,max);
                 }
+              }
             } else {
                 e = getdeg(tv->v,(P)BDY(t));
                 max = MAX(e,max);
@@ -3739,13 +4873,22 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     ishomo = 1;
     for ( in0 = 0, fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
         if ( nd_module ) {
-      if ( !nd_gentrace ) pltozpl((LIST)BDY(t),&dmy,&zpl);
-      else zpl = (LIST)BDY(t);
+          if ( OID(BDY(t)) == O_DPM ) {
+            Z cont;
+            DPM zdpm;
+
+            if ( !nd_gentrace ) dpm_ptozp((DPM)BDY(t),&cont,&zdpm);
+            else zdpm = (DPM)BDY(t);
+            c = (pointer)dpmtondv(m,zdpm);
+          } else {
+            if ( !nd_gentrace ) pltozpl((LIST)BDY(t),&dmy,&zpl);
+            else zpl = (LIST)BDY(t);
             c = (pointer)pltondv(CO,vv,zpl);
+          }
         } else {
-      if ( !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp);
-      else zp = (P)BDY(t);
-            c = (pointer)ptondv(CO,vv,zp);
+          if ( !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp);
+          else zp = (P)BDY(t);
+          c = (pointer)ptondv(CO,vv,zp);
         }
         if ( ishomo )
             ishomo = ishomo && ndv_ishomo(c);
@@ -3773,7 +4916,7 @@ 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);
         }
@@ -3785,6 +4928,11 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
             else m = get_lprime(++mindex);
             continue;
         }
+        if ( nd_gentrace ) {
+          MKVECT(hvect,nd_psn);
+          for ( i = 0; i < nd_psn; i++ )
+             ndltodp(nd_psh[i]->dl,(DP *)&BDY(hvect)[i]);
+        }
         if ( !ishomo && homo ) {
             /* dehomogenization */
             for ( t = cand; t; t = NEXT(t) ) ndv_dehomogenize((NDV)BDY(t),ord);
@@ -3837,8 +4985,11 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     nd_bpe = cbpe;
     nd_setup_parameters(nd_nvar,0);
     for ( r = cand; r; r = NEXT(r) ) {
-    if ( nd_module ) BDY(r) = ndvtopl(0,CO,vv,BDY(r),mrank);
-        else BDY(r) = (pointer)ndvtop(0,CO,vv,BDY(r));
+      if ( nd_module ) {
+        if ( retdp ) BDY(r) = ndvtodpm(0,BDY(r));
+        else BDY(r) = ndvtopl(0,CO,vv,BDY(r),mrank);
+      } else if ( retdp ) BDY(r) = ndvtodp(0,BDY(r));
+      else BDY(r) = (pointer)ndvtop(0,CO,vv,BDY(r));
     }
     if ( nd_nalg )
         cand = postprocess_algcoef(av,alist,cand);
@@ -3862,7 +5013,7 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
         MKLIST(l1,tl1); MKLIST(l2,tl2); MKLIST(l3,t); MKLIST(l4,tl3);
     MKLIST(l5,tl4);
       STOZ(nd_bpe,bpe);
-        tr = mknode(8,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe); MKLIST(*rp,tr);
+        tr = mknode(9,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe,hvect); MKLIST(*rp,tr);
     }
 }
 
@@ -3898,7 +5049,7 @@ DL ndltodl(int n,UINT *ndl)
     int i,j,l,s,ord_l;
     struct order_pair *op;
 
-    NEWDL(dl,n);
+    NEWDL_NOINIT(dl,n);
     dl->td = TD(ndl);
     d = dl->d;
     if ( nd_blockmask ) {
@@ -3914,6 +5065,27 @@ 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;
@@ -3926,6 +5098,18 @@ void nmtodp(int mod,NM m,DP *r)
     *r = dp;
 }
 
+void ndltodp(UINT *d,DP *r)
+{
+    DP dp;
+    MP mr;
+
+    NEWMP(mr); 
+    mr->dl = ndltodl(nd_nvar,d);
+    mr->c = (Obj)ONE;
+    NEXT(mr) = 0; MKDP(nd_nvar,mr,dp); dp->sugar = mr->dl->td;
+    *r = dp;
+}
+
 void ndl_print(UINT *dl)
 {
     int n;
@@ -3959,7 +5143,7 @@ void nd_print(ND p)
     else {
         for ( m = BDY(p); m; m = NEXT(m) ) {
             if ( CM(m) & 0x80000000 ) printf("+@_%d*",IFTOF(CM(m)));
-            else printf("+%d*",CM(m));
+            else printf("+%ld*",CM(m));
             ndl_print(DL(m));
         }
         printf("\n");
@@ -4090,7 +5274,7 @@ void ndv_homogenize(NDV p,int obpe,int oadv,EPOS oepos
     NMV m,mr0,mr,t;
 
     len = p->len;
-    for ( m = BDY(p), i = 0, max = 1; i < len; NMV_OADV(m), i++ )
+    for ( m = BDY(p), i = 0, max = 0; i < len; NMV_OADV(m), i++ )
         max = MAX(max,TD(DL(m)));
     mr0 = nmv_adv>oadv?(NMV)REALLOC(BDY(p),len*nmv_adv):BDY(p);
     m = (NMV)((char *)mr0+(len-1)*oadv);
@@ -4235,14 +5419,18 @@ void mpz_removecont_array(mpz_t *c,int n)
 {
   mpz_t d0,a,u,u1,gcd;
   int i,j;
-  mpz_t *q,*r;
+  static mpz_t *q,*r;
+  static int c_len = 0;
 
   for ( i = 0; i < n; i++ ) 
     if ( mpz_sgn(c[i]) ) break;
   if ( i == n ) return;
   gcdv_mpz_estimate(d0,c,n);
-  q = (mpz_t *)MALLOC(n*sizeof(mpz_t));
-  r = (mpz_t *)MALLOC(n*sizeof(mpz_t));
+  if ( n > c_len ) {
+    q = (mpz_t *)MALLOC(n*sizeof(mpz_t));
+    r = (mpz_t *)MALLOC(n*sizeof(mpz_t));
+    c_len = n;
+  }
   for ( i = 0; i < n; i++ ) {
     mpz_init(q[i]); mpz_init(r[i]);
     mpz_fdiv_qr(q[i],r[i],c[i],d0);
@@ -4414,7 +5602,7 @@ 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 */
@@ -4550,6 +5738,7 @@ 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);
     }
@@ -4568,12 +5757,14 @@ 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;
@@ -4585,6 +5776,91 @@ ND_pairs nd_reconstruct(int trace,ND_pairs d)
     return s0;
 }
 
