===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2018/engine/nd.c,v
retrieving revision 1.5
retrieving revision 1.65
diff -u -p -r1.5 -r1.65
--- OpenXM_contrib2/asir2018/engine/nd.c	2018/09/27 02:39:37	1.5
+++ OpenXM_contrib2/asir2018/engine/nd.c	2022/04/03 00:39:12	1.65
@@ -1,18 +1,27 @@
-/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.4 2018/09/25 07:36:01 noro Exp $ */
+/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.64 2022/03/09 07:50:51 noro Exp $ */
 
 #include "nd.h"
 
-struct oEGT eg_search;
+void print_siglist(NODE l);
 
+NODE nd_hpdata;
+int Nnd_add,Nf4_red,NcriB,NcriMF,Ncri2,Npairs,Nnewpair;
+struct oEGT eg_search,f4_symb,f4_conv,f4_elim1,f4_elim2;
+
 int diag_period = 6;
 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;
 
@@ -44,7 +53,7 @@ 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;
@@ -54,18 +63,37 @@ 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,nd_sba_syz,nd_sba_inputisgb,nd_sba_heu;
 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;
 
+struct comp_sig_spec {
+  int n;
+  // current_i <-> oldv[i]
+  int *oldv;
+  int *weight;
+  struct order_pair *order_pair;
+  int block_length;
+  int **matrix;
+  int row;
+  int (*cmpdl)(int n,DL d1,DL d2);
+};
+
+struct comp_sig_spec *nd_sba_modord;
+
+DL ndltodl(int n,UINT *ndl);
 NumberField get_numberfield();
 UINT *nd_det_compute_bound(NDV **dm,int n,int j);
 void nd_det_reconstruct(NDV **dm,int n,int j,NDV d);
@@ -77,15 +105,25 @@ 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);
 void finalize_tracelist(int i,P cont);
 void conv_ilist(int demand,int trace,NODE g,int **indp);
-void parse_nd_option(NODE opt);
+void parse_nd_option(VL vl,NODE opt);
 void dltondl(int n,DL dl,UINT *r);
 DP ndvtodp(int mod,NDV p);
 DP ndtodp(int mod,ND p);
+DPM ndvtodpm(int mod,NDV p);
+NDV dptondv(int mod,DP p);
+NDV dpmtondv(int mod,DPM p);
+int dp_getdeg(DP p);
+int dpm_getdeg(DPM p,int *rank);
+void dpm_ptozp(DPM p,Z *cont,DPM *r);
+int compdmm(int nv,DMM a,DMM b);
+DPM sigtodpm(SIG s);
+SIG dup_sig(SIG sig);
 
 void Pdp_set_weight(NODE,VECT *);
 void Pox_cmo_rpc(NODE,Obj *);
@@ -100,6 +138,7 @@ NODE nd_f4_red_mod64_main(int m,ND_pairs sp0,int nsp,U
 NODE nd_f4_red_lf_main(int m,ND_pairs sp0,int nsp,int trace,UINT *s0vect,int col,
         NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred);
 int nd_gauss_elim_lf(mpz_t **mat0,int *sugar,int row,int col,int *colstat);
+int nd_gauss_elim_mod_s(UINT **mat,int *sugar,ND_pairs *spactive,int row,int col,int md,int *colstat,SIG *sig);
 NODE nd_f4_lf_trace_main(int m,int **indp);
 void nd_f4_lf_trace(LIST f,LIST v,int trace,int homo,struct order_spec *ord,LIST *rp);
 
@@ -139,7 +178,6 @@ void _NM_alloc()
 matrix alloc_matrix(int row,int col)
 {
   unsigned long **a;
-  int i,len,blen;
   matrix mat;
 
   mat = (matrix)MALLOC(sizeof(struct matrix));
@@ -344,7 +382,7 @@ void ndl_dehomogenize(UINT *d)
 void ndl_lcm(UINT *d1,unsigned *d2,UINT *d)
 {
     UINT t1,t2,u,u1,u2;
-    int i,j,l;
+    int i,j;
 
     if ( nd_module && (MPOS(d1) != MPOS(d2)) )
         error("ndl_lcm : inconsistent monomials");
@@ -442,7 +480,7 @@ void ndl_lcm(UINT *d1,unsigned *d2,UINT *d)
 void ndl_max(UINT *d1,unsigned *d2,UINT *d)
 {
     UINT t1,t2,u,u1,u2;
-    int i,j,l;
+    int i,j;
 
     for ( i = nd_exporigin; i < nd_wpd; i++ ) {
         u1 = d1[i]; u2 = d2[i]; 
@@ -469,8 +507,11 @@ 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;
 }
 
@@ -479,14 +520,14 @@ int ndl_weight(UINT *d)
 int ndl_weight2(UINT *d)
 {
     int t,u;
-    int i,j;
+    int i;
 
     for ( i = 0, t = 0; i < nd_nvar; i++ ) {
         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;
 }
 
@@ -514,6 +555,13 @@ 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;
@@ -530,7 +578,7 @@ int ndl_lex_compare(UINT *d1,UINT *d2)
 
 int ndl_block_compare(UINT *d1,UINT *d2)
 {
-    int i,l,j,ord_o,ord_l;
+    int i,l,j,ord_o;
     struct order_pair *op;
     UINT t1,t2,m;
     UINT *mask;
@@ -566,41 +614,41 @@ int ndl_matrix_compare(UINT *d1,UINT *d2)
   Z t1;
   Z t,t2;
 
-    for ( j = 0; j < nd_nvar; j++ )
-        nd_work_vector[j] = GET_EXP(d1,j)-GET_EXP(d2,j);
+  for ( j = 0; j < nd_nvar; j++ )
+    nd_work_vector[j] = GET_EXP(d1,j)-GET_EXP(d2,j);
   if ( nd_top_weight ) {
     if ( OID(nd_top_weight) == O_VECT ) {
-        mat = (Z **)&BDY((VECT)nd_top_weight);
-        row = 1;
+      mat = (Z **)&BDY((VECT)nd_top_weight);
+      row = 1;
     } else {
       mat = (Z **)BDY((MAT)nd_top_weight);
-        row = ((MAT)nd_top_weight)->row;
+      row = ((MAT)nd_top_weight)->row;
     }
     for ( i = 0; i < row; i++ ) {
-        w = mat[i];
+      w = mat[i];
       for ( j = 0, t = 0; j < nd_nvar; j++ ) {
-        STOQ(nd_work_vector[j],t1);
+        STOZ(nd_work_vector[j],t1);
         mulz(w[j],t1,&t2);
         addz(t,t2,&t1);
         t = t1;
       }
-        if ( t ) {
-          s = sgnz(t); 
-            if ( s > 0 ) return 1;
-            else if ( s < 0 ) return -1;
-        }
-    }
-  }
-    for ( i = 0; i < nd_matrix_len; i++ ) {
-        v = nd_matrix[i];
-        for ( j = 0, s = 0; j < nd_nvar; j++ )
-            s += v[j]*nd_work_vector[j];
+      if ( t ) {
+        s = sgnz(t); 
         if ( s > 0 ) return 1;
         else if ( s < 0 ) return -1;
+      }
     }
+  }
+  for ( i = 0; i < nd_matrix_len; i++ ) {
+    v = nd_matrix[i];
+    for ( j = 0, s = 0; j < nd_nvar; j++ )
+      s += v[j]*nd_work_vector[j];
+    if ( s > 0 ) return 1;
+    else if ( s < 0 ) return -1;
+  }
   if ( !ndl_equal(d1,d2) )
-    error("afo");
-    return 0;
+    error("ndl_matrix_compare : invalid matrix");
+  return 0;
 }
 
 int ndl_composite_compare(UINT *d1,UINT *d2)
@@ -683,135 +731,149 @@ 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)>=(UINT)(nd_pot_nelim+1) && MPOS(d2) >= (UINT)(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,retpot;
+  DMM *in;
+  DMMstack s;
+  static DL d1=0;
+  static DL d2=0;
+  static int dlen=0;
+  extern int ReversePOT;
 
-    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 ( ReversePOT ) retpot = -1;
+  else retpot = 1;
+  pos1 = MPOS(m1); pos2 = MPOS(m2);
+  if ( pos1 == pos2 ) return (*ndl_base_compare_function)(m1,m2);
+  if ( nd_nvar > dlen ) {
+    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 retpot;
+      else if ( pos1 > pos2 ) return -retpot;
+      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
+  switch ( nd_base_ordtype ) {
+    case 0:
+      t = (*dl_base_compare_function)(nd_nvar,d1,d2);
+      if ( t ) return t;
+      else if ( pos1 < pos2 ) return retpot;
+      else if ( pos1 > pos2 ) return -retpot;
+      else return 0;
+      break;
+    case 1:
+      if ( pos1 < pos2 ) return retpot;
+      else if ( pos1 > pos2 ) return -retpot;
+      else return (*dl_base_compare_function)(nd_nvar,d1,d2);
+      break;
+    case 2:
+      if ( d1->td > d2->td  ) return 1;
+      else if ( d1->td < d2->td ) return -1;
+      else if ( pos1 < pos2 ) return retpot;
+      else if ( pos1 > pos2 ) return -retpot;
+      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)
@@ -931,7 +993,7 @@ INLINE void ndl_sub(UINT *d1,UINT *d2,UINT *d)
 
 int ndl_disjoint(UINT *d1,UINT *d2)
 {
-    UINT t1,t2,u,u1,u2;
+    UINT t1,t2,u1,u2;
     int i,j;
 
     if ( nd_module && (MPOS(d1) == MPOS(d2)) ) return 0;
@@ -1125,11 +1187,12 @@ int ndl_check_bound2(int index,UINT *d2)
 INLINE int ndl_hash_value(UINT *d)
 {
     int i;
-    int r;
+    UINT r;
 
     r = 0;
     for ( i = 0; i < nd_wpd; i++ )    
-        r = ((r<<16)+d[i])%REDTAB_LEN;
+        r = (r*1511+d[i]);
+    r %= REDTAB_LEN;
     return r;
 }
 
@@ -1167,18 +1230,99 @@ 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);
+}
+
+void print_siglist(NODE l)
+{
+  for ( ; l; l = NEXT(l) )
+   print_sig((SIG)l->body);
+}
+
+
+// assuming increasing order wrt signature 
+
+INLINE int ndl_find_reducer_s(UINT *dg,SIG sig)
+{
+  RHist r;
+  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;
+      _adddl(nd_nvar,DL(quo),nd_sba_hm[quo->pos],DL2(quo));
+      ret = comp_sig(sig,quo);
+//      if ( ret >= 0 ) { singular = 0; break; }
+      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;
-    int t,can,td1,td2;
-    ND r;
+    int c;
+    int can;
     NM m1,m2,mr0,mr,s;
 
     if ( !p1 ) return p2;
     else if ( !p2 ) return p1;
     else {
         can = 0;
-        for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
+        for (  m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
             c = DL_COMPARE(DL(m1),DL(m2));
             switch ( c ) {
                 case 0:
@@ -1211,11 +1355,11 @@ ND nd_merge(ND p1,ND p2)
 
 ND nd_add(int mod,ND p1,ND p2)
 {
-    int n,c;
-    int t,can,td1,td2;
-    ND r;
+    int c;
+    int t,can;
     NM m1,m2,mr0,mr,s;
 
+    Nnd_add++;
     if ( !p1 ) return p2;
     else if ( !p2 ) return p1;
     else if ( mod == -1 ) return nd_add_sf(p1,p2);
@@ -1223,7 +1367,7 @@ ND nd_add(int mod,ND p1,ND p2)
     else if ( !mod ) return nd_add_q(p1,p2);
     else {
         can = 0;
-        for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
+        for ( m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
             c = DL_COMPARE(DL(m1),DL(m2));
             switch ( c ) {
                 case 0:
@@ -1284,16 +1428,14 @@ int nm_destructive_add_q(NM *m1,NM *m2,NM *mr0,NM *mr)
 
 ND nd_add_q(ND p1,ND p2)
 {
-    int n,c,can;
-    ND r;
+    int c,can;
     NM m1,m2,mr0,mr,s;
-    P t;
 
     if ( !p1 ) return p2;
     else if ( !p2 ) return p1;
     else {
         can = 0;
-        for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
+        for ( m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
             c = DL_COMPARE(DL(m1),DL(m2));
             switch ( c ) {
                 case 0:
@@ -1335,8 +1477,7 @@ ND nd_add_q(ND p1,ND p2)
 
 ND nd_add_sf(ND p1,ND p2)
 {
-    int n,c,can;
-    ND r;
+    int c,can;
     NM m1,m2,mr0,mr,s;
     int t;
 
@@ -1344,7 +1485,7 @@ ND nd_add_sf(ND p1,ND p2)
     else if ( !p2 ) return p1;
     else {
         can = 0;
-        for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
+        for ( m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
             c = DL_COMPARE(DL(m1),DL(m2));
             switch ( c ) {
                 case 0:
@@ -1412,8 +1553,8 @@ ND nd_reduce2(int mod,ND d,ND g,NDV p,NM mul,NDC dn,Ob
         }
         *divp = (Obj)credp;
     } else {
-        igcd_cofactor(HCQ(g),HCQ(p),&gcd,&cg,&cred);
-        chsgnz(cg,&CQ(mul));
+        igcd_cofactor(HCZ(g),HCZ(p),&gcd,&cg,&cred);
+        chsgnz(cg,&CZ(mul));
         nd_mul_c_q(d,(P)cred); nd_mul_c_q(g,(P)cred);
         if ( dn ) {
             mulz(dn->z,cred,&tq); dn->z = tq;
@@ -1424,40 +1565,29 @@ ND nd_reduce2(int mod,ND d,ND g,NDV p,NM mul,NDC dn,Ob
 }
 
 /* ret=1 : success, ret=0 : overflow */
-int nd_nf(int mod,ND d,ND g,NDV *ps,int full,NDC dn,ND *rp)
+int nd_nf(int mod,ND d,ND g,NDV *ps,int full,ND *rp)
 {
-    NM m,mrd,tail;
+    NM m,tail;
     NM mul;
-    int n,sugar,psugar,sugar0,stat,index;
-    int c,c1,c2,dummy;
+    int n,sugar,index;
     RHist h;
-    NDV p,red;
-    Q cg,cred,gcd,tq,qq;
+    NDV p;
     Z iq;
     DP dmul;
     NODE node;
     LIST hist;
     double hmag;
-    P tp,tp1;
-    Obj tr,tr1,div;
+    Obj div;
     union oNDC hg;
     P cont;
 
-    if ( dn ) {
-        if ( mod )
-            dn->m = 1;
-        else if ( nd_vc )
-            dn->r = (R)ONE;
-        else
-            dn->z = ONE;
-    }
     if ( !g ) {
         *rp = d;
         return 1;
     }
     if ( !mod ) hmag = ((double)p_mag(HCP(g)))*nd_scale;
 
-    sugar0 = sugar = SG(g);
+    sugar = SG(g);
     n = NV(g);
     mul = (NM)MALLOC(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT));
     if ( d )
@@ -1473,26 +1603,21 @@ int nd_nf(int mod,ND d,ND g,NDV *ps,int full,NDC dn,ND
             }
             p = nd_demand ? ndv_load(index) : ps[index];
             /* d+g -> div*(d+g)+mul*p */
-            g = nd_reduce2(mod,d,g,p,mul,dn,&div);
+            g = nd_reduce2(mod,d,g,p,mul,0,&div);
             if ( nd_gentrace ) {
                 /* Trace=[div,index,mul,ONE] */
-                STOQ(index,iq);
+                STOZ(index,iq);
                 nmtodp(mod,mul,&dmul);
                 node = mknode(4,div,iq,dmul,ONE);
             }
-            sugar = MAX(sugar,SG(p)+TD(DL(mul)));
+            sugar = MAX(sugar,(int)(SG(p)+TD(DL(mul))));
             if ( !mod && g && !nd_vc && ((double)(p_mag(HCP(g))) > hmag) ) {
                 hg = HCU(g);
                 nd_removecont2(d,g);
-                if ( dn || nd_gentrace ) {
+                if ( nd_gentrace ) {
                     /* overwrite cont : Trace=[div,index,mul,cont] */
+                    /* exact division */
                     cont = ndc_div(mod,hg,HCU(g));
-                    if ( dn ) {
-                        if ( nd_vc ) {
-                            divr(nd_vc,(Obj)dn->r,(Obj)cont,&tr);
-                            reductr(nd_vc,(Obj)tr,&tr1); dn->r = (R)tr1;
-                        } else divz(dn->z,(Z)cont,&dn->z);
-                    }
                     if ( nd_gentrace && !UNIQ(cont) ) ARG3(node) = (pointer)cont;
                 }
                 hmag = ((double)p_mag(HCP(g)))*nd_scale;
@@ -1521,17 +1646,104 @@ int nd_nf(int mod,ND d,ND g,NDV *ps,int full,NDC dn,ND
     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,tail;
+    NM mul;
+    int n,sugar,index;
+    RHist h;
+    NDV p;
+    Z iq;
+    DP dmul;
+    NODE node;
+    LIST hist;
+    double hmag;
+    Obj div;
+//    union oNDC hg;
+    SIG sig;
+
+    if ( !g ) {
+        *rp = d;
+        return 1;
+    }
+    if ( !mod ) hmag = ((double)p_mag(HCP(g)))*nd_scale;
+
+    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,(int)(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;
+            }
+            if ( nd_gentrace ) {
+                /* Trace=[div,index,mul,ONE] */
+                STOZ(index,iq);
+                nmtodp(mod,mul,&dmul);
+                node = mknode(4,div,iq,dmul,ONE);
+            }
+            MKLIST(hist,node);
+            MKNODE(node,hist,nd_tracelist); nd_tracelist = node;
+        } 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;
     NDV p;
-    ND u,d,red;
-    NODE l;
-    NM mul,m,mrd,tail;
-    int sugar,psugar,n,h_reducible;
+    ND d,red;
+    NM mul,m,tail;
+    int sugar,psugar,n;
     PGeoBucket bucket;
     int c,c1,c2;
-    Z cg,cred,gcd,zzz;
+    Z cg,cred,gcd;
     RHist h;
     double hmag,gmag;
     int count = 0;
@@ -1543,7 +1755,7 @@ int nd_nf_pbucket(int mod,ND g,NDV *ps,int full,ND *rp
     }
     sugar = SG(g);
     n = NV(g);
-    if ( !mod ) hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
+    if ( !mod ) hmag = ((double)p_mag((P)HCZ(g)))*nd_scale;
     bucket = create_pbucket();
     add_pbucket(mod,bucket,g);
     d = 0;
@@ -1586,12 +1798,12 @@ int nd_nf_pbucket(int mod,ND g,NDV *ps,int full,ND *rp
                 c1 = invm(HCM(p),mod); c2 = mod-HCM(g);
                 DMAR(c1,c2,0,mod,c); CM(mul) = c;
             } else {
-                igcd_cofactor(HCQ(g),HCQ(p),&gcd,&cg,&cred);
-                chsgnz(cg,&CQ(mul));
+                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)HCQ(g));
+                gmag = (double)p_mag((P)HCZ(g));
             }
             red = ndv_mul_nm(mod,mul,p);
             bucket->body[hindex] = nd_remove_head(g);
@@ -1607,7 +1819,7 @@ int nd_nf_pbucket(int mod,ND g,NDV *ps,int full,ND *rp
                     return 1;
                 }
                 nd_removecont2(d,g);
-                hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
+                hmag = ((double)p_mag((P)HCZ(g)))*nd_scale;
                 add_pbucket(mod,bucket,g);
             }
         } else if ( !full ) {
@@ -1633,20 +1845,144 @@ 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 d,red;
+  NM mul,m,tail;
+  int sugar,psugar,n;
+  PGeoBucket bucket;
+  int c,c1,c2;
+  Z cg,cred,gcd;
+  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)
 {
-    int n,i,stat;
+    int i,stat;
     ND nf,d;
     NDV r;
     NODE t,s;
-    union oNDC dn;
     Z q;
     LIST list;
 
-    ndv_setup(m,0,cand,nd_gentrace?1:0,1);
-    n = length(cand);
+    ndv_setup(m,0,cand,nd_gentrace?1:0,1,0);
+//    n = length(cand);
 
   if ( nd_gentrace ) { nd_alltracelist = 0; nd_tracelist = 0; }
     /* membercheck : list is a subset of Id(cand) ? */
@@ -1662,7 +1998,7 @@ again:
         if ( m == -2 ) ndv_mod(m,r);
 #endif
         d = ndvtond(m,r);
-        stat = nd_nf(m,0,d,nd_ps,0,0,&nf);
+        stat = nd_nf(m,0,d,nd_ps,0,&nf);
         if ( !stat ) {
             nd_reconstruct(0,0);
             goto again;
@@ -1670,7 +2006,7 @@ again:
     if ( nd_gentrace ) {
       nd_tracelist = reverse_node(nd_tracelist);
       MKLIST(list,nd_tracelist);
-      STOQ(i,q); s = mknode(2,q,list); MKLIST(list,s);
+      STOZ(i,q); s = mknode(2,q,list); MKLIST(list,s);
       MKNODE(s,list,nd_alltracelist);
       nd_alltracelist = s; nd_tracelist = 0;
     }
@@ -1732,6 +2068,7 @@ void free_pbucket(PGeoBucket b) {
     GCFREE(b);
 }
 
+#if 0
 void add_pbucket_symbolic(PGeoBucket g,ND d)
 {
     int l,i,k,m;
@@ -1749,7 +2086,32 @@ 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,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;
@@ -1767,7 +2129,29 @@ 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,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;
@@ -1810,8 +2194,8 @@ NM remove_head_pbucket_symbolic(PGeoBucket g)
 
 int head_pbucket(int mod,PGeoBucket g)
 {
-    int j,i,c,k,nv,sum;
-    UINT *di,*dj;
+    int j,i,c,k,sum;
+    UINT *dj;
     ND gi,gj;
 
     k = g->m;
@@ -1856,7 +2240,7 @@ int head_pbucket(int mod,PGeoBucket g)
 
 int head_pbucket_q(PGeoBucket g)
 {
-    int j,i,c,k,nv;
+    int j,i,c,k;
     Z sum,t;
     ND gi,gj;
 
@@ -1868,18 +2252,18 @@ int head_pbucket_q(PGeoBucket g)
             if ( j < 0 ) {
                 j = i;
                 gj = g->body[j];
-                sum = HCQ(gj);
+                sum = HCZ(gj);
             } else {
-                nv = NV(gi);
+//               nv = NV(gi);
                 c = DL_COMPARE(HDL(gi),HDL(gj));
                 if ( c > 0 ) {
-                    if ( sum ) HCQ(gj) = sum;
+                    if ( sum ) HCZ(gj) = sum;
                     else g->body[j] = nd_remove_head(gj);
                     j = i;
                     gj = g->body[j];
-                    sum = HCQ(gj);
+                    sum = HCZ(gj);
                 } else if ( c == 0 ) {
-                    addz(sum,HCQ(gi),&t);
+                    addz(sum,HCZ(gi),&t);
                     sum = t;
                     g->body[i] = nd_remove_head(gi);
                 }
@@ -1887,7 +2271,7 @@ int head_pbucket_q(PGeoBucket g)
         }
         if ( j < 0 ) return -1;
         else if ( sum ) {
-            HCQ(gj) = sum;
+            HCZ(gj) = sum;
             return j;
         } else
             g->body[j] = nd_remove_head(gj);
@@ -1896,7 +2280,7 @@ int head_pbucket_q(PGeoBucket g)
 
 int head_pbucket_lf(PGeoBucket g)
 {
-    int j,i,c,k,nv;
+    int j,i,c,k;
     Z sum,t;
     ND gi,gj;
 
@@ -1910,7 +2294,7 @@ int head_pbucket_lf(PGeoBucket g)
                 gj = g->body[j];
                 sum = HCZ(gj);
             } else {
-                nv = NV(gi);
+//              nv = NV(gi);
                 c = DL_COMPARE(HDL(gi),HDL(gj));
                 if ( c > 0 ) {
                     if ( sum ) HCZ(gj) = sum;
@@ -1937,7 +2321,7 @@ int head_pbucket_lf(PGeoBucket g)
 ND normalize_pbucket(int mod,PGeoBucket g)
 {
     int i;
-    ND r,t;
+    ND r;
 
     r = 0;
     for ( i = 0; i <= g->m; i++ ) {
@@ -1978,7 +2362,6 @@ void register_hcf(NDV p)
 #else
 void register_hcf(NDV p)
 {
-    DCP dc,t;
     P hc,h,q;
     Q dmy;
     int c;
@@ -2012,46 +2395,46 @@ void register_hcf(NDV p)
 
 int do_diagonalize(int sugar,int m)
 {
-    int i,nh,stat;
-    NODE r,g,t;
-    ND h,nf,s,head;
-    NDV nfv;
-    Q q;
-    P nm,nmp,dn,mnp,dnp,cont,cont1;
-    union oNDC hc;
-    NODE node;
-    LIST l;
-    Z iq;
+  int i,stat;
+  ND nf,s,head;
+  NDV nfv;
+  P cont;
+  union oNDC hc;
+  NODE node;
+  LIST l;
+  Z iq;
 
-    for ( i = nd_psn-1; i >= 0 && SG(nd_psh[i]) == sugar; i-- ) {
-        if ( nd_gentrace ) {
-            /* Trace = [1,index,1,1] */
-            STOQ(i,iq); node = mknode(4,ONE,iq,ONE,ONE);
-            MKLIST(l,node); MKNODE(nd_tracelist,l,0);
-        }
-        if ( nd_demand )
-            nfv = ndv_load(i);
-        else
-            nfv = nd_ps[i];
-        s = ndvtond(m,nfv);
-        s = nd_separate_head(s,&head);
-        stat = nd_nf(m,head,s,nd_ps,1,0,&nf);
-        if ( !stat ) return 0;
-        ndv_free(nfv);
-        hc = HCU(nf); nd_removecont(m,nf);
-        cont = ndc_div(m,hc,HCU(nf));
-    if ( nd_gentrace ) finalize_tracelist(i,cont);
-        nfv = ndtondv(m,nf);
-        nd_free(nf);
-        nd_bound[i] = ndv_compute_bound(nfv);
-        if ( !m ) register_hcf(nfv);
-        if ( nd_demand ) {
-            ndv_save(nfv,i);
-            ndv_free(nfv);
-        } else
-            nd_ps[i] = nfv;
+  if ( diag_period == 0 ) return 1;
+  for ( i = nd_psn-1; i >= 0 && SG(nd_psh[i]) == sugar; i-- ) {
+    if ( nd_gentrace ) {
+      /* Trace = [1,index,1,1] */
+      STOZ(i,iq); node = mknode(4,ONE,iq,ONE,ONE);
+      MKLIST(l,node); MKNODE(nd_tracelist,l,0);
     }
-    return 1;
+    if ( nd_demand )
+      nfv = ndv_load(i);
+    else
+      nfv = nd_ps[i];
+    s = ndvtond(m,nfv);
+    s = nd_separate_head(s,&head);
+    stat = nd_nf(m,head,s,nd_ps,1,&nf);
+    if ( !stat ) return 0;
+    ndv_free(nfv);
+    hc = HCU(nf); nd_removecont(m,nf);
+    /* exact division */
+    cont = ndc_div(m,hc,HCU(nf));
+    if ( nd_gentrace ) finalize_tracelist(i,cont);
+    nfv = ndtondv(m,nf);
+    nd_free(nf);
+    nd_bound[i] = ndv_compute_bound(nfv);
+    if ( !m ) register_hcf(nfv);
+    if ( nd_demand ) {
+      ndv_save(nfv,i);
+      ndv_free(nfv);
+    } else
+      nd_ps[i] = nfv;
+  }
+  return 1;
 }
 
 LIST compute_splist()
@@ -2069,7 +2452,7 @@ LIST compute_splist()
     }
   for ( t = d, tn0 = 0; t; t = NEXT(t) ) {
     NEXTNODE(tn0,tn);
-        STOQ(t->i1,i1); STOQ(t->i2,i2);
+        STOZ(t->i1,i1); STOZ(t->i2,i2);
         node = mknode(2,i1,i2); MKLIST(l0,node);
     BDY(tn) = l0;
   }
@@ -2077,114 +2460,774 @@ LIST compute_splist()
   return l0;
 }
 
+typedef struct oHPDATA {
+  int n;
+  P hn; // HP(t)=hn(t)/((1-t^w0)*...*(1-t^w(n-1)))
+  VECT x; // BDY(x)[i] = <<0,...,1,...,0>>
+  int *w;
+} *HPDATA;
+
+void make_reduced(VECT b,int nv);
+void mhp_rec(VECT b,VECT x,P t,P *r);
+P mhp_ctop(P *r,P *plist,int n);
+DL monomial_colon(DL a,DL b,int n);
+LIST dp_monomial_hilbert_poincare(VECT b,VECT x);
+LIST dp_monomial_hilbert_poincare_weight(VECT b,VECT x,int *w);
+
+void setup_hpdata(HPDATA final,HPDATA current)
+{
+  int n,i;
+  DL *p;
+  VECT b,x;
+  DL dl;
+  LIST ret;
+  int *w;
+
+  final->n = n = nd_nvar;
+  final->hn = (P)BDY(nd_hpdata);
+#if 0
+  if ( NEXT(nd_hpdata) != 0 && (weight=(LIST)BDY(NEXT(nd_hpdata))) != 0 ) {
+    wlen = length(BDY(weight));
+    if ( n != wlen )
+      error("setup_hpdata : inconsistent weight length");
+    w = (int *)MALLOC(n*sizeof(int));
+    for ( i = 0, nd = BDY((LIST)weight); i < n; i++, nd = NEXT(nd) ) 
+      w[i] = ZTOS((Z)BDY(nd));
+  } else
+    w = 0;
+#else
+  w = current_dl_weight_vector;
+#endif
+  MKVECT(x,n);
+  for ( i = 0; i < n; i++ ) {
+    NEWDL(dl,n); dl->d[i] = 1; dl->td = 1; BDY(x)[i] = dl;
+  }
+  final->x = x;
+  final->w = w;
+
+  MKVECT(b,nd_psn); p = (DL *)BDY(b);
+  for ( i = 0; i < nd_psn; i++ ) {
+    p[i] = ndltodl(n,nd_psh[i]->dl);
+  }
+  if ( w ) {
+    ret = dp_monomial_hilbert_poincare_weight(b,x,w);
+  } else
+    ret = dp_monomial_hilbert_poincare(b,x);
+  current->n = n;
+  current->hn = (P)BDY(BDY(ret));
+  current->x = x;
+  current->w = w;
+}
+
+int comp_hn(P a, P b)
+{
+  P s;
+  DCP dc;
+
+  subp(CO,a,b,&s);
+  if ( !s ) return -1; 
+  else if ( OID(s) == 1 ) return 0;
+  else {
+    for ( dc = DC(s); NEXT(dc); dc = NEXT(dc) );
+    return (int)ZTOS((Z)dc->d);
+  }
+}
+
+void update_hpdata(HPDATA current,int nh)
+{
+  NODE data1;
+  DL new;
+  int i,n;
+  Z dz;
+  DL *p;
+  VECT b;
+  P tv,td,s,hn;
+  LIST list1;
+
+  n = nd_nvar;
+  new = ndltodl(n,nd_psh[nh]->dl);
+  MKVECT(b,nh); p = (DL *)BDY(b);
+  for ( i = 0; i < nh; i++ ) {
+    p[i] = monomial_colon(ndltodl(n,nd_psh[i]->dl),new,n);
+  }
+  // compute HP(I:new)
+  if ( current->w )
+    list1 = dp_monomial_hilbert_poincare_weight(b,current->x,current->w);
+  else
+    list1 = dp_monomial_hilbert_poincare(b,current->x);
+  data1 = BDY((LIST)list1);
+  // HP(I+<new>) = H(I)-t^d*H(I:new), d=tdeg(new)
+  makevar("t",&tv); UTOZ(new->td,dz);
+  pwrp(CO,tv,dz,&td);
+  mulp(CO,(P)ARG0(data1),td,&s);
+  subp(CO,current->hn,s,&hn);
+  current->hn = hn;
+}
+
+ND_pairs nd_remove_same_sugar( ND_pairs d, int sugar)
+{
+  struct oND_pairs root;
+  ND_pairs prev,cur;
+  int i;
+
+  root.next = d;
+  prev = &root; cur = d;
+  i = 0;
+  while ( cur ) {
+    if ( SG(cur) == sugar ) {
+      prev->next = cur->next;
+      i++;
+    } else
+      prev = cur;
+    cur = cur->next;
+  }
+  if ( DP_Print && i ) fprintf(asir_out,"[%d]",i);
+  return root.next;
+}
+
 /* return value = 0 => input is not a GB */
 
 NODE nd_gb(int m,int ishomo,int checkonly,int gensyz,int **indp)
 {
-    int i,nh,sugar,stat;
-    NODE r,g,t;
-    ND_pairs d;
-    ND_pairs l;
-    ND h,nf,s,head,nf1;
-    NDV nfv;
-    Z q;
-    union oNDC dn,hc;
-    int diag_count = 0;
-    P cont;
-    LIST list;
+  int i,nh,sugar,stat;
+  NODE g,t;
+  ND_pairs d;
+  ND_pairs l;
+  ND h,nf;
+  NDV nfv;
+  Z q;
+  union oNDC hc;
+  int diag_count = 0;
+  int Nnfnz = 0,Nnfz = 0;
+  P cont;
+  LIST list;
+  struct oHPDATA current_hpdata,final_hpdata;
 
-    g = 0; d = 0;
-    for ( i = 0; i < nd_psn; i++ ) {
-        d = update_pairs(d,g,i,gensyz);
-        g = update_base(g,i);
-    }
-    sugar = 0;
-    while ( d ) {
+struct oEGT eg1,eg2,eg_update;
+
+init_eg(&eg_update);
+  Nnd_add = 0;
+  g = 0; d = 0;
+  for ( i = 0; i < nd_psn; i++ ) {
+    d = update_pairs(d,g,i,gensyz);
+    g = update_base(g,i);
+  }
+  sugar = 0;
+  if ( nd_hpdata ) {
+    if ( DP_Print ) fprintf(asir_out,"Hilbert driven algorithm.\n");
+    setup_hpdata(&final_hpdata,&current_hpdata);
+  }
+  while ( d ) {
 again:
-        l = nd_minp(d,&d);
-        if ( MaxDeg > 0 && SG(l) > MaxDeg ) break;
-        if ( SG(l) != sugar ) {
-            if ( ishomo ) {
-                diag_count = 0;
-                stat = do_diagonalize(sugar,m);
-                if ( !stat ) {
-                    NEXT(l) = d; d = l;
-                    d = nd_reconstruct(0,d);
-                    goto again;
-                }
-            }
-            sugar = SG(l);
-            if ( DP_Print ) fprintf(asir_out,"%d",sugar);
-        }
-        stat = nd_sp(m,0,l,&h);
+    l = nd_minp(d,&d);
+    if ( MaxDeg > 0 && SG(l) > MaxDeg ) break;
+    if ( SG(l) != sugar ) {
+      if ( ishomo ) {
+        diag_count = 0;
+        stat = do_diagonalize(sugar,m);
         if ( !stat ) {
-            NEXT(l) = d; d = l;
-            d = nd_reconstruct(0,d);
-            goto again;
+          NEXT(l) = d; d = l;
+          d = nd_reconstruct(0,d);
+          goto again;
         }
+      }
+      sugar = SG(l);
+      if ( DP_Print ) fprintf(asir_out,"%d",sugar);
+    }
+    stat = nd_sp(m,0,l,&h);
+    if ( !stat ) {
+      NEXT(l) = d; d = l;
+      d = nd_reconstruct(0,d);
+      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,0,&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,0,&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 ) {
-            if ( checkonly || gensyz ) return 0;
+    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 ) {
           if ( MPOS(HDL(nf)) > 1 ) return 0;
         } else if ( !(HDL(nf)[nd_exporigin] & nd_mask[0]) ) return 0;
       }
-            if ( DP_Print ) { printf("+"); fflush(stdout); }
-            hc = HCU(nf);
-            nd_removecont(m,nf);
-            if ( !m && nd_nalg ) {
-                nd_monic(0,&nf);
-                nd_removecont(m,nf);
-            }
-            if ( nd_gentrace ) {
+      if ( DP_Print ) { printf("+"); fflush(stdout); }
+      hc = HCU(nf);
+      nd_removecont(m,nf);
+      if ( !m && nd_nalg ) {
+        nd_monic(0,&nf);
+        nd_removecont(m,nf);
+      }
+      if ( nd_gentrace ) {
+        /* exact division */
         cont = ndc_div(m,hc,HCU(nf));
         if ( m || !UNIQ(cont) ) {
-                    t = mknode(4,NULLP,NULLP,NULLP,cont);
-                    MKLIST(list,t); MKNODE(t,list,nd_tracelist);
+          t = mknode(4,NULLP,NULLP,NULLP,cont);
+          MKLIST(list,t); MKNODE(t,list,nd_tracelist);
           nd_tracelist = t;
         }
-            }
-            nfv = ndtondv(m,nf); nd_free(nf);
-            nh = ndv_newps(m,nfv,0,0);
-            if ( !m && (ishomo && ++diag_count == diag_period) ) {
-                diag_count = 0;
-                stat = do_diagonalize(sugar,m);
-                if ( !stat ) {
-                    NEXT(l) = d; d = l;
-                    d = nd_reconstruct(1,d);
-                    goto again;
-                }
-            }
-            d = update_pairs(d,g,nh,0);
-            g = update_base(g,nh);
-            FREENDP(l);
-        } else {
-        if ( nd_gentrace && gensyz ) {
-                nd_tracelist = reverse_node(nd_tracelist); 
+      }
+      nfv = ndtondv(m,nf); nd_free(nf);
+      nh = ndv_newps(m,nfv,0);
+      if ( !m && (ishomo && ++diag_count == diag_period) ) {
+        diag_count = 0;
+        stat = do_diagonalize(sugar,m);
+        if ( !stat ) {
+          NEXT(l) = d; d = l;
+          d = nd_reconstruct(1,d);
+          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);
+      if ( nd_hpdata ) {
+        int dg,sugar0;
+
+        update_hpdata(&current_hpdata,nh); 
+        dg = comp_hn(final_hpdata.hn,current_hpdata.hn);
+        if ( dg < 0 ) {
+           int d_len;
+           for ( d_len = 0; d; d = d->next, d_len++);
+           fprintf(asir_out,"[%d] We found a gb\n",d_len);
+        }
+        sugar0 = sugar;
+        while ( d && dg > sugar0 ) {
+          d = nd_remove_same_sugar(d,sugar0);
+          sugar0++;
+        }
+      }
+    } else {
+      Nnfz++;
+      if ( nd_gentrace && gensyz ) {
+        nd_tracelist = reverse_node(nd_tracelist); 
         MKLIST(list,nd_tracelist);
-                STOQ(-1,q); t = mknode(2,q,list); MKLIST(list,t);
-                MKNODE(t,list,nd_alltracelist); 
+        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);
-        }
+      if ( DP_Print ) { fprintf(asir_out,"."); fflush(asir_out); }
+        FREENDP(l);
     }
+  }
   conv_ilist(nd_demand,0,g,indp);
-    if ( !checkonly && DP_Print ) { printf("nd_gb done.\n"); fflush(stdout); }
-    return g;
+  if ( !checkonly && DP_Print ) { 
+    fprintf(asir_out,"\nnd_gb done. Nbase=%d,Nnd_add=%d,Npairs=%d, Nnfnz=%d,Nnfz=%d,",nd_psn,Nnd_add,Npairs,Nnfnz,Nnfz);
+    fprintf(asir_out,"Nremoved=%d\n",NcriB+NcriMF+Ncri2);
+    fflush(asir_out);
+  }
+  if ( DP_Print ) {
+    print_eg("update",&eg_update); fprintf(asir_out,"\n");
+  }
+  return g;
 }
 