+void nd_reconstruct_s(int trace,ND_pairs *d)
+{
+    int i,obpe,oadv,h;
+    static NM prev_nm_free_list;
+    static ND_pairs prev_ndp_free_list;
+    RHist mr0,mr;
+    RHist r;
+    RHist *old_red;
+    ND_pairs s0,s,t;
+    EPOS oepos;
+
+    obpe = nd_bpe;
+    oadv = nmv_adv;
+    oepos = nd_epos;
+    if ( obpe < 2 ) nd_bpe = 2;
+    else if ( obpe < 3 ) nd_bpe = 3;
+    else if ( obpe < 4 ) nd_bpe = 4;
+    else if ( obpe < 5 ) nd_bpe = 5;
+    else if ( obpe < 6 ) nd_bpe = 6;
+    else if ( obpe < 8 ) nd_bpe = 8;
+    else if ( obpe < 10 ) nd_bpe = 10;
+    else if ( obpe < 16 ) nd_bpe = 16;
+    else if ( obpe < 32 ) nd_bpe = 32;
+    else error("nd_reconstruct_s : exponent too large");
+
+    nd_setup_parameters(nd_nvar,0);
+    prev_nm_free_list = _nm_free_list;
+    prev_ndp_free_list = _ndp_free_list;
+    _nm_free_list = 0;
+    _ndp_free_list = 0;
+    for ( i = nd_psn-1; i >= 0; i-- ) {
+        ndv_realloc(nd_ps[i],obpe,oadv,oepos);
+        ndv_realloc(nd_ps_sym[i],obpe,oadv,oepos);
+    }
+    if ( trace )
+        for ( i = nd_psn-1; i >= 0; i-- ) {
+            ndv_realloc(nd_ps_trace[i],obpe,oadv,oepos);
+            ndv_realloc(nd_ps_trace_sym[i],obpe,oadv,oepos);
+        }
+
+    for ( i = 0; i < nd_nbase; i++ ) {
+      s0 = 0;
+      for ( t = d[i]; t; t = NEXT(t) ) {
+          NEXTND_pairs(s0,s);
+          s->i1 = t->i1;
+          s->i2 = t->i2;
+          s->sig = t->sig;
+          SG(s) = SG(t);
+          ndl_reconstruct(LCM(t),LCM(s),obpe,oepos);
+      }
+      d[i] = s0;
+    }
+    
+    old_red = (RHist *)MALLOC(REDTAB_LEN*sizeof(RHist));
+    for ( i = 0; i < REDTAB_LEN; i++ ) {
+        old_red[i] = nd_red[i];
+        nd_red[i] = 0;
+    }
+    for ( i = 0; i < REDTAB_LEN; i++ )
+        for ( r = old_red[i]; r; r = NEXT(r) ) {
+            NEWRHist(mr);
+            mr->index = r->index;
+            SG(mr) = SG(r);
+            ndl_reconstruct(DL(r),DL(mr),obpe,oepos);
+            h = ndl_hash_value(DL(mr));
+            NEXT(mr) = nd_red[h];
+            nd_red[h] = mr;
+            mr->sig = r->sig;
+        }
+    for ( i = 0; i < REDTAB_LEN; i++ ) old_red[i] = 0;
+    old_red = 0;
+    for ( i = 0; i < nd_psn; i++ ) {
+        NEWRHist(r); SG(r) = SG(nd_psh[i]);
+        ndl_reconstruct(DL(nd_psh[i]),DL(r),obpe,oepos);
+        r->sig = nd_psh[i]->sig;
+        nd_psh[i] = r;
+    }
+    if ( s0 ) NEXT(s) = 0;
+    prev_nm_free_list = 0;
+    prev_ndp_free_list = 0;
+#if 0
+    GC_gcollect();
+#endif
+}
+
 void ndl_reconstruct(UINT *d,UINT *r,int obpe,EPOS oepos)
 {
     int n,i,ei,oepw,omask0,j,s,ord_l,l;
@@ -4693,6 +5969,8 @@ 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;
 }
@@ -5071,6 +6349,7 @@ 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;
 }
 
@@ -5192,31 +6471,32 @@ NDV ptondv(VL vl,VL dvl,P p)
 
 void pltozpl(LIST l,Q *cont,LIST *pp)
 {
-    NODE nd,nd1;
-    int n;
-    P *pl;
-    Q *cl;
-    int i;
-    P dmy;
-    Z dvr;
-    LIST r;
+  NODE nd,nd1;
+  int n;
+  P *pl;
+  Q *cl;
+  int i;
+  P dmy;
+  Z dvr,inv;
+  LIST r;
 
-    nd = BDY(l); n = length(nd);
-    pl = (P *)MALLOC(n*sizeof(P));
-    cl = (Q *)MALLOC(n*sizeof(P));
-    for ( i = 0; i < n; i++, nd = NEXT(nd) )
-        ptozp((P)BDY(nd),1,&cl[i],&dmy);
-    qltozl(cl,n,&dvr);
-    nd = BDY(l);
-    for ( i = 0; i < n; i++, nd = NEXT(nd) ) {
-        divsp(CO,(P)BDY(nd),(P)dvr,&pl[i]);
-    }
-    nd = 0;
-    for ( i = n-1; i >= 0; i-- ) {
-        MKNODE(nd1,pl[i],nd); nd = nd1;
-    }
-    MKLIST(r,nd);
-    *pp = r;
+  nd = BDY(l); n = length(nd);
+  pl = (P *)MALLOC(n*sizeof(P));
+  cl = (Q *)MALLOC(n*sizeof(Q));
+  for ( i = 0; i < n; i++, nd = NEXT(nd) ) {
+    ptozp((P)BDY(nd),1,&cl[i],&dmy);
+  }
+  qltozl(cl,n,&dvr);
+  divz(ONE,dvr,&inv);
+  nd = BDY(l);
+  for ( i = 0; i < n; i++, nd = NEXT(nd) )
+    divsp(CO,(P)BDY(nd),(P)dvr,&pl[i]);
+  nd = 0;
+  for ( i = n-1; i >= 0; i-- ) {
+    MKNODE(nd1,pl[i],nd); nd = nd1;
+  }
+  MKLIST(r,nd);
+  *pp = r;
 }
 
 /* (a1,a2,...,an) -> a1*e(1)+...+an*e(n) */
@@ -5402,9 +6682,112 @@ NDV ndtondv(int mod,ND p)
     }
     MKNDV(NV(p),m0,len,d);
     SG(d) = SG(p);
+    d->sig = p->sig;
     return d;
 }
 
+static int dmm_comp_nv;
+
+int dmm_comp(DMM *a,DMM *b)
+{
+   return -compdmm(dmm_comp_nv,*a,*b);
+}
+
+void dmm_sort_by_ord(DMM *a,int len,int nv)
+{
+  dmm_comp_nv = nv;
+  qsort(a,len,sizeof(DMM),(int (*)(const void *,const void *))dmm_comp);
+}
+
+void dpm_sort(DPM p,DPM *rp)
+{
+  DMM t,t1;
+  int len,i,n;
+  DMM *a;
+  DPM d;
+ 
+  if ( !p ) *rp = 0;
+  for ( t = BDY(p), len = 0; t; t = NEXT(t), len++ );
+  a = (DMM *)MALLOC(len*sizeof(DMM));
+  for ( i = 0, t = BDY(p); i < len; i++, t = NEXT(t) ) a[i] = t;
+  n = p->nv;
+  dmm_sort_by_ord(a,len,n);  
+  t = 0;
+  for ( i = len-1; i >= 0; i-- ) {
+    NEWDMM(t1); 
+    t1->c = a[i]->c;
+    t1->dl = a[i]->dl;
+    t1->pos = a[i]->pos;
+    t1->next = t;
+    t = t1;
+  }
+  MKDPM(n,t,d);
+  SG(d) = SG(p);
+  *rp = d;
+}
+
+int dpm_comp(DPM *a,DPM *b)
+{
+  return -compdpm(CO,*a,*b);
+}
+
+NODE dpm_sort_list(NODE l)
+{
+  int i,len;
+  NODE t,t1;
+  DPM *a;
+  
+  len = length(l);
+  a = (DPM *)MALLOC(len*sizeof(DPM));
+  for ( t = l, i = 0; i < len; i++, t = NEXT(t) ) a[i] = (DPM)BDY(t);
+  qsort(a,len,sizeof(DPM),(int (*)(const void *,const void *))dpm_comp);
+  t = 0;
+  for ( i = len-1; i >= 0; i-- ) {
+    MKNODE(t1,(pointer)a[i],t); t = t1;
+  }
+  return t;
+}
+
+int nmv_comp(NMV a,NMV b)
+{
+  int t;
+  t = DL_COMPARE(a->dl,b->dl);
+  return -t;
+}
+
+NDV dpmtondv(int mod,DPM p)
+{
+  NDV d;
+  NMV m,m0;
+  DMM t;
+  DMM *a;
+  int i,len,n;
+
+  if ( !p ) return 0;
+  for ( t = BDY(p), len = 0; t; t = NEXT(t), len++ );
+  a = (DMM *)MALLOC(len*sizeof(DMM));
+  for ( i = 0, t = BDY(p); i < len; i++, t = NEXT(t) ) a[i] = t;
+  n = p->nv;
+  dmm_sort_by_ord(a,len,n);  
+  if ( mod > 0 || mod == -1 )
+    m0 = m = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(len*nmv_adv);
+  else
+    m0 = m = MALLOC(len*nmv_adv);
+#if 0
+  ndv_alloc += nmv_adv*len;
+#endif
+  for ( i = 0; i < len; i++, NMV_ADV(m) ) {
+    dltondl(n,a[i]->dl,DL(m));
+    MPOS(DL(m)) = a[i]->pos;
+    TD(DL(m)) = ndl_weight(DL(m));
+    CZ(m) = (Z)a[i]->c;
+  }
+  qsort(m0,len,nmv_adv,(int (*)(const void *,const void *))nmv_comp);
+  MKNDV(NV(p),m0,len,d);
+  SG(d) = SG(p);
+  return d;
+}
+
 ND ndvtond(int mod,NDV p)
 {
     ND d;
@@ -5423,6 +6806,7 @@ ND ndvtond(int mod,NDV p)
     NEXT(m) = 0;
     MKND(NV(p),m0,len,d);
     SG(d) = SG(p);
+    d->sig = p->sig;
     return d;
 }
 