+ND_pairs update_pairs_s(ND_pairs d,int t,NODE *syz);
+int update_pairs_array_s(ND_pairs *d,int t,NODE *syz);
+ND_pairs nd_newpairs_s(int t ,NODE *syz);
+ND_pairs *nd_newpairs_array_s(int t ,NODE *syz);
+
+int nd_nf_pbucket_s(int mod,ND g,NDV *ps,int full,ND *nf);
+int nd_nf_s(int mod,ND d,ND g,NDV *ps,int full,ND *nf);
+
+void _copydl(int n,DL d1,DL d2);
+void _subfromdl(int n,DL d1,DL d2);
+extern int (*cmpdl)(int n,DL d1,DL d2);
+int _dl_redble_ext(DL,DL,DL,int);
+
+int primitive_irred(ND p,SIG sig)
+{
+  static int wpd=0,dlen=0;
+  static DL dquo,squo;
+  static UINT *quo;
+  int i;
+
+  if ( dlen < nd_nvar ) {
+    NEWDL(dquo,nd_nvar);
+    NEWDL(squo,nd_nvar);
+    dlen = nd_nvar;
+  }
+  if ( wpd != nd_wpd ) {
+    wpd = nd_wpd;
+    quo = (UINT *)MALLOC(wpd*sizeof(UINT));
+  }
+  for ( i = 0; i < nd_psn; i++ ) {
+    if ( sig->pos == nd_psh[i]->sig->pos &&
+      _dl_redble_ext(DL(nd_psh[i]->sig),DL(sig),squo,nd_nvar) )
+      if ( ndl_reducible(HDL(p),DL(nd_psh[i])) ) {
+        if ( DP_Print ) fprintf(asir_out,"D");
+        ndl_sub(HDL(p),DL(nd_psh[i]),quo);
+        _ndltodl(quo,dquo);
+        if ( _eqdl(nd_nvar,squo,dquo) ) 
+          return 0;
+      }
+  }
+  return 1;
+}
+
+NODE insert_sig(NODE l,SIG s)
+{
+  int pos;
+  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;
+    } 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 small_lcm(ND_pairs l)
+{
+  SIG sig;
+  int i;
+  NODE t;
+  static DL lcm,mul,quo;
+  static int nvar = 0;
+
+  if ( nd_sba_largelcm ) return 0;
+  if ( nvar < nd_nvar ) {
+    nvar = nd_nvar; NEWDL(lcm,nvar); NEWDL(quo,nvar); NEWDL(mul,nvar);
+  }
+  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,quo2,minlm;
+  static int nvar = 0;
+
+  if ( nvar < nd_nvar ) {
+    nvar = nd_nvar; 
+    NEWDL(quo,nvar); NEWDL(quo2,nvar); NEWDL(mul,nvar);
+    NEWDL(minlm,nvar);
+  }
+  sig = l->sig;
+  // find mg s.t. m*s(g)=sig and m*lm(g) is minimal
+  _ndltodl(l->lcm,minlm); minindex = -1;
+  for ( t = nd_sba_pos[sig->pos]; t; t = t->next ) {
+    i = (long)BDY(t);
+    if ( _dl_redble_ext(DL(nd_psh[i]->sig),DL(sig),quo,nd_nvar) ) {
+      _ndltodl(DL(nd_psh[i]),mul);
+      _addtodl(nd_nvar,quo,mul);
+      if ( (*cmpdl)(nd_nvar,minlm,mul) > 0 ) {
+        minindex = i;
+        break;
+        _copydl(nd_nvar,mul,minlm);
+      }
+    }
+  }
+  // l->lcm is minimal; return l itself
+  if ( minindex < 0 ) return l;
+  else return 0;
+  for ( i = 0; i < nd_psn; i++ ) {
+    if ( i == minindex ) continue;
+    _ndltodl(DL(nd_psh[i]),mul);
+    if ( _dl_redble_ext(mul,minlm,quo,nd_nvar) ) {
+      _addtodl(nd_nvar,nd_ps[i]->sig->dl,quo);
+      sig1.pos = nd_ps[i]->sig->pos;
+      sig1.dl = quo;
+      sig1.dl2 = quo2;
+      _adddl(nd_nvar,sig1.dl,nd_sba_hm[sig1.pos],sig1.dl2);
+      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);
+
+// S(fj*ei-fi*ej) 
+
+void _subdl(int,DL,DL,DL);
+
+SIG trivial_sig(int i,int j)
+{
+  static DL lcm;
+  static struct oSIG sigi,sigj;
+  static int nvar = 0;
+  SIG sig;
+
+  if ( nvar != nd_nvar ) {
+    nvar = nd_nvar; NEWDL(lcm,nvar); NEWDL(sigi.dl,nvar); NEWDL(sigj.dl,nvar);
+    NEWDL(sigi.dl2,nvar); NEWDL(sigj.dl2,nvar);
+  }
+  if ( nd_sba_inputisgb != 0 ) {
+    lcm_of_DL(nd_nvar,nd_sba_hm[i],nd_sba_hm[j],lcm);
+    sigi.pos = i; _subdl(nd_nvar,lcm,nd_sba_hm[i],sigi.dl);
+    _copydl(nd_nvar,lcm,sigi.dl2);
+    sigj.pos = j; _subdl(nd_nvar,lcm,nd_sba_hm[j],sigj.dl);
+    _copydl(nd_nvar,lcm,sigj.dl2);
+    if ( comp_sig(&sigi,&sigj) > 0 ) sig = dup_sig(&sigi);
+    else sig = dup_sig(&sigj);
+  } else {
+    sigi.pos = i; _copydl(nd_nvar,nd_sba_hm[j],sigi.dl);
+    _adddl(nd_nvar,sigi.dl,nd_sba_hm[i],sigi.dl2);
+    sigj.pos = j; _copydl(nd_nvar,nd_sba_hm[i],sigj.dl);
+    _adddl(nd_nvar,sigj.dl,nd_sba_hm[j],sigj.dl2);
+    if ( comp_sig(&sigi,&sigj) > 0 ) sig = dup_sig(&sigi);
+    else sig = dup_sig(&sigj);
+  }
+  return sig;
+}
+
+int nd_minsig(ND_pairs *d) 
+{
+  int min,i,ret;
+
+  min = -1;
+  for ( i = 0; i < nd_nbase; i++ ) {
+    if ( d[i] != 0 ) {
+      if ( min < 0 ) min = i;
+      else {
+        ret = comp_sig(d[i]->sig,d[min]->sig);
+        if ( ret < 0 ) min = i;
+      }
+    }
+  }
+  return min;
+}
+
+int dlength(ND_pairs d)
+{
+  int i;
+  for ( i = 0; d; d = d->next, i++ );
+  return i;
+}
+
+NODE nd_sba_buch(int m,int ishomo,int **indp,NODE *syzp)
+{
+  int i,j,nh,sugar,stat,pos;
+  NODE g;
+  ND_pairs *d;
+  ND_pairs l,l1;
+  ND h,nf;
+  NDV nfv;
+//  union oNDC hc;
+  SIG sig;
+  NODE *syzlist;
+  int ngen,ind;
+  int Nnominimal,Nredundant;
+  DL lcm,quo,mul;
+  struct oHPDATA final_hpdata,current_hpdata;
+  struct oEGT eg1,eg2,eg3,eg4,eg_remove,eg_large,eg_nf,eg_nfzero;
+  struct oEGT eg_minsig,eg_smallest,eg_removecont,eg_hpdata,eg_updatepairs,eg_sbabuch,eg_sp;
+  int Nnfs=0,Nnfz=0,Nnfnz=0,dlen,nsyz;
+
+init_eg(&eg_remove);
+  syzlist = (NODE *)MALLOC(nd_psn*sizeof(NODE));
+  d = (ND_pairs *)MALLOC(nd_psn*sizeof(ND_pairs));
+  nd_nbase = nd_psn;
+  Nsyz = 0;
+  Nnd_add = 0;
+  Nnominimal = 0;
+  Nredundant = 0;
+  ngen = nd_psn;
+  if ( !do_weyl || nd_sba_inputisgb ) {
+    for ( i = 0; i < nd_psn; i++ )
+      for ( j = i+1; j < nd_psn; j++ ) {
+        sig = trivial_sig(i,j);
+        syzlist[sig->pos] = insert_sig(syzlist[sig->pos],sig);
+      }
+    }
+  dlen = 0;
+  for ( i = 0; i < nd_psn; i++ ) {
+    dlen += update_pairs_array_s(d,i,syzlist);
+  }
+  sugar = 0;
+  pos = 0;
+  if ( nd_hpdata ) {
+    setup_hpdata(&final_hpdata,&current_hpdata);
+  }
+  NEWDL(lcm,nd_nvar); NEWDL(quo,nd_nvar); NEWDL(mul,nd_nvar);
+init_eg(&eg_sp);
+init_eg(&eg_create);
+init_eg(&eg_merge);
+init_eg(&eg_minsig);
+init_eg(&eg_smallest);
+init_eg(&eg_large);
+init_eg(&eg_nf);
+init_eg(&eg_nfzero);
+init_eg(&eg_removecont);
+init_eg(&eg_updatepairs);
+init_eg(&eg_hpdata);
+init_eg(&eg_sbabuch);
+get_eg(&eg3);
+  while ( 1 ) {
+    if ( DP_Print && !nd_hpdata && dlen%1000 == 0 ) fprintf(asir_out,"(%d)",dlen);
+again :
+get_eg(&eg1);
+    ind = nd_minsig(d); 
+get_eg(&eg2); add_eg(&eg_minsig,&eg1,&eg2);
+    if ( ind < 0 ) break;
+    l = d[ind];
+//    printf("(%d,%d)",l->i1,l->i2); print_sig(l->sig); printf("\n");
+get_eg(&eg1);
+    l1 = find_smallest_lcm(l);
+get_eg(&eg2); add_eg(&eg_smallest,&eg1,&eg2);
+    if ( l1 == 0 ) {
+      d[ind] = d[ind]->next; dlen--;
+//      if ( DP_Print && !nd_hpdata ) fprintf(asir_out,"M");
+      Nnominimal++;
+      continue;
+    }
+    if ( SG(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;
+      }
+    }
+get_eg(&eg1);
+    stat = nd_sp(m,0,l1,&h);
+get_eg(&eg2); add_eg(&eg_sp,&eg1,&eg2);
+    if ( !stat ) {
+      nd_reconstruct_s(0,d);
+      goto again;
+    }
+get_eg(&eg1);
+#if USE_GEOBUCKET
+    stat = (m&&!nd_gentrace)?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 ) {
+      nd_reconstruct_s(0,d);
+      goto again;
+    } else if ( stat == -1 ) {
+      d[ind] = d[ind]->next; dlen--;
+      Nnfs++;
+      if ( DP_Print ) { printf("S"); fflush(stdout); }
+    } else if ( nf ) {
+      d[ind] = d[ind]->next; dlen--;
+      Nnfnz++;
+      if ( DP_Print ) { 
+        if ( nd_sba_redundant_check ) {
+          if ( ndl_find_reducer_nonsig(HDL(nf)) >= 0 ) {
+            Nredundant++;
+            printf("R"); 
+          } else 
+            printf("+"); 
+        } else
+          printf("+"); 
+        fflush(stdout); 
+      }
+      add_eg(&eg_nf,&eg1,&eg2);
+//      hc = HCU(nf);
+      get_eg(&eg1);
+      nd_removecont(m,nf);
+      get_eg(&eg2); add_eg(&eg_removecont,&eg1,&eg2);
+      nfv = ndtondv(m,nf); nd_free(nf);
+      nh = ndv_newps(m,nfv,0);
+  
+      get_eg(&eg1);
+      dlen += update_pairs_array_s(d,nh,syzlist);
+      get_eg(&eg2); add_eg(&eg_updatepairs,&eg1,&eg2);
+      nd_sba_pos[sig->pos] = append_one(nd_sba_pos[sig->pos],nh);
+      if ( nd_hpdata ) {
+        int dg,sugar0;
+
+        get_eg(&eg1);
+        update_hpdata(&current_hpdata,nh);
+        get_eg(&eg2); add_eg(&eg_hpdata,&eg1,&eg2);
+        dg = comp_hn(final_hpdata.hn,current_hpdata.hn);
+//        if ( !compp(CO,final_hpdata.hn,current_hpdata.hn) ) 
+        if ( dg < 0 ) {
+          if ( DP_Print ) { printf("\nWe found a gb.\n"); }
+            break;
+        } else if ( nd_sba_heu == 1 ) {
+          for ( i = 0; i < ngen; i++ ) {
+            sugar0 = sugar;
+            while ( d[i] && dg > sugar0 ) {
+              d[i] = nd_remove_same_sugar(d[i],sugar0);
+              sugar0++;
+            }
+          }
+        }
+      }
+    } else {
+      d[ind] = d[ind]->next; dlen--;
+      Nnfz++;
+      add_eg(&eg_nfzero,&eg1,&eg2);
+    // syzygy
+get_eg(&eg1);
+      nsyz = Nsyz;
+      d[sig->pos] = remove_spair_s(d[sig->pos],sig);
+      dlen -= Nsyz-nsyz;
+get_eg(&eg2); add_eg(&eg_remove,&eg1,&eg2);
+      syzlist[sig->pos] = insert_sig(syzlist[sig->pos],sig);
+      if ( DP_Print ) { printf("."); fflush(stdout); }
+    }
+  }
+  get_eg(&eg4); add_eg(&eg_sbabuch,&eg3,&eg4);
+  g = conv_ilist_s(nd_demand,0,indp);
+  if ( DP_Print ) { 
+    printf("\ndlen=%d,nd_sba done. nd_add=%d,Nsyz=%d,Nsamesig=%d,Nnominimal=%d\n",dlen,Nnd_add,Nsyz,Nsamesig,Nnominimal);
+    printf("Nbase=%d,Nnfnz=%d,Nnfz=%d,Nnfsingular=%d\n",nd_psn,Nnfnz,Nnfz,Nnfs);
+    fflush(stdout);
+    if ( nd_sba_redundant_check )
+      printf("Nredundant=%d\n",Nredundant);
+    fflush(stdout);
+     print_eg("sp",&eg_sp);
+     print_eg("create",&eg_create);
+     print_eg("merge",&eg_merge);
+     print_eg("minsig",&eg_minsig);
+     print_eg("smallest",&eg_smallest);
+     print_eg("remove",&eg_remove);
+     printf("\n");
+     print_eg("nf",&eg_nf);
+     print_eg("nfzero",&eg_nfzero);
+     print_eg("removecont",&eg_removecont);
+     print_eg("updatepairs",&eg_updatepairs);
+     print_eg("hpdata",&eg_hpdata);
+     print_eg("total",&eg_sbabuch);
+     printf("\n");
+  }
+  if ( nd_sba_syz ) {
+    print_eg("remove",&eg_remove);
+    print_eg("nf",&eg_nf);
+    print_eg("nfzero",&eg_nfzero);
+    printf("\n");
+  }
+  if ( nd_sba_syz ) {
+    NODE hsyz,tsyz,prev;
+
+    hsyz = 0;
+    for ( i = 0; i < ngen; i++ ) {
+      tsyz = syzlist[i];
+      for ( prev = 0; tsyz != 0; prev = tsyz, tsyz = NEXT(tsyz))
+        BDY(tsyz) = (pointer)sigtodpm((SIG)BDY(tsyz));
+      if ( prev != 0 ) {
+        prev->next = hsyz; hsyz = syzlist[i];
+      }
+    }
+    *syzp = hsyz;
+  } else *syzp = 0;
+  return g;
+}
+
 /* splist = [[i1,i2],...] */
 
 int check_splist(int m,NODE splist)
@@ -2196,30 +3239,30 @@ int check_splist(int m,NODE splist)
 
   for ( d = 0, t = splist; t; t = NEXT(t) ) {
     p = BDY((LIST)BDY(t));
-        NEXTND_pairs(d,r);
-        r->i1 = QTOS((Q)ARG0(p)); r->i2 = QTOS((Q)ARG1(p));
-        ndl_lcm(DL(nd_psh[r->i1]),DL(nd_psh[r->i2]),r->lcm);
+    NEXTND_pairs(d,r);
+    r->i1 = (int)ZTOS((Q)ARG0(p)); r->i2 = (int)ZTOS((Q)ARG1(p));
+    ndl_lcm(DL(nd_psh[r->i1]),DL(nd_psh[r->i2]),r->lcm);
     SG(r) = TD(LCM(r)); /* XXX */
   }
   if ( d ) NEXT(r) = 0;
 
-    while ( d ) {
+  while ( d ) {
 again:
-        l = nd_minp(d,&d);
-        stat = nd_sp(m,0,l,&h);
-        if ( !stat ) {
-            NEXT(l) = d; d = l;
-            d = nd_reconstruct(0,d);
-            goto again;
-        }
-        stat = nd_nf(m,0,h,nd_ps,!Top,0,&nf);
-        if ( !stat ) {
-            NEXT(l) = d; d = l;
-            d = nd_reconstruct(0,d);
-            goto again;
-        } else if ( nf ) return 0;
-    if ( DP_Print) { printf("."); fflush(stdout); }
+    l = nd_minp(d,&d);
+    stat = nd_sp(m,0,l,&h);
+    if ( !stat ) {
+      NEXT(l) = d; d = l;
+      d = nd_reconstruct(0,d);
+      goto again;
     }
+    stat = nd_nf(m,0,h,nd_ps,!nd_top&&!Top,&nf);
+    if ( !stat ) {
+      NEXT(l) = d; d = l;
+      d = nd_reconstruct(0,d);
+      goto again;
+    } else if ( nf ) return 0;
+    if ( DP_Print) { printf("."); fflush(stdout); }
+  }
   if ( DP_Print) { printf("done.\n"); fflush(stdout); }
   return 1;
 }
@@ -2227,96 +3270,96 @@ again:
 int check_splist_f4(int m,NODE splist)
 {
   UINT *s0vect;
-    PGeoBucket bucket;
+  PGeoBucket bucket;
   NODE p,rp0,t;
   ND_pairs d,r,l,ll;
   int col,stat;
 
   for ( d = 0, t = splist; t; t = NEXT(t) ) {
     p = BDY((LIST)BDY(t));
-        NEXTND_pairs(d,r);
-        r->i1 = QTOS((Q)ARG0(p)); r->i2 = QTOS((Q)ARG1(p));
-        ndl_lcm(DL(nd_psh[r->i1]),DL(nd_psh[r->i2]),r->lcm);
+    NEXTND_pairs(d,r);
+    r->i1 = (int)ZTOS((Q)ARG0(p)); r->i2 = (int)ZTOS((Q)ARG1(p));
+    ndl_lcm(DL(nd_psh[r->i1]),DL(nd_psh[r->i2]),r->lcm);
     SG(r) = TD(LCM(r)); /* XXX */
   }
   if ( d ) NEXT(r) = 0;
 
-    while ( d ) {
-        l = nd_minsugarp(d,&d);
-        bucket = create_pbucket();
-        stat = nd_sp_f4(m,0,l,bucket);
-        if ( !stat ) {
-            for ( ll = l; NEXT(ll); ll = NEXT(ll) );
-            NEXT(ll) = d; d = l;
-            d = nd_reconstruct(0,d);
-            continue;
-        }
-        if ( bucket->m < 0 ) continue;
-        col = nd_symbolic_preproc(bucket,0,&s0vect,&rp0);
-        if ( !col ) {
-            for ( ll = l; NEXT(ll); ll = NEXT(ll) );
-            NEXT(ll) = d; d = l;
-            d = nd_reconstruct(0,d);
-            continue;
-        }
-        if ( nd_f4_red(m,l,0,s0vect,col,rp0,0) ) return 0;
+  while ( d ) {
+    l = nd_minsugarp(d,&d);
+    bucket = create_pbucket();
+    stat = nd_sp_f4(m,0,l,bucket);
+    if ( !stat ) {
+      for ( ll = l; NEXT(ll); ll = NEXT(ll) );
+      NEXT(ll) = d; d = l;
+      d = nd_reconstruct(0,d);
+      continue;
     }
-    return 1;
+    if ( bucket->m < 0 ) continue;
+    col = nd_symbolic_preproc(bucket,0,&s0vect,&rp0);
+    if ( !col ) {
+      for ( ll = l; NEXT(ll); ll = NEXT(ll) );
+      NEXT(ll) = d; d = l;
+      d = nd_reconstruct(0,d);
+      continue;
+    }
+    if ( nd_f4_red(m,l,0,s0vect,col,rp0,0) ) return 0;
+  }
+  return 1;
 }
 
 int do_diagonalize_trace(int sugar,int m)
 {
-    int i,nh,stat;
-    NODE r,g,t;
-    ND h,nf,nfq,s,head;
-    NDV nfv,nfqv;
-    Q q,den,num;
-    union oNDC hc;
-    NODE node;
-    LIST l;
-    Z iq;
-    P cont,cont1;
+  int i,stat;
+  ND nf,s,head;
+  NDV nfv;
+  union oNDC hc;
+  NODE node;
+  LIST l;
+  Z iq;
+  P cont;
 
-    for ( i = nd_psn-1; i >= 0 && SG(nd_psh[i]) == sugar; i-- ) {
-        if ( nd_gentrace ) {
-            /* Trace = [1,index,1,1] */
-            STOQ(i,iq); node = mknode(4,ONE,iq,ONE,ONE);
-            MKLIST(l,node); MKNODE(nd_tracelist,l,0);
-        }
-        /* for nd_ps */
-        s = ndvtond(m,nd_ps[i]);
-        s = nd_separate_head(s,&head);
-        stat = nd_nf_pbucket(m,s,nd_ps,1,&nf);
-        if ( !stat ) return 0;
-        nf = nd_add(m,head,nf);
-        ndv_free(nd_ps[i]);
-        nd_ps[i] = ndtondv(m,nf);
-        nd_free(nf);
+  if ( diag_period == 0 ) return 1;
+  for ( i = nd_psn-1; i >= 0 && SG(nd_psh[i]) == sugar; i-- ) {
+    if ( nd_gentrace ) {
+        /* Trace = [1,index,1,1] */
+        STOZ(i,iq); node = mknode(4,ONE,iq,ONE,ONE);
+        MKLIST(l,node); MKNODE(nd_tracelist,l,0);
+    }
+    /* for nd_ps */
+    s = ndvtond(m,nd_ps[i]);
+    s = nd_separate_head(s,&head);
+    stat = nd_nf_pbucket(m,s,nd_ps,1,&nf);
+    if ( !stat ) return 0;
+    nf = nd_add(m,head,nf);
+    ndv_free(nd_ps[i]);
+    nd_ps[i] = ndtondv(m,nf);
+    nd_free(nf);
 
-        /* for nd_ps_trace */
-        if ( nd_demand )
-            nfv = ndv_load(i);
-        else
-            nfv = nd_ps_trace[i];
-        s = ndvtond(0,nfv);
-        s = nd_separate_head(s,&head);
-        stat = nd_nf(0,head,s,nd_ps_trace,1,0,&nf);
-        if ( !stat ) return 0;
-        ndv_free(nfv);
-        hc = HCU(nf); nd_removecont(0,nf);
+    /* for nd_ps_trace */
+    if ( nd_demand )
+        nfv = ndv_load(i);
+    else
+        nfv = nd_ps_trace[i];
+    s = ndvtond(0,nfv);
+    s = nd_separate_head(s,&head);
+    stat = nd_nf(0,head,s,nd_ps_trace,1,&nf);
+    if ( !stat ) return 0;
+    ndv_free(nfv);
+    hc = HCU(nf); nd_removecont(0,nf);
+    /* exact division */
     cont = ndc_div(0,hc,HCU(nf));
-        if ( nd_gentrace ) finalize_tracelist(i,cont);
-        nfv = ndtondv(0,nf);
-        nd_free(nf);
-        nd_bound[i] = ndv_compute_bound(nfv);
-        register_hcf(nfv);
-        if ( nd_demand ) {
-            ndv_save(nfv,i);
-            ndv_free(nfv);
-        } else
-            nd_ps_trace[i] = nfv;
-    }
-    return 1;
+    if ( nd_gentrace ) finalize_tracelist(i,cont);
+    nfv = ndtondv(0,nf);
+    nd_free(nf);
+    nd_bound[i] = ndv_compute_bound(nfv);
+    register_hcf(nfv);
+    if ( nd_demand ) {
+    ndv_save(nfv,i);
+    ndv_free(nfv);
+    } else
+    nd_ps_trace[i] = nfv;
+  }
+  return 1;
 }
 
 static struct oEGT eg_invdalg;
@@ -2335,139 +3378,162 @@ void nd_subst_vector(VL vl,P p,NODE subst,P *r)
 
 NODE nd_gb_trace(int m,int ishomo,int **indp)
 {
-    int i,nh,sugar,stat;
-    NODE r,g,t;
-    ND_pairs d;
-    ND_pairs l;
-    ND h,nf,nfq,s,head;
-    NDV nfv,nfqv;
-    Z q,den,num;
-    P hc;
-    union oNDC dn,hnfq;
-    struct oEGT eg_monic,egm0,egm1;
-    int diag_count = 0;
-    P cont;
-    LIST list;
+  int i,nh,sugar,stat;
+  NODE g,t;
+  ND_pairs d;
+  ND_pairs l;
+  ND h,nf,nfq;
+  NDV nfv,nfqv;
+  Z q;
+  P hc;
+  union oNDC hnfq;
+  struct oEGT eg_monic,egm0,egm1;
+  int diag_count = 0;
+  P cont;
+  LIST list;
+  struct oHPDATA current_hpdata,final_hpdata;
 
-    init_eg(&eg_monic);
-    init_eg(&eg_invdalg);
-    init_eg(&eg_le);
-    g = 0; d = 0;
-    for ( i = 0; i < nd_psn; i++ ) {
-        d = update_pairs(d,g,i,0);
-        g = update_base(g,i);
-    }
-    sugar = 0;
-    while ( d ) {
+  init_eg(&eg_monic);
+  init_eg(&eg_invdalg);
+  init_eg(&eg_le);
+  g = 0; d = 0;
+  for ( i = 0; i < nd_psn; i++ ) {
+    d = update_pairs(d,g,i,0);
+    g = update_base(g,i);
+  }
+  sugar = 0;
+  if ( nd_hpdata ) {
+    if ( DP_Print ) fprintf(asir_out,"Hilbert driven algorithm.\n");
+    setup_hpdata(&final_hpdata,&current_hpdata);
+  }
+
+  while ( d ) {
 again:
-        l = nd_minp(d,&d);
-        if ( MaxDeg > 0 && SG(l) > MaxDeg ) break;
-        if ( SG(l) != sugar ) {
+    l = nd_minp(d,&d);
+    if ( MaxDeg > 0 && SG(l) > MaxDeg ) break;
+    if ( SG(l) != sugar ) {
 #if 1
-            if ( ishomo ) {
-                if ( DP_Print > 2 ) fprintf(asir_out,"|");
-                stat = do_diagonalize_trace(sugar,m);
-                if ( DP_Print > 2 ) fprintf(asir_out,"|");
-                diag_count = 0;
-                if ( !stat ) {
-                    NEXT(l) = d; d = l;
-                    d = nd_reconstruct(1,d);
-                    goto again;
-                }
-            }
-#endif
-            sugar = SG(l);
-            if ( DP_Print ) fprintf(asir_out,"%d",sugar);
-        }
-        stat = nd_sp(m,0,l,&h);
+      if ( ishomo ) {
+        if ( DP_Print > 2 ) fprintf(asir_out,"|");
+        stat = do_diagonalize_trace(sugar,m);
+        if ( DP_Print > 2 ) fprintf(asir_out,"|");
+        diag_count = 0;
         if ( !stat ) {
-            NEXT(l) = d; d = l;
-            d = nd_reconstruct(1,d);
-            goto again;
+          NEXT(l) = d; d = l;
+          d = nd_reconstruct(1,d);
+          goto again;
         }
+      }
+#endif
+      sugar = SG(l);
+      if ( DP_Print ) fprintf(asir_out,"%d",sugar);
+    }
+    stat = nd_sp(m,0,l,&h);
+    if ( !stat ) {
+      NEXT(l) = d; d = l;
+      d = nd_reconstruct(1,d);
+      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,0,&nf);
+    stat = nd_nf(m,0,h,nd_ps,!nd_top&&!Top,&nf);
 #endif
-        if ( !stat ) {
+    if ( !stat ) {
+      NEXT(l) = d; d = l;
+      d = nd_reconstruct(1,d);
+      goto again;
+    } else if ( nf ) {
+      if ( nd_demand ) {
+        nfqv = ndv_load(nd_psn);
+        nfq = ndvtond(0,nfqv);
+      } else
+        nfq = 0;
+      if ( !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;
+        }
+      }
+      if ( nfq ) {
+        /* m|HC(nfq) => failure */
+        if ( nd_vc ) {
+          nd_subst_vector(nd_vc,HCP(nfq),nd_subst,&hc); q = (Z)hc;
+        } else
+          q = HCZ(nfq);
+        if ( !remqi((Q)q,m) ) return 0;
+
+        if ( DP_Print ) { printf("+"); fflush(stdout); }
+        hnfq = HCU(nfq);
+        if ( nd_nalg ) {
+          /* m|DN(HC(nf)^(-1)) => failure */
+          get_eg(&egm0);
+          if ( !nd_monic(m,&nfq) ) return 0;
+          get_eg(&egm1); add_eg(&eg_monic,&egm0,&egm1);
+          nd_removecont(0,nfq); nfqv = ndtondv(0,nfq); nd_free(nfq);
+          nfv = ndv_dup(0,nfqv); ndv_mod(m,nfv); nd_free(nf);
+        } else {
+          nd_removecont(0,nfq); nfqv = ndtondv(0,nfq); nd_free(nfq);
+          nd_removecont(m,nf); nfv = ndtondv(m,nf); nd_free(nf);
+        }
+        if ( nd_gentrace ) {
+          /* exact division */
+          cont = ndc_div(0,hnfq,HCU(nfqv));
+          if ( !UNIQ(cont) ) {
+            t = mknode(4,NULLP,NULLP,NULLP,cont);
+            MKLIST(list,t); MKNODE(t,list,nd_tracelist);
+            nd_tracelist = t;
+          }
+        }
+        nh = ndv_newps(0,nfv,nfqv);
+        if ( ishomo && ++diag_count == diag_period ) {
+          diag_count = 0;
+          if ( DP_Print > 2 ) fprintf(asir_out,"|");
+          stat = do_diagonalize_trace(sugar,m);
+          if ( DP_Print > 2 ) fprintf(asir_out,"|");
+          if ( !stat ) {
             NEXT(l) = d; d = l;
             d = nd_reconstruct(1,d);
             goto again;
-        } else if ( nf ) {
-            if ( nd_demand ) {
-                nfqv = ndv_load(nd_psn);
-                nfq = ndvtond(0,nfqv);
-            } else
-                nfq = 0;
-            if ( !nfq ) {
-                if ( !nd_sp(0,1,l,&h) || !nd_nf(0,0,h,nd_ps_trace,!Top,0,&nfq) ) {
-                    NEXT(l) = d; d = l;
-                    d = nd_reconstruct(1,d);
-                    goto again;
-                }
-            }
-            if ( nfq ) {
-                /* m|HC(nfq) => failure */
-                if ( nd_vc ) {
-                    nd_subst_vector(nd_vc,HCP(nfq),nd_subst,&hc); q = (Z)hc;
-                } else
-                    q = HCQ(nfq);
-                if ( !remqi((Q)q,m) ) return 0;
+          }
+        }
+        d = update_pairs(d,g,nh,0);
+        g = update_base(g,nh);
+        if ( nd_hpdata ) {
+          int dg,sugar0;
 
-                if ( DP_Print ) { printf("+"); fflush(stdout); }
-                hnfq = HCU(nfq);
-                if ( nd_nalg ) {
-                    /* m|DN(HC(nf)^(-1)) => failure */
-                    get_eg(&egm0);
-                    if ( !nd_monic(m,&nfq) ) return 0;
-                    get_eg(&egm1); add_eg(&eg_monic,&egm0,&egm1);
-                    nd_removecont(0,nfq); nfqv = ndtondv(0,nfq); nd_free(nfq);
-                    nfv = ndv_dup(0,nfqv); ndv_mod(m,nfv); nd_free(nf);
-                } else {
-                    nd_removecont(0,nfq); nfqv = ndtondv(0,nfq); nd_free(nfq);
-                    nd_removecont(m,nf); nfv = ndtondv(m,nf); nd_free(nf);
-                }
-                if ( nd_gentrace ) {
-           cont = ndc_div(0,hnfq,HCU(nfqv));
-           if ( !UNIQ(cont) ) {
-                       t = mknode(4,NULLP,NULLP,NULLP,cont);
-                       MKLIST(list,t); MKNODE(t,list,nd_tracelist);
-             nd_tracelist = t;
-           }
-                }
-                nh = ndv_newps(0,nfv,nfqv,0);
-                if ( ishomo && ++diag_count == diag_period ) {
-                    diag_count = 0;
-                    if ( DP_Print > 2 ) fprintf(asir_out,"|");
-                    stat = do_diagonalize_trace(sugar,m);
-                    if ( DP_Print > 2 ) fprintf(asir_out,"|");
-                    if ( !stat ) {
-                        NEXT(l) = d; d = l;
-                        d = nd_reconstruct(1,d);
-                        goto again;
-                    }
-                }
-                d = update_pairs(d,g,nh,0);
-                g = update_base(g,nh);
-            } else {
-                if ( DP_Print ) { printf("*"); fflush(stdout); }
-            }
-        } else {
-            if ( DP_Print ) { printf("."); fflush(stdout); }
+          update_hpdata(&current_hpdata,nh);
+          dg = comp_hn(final_hpdata.hn,current_hpdata.hn);
+          if ( dg < 0 ) {
+             int d_len;
+             for ( d_len = 0; d; d = d->next, d_len++);
+             fprintf(asir_out,"[%d] We found a gb\n",d_len);
+          }
+          sugar0 = sugar;
+          while ( d && dg > sugar0 ) {
+            d = nd_remove_same_sugar(d,sugar0);
+            sugar0++;
+          }
         }
-        FREENDP(l);
+      } else {
+        if ( DP_Print ) { fprintf(asir_out,"*"); fflush(asir_out); }
+      }
+    } else {
+      if ( DP_Print ) { fprintf(asir_out,"."); fflush(asir_out); }
     }
-    if ( nd_nalg ) {
-        if ( DP_Print ) {
-          print_eg("monic",&eg_monic);
-          print_eg("invdalg",&eg_invdalg);
-          print_eg("le",&eg_le);
-        }
+    FREENDP(l);
+  }
+  if ( nd_nalg ) {
+    if ( DP_Print ) {
+      print_eg("monic",&eg_monic);
+      print_eg("invdalg",&eg_invdalg);
+      print_eg("le",&eg_le);
     }
+  }
   conv_ilist(nd_demand,1,g,indp);
-    if ( DP_Print ) { printf("nd_gb_trace done.\n"); fflush(stdout); }
-    return g;
+  if ( DP_Print ) { fprintf(asir_out,"\nnd_gb_trace done. Nbase=%d\n",nd_psn); fflush(asir_out); }
+  return g;
 }
 
 int ndv_compare(NDV *p1,NDV *p2)
@@ -2495,32 +3561,30 @@ NODE ndv_reduceall(int m,NODE f)
   int i,j,n,stat;
   ND nf,g,head;
   NODE t,a0,a;
-  union oNDC dn;
-  Q q,num,den;
   NODE node;
   LIST l;
   Z iq,jq;
   int *perm;
   union oNDC hc;
-  P cont,cont1;
+  P cont;
 
   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) )
-      perm[i] = QTOS((Q)ARG1(BDY((LIST)BDY(t))));
+      perm[i] = (int)ZTOS((Q)ARG1(BDY((LIST)BDY(t))));
   }
   for ( i = 0; i < n; ) {
     if ( nd_gentrace ) {
       /* Trace = [1,index,1,1] */
-      STOQ(i,iq); node = mknode(4,ONE,iq,ONE,ONE);
+      STOZ(i,iq); node = mknode(4,ONE,iq,ONE,ONE);
       MKLIST(l,node); MKNODE(nd_tracelist,l,0);
     }
     g = ndvtond(m,nd_ps[i]);
     g = nd_separate_head(g,&head);
-    stat = nd_nf(m,head,g,nd_ps,1,0,&nf);
+    stat = nd_nf(m,head,g,nd_ps,1,&nf);
     if ( !stat )
       nd_reconstruct(0,0);
     else {
@@ -2529,9 +3593,10 @@ NODE ndv_reduceall(int m,NODE f)
       hc = HCU(nf); nd_removecont(m,nf);
       if ( nd_gentrace ) {
         for ( t = nd_tracelist; t; t = NEXT(t) ) {
-          jq = ARG1(BDY((LIST)BDY(t))); j = QTOS(jq);
-          STOQ(perm[j],jq); ARG1(BDY((LIST)BDY(t))) = jq;
+          jq = ARG1(BDY((LIST)BDY(t))); j = (int)ZTOS(jq);
+          STOZ(perm[j],jq); ARG1(BDY((LIST)BDY(t))) = jq;
         }
+        /* exact division */
         cont = ndc_div(m,hc,HCU(nf));
         finalize_tracelist(perm[i],cont);
       }
@@ -2553,9 +3618,17 @@ 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 */
@@ -2572,8 +3645,10 @@ 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 {
@@ -2583,7 +3658,7 @@ 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);
       }
@@ -2599,7 +3674,39 @@ 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;
+}
+
+int update_pairs_array_s( ND_pairs *d, int t,NODE *syz)
+{
+  ND_pairs *d1;
+  struct oEGT eg1,eg2,eg3;
+  int i;
+
+  if ( !t ) return 0;
+get_eg(&eg1);
+  Nnewpair = 0;
+  d1 = nd_newpairs_array_s(t,syz);
+get_eg(&eg2); add_eg(&eg_create,&eg1,&eg2);
+  for ( i = 0; i < nd_nbase; i++ )
+    d[i] = merge_pairs_s(d[i],d1[i]);
+get_eg(&eg3); add_eg(&eg_merge,&eg2,&eg3);
+  return Nnewpair;
+}
+
 ND_pairs nd_newpairs( NODE g, int t )
 {
   NODE h;
@@ -2609,7 +3716,7 @@ 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) > (UINT)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;
@@ -2623,7 +3730,7 @@ 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);
@@ -2637,6 +3744,455 @@ ND_pairs nd_newpairs( NODE g, int t )
   return r0;
 }
 