@@ -5447,6 +6831,29 @@ DP ndvtodp(int mod,NDV p)
     return d;
 }
 
+DPM ndvtodpm(int mod,NDV p)
+{
+  DMM m,m0;
+  DPM d;
+  NMV t;
+  int i,len;
+
+  if ( !p ) return 0;
+  m0 = 0;
+  len = p->len;
+  for ( t = BDY(p), i = 0; i < len; NMV_ADV(t), i++ ) {
+    NEXTDMM(m0,m);
+    m->dl = ndltodl(nd_nvar,DL(t));
+    m->c = (Obj)ndctop(mod,t->c);
+    m->pos = MPOS(DL(t));
+  }
+  NEXT(m) = 0;
+  MKDPM(nd_nvar,m0,d);
+  SG(d) = SG(p);
+  return d;
+}
+
+
 DP ndtodp(int mod,ND p)
 {
     MP m,m0;
@@ -5478,7 +6885,7 @@ void ndv_print(NDV p)
         len = LEN(p);
         for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
             if ( CM(m) & 0x80000000 ) printf("+@_%d*",IFTOF(CM(m)));
-            else printf("+%d*",CM(m));
+            else printf("+%ld*",CM(m));
             ndl_print(DL(m));
         }
         printf("\n");
@@ -5509,6 +6916,7 @@ NODE ndv_reducebase(NODE x,int *perm)
     NDVI w;
     NODE t,t0;
 
+    if ( nd_norb ) return x;
     len = length(x);
     w = (NDVI)MALLOC(len*sizeof(struct oNDVI));
     for ( i = 0, t = x; i < len; i++, t = NEXT(t) ) {
@@ -5534,12 +6942,15 @@ NODE ndv_reducebase(NODE x,int *perm)
 
 /* XXX incomplete */
 
+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;
@@ -5603,40 +7014,73 @@ 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;
 }
@@ -5672,7 +7116,7 @@ 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;
@@ -5775,7 +7219,7 @@ 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 )
@@ -6056,7 +7500,6 @@ int ndv_reduce_vect_q(Z *svect,int trace,int col,IndAr
 int ndv_reduce_vect_q(Z *svect0,int trace,int col,IndArray *imat,NM_ind_pair *rp0,int nred)
 {
     int i,j,k,len,pos,prev;
-    mpz_t *svect;
     mpz_t cs,cr,gcd;
     IndArray ivect;
     unsigned char *ivc;
@@ -6068,12 +7511,17 @@ int ndv_reduce_vect_q(Z *svect0,int trace,int col,IndA
     int maxrs;
     double hmag;
     int l;
+    static mpz_t *svect;
+    static int svect_len=0;
 
     maxrs = 0;
     for ( i = 0; i < col && !svect0[i]; i++ );
     if ( i == col ) return maxrs;
     hmag = p_mag((P)svect0[i])*nd_scale;
-    svect = (mpz_t *)MALLOC(col*sizeof(mpz_t));
+    if ( col > svect_len ) {
+      svect = (mpz_t *)MALLOC(col*sizeof(mpz_t));
+      svect_len = col;
+    }
     for ( i = 0; i < col; i++ ) {
       mpz_init(svect[i]);
       if ( svect0[i] )
@@ -6144,7 +7592,7 @@ int ndv_reduce_vect_q(Z *svect0,int trace,int col,IndA
 }
 #endif
 
-int ndv_reduce_vect(int m,UINT *svect,int col,IndArray *imat,NM_ind_pair *rp0,int nred)
+int ndv_reduce_vect(int m,UINT *svect,int col,IndArray *imat,NM_ind_pair *rp0,int nred,SIG sig)
 {
     int i,j,k,len,pos,prev;
     UINT c,c1,c2,c3,up,lo,dmy;
@@ -6161,7 +7609,7 @@ int ndv_reduce_vect(int m,UINT *svect,int col,IndArray
     for ( i = 0; i < nred; i++ ) {
         ivect = imat[i];
         k = ivect->head; svect[k] %= m;
-        if ( (c = svect[k]) != 0 ) {
+        if ( (c = svect[k]) != 0 && (sig == 0 || comp_sig(sig,rp0[i]->sig) > 0 ) ) {
             maxrs = MAX(maxrs,rp0[i]->sugar);
             c = m-c; redv = nd_ps[rp0[i]->index];
             len = LEN(redv); mr = BDY(redv);
@@ -6171,12 +7619,12 @@ int ndv_reduce_vect(int m,UINT *svect,int col,IndArray
                     ivc = ivect->index.c;
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivc[j]; c1 = CM(mr); prev = pos;
-            if ( c1 ) {
-              c2 = svect[pos];
+                        if ( c1 ) {
+                          c2 = svect[pos];
                           DMA(c1,c,c2,up,lo);
                           if ( up ) { DSAB(m,up,lo,dmy,c3); svect[pos] = c3;
                           } else svect[pos] = lo;
-            }
+                        }
                     }
                     break;
                 case 2:
@@ -6184,12 +7632,12 @@ int ndv_reduce_vect(int m,UINT *svect,int col,IndArray
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivs[j]; c1 = CM(mr);
                         prev = pos;
-            if ( c1 ) {
-              c2 = svect[pos];
+                        if ( c1 ) {
+                          c2 = svect[pos];
                           DMA(c1,c,c2,up,lo);
                           if ( up ) { DSAB(m,up,lo,dmy,c3); svect[pos] = c3;
                           } else svect[pos] = lo;
-            }
+                        }
                     }
                     break;
                 case 4:
@@ -6197,12 +7645,12 @@ int ndv_reduce_vect(int m,UINT *svect,int col,IndArray
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivi[j]; c1 = CM(mr);
                         prev = pos;
-            if ( c1 ) {
-              c2 = svect[pos];
+                        if ( c1 ) {
+                          c2 = svect[pos];
                           DMA(c1,c,c2,up,lo);
                           if ( up ) { DSAB(m,up,lo,dmy,c3); svect[pos] = c3;
                           } else svect[pos] = lo;
-            }
+                        }
                     }
                     break;
             }
@@ -6470,6 +7918,29 @@ NDV vect_to_ndv(UINT *vect,int spcol,int col,int *rhea
     }
 }
 
+NDV vect_to_ndv_s(UINT *vect,int col,UINT *s0vect)
+{
+    int j,k,len;
+    UINT *p;
+    UINT c;
+    NDV r;
+    NMV mr0,mr;
+
+    for ( j = 0, len = 0; j < col; j++ ) if ( vect[j] ) len++;
+    if ( !len ) return 0;
+    else {
+        mr0 = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(nmv_adv*len);
+        mr = mr0; 
+        p = s0vect;
+        for ( j = k = 0; j < col; j++, p += nd_wpd )
+          if ( (c = vect[k++]) != 0 ) {
+            ndl_copy(p,DL(mr)); CM(mr) = c; NMV_ADV(mr);
+          }
+        MKNDV(nd_nvar,mr0,len,r);
+        return r;
+    }
+}
+
 NDV vect_to_ndv_2(unsigned long *vect,int col,UINT *s0vect)
 {
     int j,k,len;
@@ -6631,7 +8102,7 @@ int nd_symbolic_preproc(PGeoBucket bucket,int trace,UI
             if ( ndl_check_bound2(index,DL(mul)) ) 
                 return 0;
             sugar = TD(DL(mul))+SG(ps[index]);
-            MKNM_ind_pair(pair,mul,index,sugar);
+            MKNM_ind_pair(pair,mul,index,sugar,0);
             red = ndv_mul_nm_symbolic(mul,ps[index]);
             add_pbucket_symbolic(bucket,nd_remove_head(red));
             NEXTNODE(rp0,rp); BDY(rp) = (pointer)pair;
@@ -6679,6 +8150,8 @@ NODE nd_f4(int m,int checkonly,int **indp)
     PGeoBucket bucket;
     struct oEGT eg0,eg1,eg_f4;
     Z i1,i2,sugarq;
+
+    init_eg(&f4_symb); init_eg(&f4_conv); init_eg(&f4_conv); init_eg(&f4_elim1); init_eg(&f4_elim2);
 #if 0
     ndv_alloc = 0;
 #endif
@@ -6724,7 +8197,7 @@ NODE nd_f4(int m,int checkonly,int **indp)
             d = nd_reconstruct(0,d);
             continue;
         }
-        get_eg(&eg1); init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg1);
+        get_eg(&eg1); init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg1); add_eg(&f4_symb,&eg0,&eg1);
         if ( DP_Print )
             fprintf(asir_out,"sugar=%d,symb=%.3fsec,",
                 sugar,eg_f4.exectime);
@@ -6734,6 +8207,7 @@ NODE nd_f4(int m,int checkonly,int **indp)
         if ( nflist ) nd_last_nonzero = f4red;
         for ( r = nflist; r; r = NEXT(r) ) {
             nf = (NDV)BDY(r);
+            if ( nd_f4_td ) SG(nf) = nd_tdeg(nf);
             ndv_removecont(m,nf);
             if ( !m && nd_nalg ) {
                 ND nf1;
@@ -6743,7 +8217,7 @@ 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);
         }
@@ -6773,8 +8247,12 @@ NODE nd_f4(int m,int checkonly,int **indp)
 #if 0
     fprintf(asir_out,"ndv_alloc=%d\n",ndv_alloc);
 #endif
-  if ( DP_Print )
-    fprintf(asir_out,"number of red=%d\n",Nf4_red);
+  if ( DP_Print ) {
+    fprintf(asir_out,"number of red=%d,",Nf4_red);
+    fprintf(asir_out,"symb=%.3fsec,conv=%.3fsec,elim1=%.3fsec,elim2=%.3fsec\n",
+      f4_symb.exectime,f4_conv.exectime,f4_elim1.exectime,f4_elim2.exectime);
+    fprintf(asir_out,"number of removed pairs=%d\n,",NcriB+NcriMF+Ncri2);
+  }
   conv_ilist(nd_demand,0,g,indp);
     return g;
 }
@@ -6868,7 +8346,7 @@ 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);
         }
@@ -7083,7 +8561,7 @@ NODE nd_f4_red(int m,ND_pairs sp0,int trace,UINT *s0ve
         rhead[imat[i]->head] = 1;
         start = imat[i]->head;
     }
-    get_eg(&eg1); init_eg(&eg_conv); add_eg(&eg_conv,&eg0,&eg1);
+    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);
@@ -7135,7 +8613,7 @@ NODE nd_f4_red_main(int m,ND_pairs sp0,int nsp,UINT *s
         if ( m == -1 ) 
             maxrs = ndv_reduce_vect_sf(m,svect,col,imat,rvect,nred);
         else
-            maxrs = ndv_reduce_vect(m,svect,col,imat,rvect,nred);
+            maxrs = ndv_reduce_vect(m,svect,col,imat,rvect,nred,0);
         for ( i = 0; i < col; i++ ) if ( svect[i] ) break;
         if ( i < col ) {
             spmat[sprow] = v = (UINT *)MALLOC_ATOMIC(spcol*sizeof(UINT));
@@ -7191,7 +8669,84 @@ NODE nd_f4_red_main(int m,ND_pairs sp0,int nsp,UINT *s
     return r0;
 }
 
+NODE nd_f4_red_main_s(int m,ND_pairs sp0,int nsp,UINT *s0vect,int col,
+        NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred,NODE *syzlistp)
+{
+    int spcol,sprow,a;
+    int i,j,k,l,rank;
+    NODE r0,r;
+    ND_pairs sp;
+    ND spol;
+    UINT **spmat;
+    UINT *svect,*cvect;
+    UINT *v;
+    int *colstat;
+    struct oEGT eg0,eg1,eg2,eg_f4,eg_f4_1,eg_f4_2;
+    int maxrs;
+    int *spsugar;
+    ND_pairs *spactive;
+    SIG *spsig;
 
+    get_eg(&eg0);
+    /* elimination (1st step) */
+    spmat = (UINT **)MALLOC(nsp*sizeof(UINT *));
+    spsugar = (int *)MALLOC(nsp*sizeof(int));
+    spsig = (SIG *)MALLOC(nsp*sizeof(SIG));
+    for ( a = sprow = 0, sp = sp0; a < nsp; a++, sp = NEXT(sp) ) {
+        nd_sp(m,0,sp,&spol);
+        if ( !spol ) {
+          syzlistp[sp->sig->pos] = insert_sig(syzlistp[sp->sig->pos],sp->sig);
+          continue;
+        }
+        svect = (UINT *)MALLOC(col*sizeof(UINT));
+        nd_to_vect(m,s0vect,col,spol,svect);
+        maxrs = ndv_reduce_vect(m,svect,col,imat,rvect,nred,spol->sig);
+        for ( i = 0; i < col; i++ ) if ( svect[i] ) break;
+        if ( i < col ) {
+            spmat[sprow] = svect;
+            spsugar[sprow] = MAX(maxrs,SG(spol));
+            spsig[sprow] = sp->sig;
+            sprow++;
+        } else {
+          syzlistp[sp->sig->pos] = insert_sig(syzlistp[sp->sig->pos],sp->sig);
+        }
+        nd_free(spol);
+    }
+    get_eg(&eg1); init_eg(&eg_f4_1); add_eg(&eg_f4_1,&eg0,&eg1); add_eg(&f4_elim1,&eg0,&eg1);
+    if ( DP_Print ) {
+        fprintf(asir_out,"elim1=%.3fsec,",eg_f4_1.exectime);
+        fflush(asir_out);
+    }
+    /* free index arrays */
+    for ( i = 0; i < nred; i++ ) GCFREE(imat[i]->index.c);
+
+    /* elimination (2nd step) */
+    colstat = (int *)MALLOC(col*sizeof(int));
+    rank = nd_gauss_elim_mod_s(spmat,spsugar,0,sprow,col,m,colstat,spsig);
+    r0 = 0;
+    for ( i = 0; i < sprow; i++ ) {
+        if ( spsugar[i] >= 0 ) {
+          NEXTNODE(r0,r);
+          BDY(r) = vect_to_ndv_s(spmat[i],col,s0vect);
+          SG((NDV)BDY(r)) = spsugar[i];
+          ((NDV)BDY(r))->sig = spsig[i];
+        } else
+          syzlistp[spsig[i]->pos] = insert_sig(syzlistp[spsig[i]->pos],spsig[i]);
+        GCFREE(spmat[i]);
+    }
+    if ( r0 ) NEXT(r) = 0;
+    get_eg(&eg2); init_eg(&eg_f4_2); add_eg(&eg_f4_2,&eg1,&eg2); add_eg(&f4_elim2,&eg1,&eg2);
+    init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg2);
+    if ( DP_Print ) {
+        fprintf(asir_out,"elim2=%.3fsec,",eg_f4_2.exectime);
+        fprintf(asir_out,"nsp=%d,nred=%d,spmat=(%d,%d),rank=%d ",
+            nsp,nred,sprow,col,rank);
+        fprintf(asir_out,"%.3fsec,",eg_f4.exectime);
+    }
+    return r0;
+}
+
+
 /* for small finite fields */
 
 NODE nd_f4_red_sf_main(int m,ND_pairs sp0,int nsp,UINT *s0vect,int col,
@@ -7603,7 +9158,57 @@ int nd_gauss_elim_mod(UINT **mat0,int *sugar,ND_pairs 
     return rank;
 }
 
+int nd_gauss_elim_mod_s(UINT **mat,int *sugar,ND_pairs *spactive,int row,int col,int md,int *colstat,SIG *sig)
+{
+  int i,j,k,l,rank,s,imin;
+  UINT inv;
+  UINT a;
+  UINT *t,*pivot,*pk;
+  UINT *ck;
+  UINT *ct;
+  ND_pairs pair;
+  SIG sg;
+  int *used;
 