+int sig_cmpdl_op(int n,DL d1,DL d2)
+{
+  int e1,e2,i,j,l;
+  int *t1,*t2;
+  int len;
+  struct order_pair *pair;
+
+  len = nd_sba_modord->block_length;
+  pair = nd_sba_modord->order_pair;
+
+  for ( i = 0, t1 = d1->d, t2 = d2->d; i < len; i++ ) {
+    l = pair[i].length;
+    switch ( pair[i].order ) {
+      case 0:
+        for ( j = 0, e1 = e2 = 0; j < l; j++ ) {
+          e1 += t1[j];
+          e2 += t2[j];
+        }
+        if ( e1 > e2 )
+          return 1;
+        else if ( e1 < e2 )
+          return -1;
+        else {
+          for ( j = l - 1; j >= 0 && t1[j] == t2[j]; j-- );
+          if ( j >= 0 )
+            return t1[j] < t2[j] ? 1 : -1;
+        }
+        break;
+      case 1:
+        for ( j = 0, e1 = e2 = 0; j < l; j++ ) {
+          e1 += t1[j];
+          e2 += t2[j];
+        }
+        if ( e1 > e2 )
+          return 1;
+        else if ( e1 < e2 )
+          return -1;
+        else {
+          for ( j = 0; j < l && t1[j] == t2[j]; j++ );
+          if ( j < l )
+            return t1[j] > t2[j] ? 1 : -1;
+        }
+        break;
+      case 2:
+        for ( j = 0; j < l && t1[j] == t2[j]; j++ );
+        if ( j < l )
+          return t1[j] > t2[j] ? 1 : -1;
+        break;
+      default:
+        error("sig_cmpdl_op : invalid order"); break;
+    }
+    t1 += l; t2 += l; // head += l;
+  }
+  return 0;
+}
+
+int sig_cmpdl_mat(int n,DL d1,DL d2)
+{
+  int *v,*t1,*t2;
+  int s,i,j,len;
+  int **matrix;
+  static int *w;
+  static int nvar = 0;
+
+  if ( nvar != n ) {
+    nvar = n; w = (int *)MALLOC(n*sizeof(int));
+  }
+  for ( i = 0, t1 = d1->d, t2 = d2->d; i < n; i++ )
+    w[i] = t1[i]-t2[i];
+  len = nd_sba_modord->row;
+  matrix = nd_sba_modord->matrix;
+  for ( j = 0; j < len; j++ ) {
+    v = matrix[j];
+    for ( i = 0, s = 0; i < n; i++ )
+      s += v[i]*w[i];
+    if ( s > 0 )
+      return 1;
+    else if ( s < 0 )
+      return -1;
+  }
+  return 0;
+}
+
+struct comp_sig_spec *create_comp_sig_spec(VL current_vl,VL old_vl,Obj ord,Obj weight)
+{
+  struct comp_sig_spec *spec;
+  VL ovl,vl;
+  V ov;
+  int i,j,n,nvar,s;
+  NODE node,t,tn;
+  struct order_pair *l;
+  MAT m;
+  Obj **b;
+  int **w;
+  int *a;
+
+  spec = (struct comp_sig_spec *)MALLOC(sizeof(struct comp_sig_spec));
+  for ( i = 0, vl = current_vl; vl; vl = NEXT(vl), i++ );
+  spec->n = nvar = i;
+  if ( old_vl != 0 ) {
+    spec->oldv = (int *)MALLOC(nvar*sizeof(int));
+    for ( i = 0, ovl = old_vl; i < nvar; ovl = NEXT(ovl), i++ ) {
+      ov = ovl->v;
+      for ( j = 0, vl = current_vl; vl; vl = NEXT(vl), j++ )
+        if ( ov == vl->v ) break;
+      spec->oldv[i] = j;
+    }
+  } else
+    spec->oldv = 0;
+  if ( !ord || NUM(ord) ) {
+    switch ( ZTOS((Z)ord) ) {
+      case 0:
+        spec->cmpdl = cmpdl_revgradlex; break;
+      case 1:
+        spec->cmpdl = cmpdl_gradlex; break;
+      case 2:
+        spec->cmpdl = cmpdl_lex; break;
+      default:
+        error("create_comp_sig_spec : invalid spec"); break;
+    }
+  } else if ( OID(ord) == O_LIST ) {
+    node = BDY((LIST)ord);
+    for ( n = 0, t = node; t; t = NEXT(t), n++ );
+    l = (struct order_pair *)MALLOC_ATOMIC(n*sizeof(struct order_pair));
+    for ( i = 0, t = node, s = 0; i < n; t = NEXT(t), i++ ) {
+      tn = BDY((LIST)BDY(t)); l[i].order = (int)ZTOS((Q)BDY(tn));
+      tn = NEXT(tn); l[i].length = (int)ZTOS((Q)BDY(tn));
+      s += l[i].length;
+    }
+    if ( s != nvar )
+      error("create_comp_sig_spec : invalid spec");
+    spec->order_pair = l;
+    spec->block_length = n;
+    spec->cmpdl = sig_cmpdl_op;
+  } else if ( OID(ord) == O_MAT ) {
+    m = (MAT)ord; b = (Obj **)BDY(m);
+    if ( m->col != nvar )
+      error("create_comp_sig_spec : invalid spec");
+    w = almat(m->row,m->col);
+    for ( i = 0; i < m->row; i++ )
+      for ( j = 0; j < m->col; j++ )
+        w[i][j] = (int)ZTOS((Q)b[i][j]);
+    spec->row = m->row;
+    spec->matrix = w;
+    spec->cmpdl = sig_cmpdl_mat;
+  } else
+    error("create_comp_sig_spec : invalid spec");
+  if ( weight != 0 ) {
+    node = BDY((LIST)weight);
+    a = (int *)MALLOC(nvar*sizeof(int));
+    for ( i = 0; i < nvar; i++, node = NEXT(node) )
+      a[i] = (int)ZTOS((Z)BDY(node));
+    spec->weight = a;
+  }
+  return spec;
+}
+
+#define SIG_MUL_WEIGHT(a,i) (weight?(a)*weight[i]:(a))
+  
+int comp_sig_monomial(int n,DL d1,DL d2)
+{
+  static DL m1,m2;
+  static int nvar = 0;
+  int *oldv,*weight;
+  int i,w1,w2;
+ 
+  if ( nvar != n ) {
+    nvar = n; NEWDL(m1,nvar); NEWDL(m2,nvar);
+  }
+  if ( !nd_sba_modord )
+    return (*cmpdl)(n,d1,d2);
+  else if ( !nd_sba_modord->weight && !nd_sba_modord->oldv ) {
+    return (*nd_sba_modord->cmpdl)(n,d1,d2);
+  } else {
+    weight = nd_sba_modord->weight;
+    oldv = nd_sba_modord->oldv;
+    if ( oldv ) {
+      for ( i = 0; i < n; i++ ) {
+        m1->d[i] = d1->d[oldv[i]]; m2->d[i] = d2->d[oldv[i]];
+      }
+    } else {
+      for ( i = 0; i < n; i++ ) {
+        m1->d[i] = d1->d[i]; m2->d[i] = d2->d[i];
+      }
+    }
+    for ( i = 0, w1 = w2 = 0; i < n; i++ ) {
+      w1 += SIG_MUL_WEIGHT(m1->d[i],i); 
+      w2 += SIG_MUL_WEIGHT(m2->d[i],i);
+    }
+    m1->td = w1; m2->td = w2;
+    return (*nd_sba_modord->cmpdl)(n,m1,m2);
+  }
+}
+
+int comp_sig(SIG s1,SIG s2)
+{
+  if ( nd_sba_pot ) {
+    if ( s1->pos > s2->pos ) return 1;
+    else if ( s1->pos < s2->pos ) return -1;
+    else return comp_sig_monomial(nd_nvar,DL(s1),DL(s2));
+  } else {
+    static DL m1,m2;
+    static int nvar = 0;
+    int ret;
+  
+    if ( nvar != nd_nvar ) {
+      nvar = nd_nvar; NEWDL(m1,nvar); NEWDL(m2,nvar);
+    }
+    if ( !nd_sba_modord )
+      ret = (*cmpdl)(nd_nvar,DL2(s1),DL2(s2));
+    else
+      ret = comp_sig_monomial(nd_nvar,DL2(s1),DL2(s2));
+    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);
+#if 0
+  s1 = SG(p1)-TD(DL(p1));
+  s2 = SG(p2)-TD(DL(p2));
+  SG(sp) = MAX(s1,s2) + TD(sp->lcm);
+#endif
+
+  if ( wpd != nd_wpd ) {
+    wpd = nd_wpd;
+    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;
+  _adddl(nd_nvar,DL(sig1),nd_sba_hm[sig1->pos],DL2(sig1));
+
+  // 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;
+  _adddl(nd_nvar,DL(sig2),nd_sba_hm[sig2->pos],DL2(sig2));
+
+  ret = comp_sig(sig1,sig2);
+  if ( ret == 0 ) return 0;
+  else if ( ret > 0 ) sp->sig = sig1;
+  else sp->sig = sig2;
+
+  s1 = DL(sig1)->td+nd_sba_hm[p1->sig->pos]->td;
+  s2 = DL(sig2)->td+nd_sba_hm[p2->sig->pos]->td;
+  SG(sp) = MAX(s1,s2);
+
+  return 1;
+}
+
+SIG dup_sig(SIG sig)
+{
+  SIG r;
+
+  if ( !sig ) return 0;
+  else {
+    NEWSIG(r);
+    _copydl(nd_nvar,DL(sig),DL(r));
+    _copydl(nd_nvar,DL2(sig),DL2(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,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 {
+      Nnewpair--;
+      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=1;
+
+  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
+    Nnewpair++;
+    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 s;
+  int ret,i;
+  ND_pairs r0,_sp,sp;
+  SIG spsig,tsig;
+  static int nvar = 0;
+  static SIG _sig1,_sig2;
+
+  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;
+}
+
+ND_pairs *nd_newpairs_array_s(int t, NODE *syz)
+{
+  NODE s;
+  int ret,i;
+  ND_pairs _sp,sp;
+  ND_pairs *d;
+  SIG spsig,tsig;
+  static int nvar = 0;
+  static SIG _sig1,_sig2;
+
+  NEWND_pairs(_sp);
+  if ( !_sig1 || nvar != nd_nvar ) {
+    nvar = nd_nvar; NEWSIG(_sig1); NEWSIG(_sig2);
+  }
+  d = (ND_pairs *)MALLOC(nd_nbase*sizeof(ND_pairs));
+  Nnewpair = 0;
+  for ( i = 0; i < t; i++ ) {
+    ret = _create_spair_s(i,t,_sp,_sig1,_sig2);
+    if ( ret ) {
+      spsig = _sp->sig;
+      for ( s = syz[spsig->pos]; s; s = s->next ) {
+        tsig = (SIG)s->body;
+        if ( _dl_redble(DL(tsig),DL(spsig),nd_nvar) )
+          break;
+      }
+      if ( s == 0 ) {
+        NEWND_pairs(sp);
+        dup_ND_pairs(sp,_sp);
+        d[spsig->pos] = insert_pair_s(d[spsig->pos],sp);
+      } else
+        Nsyz++;
+    }
+  }
+  return d;
+}
+
 /* ipair = [i1,i2],[i1,i2],... */
 ND_pairs nd_ipairtospair(NODE ipair)
 {
@@ -2647,8 +4203,8 @@ ND_pairs nd_ipairtospair(NODE ipair)
   for ( r0 = 0, t = ipair; t; t = NEXT(t) ) {
     NEXTND_pairs(r0,r);
     tn = BDY((LIST)BDY(t));
-    r->i1 = QTOS((Q)ARG0(tn));
-    r->i2 = QTOS((Q)ARG1(tn));
+    r->i1 = (int)ZTOS((Q)ARG0(tn));
+    r->i2 = (int)ZTOS((Q)ARG1(tn));
     ndl_lcm(DL(nd_psh[r->i1]),DL(nd_psh[r->i2]),r->lcm);
     s1 = SG(nd_psh[r->i1])-TD(DL(nd_psh[r->i1]));
     s2 = SG(nd_psh[r->i2])-TD(DL(nd_psh[r->i2]));
@@ -2667,7 +4223,6 @@ ND_pairs crit_B( ND_pairs d, int s )
 {
   ND_pairs cur,head,prev,remove;
   UINT *t,*tl,*lcm;
-  int td,tdl;
 
   if ( !d ) return 0;
   t = DL(nd_psh[s]);
@@ -2687,7 +4242,7 @@ 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);
         }
@@ -2833,8 +4388,7 @@ NODE update_base(NODE nd,int ndp)
 ND_pairs nd_minp( ND_pairs d, ND_pairs *prest )
 {
     ND_pairs m,ml,p,l;
-    UINT *lcm;
-    int s,td,len,tlen,c,c1;
+    int s;
 
     if ( !(p = NEXT(m = d)) ) {
         *prest = p;
@@ -2914,6 +4468,18 @@ 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;
@@ -2922,15 +4488,13 @@ int nd_tdeg(NDV c)
 
   len = LEN(c);
   for ( a = BDY(c), i = 0; i < len; i++, NMV_ADV(a) )
-    wmax = MAX(TD(DL(a)),wmax);
+    wmax = MAX((int)TD(DL(a)),wmax);
   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;
-    NDV b;
     NODE tn;
     LIST l;
     Z iq;
@@ -2962,6 +4526,7 @@ 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);
@@ -2971,6 +4536,7 @@ 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 ) {
@@ -2987,116 +4553,158 @@ int ndv_newps(int m,NDV a,NDV aq,int f4)
     if ( nd_gentrace ) {
         /* reverse the tracelist and append it to alltracelist */
         nd_tracelist = reverse_node(nd_tracelist); MKLIST(l,nd_tracelist);
-        STOQ(nd_psn,iq); tn = mknode(2,iq,l); MKLIST(l,tn);
+        STOZ(nd_psn,iq); tn = mknode(2,iq,l); MKLIST(l,tn);
         MKNODE(tn,l,nd_alltracelist); nd_alltracelist = tn; nd_tracelist = 0;
     }
     return nd_psn++;
 }
 
+// find LM wrt the specified modord
+void ndv_lm_modord(NDV p,DL d)
+{
+  NMV m;
+  DL tmp;
+  int len,i,ret;
+
+  NEWDL(tmp,nd_nvar);
+  m = BDY(p); len = LEN(p);
+  _ndltodl(DL(m),d); // printdl(d); printf("->");
+  for ( i = 1, NMV_ADV(m); i < len; i++, NMV_ADV(m) ) {
+    _ndltodl(DL(m),tmp);
+    ret = comp_sig_monomial(nd_nvar,tmp,d);
+    if ( ret > 0 ) _copydl(nd_nvar,tmp,d);
+  }
+//   printdl(d); printf("\n");
+}
+
 /* nd_tracelist = [[0,index,div],...,[nd_psn-1,index,div]] */
 /* return 1 if success, 0 if failure (HC(a mod p)) */
 
-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;
-    UINT *d;
-    RHist r;
-    NDVI w;
-    NDV a,am;
-    union oNDC hc;
-    NODE node;
-    P hcp;
-    Z iq,jq;
-    LIST l;
+  int i,j;
+  NODE s,tn;
+  RHist r;
+  NDVI w;
+  NDV a,am;
+  union oNDC hc;
+  NODE node;
+  Z iq,jq;
+  LIST l;
 
-    nd_found = 0; nd_notfirst = 0; nd_create = 0;
-    /* initialize the tracelist */
-    nd_tracelist = 0;
+  nd_found = 0; nd_notfirst = 0; nd_create = 0;
+  /* initialize the tracelist */
+  nd_tracelist = 0;
 
-    for ( nd_psn = 0, s = f; s; s = NEXT(s) ) if ( BDY(s) ) nd_psn++;
-    w = (NDVI)MALLOC(nd_psn*sizeof(struct oNDVI));
-    for ( i = j = 0, s = f; s; s = NEXT(s), j++ ) 
-        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) )
-            qsort(w,nd_psn,sizeof(struct oNDVI),
-                (int (*)(const void *,const void *))ndvi_compare_rev);
-        else
-            qsort(w,nd_psn,sizeof(struct oNDVI),
-                (int (*)(const void *,const void *))ndvi_compare);
-    }
-    nd_pslen = 2*nd_psn;
-    nd_ps = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
-    nd_ps_trace = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
-    nd_ps_sym = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
-    nd_ps_trace_sym = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
-    nd_psh = (RHist *)MALLOC(nd_pslen*sizeof(RHist));
-    nd_bound = (UINT **)MALLOC(nd_pslen*sizeof(UINT *));
-    nd_hcf = 0;
-
-    if ( trace && nd_vc )
-        makesubst(nd_vc,&nd_subst);
+  for ( nd_psn = 0, s = f; s; s = NEXT(s) ) if ( BDY(s) ) nd_psn++;
+  w = (NDVI)MALLOC(nd_psn*sizeof(struct oNDVI));
+  for ( i = j = 0, s = f; s; s = NEXT(s), j++ ) 
+    if ( BDY(s) ) { w[i].p = BDY(s); w[i].i = j; i++; }
+  if ( !dont_sort ) {
+    /* XXX heuristic */
+    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
-        nd_subst = 0;
+      qsort(w,nd_psn,sizeof(struct oNDVI),
+        (int (*)(const void *,const void *))ndvi_compare);
+  }
+  nd_pslen = 2*nd_psn;
+  nd_ps = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
+  nd_ps_trace = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
+  nd_ps_sym = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
+  nd_ps_trace_sym = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
+  nd_psh = (RHist *)MALLOC(nd_pslen*sizeof(RHist));
+  nd_bound = (UINT **)MALLOC(nd_pslen*sizeof(UINT *));
+  nd_hcf = 0;
 