+  used = (int *)MALLOC(row*sizeof(int));
+  for ( j = 0; j < col; j++ ) {
+    for ( i = 0; i < row; i++ )
+      a = mat[i][j] %= md;
+    for ( i = 0; i < row; i++ )
+      if ( !used[i] && mat[i][j] ) break;
+    if ( i == row ) {
+      colstat[j] = 0;
+      continue;
+    } else {
+      colstat[j] = 1;
+      used[i] = 1;
+    }
+    /* column j is normalized */
+    s = sugar[i];
+    inv = invm(mat[i][j],md);
+    /* normalize pivot row */
+    for ( k = j, pk = mat[i]+j; k < col; k++, pk++, ck++ ) {
+      DMAR(*pk,inv,0,md,*pk);
+    }
+    for ( k = i+1; k < row; k++ ) {
+      if ( (a = mat[k][j]) != 0 ) {
+        sugar[k] = MAX(sugar[k],s);
+        red_by_vect(md,mat[k]+j,mat[i]+j,(int)(md-a),col-j);
+        Nf4_red++;
+      }
+    }
+  }
+  rank = 0;
+  for ( i = 0; i < row; i++ ) {
+    for ( j = 0; j < col; j++ )
+      if ( mat[i][j] ) break;
+    if ( j == col ) sugar[i] = -1;
+    else rank++;
+  }
+  return rank;
+}
+
+
 int nd_gauss_elim_sf(UINT **mat0,int *sugar,int row,int col,int md,int *colstat)
 {
     int i,j,k,l,inv,a,rank,s;
@@ -7666,7 +9271,9 @@ int ndv_ishomo(NDV p)
     h = TD(DL(m));
     NMV_ADV(m);
     for ( len--; len; len--, NMV_ADV(m) )
-        if ( TD(DL(m)) != h ) return 0;
+        if ( TD(DL(m)) != h ) {
+          return 0;
+        }
     return 1;
 }
 
@@ -8277,69 +9884,107 @@ void conv_ilist(int demand,int trace,NODE g,int **indp
   if ( indp ) *indp = ind;
 }
 
+NODE conv_ilist_s(int demand,int trace,int **indp)
+{
+  int n,i,j;
+  int *ind;
+  NODE g0,g;
+
+  n = nd_psn;
+  ind = (int *)MALLOC(n*sizeof(int));
+  g0 = 0;
+  for ( i = 0; i < n; i++ ) {
+    ind[i] = i;
+    NEXTNODE(g0,g);
+    BDY(g) = (pointer)(demand?ndv_load(i):(trace?nd_ps_trace[i]:nd_ps[i]));
+  }
+  if ( g0 ) NEXT(g) = 0;
+  if ( indp ) *indp = ind;
+  return g0;
+}
+
 void parse_nd_option(NODE opt)
 {
-    NODE t,p,u;
+  NODE t,p,u;
   int i,s,n;
-    char *key;
-    Obj value;
+  char *key;
+  Obj value;
 
-    nd_gentrace = 0; nd_gensyz = 0; nd_nora = 0; nd_gbblock = 0;
+  nd_gentrace = 0; nd_gensyz = 0; nd_nora = 0; nd_norb = 0; nd_gbblock = 0;
   nd_newelim = 0; nd_intersect = 0; nd_nzlist = 0;
   nd_splist = 0; nd_check_splist = 0;
-    nd_sugarweight = 0;
-    nd_f4red =0;
-    nd_rank0 = 0;
-    for ( t = opt; t; t = NEXT(t) ) {
-        p = BDY((LIST)BDY(t));
-        key = BDY((STRING)BDY(p));
-        value = (Obj)BDY(NEXT(p));
-        if ( !strcmp(key,"gentrace") )
-            nd_gentrace = value?1:0;
-        else if ( !strcmp(key,"gensyz") )
-            nd_gensyz = value?1:0;
-        else if ( !strcmp(key,"nora") )
-            nd_nora = value?1:0;
-        else if ( !strcmp(key,"gbblock") ) {
-            if ( value && OID(value) == O_LIST ) {
+  nd_sugarweight = 0; nd_f4red =0; nd_rank0 = 0;
+  nd_f4_td = 0; nd_sba_f4step = 2; nd_sba_pot = 0; nd_sba_largelcm = 0;
+  nd_sba_dontsort = 0; nd_top = 0; nd_sba_redundant_check = 0;
+
+  for ( t = opt; t; t = NEXT(t) ) {
+    p = BDY((LIST)BDY(t));
+    key = BDY((STRING)BDY(p));
+    value = (Obj)BDY(NEXT(p));
+    if ( !strcmp(key,"gentrace") )
+      nd_gentrace = value?1:0;
+    else if ( !strcmp(key,"gensyz") )
+      nd_gensyz = value?1:0;
+    else if ( !strcmp(key,"nora") )
+      nd_nora = value?1:0;
+    else if ( !strcmp(key,"norb") )
+      nd_norb = value?1:0;
+    else if ( !strcmp(key,"gbblock") ) {
+      if ( value && OID(value) == O_LIST ) {
         u = BDY((LIST)value);
-              nd_gbblock = MALLOC((2*length(u)+1)*sizeof(int));
+        nd_gbblock = MALLOC((2*length(u)+1)*sizeof(int));
         for ( i = 0; u; u = NEXT(u) ) {
           p = BDY((LIST)BDY(u));
           s = nd_gbblock[i++] = ZTOS((Q)BDY(p));
           nd_gbblock[i++] = s+ZTOS((Q)BDY(NEXT(p)))-1;
         }
         nd_gbblock[i] = -1;
-            } else
-              nd_gbblock = 0;
+      } else
+        nd_gbblock = 0;
     } else if ( !strcmp(key,"newelim") )
             nd_newelim = value?1:0;
     else if ( !strcmp(key,"intersect") )
             nd_intersect = value?1:0;
+    else if ( !strcmp(key,"syzgen") )
+            nd_intersect = ZTOS((Q)value);
     else if ( !strcmp(key,"lf") )
             nd_lf = value?1:0;
     else if ( !strcmp(key,"trace") ) {
-           if ( value ) {
-               u = BDY((LIST)value);
-           nd_nzlist = BDY((LIST)ARG2(u));
-           nd_bpe = ZTOS((Q)ARG3(u));
-           }
+      if ( value ) {
+        u = BDY((LIST)value);
+        nd_nzlist = BDY((LIST)ARG2(u));
+        nd_bpe = ZTOS((Q)ARG3(u));
+      }
     } else if ( !strcmp(key,"f4red") ) {
-       nd_f4red = ZTOS((Q)value);
+      nd_f4red = ZTOS((Q)value);
     } else if ( !strcmp(key,"rank0") ) {
-            nd_rank0 = value?1:0;
+      nd_rank0 = value?1:0;
     } else if ( !strcmp(key,"splist") ) {
-            nd_splist = value?1:0;
+      nd_splist = value?1:0;
     } else if ( !strcmp(key,"check_splist") ) {
       nd_check_splist = BDY((LIST)value);
     } else if ( !strcmp(key,"sugarweight") ) {
       u = BDY((LIST)value);
-            n = length(u);
-            nd_sugarweight = MALLOC(n*sizeof(int));
+      n = length(u);
+      nd_sugarweight = MALLOC(n*sizeof(int));
       for ( i = 0; i < n; i++, u = NEXT(u) ) 
-                nd_sugarweight[i] = ZTOS((Q)BDY(u));
+        nd_sugarweight[i] = ZTOS((Q)BDY(u));
+    } else if ( !strcmp(key,"f4_td") ) {
+      nd_f4_td = value?1:0;
+    } else if ( !strcmp(key,"sba_f4step") ) {
+      nd_sba_f4step = value?ZTOS((Q)value):0;
+    } else if ( !strcmp(key,"sba_pot") ) {
+      nd_sba_pot = value?1:0;
+    } else if ( !strcmp(key,"sba_largelcm") ) {
+      nd_sba_largelcm = value?1:0;
+    } else if ( !strcmp(key,"sba_dontsort") ) {
+      nd_sba_dontsort = value?1:0;
+    } else if ( !strcmp(key,"sba_redundant_check") ) {
+      nd_sba_redundant_check = value?1:0;
+    } else if ( !strcmp(key,"top") ) {
+      nd_top = value?1:0;
     }
-    }
+  }
 }
 
 ND mdptond(DP d);
@@ -8871,7 +10516,7 @@ 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 ) {
@@ -8987,7 +10632,7 @@ 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);
         }
@@ -9027,6 +10672,29 @@ NDV vect64_to_ndv(mp_limb_t *vect,int spcol,int col,in
     }
 }
 
+NDV vect64_to_ndv_s(mp_limb_t *vect,int col,UINT *s0vect)
+{
+    int j,k,len;
+    UINT *p;
+    UINT c;
+    NDV r;
+    NMV mr0,mr;
+
+    for ( j = 0, len = 0; j < col; j++ ) if ( vect[j] ) len++;
+    if ( !len ) return 0;
+    else {
+        mr0 = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(nmv_adv*len);
+        mr = mr0; 
+        p = s0vect;
+        for ( j = k = 0; j < col; j++, p += nd_wpd )
+          if ( (c = (UINT)vect[k++]) != 0 ) {
+            ndl_copy(p,DL(mr)); CM(mr) = c; NMV_ADV(mr);
+          }
+        MKNDV(nd_nvar,mr0,len,r);
+        return r;
+    }
+}
+
 int nd_to_vect64(int mod,UINT *s0,int n,ND d,mp_limb_t *r)
 {
     NM m;
@@ -9056,7 +10724,7 @@ int nd_to_vect64(int mod,UINT *s0,int n,ND d,mp_limb_t
 
 #define MOD128(a,c,m) ((a)=(((c)!=0||((a)>=(m)))?(((((U128)(c))<<64)+(a))%(m)):(a)))
 
-int ndv_reduce_vect64(int m,mp_limb_t *svect,mp_limb_t *cvect,int col,IndArray *imat,NM_ind_pair *rp0,int nred)
+int ndv_reduce_vect64(int m,mp_limb_t *svect,mp_limb_t *cvect,int col,IndArray *imat,NM_ind_pair *rp0,int nred,SIG sig)
 {
     int i,j,k,len,pos,prev;
     mp_limb_t a,c,c1,c2;
@@ -9077,7 +10745,7 @@ int ndv_reduce_vect64(int m,mp_limb_t *svect,mp_limb_t
         a = svect[k]; c = cvect[k];
         MOD128(a,c,m);
         svect[k] = a; cvect[k] = 0;
-        if ( (c = svect[k]) != 0 ) {
+        if ( (c = svect[k]) != 0 && (sig == 0 || comp_sig(sig,rp0[i]->sig) > 0 ) ) {
             Nf4_red++;
             maxrs = MAX(maxrs,rp0[i]->sugar);
             c = m-c; redv = nd_ps[rp0[i]->index];
@@ -9088,33 +10756,27 @@ int ndv_reduce_vect64(int m,mp_limb_t *svect,mp_limb_t
                     ivc = ivect->index.c;
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivc[j]; c1 = CM(mr); prev = pos;
-                        if ( c1 ) {
-                          c2 = svect[pos]+c1*c;
-                          if ( c2 < svect[pos] ) cvect[pos]++;
-                          svect[pos] = c2;
-                        }
+                        c2 = svect[pos]+c1*c;
+                        if ( c2 < svect[pos] ) cvect[pos]++;
+                        svect[pos] = c2;
                     }
                     break;
                 case 2:
                     ivs = ivect->index.s; 
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivs[j]; c1 = CM(mr); prev = pos;
-                        if ( c1 ) {
-                          c2 = svect[pos]+c1*c;
-                          if ( c2 < svect[pos] ) cvect[pos]++;
-                          svect[pos] = c2;
-                        }
+                        c2 = svect[pos]+c1*c;
+                        if ( c2 < svect[pos] ) cvect[pos]++;
+                        svect[pos] = c2;
                     }
                     break;
                 case 4:
                     ivi = ivect->index.i;
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivi[j]; c1 = CM(mr); prev = pos;
-                        if ( c1 ) {
-                          c2 = svect[pos]+c1*c;
-                          if ( c2 < svect[pos] ) cvect[pos]++;
-                          svect[pos] = c2;
-                        }
+                        c2 = svect[pos]+c1*c;
+                        if ( c2 < svect[pos] ) cvect[pos]++;
+                        svect[pos] = c2;
                     }
                     break;
             }
@@ -9157,7 +10819,7 @@ NODE nd_f4_red_mod64_main(int m,ND_pairs sp0,int nsp,U
         nd_sp(m,0,sp,&spol);
         if ( !spol ) continue;
         nd_to_vect64(m,s0vect,col,spol,svect);
-        maxrs = ndv_reduce_vect64(m,svect,cvect,col,imat,rvect,nred);
+        maxrs = ndv_reduce_vect64(m,svect,cvect,col,imat,rvect,nred,0);
         for ( i = 0; i < col; i++ ) if ( svect[i] ) break;
         if ( i < col ) {
             spmat[sprow] = v = (mp_limb_t *)MALLOC_ATOMIC(spcol*sizeof(mp_limb_t));
@@ -9170,7 +10832,7 @@ NODE nd_f4_red_mod64_main(int m,ND_pairs sp0,int nsp,U
         }
         nd_free(spol);
     }
-    get_eg(&eg1); init_eg(&eg_f4_1); add_eg(&eg_f4_1,&eg0,&eg1);
+    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);
@@ -9191,7 +10853,7 @@ NODE nd_f4_red_mod64_main(int m,ND_pairs sp0,int nsp,U
     if ( r0 ) NEXT(r) = 0;
 