-    if ( !nd_red )
-        nd_red = (RHist *)MALLOC(REDTAB_LEN*sizeof(RHist));
-    for ( i = 0; i < REDTAB_LEN; i++ ) nd_red[i] = 0;
-    for ( i = 0; i < nd_psn; i++ ) {
-        hc = HCU(w[i].p);
-        if ( trace ) {
-            if ( mod == -2 ) {
-              /* over a large finite field */
-              /* trace = small modulus */
-              a = nd_ps_trace[i] = ndv_dup(-2,w[i].p);
-              ndv_mod(-2,a);
-              if ( !dont_removecont) ndv_removecont(-2,a);
-              am = nd_ps[i] = ndv_dup(trace,w[i].p);
-              ndv_mod(trace,am);
-            if ( DL_COMPARE(HDL(am),HDL(a)) ) 
-              return 0;
-              ndv_removecont(trace,am);
-            } else {
-              a = nd_ps_trace[i] = ndv_dup(0,w[i].p);
-              if ( !dont_removecont) ndv_removecont(0,a);
-              register_hcf(a);
-              am = nd_ps[i] = ndv_dup(mod,a);
-              ndv_mod(mod,am);
-            if ( DL_COMPARE(HDL(am),HDL(a)) ) 
-              return 0;
-              ndv_removecont(mod,am);
-            }
-        } else {
-            a = nd_ps[i] = ndv_dup(mod,w[i].p);
-            if ( mod || !dont_removecont ) ndv_removecont(mod,a);
-            if ( !mod ) register_hcf(a);
-        }
-        if ( nd_gentrace ) {
-            STOQ(i,iq); STOQ(w[i].i,jq); node = mknode(3,iq,jq,ONE);
+  if ( trace && nd_vc )
+    makesubst(nd_vc,&nd_subst);
+  else
+    nd_subst = 0;
+
+  if ( !nd_red )
+    nd_red = (RHist *)MALLOC(REDTAB_LEN*sizeof(RHist));
+  for ( i = 0; i < REDTAB_LEN; i++ ) nd_red[i] = 0;
+  for ( i = 0; i < nd_psn; i++ ) {
+    hc = HCU(w[i].p);
+    if ( trace ) {
+      if ( mod == -2 ) {
+        /* over a large finite field */
+        /* trace = small modulus */
+        a = nd_ps_trace[i] = ndv_dup(-2,w[i].p);
+        ndv_mod(-2,a);
+        if ( !dont_removecont) ndv_removecont(-2,a);
+        am = nd_ps[i] = ndv_dup(trace,w[i].p);
+        ndv_mod(trace,am);
+        if ( DL_COMPARE(HDL(am),HDL(a)) ) return 0;
+        ndv_removecont(trace,am);
+      } else {
+        a = nd_ps_trace[i] = ndv_dup(0,w[i].p);
+        if ( !dont_removecont) ndv_removecont(0,a);
+        register_hcf(a);
+        am = nd_ps[i] = ndv_dup(mod,a);
+        ndv_mod(mod,am);
+        if ( DL_COMPARE(HDL(am),HDL(a)) ) return 0;
+        ndv_removecont(mod,am);
+      }
+    } else {
+      a = nd_ps[i] = ndv_dup(mod,w[i].p);
+      if ( mod || !dont_removecont ) ndv_removecont(mod,a);
+      if ( !mod ) register_hcf(a);
+    }
+    if ( nd_gentrace ) {
+      STOZ(i,iq); STOZ(w[i].i,jq); node = mknode(3,iq,jq,ONE);
+      /* exact division */
       if ( !dont_removecont )
-                ARG2(node) = (pointer)ndc_div(trace?0:mod,hc,HCU(a));
-            MKLIST(l,node); NEXTNODE(nd_tracelist,tn); BDY(tn) = l;
-        }
-        NEWRHist(r); SG(r) = HTD(a); ndl_copy(HDL(a),DL(r));
-        nd_bound[i] = ndv_compute_bound(a);
-        nd_psh[i] = r;
-        if ( nd_demand ) {
-            if ( trace ) {
-                ndv_save(nd_ps_trace[i],i);
-                nd_ps_sym[i] = ndv_symbolic(mod,nd_ps_trace[i]);
-                nd_ps_trace_sym[i] = ndv_symbolic(mod,nd_ps_trace[i]);
-                nd_ps_trace[i] = 0;
-            } else {
-                ndv_save(nd_ps[i],i);
-                nd_ps_sym[i] = ndv_symbolic(mod,nd_ps[i]);
-                nd_ps[i] = 0;
-            }
-        }
+        ARG2(node) = (pointer)ndc_div(trace?0:mod,hc,HCU(a));
+      MKLIST(l,node); NEXTNODE(nd_tracelist,tn); BDY(tn) = l;
     }
-    if ( nd_gentrace && nd_tracelist ) NEXT(tn) = 0;
-    return 1;
+    NEWRHist(r); SG(r) = HTD(a); ndl_copy(HDL(a),DL(r));
+    nd_bound[i] = ndv_compute_bound(a);
+    nd_psh[i] = r;
+    if ( nd_demand ) {
+      if ( trace ) {
+        ndv_save(nd_ps_trace[i],i);
+        nd_ps_sym[i] = ndv_symbolic(mod,nd_ps_trace[i]);
+        nd_ps_trace_sym[i] = ndv_symbolic(mod,nd_ps_trace[i]);
+        nd_ps_trace[i] = 0;
+      } else {
+        ndv_save(nd_ps[i],i);
+        nd_ps_sym[i] = ndv_symbolic(mod,nd_ps[i]);
+        nd_ps[i] = 0;
+      }
+    }
+  }
+  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);
+      if ( nd_sba_modord )
+        ndv_lm_modord(nd_ps[i],nd_sba_hm[i]);
+      else
+        _ndltodl(DL(nd_psh[i]),nd_sba_hm[i]);
+      _adddl(nd_nvar,DL(sig),nd_sba_hm[i],DL2(sig));
+    }
+    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;
 }
 
 struct order_spec *append_block(struct order_spec *spec,
@@ -3108,7 +4716,7 @@ static VECT prev_weight_vector_obj;
 void preprocess_algcoef(VL vv,VL av,struct order_spec *ord,LIST f,
     struct order_spec **ord1p,LIST *f1p,NODE *alistp)
 {
-    NODE alist,t,s,r0,r,arg;
+    NODE alist,t,s,arg;
     VL tv;
     P poly;
     DP d;
@@ -3117,8 +4725,7 @@ void preprocess_algcoef(VL vv,VL av,struct order_spec 
     MP m;
     int i,nvar,nalg,n;
     NumberField nf;
-    LIST f1,f2;
-    struct order_spec *current_spec;
+    LIST f1;
     VECT obj,obj0;
     VECT tmp;
 
@@ -3207,184 +4814,217 @@ NODE postprocess_algcoef(VL av,NODE alist,NODE r)
 
 void nd_gr(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,alist;
-    int e,max,nvar,i;
-    NDV b;
-    int ishomo,nalg,mrank,trank,wmax,len;
+  VL tv,fv,vv,av;
+  NODE fd,fd0,r0,t,x,s,xx,alist,r;
+  int e,max,nvar,i;
+  NDV b;
+  int ishomo,nalg,mrank,trank,wmax,len;
   NMV a;
-    Alg alpha,dp;
-    P p,zp;
-    Q dmy;
-    LIST f1,f2,zpl;
-    Obj obj;
-    NumberField nf;
-    struct order_spec *ord1;
-    NODE tr,tl1,tl2,tl3,tl4,nzlist;
-    LIST l1,l2,l3,l4,l5;
+  P zp;
+  Q dmy;
+  LIST f1,zpl;
+  struct order_spec *ord1;
+  NODE tr,tl1,tl2,tl3,tl4,nzlist;
+  LIST l1,l2,l3,l4,l5;
   int j;
   Z jq,bpe,last_nonzero;
-    int *perm;
-    EPOS oepos;
-    int obpe,oadv,ompos,cbpe;
+  int *perm;
+  EPOS oepos;
+  int obpe,oadv,ompos,cbpe;
+  VECT hvect;
 
-    nd_module = 0;
-    if ( !m && Demand ) nd_demand = 1;
-    else nd_demand = 0;
-    parse_nd_option(current_option);
+  NcriB = NcriMF = Ncri2 = 0;
+  nd_module = 0;
+  if ( !m && Demand ) nd_demand = 1;
+  else nd_demand = 0;
 
-    if ( DP_Multiple )
-        nd_scale = ((double)DP_Multiple)/(double)(Denominator?Denominator:1);
+  if ( DP_Multiple )
+    nd_scale = ((double)DP_Multiple)/(double)(Denominator?Denominator:1);
 #if 0
-    ndv_alloc = 0;
+  ndv_alloc = 0;
 #endif
-    get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
-    if ( m && nd_vc )
-       error("nd_{gr,f4} : computation over Fp(X) is unsupported. Use dp_gr_mod_main().");
-    for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
-    switch ( ord->id ) {
-        case 1:
-            if ( ord->nv != nvar )
-                error("nd_{gr,f4} : invalid order specification");
-            break;
-        default:
-            break;
+  get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+  parse_nd_option(vv,current_option);
+  if ( m && nd_vc )
+    error("nd_{gr,f4} : computation over Fp(X) is unsupported. Use dp_gr_mod_main().");
+  for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
+  switch ( ord->id ) {
+    case 1:
+      if ( ord->nv != nvar )
+        error("nd_{gr,f4} : invalid order specification");
+      break;
+    default:
+      break;
+  }
+  nd_nalg = 0;
+  av = 0;
+  if ( !m ) {
+    get_algtree((Obj)f,&av);
+    for ( nalg = 0, tv = av; tv; tv = NEXT(tv), nalg++ );
+    nd_ntrans = nvar;
+    nd_nalg = nalg;
+    /* #i -> t#i */
+    if ( nalg ) {
+      preprocess_algcoef(vv,av,ord,f,&ord1,&f1,&alist);
+      ord = ord1;
+      f = f1;
     }
-    nd_nalg = 0;
-    av = 0;
-    if ( !m ) {
-        get_algtree((Obj)f,&av);
-        for ( nalg = 0, tv = av; tv; tv = NEXT(tv), nalg++ );
-        nd_ntrans = nvar;
-        nd_nalg = nalg;
-        /* #i -> t#i */
-        if ( nalg ) {
-            preprocess_algcoef(vv,av,ord,f,&ord1,&f1,&alist);
-            ord = ord1;
-            f = f1;
+    nvar += nalg;
+  }
+  nd_init_ord(ord);
+  mrank = 0;
+  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);
+          for ( ; s; s = NEXT(s) ) {
+            e = getdeg(tv->v,(P)BDY(s));
+            max = MAX(e,max);
+          }
         }
-        nvar += nalg;
-    }
-    nd_init_ord(ord);
-    mrank = 0;
-    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);
-                }
-            } else {
-                e = getdeg(tv->v,(P)BDY(t));
-                max = MAX(e,max);
-            }
+      } else {
+        if ( OID(BDY(t)) == O_DP ) {
+          e = dp_getdeg((DP)BDY(t));
+          max = MAX(e,max);
+        } else {
+          e = getdeg(tv->v,(P)BDY(t));
+          max = MAX(e,max);
         }
-    nd_setup_parameters(nvar,nd_nzlist?0: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 ( nd_module ) {
+      }
+    }
+  nd_setup_parameters(nvar,nd_nzlist?0: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 ( nd_module ) {
+      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);
+        b = (pointer)pltondv(CO,vv,zpl);
+      }
+    } else {
+      if ( OID(BDY(t)) == O_DP ) {
+        DP zdp;
+
+        if ( !m && !nd_gentrace ) dp_ptozp((DP)BDY(t),&zdp);
+        else zdp = (DP)BDY(t);
+        b = (pointer)dptondv(m,zdp);
       } else {
         if ( !m && !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp);
         else zp = (P)BDY(t);
         b = (pointer)ptondv(CO,vv,zp);
       }
-      if ( ishomo )
-        ishomo = ishomo && ndv_ishomo(b);
-      if ( m ) ndv_mod(m,b);
-      if ( b ) { NEXTNODE(fd0,fd); BDY(fd) = (pointer)b; }
     }
-    if ( fd0 ) NEXT(fd) = 0;
+    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);
+                wmax = MAX((int)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_gbblock||nd_splist||nd_check_splist)?1:0,0);
-    if ( nd_gentrace ) {
-        MKLIST(l1,nd_tracelist); MKNODE(nd_alltracelist,l1,0);
-    }
+  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);
+  }
   if ( nd_splist ) {
     *rp = compute_splist();
     return;
   }
   if ( nd_check_splist ) {
-        if ( f4 ) {
-            if ( check_splist_f4(m,nd_check_splist) ) *rp = (LIST)ONE;
-            else *rp = 0;
-        } else {
-            if ( check_splist(m,nd_check_splist) ) *rp = (LIST)ONE;
-            else *rp = 0;
-        }
+    if ( f4 ) {
+      if ( check_splist_f4(m,nd_check_splist) ) *rp = (LIST)ONE;
+      else *rp = 0;
+    } else {
+      if ( check_splist(m,nd_check_splist) ) *rp = (LIST)ONE;
+      else *rp = 0;
+    }
     return;
   }
-    x = f4?nd_f4(m,0,&perm):nd_gb(m,ishomo || homo,0,0,&perm);
+  x = f4?nd_f4(m,0,&perm):nd_gb(m,ishomo || homo,0,0,&perm);
   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);
     nd_init_ord(ord);
     nd_setup_parameters(nvar,0);
   }
-    nd_demand = 0;
+  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])) > (UINT)nd_intersect ) { 
         MKNODE(xx,(pointer)((unsigned long)j),x); x = xx; 
       }
     conv_ilist(nd_demand,0,x,0);
     goto FINAL;
   }
-    if ( nd_gentrace  && f4 ) { nzlist = nd_alltracelist; }
-    x = ndv_reducebase(x,perm);
-    if ( nd_gentrace  && !f4 ) { tl1 = nd_alltracelist; nd_alltracelist = 0; }
-    x = ndv_reduceall(m,x);
-    cbpe = nd_bpe;
-    if ( nd_gentrace && !f4 ) { 
-        tl2 = nd_alltracelist; nd_alltracelist = 0;
-        ndv_check_membership(m,fd0,obpe,oadv,oepos,x);
-        tl3 = nd_alltracelist; nd_alltracelist = 0; 
-        if ( nd_gensyz ) { 
-          nd_gb(m,0,1,1,0);
-            tl4 = nd_alltracelist; nd_alltracelist = 0; 
-        } else tl4 = 0;
-    }
-    nd_bpe = cbpe;
-    nd_setup_parameters(nd_nvar,0);
+  if ( nd_gentrace  && f4 ) { nzlist = nd_alltracelist; }
+  x = ndv_reducebase(x,perm);
+  if ( nd_gentrace  && !f4 ) { tl1 = nd_alltracelist; nd_alltracelist = 0; }
+  x = ndv_reduceall(m,x);
+  cbpe = nd_bpe;
+  if ( nd_gentrace && !f4 ) { 
+    tl2 = nd_alltracelist; nd_alltracelist = 0;
+    ndv_check_membership(m,fd0,obpe,oadv,oepos,x);
+    tl3 = nd_alltracelist; nd_alltracelist = 0; 
+    if ( nd_gensyz ) { 
+      nd_gb(m,0,1,1,0);
+      tl4 = nd_alltracelist; nd_alltracelist = 0; 
+    } else tl4 = 0;
+  }
+  nd_bpe = cbpe;
+  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));
+  for ( r0 = 0, t = x; t; t = NEXT(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 )
+  }
+  if ( r0 ) NEXT(r) = 0;
+  if ( !m && nd_nalg )
         r0 = postprocess_algcoef(av,alist,r0);
-    MKLIST(*rp,r0);
-    if ( nd_gentrace ) {
+  MKLIST(*rp,r0);
+  if ( nd_gentrace ) {
   if ( f4 ) {
-            STOQ(16,bpe);
-            STOQ(nd_last_nonzero,last_nonzero);
-            tr = mknode(5,*rp,(!ishomo&&homo)?ONE:0,BDY(nzlist),bpe,last_nonzero); MKLIST(*rp,tr);
-            
+            STOZ(16,bpe);
+            STOZ(nd_last_nonzero,last_nonzero);
+            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);
@@ -3392,19 +5032,19 @@ FINAL:
             for ( t = tl2; t; t = NEXT(t) ) {
             /* s = [i,[*,j,*,*],...] */
                 s = BDY((LIST)BDY(t));
-                j = perm[QTOS((Q)ARG0(s))]; STOQ(j,jq); ARG0(s) = (pointer)jq;
+                j = perm[ZTOS((Q)ARG0(s))]; STOZ(j,jq); ARG0(s) = (pointer)jq;
                 for ( s = BDY((LIST)ARG1(s)); s; s = NEXT(s) ) {
-                    j = perm[QTOS((Q)ARG1(BDY((LIST)BDY(s))))]; STOQ(j,jq); 
+                    j = perm[ZTOS((Q)ARG1(BDY((LIST)BDY(s))))]; STOZ(j,jq); 
                     ARG1(BDY((LIST)BDY(s))) = (pointer)jq;
                 }
             }
             for ( j = length(x)-1, t = 0; j >= 0; j-- ) {
-                STOQ(perm[j],jq); MKNODE(s,jq,t); t = s;
+                STOZ(perm[j],jq); MKNODE(s,jq,t); t = s;
             }
             MKLIST(l1,tl1); MKLIST(l2,tl2); MKLIST(l3,t); MKLIST(l4,tl3);
             MKLIST(l5,tl4);
-            STOQ(nd_bpe,bpe);
-            tr = mknode(8,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe); MKLIST(*rp,tr);
+            STOZ(nd_bpe,bpe);
+            tr = mknode(9,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe,hvect); MKLIST(*rp,tr);
         }
     }
 #if 0
@@ -3412,24 +5052,165 @@ 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;
+  NODE fd,fd0,r,r0,t,x,nd,nd1,syz;
+  int e,max,nvar,i;
+  NDV b;
+  int ishomo,wmax,len;
+  NMV a;
+  P zp;
+  Q dmy;
+  struct order_spec *ord1;
+  int *perm;
+  EPOS oepos;
+  int obpe,oadv,ompos;
+  struct oEGT eg0,eg1,egconv,egintred;
+  LIST l1,redind;
+  Z z;
+
+  nd_module = 0;
+  nd_demand = 0;
+  Nsamesig = 0;
+  if ( DP_Multiple )
+    nd_scale = ((double)DP_Multiple)/(double)(Denominator?Denominator:1);
+  get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+  parse_nd_option(vv,current_option);
+  if ( m && nd_vc )
+    error("nd_sba : computation over Fp(X) is unsupported. Use dp_gr_mod_main().");
+  for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
+  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) ) {
+      if ( OID(BDY(t)) == O_DP ) {
+        e = dp_getdeg((DP)BDY(t));
+        max = MAX(e,max);
+      } else {
+        e = getdeg(tv->v,(P)BDY(t));
+        max = MAX(e,max);
+      }
+    }
+  }
+  nd_setup_parameters(nvar,max);
+  obpe = nd_bpe; oadv = nmv_adv; oepos = nd_epos; ompos = nd_mpos;
+  ishomo = 1;
+  for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
+    if ( OID(BDY(t)) == O_DP ) {
+      DP zdp;
+
+      if ( !m ) dp_ptozp((DP)BDY(t),&zdp);
+      else zdp = (DP)BDY(t);
+      b = (pointer)dptondv(m,zdp);
+    } else {
+      if ( !m ) ptozp((P)BDY(t),1,&dmy,&zp);
+      else zp = (P)BDY(t);
+      b = (pointer)ptondv(CO,vv,zp);
+    }
+    if ( ishomo )
+      ishomo = ishomo && ndv_ishomo(b);
+    if ( m ) ndv_mod(m,b);
+    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((int)TD(DL(a)),wmax);
+      }
+      homogenize_order(ord,nvar,&ord1);
+      nd_init_ord(ord1);
+      // for SIG comparison
+      initd(ord1);
+      nd_setup_parameters(nvar+1,nd_nzlist?0:wmax);
+      for ( t = fd0; t; t = NEXT(t) )
+        ndv_homogenize((NDV)BDY(t),obpe,oadv,oepos,ompos);
+  }
+
+  ndv_setup(m,0,fd0,nd_sba_dontsort,0,1);
+  if ( nd_gentrace ) {
+    MKLIST(l1,nd_tracelist); MKNODE(nd_alltracelist,l1,0);
+  }
+  x = f4 ? nd_sba_f4(m,&perm) : nd_sba_buch(m,ishomo || homo,&perm,&syz);
+  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);
+    // for SIG comparison
+    initd(ord);
+    nd_setup_parameters(nvar,0);
+  }
+  nd_demand = 0;
+  get_eg(&eg0);
+  x = ndv_reducebase(x,perm);
+  for ( nd = 0, i = length(x)-1; i >= 0; i-- ) {
+    STOZ(perm[i],z); MKNODE(nd1,z,nd); nd = nd1;
+  }
+  MKLIST(redind,nd);
+  x = ndv_reduceall(m,x);
+  get_eg(&eg1); init_eg(&egintred); add_eg(&egintred,&eg0,&eg1);
+  nd_setup_parameters(nd_nvar,0);
+  get_eg(&eg0);
+  for ( r0 = 0, t = x; t; t = NEXT(t) ) {
+    NEXTNODE(r0,r); 
+    if ( retdp ) BDY(r) = ndvtodp(m,BDY(t));
+    else BDY(r) = ndvtop(m,CO,vv,BDY(t));
+  }
+  if ( r0 ) NEXT(r) = 0;
+  if ( nd_sba_syz ) {
+    LIST gb,hsyz;
+
+    MKLIST(gb,r0);
+    MKLIST(hsyz,syz);
+    nd = mknode(2,gb,hsyz);
+    MKLIST(*rp,nd);
+  } else if ( nd_gentrace ) {
+    LIST gb,trace;
+
+    MKLIST(trace,nd_alltracelist);
+    MKLIST(gb,r0);
+    nd = mknode(3,gb,redind,trace);
+    MKLIST(*rp,nd);
+  } else
+    MKLIST(*rp,r0);
+  get_eg(&eg1); init_eg(&egconv); add_eg(&egconv,&eg0,&eg1);
+  print_eg("intred",&egintred); fprintf(asir_out,"\n");
+  print_eg("conv",&egconv); fprintf(asir_out,"\n");
+}
+
 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;
-    NODE fd,fd0,r,r0,t,x,s,xx,alist;
-    int e,max,nvar,i;
+    VL tv,fv,vv,av;
+    NODE fd,fd0,r,r0,t,x,alist;
+    int e,max,nvar,i,nalg;
     NDV b;
-    int ishomo,nalg;
-    Alg alpha,dp;
-    P p,zp;
+    int ishomo;
+    P zp;
     Q dmy;
-    LIST f1,f2;
-    Obj obj;
-    NumberField nf;
+    LIST f1;
     struct order_spec *ord1;
     int *perm;
 