     for ( ; i < sprow; i++ ) GCFREE(spmat[i]);
-    get_eg(&eg2); init_eg(&eg_f4_2); add_eg(&eg_f4_2,&eg1,&eg2);
+    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);
@@ -9287,5 +10949,432 @@ int nd_gauss_elim_mod64(mp_limb_t **mat,int *sugar,ND_
   GCFREE(cmat);
   return rank;
 }
+
+int nd_gauss_elim_mod64_s(mp_limb_t **mat,int *sugar,ND_pairs *spactive,int row,int col,int md,int *colstat,SIG *sig)
+{
+  int i,j,k,l,rank,s,imin;
+  mp_limb_t inv;
+  mp_limb_t a;
+  UINT c;
+  mp_limb_t *t,*pivot,*pk;
+  UINT *ck;
+  UINT **cmat;
+  UINT *ct;
+  ND_pairs pair;
+  SIG sg;
+  int *used;
+
+  used = (int *)MALLOC(row*sizeof(int));
+  cmat = (UINT **)MALLOC(row*sizeof(UINT *));
+  for ( i = 0; i < row; i++ ) {
+    cmat[i] = MALLOC_ATOMIC(col*sizeof(UINT));
+    bzero(cmat[i],col*sizeof(UINT));
+  }
+
+  for ( j = 0; j < col; j++ ) {
+    for ( i = 0; i < row; i++ ) {
+      a = mat[i][j]; c = cmat[i][j];
+      MOD128(a,c,md);
+      mat[i][j] = a; cmat[i][j] = 0;
+    }
+    for ( i = 0; i < row; i++ )
+      if ( !used[i] && mat[i][j] ) break;
+    if ( i == row ) {
+      colstat[j] = 0;
+      continue;
+    } else {
+      colstat[j] = 1;
+      used[i] = 1;
+    }
+    /* column j is normalized */
+    s = sugar[i];
+    inv = invm((UINT)mat[i][j],md);
+    /* normalize pivot row */
+    for ( k = j, pk = mat[i]+j, ck = cmat[i]+j; k < col; k++, pk++, ck++ ) {
+      a = *pk; c = *ck; MOD128(a,c,md); *pk = (a*inv)%md; *ck = 0;
+    }
+    for ( k = i+1; k < row; k++ ) {
+      if ( (a = mat[k][j]) != 0 ) {
+        sugar[k] = MAX(sugar[k],s);
+        red_by_vect64(md,mat[k]+j,cmat[k]+j,mat[i]+j,(int)(md-a),col-j);
+        Nf4_red++;
+      }
+    }
+  }
+  rank = 0;
+  for ( i = 0; i < row; i++ ) {
+    for ( j = 0; j < col; j++ )
+      if ( mat[i][j] ) break;
+    if ( j == col ) sugar[i] = -1;
+    else rank++;
+  }
+  for ( i = 0; i < row; i++ ) GCFREE(cmat[i]);
+  GCFREE(cmat);
+  return rank;
+}
+
+NODE nd_f4_red_mod64_main_s(int m,ND_pairs sp0,int nsp,UINT *s0vect,int col,
+        NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred,NODE *syzlistp)
+{
+    int spcol,sprow,a;
+    int i,j,k,l,rank;
+    NODE r0,r;
+    ND_pairs sp;
+    ND spol;
+    mp_limb_t **spmat;
+    mp_limb_t *svect,*cvect;
+    mp_limb_t *v;
+    int *colstat;
+    struct oEGT eg0,eg1,eg2,eg_f4,eg_f4_1,eg_f4_2;
+    int maxrs;
+    int *spsugar;
+    ND_pairs *spactive;
+    SIG *spsig;
+
+    get_eg(&eg0);
+    /* elimination (1st step) */
+    spmat = (mp_limb_t **)MALLOC(nsp*sizeof(mp_limb_t *));
+    cvect = (mp_limb_t *)MALLOC(col*sizeof(mp_limb_t));
+    spsugar = (int *)MALLOC(nsp*sizeof(int));
+    spsig = (SIG *)MALLOC(nsp*sizeof(SIG));
+    for ( a = sprow = 0, sp = sp0; a < nsp; a++, sp = NEXT(sp) ) {
+        nd_sp(m,0,sp,&spol);
+        if ( !spol ) {
+          syzlistp[sp->sig->pos] = insert_sig(syzlistp[sp->sig->pos],sp->sig);
+          continue;
+        }
+        svect = (mp_limb_t *)MALLOC(col*sizeof(mp_limb_t));
+        nd_to_vect64(m,s0vect,col,spol,svect);
+        maxrs = ndv_reduce_vect64(m,svect,cvect,col,imat,rvect,nred,spol->sig);
+        for ( i = 0; i < col; i++ ) if ( svect[i] ) break;
+        if ( i < col ) {
+            spmat[sprow] = svect;
+            spsugar[sprow] = MAX(maxrs,SG(spol));
+            spsig[sprow] = sp->sig;
+            sprow++;
+        } else {
+          syzlistp[sp->sig->pos] = insert_sig(syzlistp[sp->sig->pos],sp->sig);
+        }
+        nd_free(spol);
+    }
+    get_eg(&eg1); init_eg(&eg_f4_1); add_eg(&eg_f4_1,&eg0,&eg1); add_eg(&f4_elim1,&eg0,&eg1);
+    if ( DP_Print ) {
+        fprintf(asir_out,"elim1=%.3fsec,",eg_f4_1.exectime);
+        fflush(asir_out);
+    }
+    /* free index arrays */
+    for ( i = 0; i < nred; i++ ) GCFREE(imat[i]->index.c);
+
+    /* elimination (2nd step) */
+    colstat = (int *)MALLOC(col*sizeof(int));
+    rank = nd_gauss_elim_mod64_s(spmat,spsugar,0,sprow,col,m,colstat,spsig);
+    r0 = 0;
+    for ( i = 0; i < sprow; i++ ) {
+        if ( spsugar[i] >= 0 ) {
+          NEXTNODE(r0,r);
+          BDY(r) = vect64_to_ndv_s(spmat[i],col,s0vect);
+          SG((NDV)BDY(r)) = spsugar[i];
+          ((NDV)BDY(r))->sig = spsig[i];
+        } else
+          syzlistp[spsig[i]->pos] = insert_sig(syzlistp[spsig[i]->pos],spsig[i]);
+        GCFREE(spmat[i]);
+    }
+    if ( r0 ) NEXT(r) = 0;
+    get_eg(&eg2); init_eg(&eg_f4_2); add_eg(&eg_f4_2,&eg1,&eg2); add_eg(&f4_elim2,&eg1,&eg2);
+    init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg2);
+    if ( DP_Print ) {
+        fprintf(asir_out,"elim2=%.3fsec,",eg_f4_2.exectime);
+        fprintf(asir_out,"nsp=%d,nred=%d,spmat=(%d,%d),rank=%d ",
+            nsp,nred,sprow,col,rank);
+        fprintf(asir_out,"%.3fsec,",eg_f4.exectime);
+    }
+    return r0;
+}
 #endif
 