-    parse_nd_option(current_option);
     get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+    parse_nd_option(vv,current_option);
     for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
     switch ( ord->id ) {
         case 1:
@@ -3471,7 +5252,7 @@ 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 ) {
@@ -3512,16 +5293,14 @@ NDV recompute_trace(NODE ti,NDV *p,int mod)
   NODE sj;
   NDV red;
   Obj mj;
-  static int afo=0;
 
-  afo++;
   mul = (NM)MALLOC(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT));
   CM(mul) = 1;
   tail = 0;
   for ( i = 0, d = r = 0; ti; ti = NEXT(ti), i++ ) {
     sj = BDY((LIST)BDY(ti));
     if ( ARG0(sj) ) {
-      red = p[QTOS((Q)ARG1(sj))];
+      red = p[ZTOS((Q)ARG1(sj))];
       mj = (Obj)ARG2(sj);
       if ( OID(mj) != O_DP ) ndl_zero(DL(mul));
       else dltondl(nd_nvar,BDY((DP)mj)->dl,DL(mul));
@@ -3562,46 +5341,40 @@ NDV recompute_trace(NODE ti,NDV *p,int mod)
 
 void nd_gr_recompute_trace(LIST f,LIST v,int m,struct order_spec *ord,LIST tlist,LIST *rp)
 {
-    VL tv,fv,vv,vc,av;
-    NODE fd,fd0,r,r0,t,x,s,xx,alist;
-    int e,max,nvar,i;
-    NDV b;
-    int ishomo,nalg;
-    Alg alpha,dp;
-    P p,zp;
-    Q dmy;
-    LIST f1,f2;
-    Obj obj;
-    NumberField nf;
-    struct order_spec *ord1;
+  VL tv,fv,vv;
+  NODE r,r0,t;
+  int nvar,i;
+  NDV b;
+  P zp;
+  Q dmy;
   NODE permtrace,intred,ind,perm,trace,ti;
   int len,n,j;
   NDV *db,*pb;
 
-    parse_nd_option(current_option);
-    get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
-    for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
-    switch ( ord->id ) {
-        case 1:
-            if ( ord->nv != nvar )
-                error("nd_check : invalid order specification");
-            break;
-        default:
-            break;
-    }
-    nd_init_ord(ord);
-  nd_bpe = QTOS((Q)ARG7(BDY(tlist)));
-    nd_setup_parameters(nvar,0);
+  get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+  parse_nd_option(vv,current_option);
+  for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
+  switch ( ord->id ) {
+    case 1:
+      if ( ord->nv != nvar )
+        error("nd_check : invalid order specification");
+      break;
+    default:
+      break;
+  }
+  nd_init_ord(ord);
+  nd_bpe = (int)ZTOS((Q)ARG7(BDY(tlist)));
+  nd_setup_parameters(nvar,0);
 
   len = length(BDY(f));
   db = (NDV *)MALLOC(len*sizeof(NDV *));
   for ( i = 0, t = BDY(f); t; i++, t = NEXT(t) ) {
-      ptozp((P)BDY(t),1,&dmy,&zp);
-      b = ptondv(CO,vv,zp);
-        ndv_mod(m,b);
+    ptozp((P)BDY(t),1,&dmy,&zp);
+    b = ptondv(CO,vv,zp);
+    ndv_mod(m,b);
     ndv_mul_c(m,b,invm(HCM(b),m));
     db[i] = b;
-    }
+  }
 
   permtrace = BDY((LIST)ARG2(BDY(tlist))); 
   intred = BDY((LIST)ARG3(BDY(tlist))); 
@@ -3610,73 +5383,72 @@ void nd_gr_recompute_trace(LIST f,LIST v,int m,struct 
   trace = NEXT(permtrace);
 
   for ( i = length(perm)-1, t = trace; t; t = NEXT(t) ) {
-    j = QTOS((Q)ARG0(BDY((LIST)BDY(t))));
+    j = (int)ZTOS((Q)ARG0(BDY((LIST)BDY(t))));
     if ( j > i ) i = j;
   }
   n = i+1;
   pb = (NDV *)MALLOC(n*sizeof(NDV *));
   for ( t = perm, i = 0; t; t = NEXT(t), i++ ) {
     ti = BDY((LIST)BDY(t));
-    pb[QTOS((Q)ARG0(ti))] = db[QTOS((Q)ARG1(ti))];
+    pb[ZTOS((Q)ARG0(ti))] = db[ZTOS((Q)ARG1(ti))];
   }
   for ( t = trace; t; t = NEXT(t) ) {
     ti = BDY((LIST)BDY(t));
-    pb[QTOS((Q)ARG0(ti))] = recompute_trace(BDY((LIST)ARG1(ti)),pb,m);
-    if ( !pb[QTOS((Q)ARG0(ti))] ) { *rp = 0; return; }
+    pb[ZTOS((Q)ARG0(ti))] = recompute_trace(BDY((LIST)ARG1(ti)),pb,m);
+    if ( !pb[ZTOS((Q)ARG0(ti))] ) { *rp = 0; return; }
       if ( DP_Print ) { 
            fprintf(asir_out,"."); fflush(asir_out);
       }
   }
   for ( t = intred; t; t = NEXT(t) ) {
     ti = BDY((LIST)BDY(t));
-    pb[QTOS((Q)ARG0(ti))] = recompute_trace(BDY((LIST)ARG1(ti)),pb,m);
-    if ( !pb[QTOS((Q)ARG0(ti))] ) { *rp = 0; return; }
+    pb[ZTOS((Q)ARG0(ti))] = recompute_trace(BDY((LIST)ARG1(ti)),pb,m);
+    if ( !pb[ZTOS((Q)ARG0(ti))] ) { *rp = 0; return; }
       if ( DP_Print ) { 
-           fprintf(asir_out,"*"); fflush(asir_out);
-      }
+        fprintf(asir_out,"*"); fflush(asir_out);
+    }
   }
-    for ( r0 = 0, t = ind; t; t = NEXT(t) ) {
-        NEXTNODE(r0,r); 
-    b = pb[QTOS((Q)BDY(t))];
-        ndv_mul_c(m,b,invm(HCM(b),m));
+  for ( r0 = 0, t = ind; t; t = NEXT(t) ) {
+    NEXTNODE(r0,r); 
+    b = pb[ZTOS((Q)BDY(t))];
+    ndv_mul_c(m,b,invm(HCM(b),m));
 #if 0
-        BDY(r) = ndvtop(m,CO,vv,pb[QTOS((Q)BDY(t))]);
+    BDY(r) = ndvtop(m,CO,vv,pb[ZTOS((Q)BDY(t))]);
 #else
-        BDY(r) = ndvtodp(m,pb[QTOS((Q)BDY(t))]);
+    BDY(r) = ndvtodp(m,pb[ZTOS((Q)BDY(t))]);
 #endif
-    }
-    if ( r0 ) NEXT(r) = 0;
-    MKLIST(*rp,r0);
-    if ( DP_Print ) fprintf(asir_out,"\n");
+  }
+  if ( r0 ) NEXT(r) = 0;
+  MKLIST(*rp,r0);
+  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;
+    VL tv,fv,vv,av;
+    NODE fd,fd0,in0,in,r,t,s,cand,alist;
     int m,nocheck,nvar,mindex,e,max;
     NDV c;
     NMV a;
-    P p,zp;
+    P zp;
     Q dmy;
     EPOS oepos;
     int obpe,oadv,wmax,i,len,cbpe,ishomo,nalg,mrank,trank,ompos;
-    Alg alpha,dp;
-    P poly;
-    LIST f1,f2,zpl;
-    Obj obj;
-    NumberField nf;
+    LIST f1,zpl;
     struct order_spec *ord1;
-    struct oEGT eg_check,eg0,eg1;
+    struct oEGT eg_check,eg_gb,eg_intred,eg0,eg1;
     NODE tr,tl1,tl2,tl3,tl4;
     LIST l1,l2,l3,l4,l5;
     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);
+    get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+    parse_nd_option(vv,current_option);
     if ( nd_lf ) {
       if ( f4 )
         nd_f4_lf_trace(f,v,trace,homo,ord,rp);
@@ -3687,7 +5459,6 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     if ( DP_Multiple )
         nd_scale = ((double)DP_Multiple)/(double)(Denominator?Denominator:1);
 
-    get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
     for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
     switch ( ord->id ) {
         case 1:
@@ -3727,6 +5498,11 @@ 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);
@@ -3734,9 +5510,15 @@ 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 {
+              if ( OID(BDY(t)) == O_DP ) {
+                e = dp_getdeg((DP)BDY(t));
+                max = MAX(e,max);
+              } else {
                 e = getdeg(tv->v,(P)BDY(t));
                 max = MAX(e,max);
+              }
             }
         }
     nd_setup_parameters(nvar,max);
@@ -3744,13 +5526,30 @@ 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);
+          if ( OID(BDY(t)) == O_DP ) {
+            DP zdp;
+
+            if ( !nd_gentrace ) dp_ptozp((DP)BDY(t),&zdp);
+            else zdp = (DP)BDY(t);
+            c = (pointer)dptondv(m,zdp);
+          } else {
+            if ( !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp);
+            else zp = (P)BDY(t);
             c = (pointer)ptondv(CO,vv,zp);
+          }
         }
         if ( ishomo )
             ishomo = ishomo && ndv_ishomo(c);
@@ -3765,7 +5564,7 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
         for ( t = in0, wmax = max; t; t = NEXT(t) ) {
             c = (NDV)BDY(t); len = LEN(c);
             for ( a = BDY(c), i = 0; i < len; i++, NMV_ADV(a) )
-                wmax = MAX(TD(DL(a)),wmax);
+                wmax = MAX((int)TD(DL(a)),wmax);
         }
         homogenize_order(ord,nvar,&ord1);
         nd_init_ord(ord1);
@@ -3775,10 +5574,11 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     }
     if ( MaxDeg > 0 ) nocheck = 1;
     while ( 1 ) {
-    tl1 = tl2 = tl3 = tl4 = 0;
+        get_eg(&eg0);
+        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);
         }
@@ -3790,16 +5590,24 @@ 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);
             nd_init_ord(ord);
             nd_setup_parameters(nvar,0);
         }
+        get_eg(&eg1); init_eg(&eg_gb); add_eg(&eg_gb,&eg0,&eg1);
         nd_demand = 0;
         cand = ndv_reducebase(cand,perm);
         if ( nd_gentrace ) { tl1 = nd_alltracelist; nd_alltracelist = 0; }
+        get_eg(&eg0);
         cand = ndv_reduceall(0,cand);
+        get_eg(&eg1); init_eg(&eg_intred); add_eg(&eg_intred,&eg0,&eg1);
         cbpe = nd_bpe;
         if ( nd_gentrace ) { tl2 = nd_alltracelist; nd_alltracelist = 0; }
         get_eg(&eg0);
@@ -3810,7 +5618,7 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
           tl3 = nd_alltracelist; nd_alltracelist = 0; 
         } else tl3 = 0;
             /* gbcheck : cand is a GB of Id(cand) ? */
-            if ( nd_vc || nd_gentrace || nd_gensyz )
+            if ( nd_vc || nd_gentrace || nd_gensyz || do_weyl )
               ret = nd_gb(0,0,1,nd_gensyz?1:0,0)!=0;
             else
               ret = nd_f4(0,1,0)!=0;
@@ -3837,13 +5645,17 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     }
     get_eg(&eg1); init_eg(&eg_check); add_eg(&eg_check,&eg0,&eg1);
     if ( DP_Print )
-        fprintf(asir_out,"check=%.3fsec,",eg_check.exectime);
+        fprintf(asir_out,"gb=%.3fsec,check=%.3fsec,intred=%.3fsec\n",
+          eg_gb.exectime,eg_check.exectime,eg_intred.exectime);
     /* dp->p */
     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);
@@ -3855,19 +5667,19 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
         for ( t = tl2; t; t = NEXT(t) ) {
       /* s = [i,[*,j,*,*],...] */
             s = BDY((LIST)BDY(t));
-            j = perm[QTOS((Q)ARG0(s))]; STOQ(j,jq); ARG0(s) = (pointer)jq;
+            j = perm[ZTOS((Q)ARG0(s))]; STOZ(j,jq); ARG0(s) = (pointer)jq;
       for ( s = BDY((LIST)ARG1(s)); s; s = NEXT(s) ) {
-                j = perm[QTOS((Q)ARG1(BDY((LIST)BDY(s))))]; STOQ(j,jq); 
+                j = perm[ZTOS((Q)ARG1(BDY((LIST)BDY(s))))]; STOZ(j,jq); 
         ARG1(BDY((LIST)BDY(s))) = (pointer)jq;
             }
     }
     for ( j = length(cand)-1, t = 0; j >= 0; j-- ) {
-        STOQ(perm[j],jq); MKNODE(s,jq,t); t = s;
+        STOZ(perm[j],jq); MKNODE(s,jq,t); t = s;
     }
         MKLIST(l1,tl1); MKLIST(l2,tl2); MKLIST(l3,t); MKLIST(l4,tl3);
     MKLIST(l5,tl4);
-      STOQ(nd_bpe,bpe);
-        tr = mknode(8,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe); MKLIST(*rp,tr);
+      STOZ(nd_bpe,bpe);
+        tr = mknode(9,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe,hvect); MKLIST(*rp,tr);
     }
 }
 
@@ -3903,7 +5715,7 @@ 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 ) {
@@ -3919,6 +5731,27 @@ 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;
@@ -3931,6 +5764,18 @@ 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;
@@ -3964,7 +5809,7 @@ 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");
@@ -3980,7 +5825,7 @@ void nd_print_q(ND p)
     else {
         for ( m = BDY(p); m; m = NEXT(m) ) {
             printf("+");
-            printexpr(CO,(Obj)CQ(m));
+            printexpr(CO,(Obj)CZ(m));
             printf("*");
             ndl_print(DL(m));
         }
@@ -4014,9 +5859,9 @@ void nd_removecont(int mod,ND p)
         w = (Z *)MALLOC(n*sizeof(Q));
         v.len = n;
         v.body = (pointer *)w;
-        for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) w[i] = CQ(m);
+        for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) w[i] = CZ(m);
         removecont_array((P *)w,n,1);
-        for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) CQ(m) = w[i];    
+        for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) CZ(m) = w[i];    
     }
 }
 
@@ -4035,15 +5880,15 @@ void nd_removecont2(ND p1,ND p2)
     v.body = (pointer *)w;
     i = 0;
     if ( p1 )
-        for ( m = BDY(p1); i < n1; m = NEXT(m), i++ ) w[i] = CQ(m);
+        for ( m = BDY(p1); i < n1; m = NEXT(m), i++ ) w[i] = CZ(m);
     if ( p2 )
-        for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) w[i] = CQ(m);
+        for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) w[i] = CZ(m);
     removecont_array((P *)w,n,1);
     i = 0;
     if ( p1 )
-        for ( m = BDY(p1); i < n1; m = NEXT(m), i++ ) CQ(m) = w[i];    
+        for ( m = BDY(p1); i < n1; m = NEXT(m), i++ ) CZ(m) = w[i];    
     if ( p2 )
-        for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) CQ(m) = w[i];    
+        for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) CZ(m) = w[i];    
 }
 
 void ndv_removecont(int mod,NDV p)
@@ -4051,7 +5896,7 @@ void ndv_removecont(int mod,NDV p)
     int i,len,all_p;
     Z *c;
     P *w;
-    Z dvr,t;
+    Z dvr;
     P g,cont,tp;
     NMV m;
 
@@ -4095,15 +5940,15 @@ 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++ )
-        max = MAX(max,TD(DL(m)));
+    for ( m = BDY(p), i = 0, max = 0; i < len; NMV_OADV(m), i++ )
+        max = MAX(max,(int)TD(DL(m)));
     mr0 = nmv_adv>oadv?(NMV)REALLOC(BDY(p),len*nmv_adv):BDY(p);
     m = (NMV)((char *)mr0+(len-1)*oadv);
     mr = (NMV)((char *)mr0+(len-1)*nmv_adv);
     t = (NMV)MALLOC(nmv_adv);
     for ( i = 0; i < len; i++, NMV_OPREV(m), NMV_PREV(mr) ) {
         ndl_homogenize(DL(m),DL(t),obpe,oepos,ompos,max);
-        CQ(mr) = CQ(m);
+        CZ(mr) = CZ(m);
         ndl_copy(DL(t),DL(mr));
     }
     NV(p)++;
@@ -4114,8 +5959,6 @@ void ndv_dehomogenize(NDV p,struct order_spec *ord)
 {
     int i,j,adj,len,newnvar,newwpd,newadv,newexporigin,newmpos;
     int pos;
-    Q *w;
-    Q dvr,t;
     NMV m,r;
 
     len = p->len;
@@ -4128,7 +5971,7 @@ void ndv_dehomogenize(NDV p,struct order_spec *ord)
     if ( newwpd != nd_wpd ) {
         newadv = ROUND_FOR_ALIGN(sizeof(struct oNMV)+(newwpd-1)*sizeof(UINT));
         for ( m = r = BDY(p), i = 0; i < len; NMV_ADV(m), NDV_NADV(r), i++ ) {
-            CQ(r) = CQ(m);
+            CZ(r) = CZ(m);
             if ( nd_module ) pos = MPOS(DL(m));
             for ( j = 0; j < newexporigin; j++ ) DL(r)[j] = DL(m)[j];
             adj = nd_exporigin-newexporigin;
@@ -4175,7 +6018,7 @@ void nd_heu_nezgcdnpz(VL vl,P *pl,int m,int full,P *pr
 
 void removecont_array(P *p,int n,int full)
 {
-    int all_p,all_q,i;
+    int all_q,i;
     Z *c;
     P *w;
     P t,s;
@@ -4204,7 +6047,7 @@ void removecont_array_q(Z *c,int n)
 {
   struct oVECT v;
   Z d0,d1,a,u,u1,gcd;
-  int i,j;
+  int i;
   Z *q,*r;
 
   q = (Z *)MALLOC(n*sizeof(Z));
@@ -4219,11 +6062,13 @@ void removecont_array_q(Z *c,int n)
     v.id = O_VECT; v.len = n; v.body = (pointer *)r;
     gcdvz(&v,&d1);
     gcdz(d0,d1,&gcd);
-    divz(d0,gcd,&a);
+    /* exact division */
+    divsz(d0,gcd,&a);
     for ( i = 0; i < n; i++ ) {
       mulz(a,q[i],&u);
       if ( r[i] ) {
-        divz(r[i],gcd,&u1);
+        /* exact division */
+        divsz(r[i],gcd,&u1);
         addz(u,u1,&q[i]);
       } else
         q[i] = u;
@@ -4238,14 +6083,18 @@ 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);
@@ -4342,7 +6191,7 @@ void ndv_free(NDV p)
 
 void nd_append_red(UINT *d,int i)
 {
-    RHist m,m0;
+    RHist m;
     int h;
 