+NODE nd_f4_red_s(int m,ND_pairs sp0,int trace,UINT *s0vect,int col,NODE rp0,NODE *syzlistp)
+{
+  IndArray *imat;
+  int nsp,nred,i,start;
+  int *rhead;
+  NODE r0,rp;
+  ND_pairs sp;
+  NM_ind_pair *rvect;
+  UINT *s;
+  int *s0hash;
+  struct oEGT eg0,eg1,eg_conv;
+
+  for ( sp = sp0, nsp = 0; sp; sp = NEXT(sp), nsp++ );
+  nred = length(rp0);
+  imat = (IndArray *)MALLOC(nred*sizeof(IndArray));
+  rhead = (int *)MALLOC(col*sizeof(int));
+  for ( i = 0; i < col; i++ ) rhead[i] = 0;
+
+  /* construction of index arrays */
+  get_eg(&eg0);
+  if ( DP_Print ) {
+    fprintf(asir_out,"%dx%d,",nsp+nred,col);
+    fflush(asir_out);
+  }
+  rvect = (NM_ind_pair *)MALLOC(nred*sizeof(NM_ind_pair));
+  for ( start = 0, rp = rp0, i = 0; rp; i++, rp = NEXT(rp) ) {
+    rvect[i] = (NM_ind_pair)BDY(rp);
+    imat[i] = nm_ind_pair_to_vect_compress(trace,s0vect,col,rvect[i],start);
+    rhead[imat[i]->head] = 1;
+    start = imat[i]->head;
+  }
+  get_eg(&eg1); init_eg(&eg_conv); add_eg(&eg_conv,&eg0,&eg1); add_eg(&f4_conv,&eg0,&eg1);
+  if ( DP_Print ) {
+    fprintf(asir_out,"conv=%.3fsec,",eg_conv.exectime);
+    fflush(asir_out);
+  }
+  if ( m > 0 )
+#if SIZEOF_LONG==8
+    r0 = nd_f4_red_mod64_main_s(m,sp0,nsp,s0vect,col,rvect,rhead,imat,nred,syzlistp);
+#else
+    r0 = nd_f4_red_main_s(m,sp0,nsp,s0vect,col,rvect,rhead,imat,nred,syzlistp);
+#endif
+  else
+//    r0 = nd_f4_red_q_main_s(sp0,nsp,trace,s0vect,col,rvect,rhead,imat,nred);
+    error("nd_f4_red_q_main_s : not implemented yet");
+  return r0;
+}
+
+INLINE int ndl_find_reducer_minsig(UINT *dg)
+{
+  RHist r;
+  int i,singular,ret,d,k,imin;
+  SIG t;
+  static int wpd,nvar;
+  static SIG quo,quomin;
+  static UINT *tmp;
+
+  if ( !quo || nvar != nd_nvar ) { NEWSIG(quo); NEWSIG(quomin); }
+  if ( wpd != nd_wpd ) {
+    wpd = nd_wpd;
+    tmp = (UINT *)MALLOC(wpd*sizeof(UINT));
+  }
+#if 0
+  d = ndl_hash_value(dg);
+  for ( r = nd_red[d], k = 0; r; r = NEXT(r), k++ ) {
+    if ( ndl_equal(dg,DL(r)) ) {
+      return r->index;
+    }
+  }
+#endif
+  imin = -1;
+  for ( i = 0; i < nd_psn; i++ ) {
+    r = nd_psh[i];
+    if ( ndl_reducible(dg,DL(r)) ) {
+      ndl_sub(dg,DL(r),tmp);
+      _ndltodl(tmp,DL(quo));
+      _addtodl(nd_nvar,DL(nd_psh[i]->sig),DL(quo));
+      quo->pos = nd_psh[i]->sig->pos;
+      if ( imin < 0 || comp_sig(quomin,quo) > 0 ) {
+        t = quo; quo = quomin; quomin = t;
+        imin = i;
+      }
+    }
+  }
+  if ( imin == -1 ) return nd_psn;
+  else {
+#if 0
+    nd_append_red(dg,i);
+#endif
+    return imin;
+  }
+}
+
+int nd_symbolic_preproc_s(PGeoBucket bucket,int trace,UINT **s0vect,NODE *r)
+{
+  NODE rp0,rp;
+  NM mul,head,s0,s;
+  int index,col,i,sugar;
+  RHist h;
+  UINT *s0v,*p;
+  NM_ind_pair pair;
+  ND red;
+  NDV *ps;
+  SIG sig;
+
+  s0 = 0; rp0 = 0; col = 0;
+  if ( nd_demand )
+    ps = trace?nd_ps_trace_sym:nd_ps_sym;
+  else
+    ps = trace?nd_ps_trace:nd_ps;
+  while ( 1 ) {
+    head = remove_head_pbucket_symbolic(bucket);
+    if ( !head ) break;
+    if ( !s0 ) s0 = head;
+    else NEXT(s) = head;
+    s = head;
+    index = ndl_find_reducer_minsig(DL(head));
+    if ( index >= 0 && index < nd_psn ) {
+      h = nd_psh[index];
+      NEWNM(mul);
+      ndl_sub(DL(head),DL(h),DL(mul));
+      if ( ndl_check_bound2(index,DL(mul)) ) 
+        return 0;
+      sugar = TD(DL(mul))+SG(ps[index]);
+      NEWSIG(sig);
+      _ndltodl(DL(mul),DL(sig));
+      _addtodl(nd_nvar,DL(nd_psh[index]->sig),DL(sig));
+      sig->pos = nd_psh[index]->sig->pos;
+      MKNM_ind_pair(pair,mul,index,sugar,sig);
+      red = ndv_mul_nm_symbolic(mul,ps[index]);
+      add_pbucket_symbolic(bucket,nd_remove_head(red));
+      NEXTNODE(rp0,rp); BDY(rp) = (pointer)pair;
+    }
+    col++;
+  }
+  if ( rp0 ) NEXT(rp) = 0;
+  NEXT(s) = 0;
+  s0v = (UINT *)MALLOC_ATOMIC(col*nd_wpd*sizeof(UINT));
+  for ( i = 0, p = s0v, s = s0; i < col;
+    i++, p += nd_wpd, s = NEXT(s) ) ndl_copy(DL(s),p);
+  *s0vect = s0v;        
+  *r = rp0;
+
+  return col;
+}
+
+NODE nd_sba_f4(int m,int **indp)
+{
+  int i,nh,stat,index,f4red,f4step;
+  int col,rank,len,k,j,a,sugar,nbase,psugar,ms;
+  NODE r,g,rp0,nflist;
+  ND_pairs d,l,t,l1;
+  ND h,nf;
+  NDV nfv;
+  union oNDC hc;
+  UINT *s0vect;
+  UINT c;
+  PGeoBucket bucket;
+  NODE *syzlist;
+  SIG sig;
+  struct oEGT eg0,eg1,eg_f4;
+  struct oEGT eg2,eg_update,eg_remove,eg_large,eg_nf,eg_nfzero;
+
+  Nf4_red=0;
+  d = 0;
+  syzlist = (NODE *)MALLOC(nd_psn*sizeof(NODE));
+  for ( i = 0; i < nd_psn; i++ ) {
+    d = update_pairs_s(d,i,syzlist);
+  }
+  nd_nbase = nd_psn;
+  f4red = 1;
+  psugar = 0;
+  f4step = 0;
+  while ( d ) {
+    for ( t = d, ms = SG(d); t; t = NEXT(t) )
+      if ( SG(t) < ms ) ms = SG(t);
+    if ( ms == psugar && f4step >= nd_sba_f4step ) {
+again:
+      l = d; d = d->next;
+#if 0
+      if ( small_lcm(l) ) {
+        if ( DP_Print ) fprintf(asir_out,"M");
+        continue;
+      }
+      sig = l->sig;
+      stat = nd_sp(m,0,l,&h);
+#else
+      l1 = find_smallest_lcm(l);
+      if ( l1 == 0 ) {
+        if ( DP_Print ) fprintf(asir_out,"M");
+        continue;
+      }
+      sig = l1->sig;
+      stat = nd_sp(m,0,l1,&h);
+#endif
+      if ( !stat ) {
+        NEXT(l) = d; d = l;
+        d = nd_reconstruct(0,d);
+        goto again;
+      }
+  get_eg(&eg1);
+  #if USE_GEOBUCKET
+      stat = m?nd_nf_pbucket_s(m,h,nd_ps,!nd_top&&!Top,&nf):nd_nf_s(m,0,h,nd_ps,!nd_top&&!Top,&nf);
+  #else
+      stat = nd_nf_s(m,0,h,nd_ps,!nd_top&&!Top,&nf);
+  #endif
+  get_eg(&eg2); 
+      if ( !stat ) {
+        NEXT(l) = d; d = l;
+        d = nd_reconstruct(0,d);
+        goto again;
+      } else if ( stat == -1 ) {
+        if ( DP_Print ) { printf("S"); fflush(stdout); }
+        FREENDP(l);
+      } else if ( nf ) {
+        if ( DP_Print ) { printf("+"); fflush(stdout); }
+        add_eg(&eg_nf,&eg1,&eg2);
+        hc = HCU(nf);
+        nd_removecont(m,nf);
+        nfv = ndtondv(m,nf); nd_free(nf);
+        nh = ndv_newps(m,nfv,0);
+  
+        d = update_pairs_s(d,nh,syzlist);
+        nd_sba_pos[sig->pos] = append_one(nd_sba_pos[sig->pos],nh);
+        FREENDP(l);
+      } else {
+        add_eg(&eg_nfzero,&eg1,&eg2);
+       // syzygy
+  get_eg(&eg1);
+        d = remove_spair_s(d,sig);
+  get_eg(&eg2); add_eg(&eg_remove,&eg1,&eg2);
+        syzlist[sig->pos] = insert_sig(syzlist[sig->pos],sig);
+        if ( DP_Print ) { printf("."); fflush(stdout); }
+        FREENDP(l);
+      }
+    } else {
+      if ( ms != psugar ) f4step = 1;
+      else f4step++;
+again2:
+      psugar = ms;
+      l = nd_minsugarp_s(d,&d);
+      sugar = nd_sugarweight?d->sugar2:SG(d);
+      bucket = create_pbucket();
+      stat = nd_sp_f4(m,0,l,bucket);
+      if ( !stat ) {
+        for ( t = l; NEXT(t); t = NEXT(t) );
+        NEXT(t) = d; d = l;
+        d = nd_reconstruct(0,d);
+        goto again2;
+      }
+      if ( bucket->m < 0 ) continue;
+      col = nd_symbolic_preproc_s(bucket,0,&s0vect,&rp0);
+      if ( !col ) {
+        for ( t = l; NEXT(t); t = NEXT(t) )
+          ;
+        NEXT(t) = d; d = l;
+        d = nd_reconstruct(0,d);
+        goto again2;
+      }
+      if ( DP_Print ) fprintf(asir_out,"\nsugar=%d,",psugar);
+      nflist = nd_f4_red_s(m,l,0,s0vect,col,rp0,syzlist);
+      /* adding new bases */
+      for ( r = nflist; r; r = NEXT(r) ) {
+        nfv = (NDV)BDY(r);
+        if ( nd_f4_td ) SG(nfv) = nd_tdeg(nfv);
+        ndv_removecont(m,nfv);
+        nh = ndv_newps(m,nfv,0);
+        d = update_pairs_s(d,nh,syzlist);
+        nd_sba_pos[nfv->sig->pos] = append_one(nd_sba_pos[nfv->sig->pos],nh);
+      }
+      for ( i = 0; i < nd_nbase; i++ )
+        for ( r = syzlist[i]; r; r = NEXT(r) )
+            d = remove_spair_s(d,(SIG)BDY(r));
+      d = remove_large_lcm(d);
+      if ( DP_Print ) { 
+        fprintf(asir_out,"f4red=%d,gblen=%d",f4red,nd_psn); fflush(asir_out);
+      }
+      f4red++;
+    }
+  }
+  if ( DP_Print ) {
+    fprintf(asir_out,"\nnumber of red=%d,",Nf4_red);
+  }
+  g = conv_ilist_s(nd_demand,0,indp);
+  return g;
+}