     NEWRHist(m);
@@ -4386,14 +6235,13 @@ UINT *nd_compute_bound(ND p)
 {
     UINT *d1,*d2,*t;
     UINT u;
-    int i,j,k,l,len,ind;
+    int i,j,k,l,ind;
     NM m;
 
     if ( !p )
         return 0;
     d1 = (UINT *)MALLOC(nd_wpd*sizeof(UINT));
     d2 = (UINT *)MALLOC(nd_wpd*sizeof(UINT));
-    len = LEN(p);
     m = BDY(p); ndl_copy(DL(m),d1); m = NEXT(m);
     for ( m = NEXT(m); m; m = NEXT(m) ) {
         ndl_lcm(DL(m),d1,d2);
@@ -4417,7 +6265,7 @@ 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 */
@@ -4437,10 +6285,11 @@ int nd_get_exporigin(struct order_spec *ord)
 }
 
 void nd_setup_parameters(int nvar,int max) {
-    int i,j,n,elen,ord_o,ord_l,l,s,wpd;
-    struct order_pair *op;
+    int i,j,elen,wpd;
+    extern int CNVars;
 
     nd_nvar = nvar;
+    CNVars = nvar;
     if ( max ) {
         /* XXX */
         if ( do_weyl ) nd_bpe = 32;
@@ -4457,20 +6306,20 @@ void nd_setup_parameters(int nvar,int max) {
     }
     if ( !do_weyl && weight_check && (current_dl_weight_vector || nd_matrix) ) {
         UINT t;
-    int st;
+        int st;
         int *v;
   /* t = max(weights) */
         t = 0;
         if ( current_dl_weight_vector )
             for ( i = 0, t = 0; i < nd_nvar; i++ ) {
                 if ( (st=current_dl_weight_vector[i]) < 0 ) st = -st;
-                if ( t < st ) t = st;
+                if ( t < (UINT)st ) t = st;
             }
         if ( nd_matrix )
             for ( i = 0; i < nd_matrix_len; i++ )
                 for ( j = 0, v = nd_matrix[i]; j < nd_nvar; j++ ) {
                     if ( (st=v[j]) < 0 ) st = -st;
-                    if ( t < st ) t = st;
+                    if ( t < (UINT)st ) t = st;
         }
         /* i = bitsize of t */
         for ( i = 0; t; t >>=1, i++ );
@@ -4514,7 +6363,7 @@ ND_pairs nd_reconstruct(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 mr;
     RHist r;
     RHist *old_red;
     ND_pairs s0,s,t;
@@ -4553,6 +6402,7 @@ 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);
     }
@@ -4571,12 +6421,14 @@ 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;
@@ -4588,13 +6440,99 @@ 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 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);
+      }
+      if ( s0 ) NEXT(s) = 0;
+      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;
+    int n,i,ei,omask0,j,s,ord_l,l;
     struct order_pair *op;
 
     n = nd_nvar;
-    oepw = (sizeof(UINT)*8)/obpe;
+//    oepw = (sizeof(UINT)*8)/obpe;
     omask0 = (1<<obpe)-1;
     TD(r) = TD(d);
     for ( i = nd_exporigin; i < nd_wpd; i++ ) r[i] = 0;
@@ -4622,7 +6560,6 @@ void ndl_reconstruct(UINT *d,UINT *r,int obpe,EPOS oep
 ND nd_copy(ND p)
 {
     NM m,mr,mr0;
-    int c,n;
     ND r;
 
     if ( !p )
@@ -4649,7 +6586,6 @@ int nd_sp(int mod,int trace,ND_pairs p,ND *rp)
     P gp,tp;
     Z g,t;
     Z iq;
-    int td;
     LIST hist;
     NODE node;
     DP d;
@@ -4684,18 +6620,20 @@ int nd_sp(int mod,int trace,ND_pairs p,ND *rp)
         divsp(nd_vc,HCP(p2),gp,&CP(m1));
         divsp(nd_vc,HCP(p1),gp,&tp); chsgnp(tp,&CP(m2));
     } else {
-        igcd_cofactor(HCQ(p1),HCQ(p2),&g,&t,&CQ(m1)); chsgnz(t,&CQ(m2));
+        igcd_cofactor(HCZ(p1),HCZ(p2),&g,&t,&CZ(m1)); chsgnz(t,&CZ(m2));
     }
     t1 = ndv_mul_nm(mod,m1,p1); t2 = ndv_mul_nm(mod,m2,p2);
     *rp = nd_add(mod,t1,t2);
     if ( nd_gentrace ) {
         /* nd_tracelist is initialized */
-        STOQ(p->i1,iq); nmtodp(mod,m1,&d); node = mknode(4,ONE,iq,d,ONE);
+        STOZ(p->i1,iq); nmtodp(mod,m1,&d); node = mknode(4,ONE,iq,d,ONE);
         MKLIST(hist,node); MKNODE(nd_tracelist,hist,0);
-        STOQ(p->i2,iq); nmtodp(mod,m2,&d); node = mknode(4,ONE,iq,d,ONE);
+        STOZ(p->i2,iq); nmtodp(mod,m2,&d); node = mknode(4,ONE,iq,d,ONE);
         MKLIST(hist,node); MKNODE(node,hist,nd_tracelist);
         nd_tracelist = node;
     }
+    if ( *rp )
+      (*rp)->sig = p->sig;
     FREENM(m1); FREENM(m2);
     return 1;
 }
@@ -4739,7 +6677,7 @@ void ndv_mul_c_q(NDV p,Z mul)
     if ( !p ) return;
     len = LEN(p);
     for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
-        mulz(CQ(m),mul,&c); CQ(m) = c;
+        mulz(CZ(m),mul,&c); CZ(m) = c;
     }
 }
 
@@ -4805,7 +6743,7 @@ void weyl_mul_nm_nmv(int n,int mod,NM m0,NMV m1,NM *ta
     } else if ( nd_vc )
         mulp(nd_vc,CP(m0),CP(m1),&CP(m));
   else
-        mulz(CQ(m0),CQ(m1),&CQ(m));
+        mulz(CZ(m0),CZ(m1),&CZ(m));
     for ( i = 0; i < nd_wpd; i++ ) d[i] = 0;
     homo = n&1 ? 1 : 0;
     if ( homo ) {
@@ -4862,7 +6800,7 @@ void weyl_mul_nm_nmv(int n,int mod,NM m0,NMV m1,NM *ta
                         } else if ( nd_vc )
                             mulp(nd_vc,CP(tab[u]),(P)q,&CP(tab[u]));
             else {
-                            mulz(CQ(tab[u]),q,&q1); CQ(tab[u]) = q1;
+                            mulz(CZ(tab[u]),q,&q1); CZ(tab[u]) = q1;
                         }
                     }
                 }
@@ -4876,7 +6814,7 @@ void weyl_mul_nm_nmv(int n,int mod,NM m0,NMV m1,NM *ta
                         } else if ( nd_vc )
                             mulp(nd_vc,CP(tab[u]),(P)q,&CP(t));
             else
-                            mulz(CQ(tab[u]),q,&CQ(t));
+                            mulz(CZ(tab[u]),q,&CZ(t));
                         *p = t;
                     }
                 }
@@ -4900,19 +6838,16 @@ ND ndv_mul_nm_symbolic(NM m0,NDV p)
 {
     NM mr,mr0;
     NMV m;
-    UINT *d,*dt,*dm;
-    int c,n,td,i,c1,c2,len;
-    Q q;
+    UINT *d;
+    int i,len;
     ND r;
 
     if ( !p ) return 0;
     else {
-        n = NV(p); m = BDY(p);
+        m = BDY(p);
         d = DL(m0);
         len = LEN(p);
         mr0 = 0;
-        td = TD(d);
-        c = CM(m0);
         for ( i = 0; i < len; i++, NMV_ADV(m) ) {
             NEXTNM(mr0,mr);
             CM(mr) = 1;
@@ -4929,8 +6864,8 @@ ND ndv_mul_nm(int mod,NM m0,NDV p)
 {
     NM mr,mr0;
     NMV m;
-    UINT *d,*dt,*dm;
-    int c,n,td,i,c1,c2,len;
+    UINT *d;
+    int c,i,c1,c2,len;
     P q;
     ND r;
 
@@ -4942,11 +6877,10 @@ ND ndv_mul_nm(int mod,NM m0,NDV p)
         } else
             return weyl_ndv_mul_nm(mod,m0,p);
     } else {
-        n = NV(p); m = BDY(p);
+        m = BDY(p);
         d = DL(m0);
         len = LEN(p);
         mr0 = 0;
-        td = TD(d);
         if ( mod == -1 ) {
             c = CM(m0);
             for ( i = 0; i < len; i++, NMV_ADV(m) ) {
@@ -4990,8 +6924,7 @@ ND nd_quo(int mod,PGeoBucket bucket,NDV d)
 {
     NM mq0,mq;
     NMV tm;
-    Q q;
-    int i,nv,sg,c,c1,c2,hindex;
+    int i,nv,c,c1,c2,hindex;
     ND p,t,r;
 
     if ( bucket->m < 0 ) return 0;
@@ -5016,8 +6949,8 @@ ND nd_quo(int mod,PGeoBucket bucket,NDV d)
                 DMAR(c1,c2,0,mod,c); CM(mq) = c;
                 CM(tm) = mod-c;
             } else {
-                divsz(HCQ(p),HCQ(d),&CQ(mq));
-                chsgnz(CQ(mq),&CQ(tm));
+                divsz(HCZ(p),HCZ(d),&CZ(mq));
+                chsgnz(CZ(mq),&CZ(tm));
             }
             t = ndv_mul_nmv_trunc(mod,tm,d,HDL(d));
             bucket->body[hindex] = nd_remove_head(p);
@@ -5049,10 +6982,10 @@ void ndv_realloc(NDV p,int obpe,int oadv,EPOS oepos)
     mr = (NMV)((char *)mr0+(len-1)*nmv_adv);
     t = (NMV)MALLOC(nmv_adv);
     for ( i = 0; i < len; i++, NMV_OPREV(m), NMV_PREV(mr) ) {
-        CQ(t) = CQ(m);
+        CZ(t) = CZ(m);
         for ( k = 0; k < nd_wpd; k++ ) DL(t)[k] = 0;
         ndl_reconstruct(DL(m),DL(t),obpe,oepos);
-        CQ(mr) = CQ(t);
+        CZ(mr) = CZ(t);
         ndl_copy(DL(t),DL(mr));
     }
     BDY(p) = mr0;
@@ -5070,10 +7003,11 @@ NDV ndv_dup_realloc(NDV p,int obpe,int oadv,EPOS oepos
     for ( i = 0; i < len; i++, NMV_OADV(m), NMV_ADV(mr) ) {
         ndl_zero(DL(mr));
         ndl_reconstruct(DL(m),DL(mr),obpe,oepos);
-        CQ(mr) = CQ(m);
+        CZ(mr) = CZ(m);
     }
     MKNDV(NV(p),mr0,len,r);
     SG(r) = SG(p);
+    r->sig = p->sig;
     return r;
 }
 
@@ -5090,7 +7024,7 @@ NDV ndv_dup(int mod,NDV p)
     m0 = m = (NMV)((mod>0 || mod==-1)?MALLOC_ATOMIC(len*nmv_adv):MALLOC(len*nmv_adv));
     for ( t = BDY(p), i = 0; i < len; i++, NMV_ADV(t), NMV_ADV(m) ) {
         ndl_copy(DL(t),DL(m));
-        CQ(m) = CQ(t);
+        CZ(m) = CZ(t);
     }
     MKNDV(NV(p),m0,len,d);
     SG(d) = SG(p);
@@ -5108,7 +7042,7 @@ NDV ndv_symbolic(int mod,NDV p)
     m0 = m = (NMV)((mod>0||mod==-1)?MALLOC_ATOMIC(len*nmv_adv):MALLOC(len*nmv_adv));
     for ( t = BDY(p), i = 0; i < len; i++, NMV_ADV(t), NMV_ADV(m) ) {
         ndl_copy(DL(t),DL(m));
-        CQ(m) = ONE;
+        CZ(m) = ONE;
     }
     MKNDV(NV(p),m0,len,d);
     SG(d) = SG(p);
@@ -5124,7 +7058,7 @@ ND nd_dup(ND p)
     for ( m0 = 0, t = BDY(p); t; t = NEXT(t) ) {
         NEXTNM(m0,m);
         ndl_copy(DL(t),DL(m));
-        CQ(m) = CQ(t);
+        CZ(m) = CZ(t);
     }
     if ( m0 ) NEXT(m) = 0;
     MKND(NV(p),m0,LEN(p),d);
@@ -5137,7 +7071,7 @@ ND nd_dup(ND p)
 void ndv_mod(int mod,NDV p)
 {
     NMV t,d;
-    int r,s,u;
+    int r;
     int i,len,dlen;
     P cp;
     Z c;
@@ -5173,7 +7107,7 @@ void ndv_mod(int mod,NDV p)
                 nd_subst_vector(nd_vc,CP(t),nd_subst,&cp);
                 c = (Z)cp;
             } else
-                c = CQ(t);
+                c = CZ(t);
             r = remqi((Q)c,mod);
             if ( r ) {
                 CM(d) = r;
@@ -5195,31 +7129,32 @@ 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) */
@@ -5248,14 +7183,13 @@ NDV pltondv(VL vl,VL dvl,LIST p)
 
 ND ptond(VL vl,VL dvl,P p)
 {
-    int n,i,j,k,e;
+    int j,k,e,i;
     VL tvl;
     V v;
     DCP dc;
     DCP *w;
-    ND r,s,t,u;
+    ND r,t,s;
     P x;
-    int c;
     UINT *d;
     NM m,m0;
 
@@ -5264,9 +7198,9 @@ ND ptond(VL vl,VL dvl,P p)
     else if ( NUM(p) ) {
         NEWNM(m);
         ndl_zero(DL(m));
-        if ( !INT((Q)p) )
+        if ( RATN(p) && !INT((Q)p) )
           error("ptond : input must be integer-coefficient");
-        CQ(m) = (Z)p;
+        CZ(m) = (Z)p;
         NEXT(m) = 0;
         MKND(nd_nvar,m,1,r);
         SG(r) = 0;
@@ -5287,7 +7221,7 @@ ND ptond(VL vl,VL dvl,P p)
         } else {
             NEWNM(m0); d = DL(m0);
             for ( j = k-1, s = 0; j >= 0; j-- ) {
-                ndl_zero(d); e = QTOS(DEG(w[j])); PUT_EXP(d,i,e);
+                ndl_zero(d); e = (int)ZTOS(DEG(w[j])); PUT_EXP(d,i,e);
                 TD(d) = MUL_WEIGHT(e,i);
                 if ( nd_blockmask) ndl_weight_mask(d);
                 if ( nd_module ) MPOS(d) = 0;
@@ -5325,12 +7259,12 @@ P ndvtop(int mod,VL vl,VL dvl,NDV p)
             } else if ( mod == -2 ) {
                c = (P)CZ(m);
             } else if ( mod > 0 ) {
-                STOQ(CM(m),q); c = (P)q;
+                STOZ(CM(m),q); c = (P)q;
             } else
                 c = CP(m);
             d = DL(m);
             for ( i = 0, t = c, tvl = dvl; i < n; tvl = NEXT(tvl), i++ ) {
-                MKV(tvl->v,r); e = GET_EXP(d,i); STOQ(e,q);
+                MKV(tvl->v,r); e = GET_EXP(d,i); STOZ(e,q);
                 pwrp(vl,r,q,&u); mulp(vl,t,u,&w); t = w;
             }
             addp(vl,s,t,&u); s = u;
@@ -5347,7 +7281,7 @@ LIST ndvtopl(int mod,VL vl,VL dvl,NDV p,int rank)
     Z q;
     P c;
     UINT *d;
-    P s,r,u,t,w;
+    P r,u,t,w;
     GFS gfs;
     P *a;
     LIST l;
@@ -5364,12 +7298,12 @@ LIST ndvtopl(int mod,VL vl,VL dvl,NDV p,int rank)
             if ( mod == -1 ) {
                 e = IFTOF(CM(m)); MKGFS(e,gfs); c = (P)gfs;
             } else if ( mod ) {
-                STOQ(CM(m),q); c = (P)q;
+                STOZ(CM(m),q); c = (P)q;
             } else
                 c = CP(m);
             d = DL(m);
             for ( i = 0, t = c, tvl = dvl; i < n; tvl = NEXT(tvl), i++ ) {
-                MKV(tvl->v,r); e = GET_EXP(d,i); STOQ(e,q);
+                MKV(tvl->v,r); e = GET_EXP(d,i); STOZ(e,q);
                 pwrp(vl,r,q,&u); mulp(vl,t,u,&w); t = w;
             }
             addp(vl,a[MPOS(d)],t,&u); a[MPOS(d)] = u;
@@ -5401,13 +7335,141 @@ NDV ndtondv(int mod,ND p)
 #endif
     for ( t = BDY(p), i = 0; t; t = NEXT(t), i++, NMV_ADV(m) ) {
         ndl_copy(DL(t),DL(m));
-        CQ(m) = CQ(t);
+        CZ(m) = CZ(t);
     }
     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 dptondv(int mod,DP p)
+{
+  NDV d;
+  NMV m,m0;
+  MP t;
+  int i,len,n;
+
+  if ( !p ) return 0;
+  for ( t = BDY(p), len = 0; t; t = NEXT(t), len++ );
+  n = p->nv;
+  if ( mod > 0 || mod == -1 )
+    m0 = m = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(len*nmv_adv);
+  else
+    m0 = m = MALLOC(len*nmv_adv);
+  for ( i = 0, t = BDY(p); i < len; i++, NMV_ADV(m), t = NEXT(t) ) {
+    dltondl(n,t->dl,DL(m));
+    TD(DL(m)) = ndl_weight(DL(m));
+    CZ(m) = (Z)t->c;
+  }
+  qsort(m0,len,nmv_adv,(int (*)(const void *,const void *))nmv_comp);
+  MKNDV(NV(p),m0,len,d);
+  SG(d) = SG(p);
+  return d;
+}
+
+NDV dpmtondv(int mod,DPM p)
+{
+  NDV d;
+  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;
@@ -5421,11 +7483,12 @@ ND ndvtond(int mod,NDV p)
     for ( t = BDY(p), i = 0; i < len; NMV_ADV(t), i++ ) {
         NEXTNM(m0,m);
         ndl_copy(DL(t),DL(m));
-        CQ(m) = CQ(t);
+        CZ(m) = CZ(t);
     }
     NEXT(m) = 0;
     MKND(NV(p),m0,len,d);
     SG(d) = SG(p);
+    d->sig = p->sig;
     return d;
 }
 
@@ -5450,25 +7513,61 @@ DP ndvtodp(int mod,NDV p)
     return d;
 }
 
+DPM sigtodpm(SIG s)
+{
+  DMM m;
+  DPM d;
+
+  NEWDMM(m); 
+  m->c = (Obj)ONE;
+  m->dl = s->dl;
+  m->pos = s->pos+1;
+  m->next = 0;
+  MKDPM(nd_nvar,m,d);
+  SG(d) = s->dl->td;
+  return d;
+}
+
+DPM ndvtodpm(int mod,NDV p)
+{
+  DMM m,m0;
+  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;
+  MP m,m0;
   DP d;
-    NM t;
-    int i,len;
+  NM t;
 
-    if ( !p ) return 0;
-    m0 = 0;
-    len = p->len;
-    for ( t = BDY(p); t; t = NEXT(t) ) {
-        NEXTMP(m0,m);
-      m->dl = ndltodl(nd_nvar,DL(t));
-      m->c = (Obj)ndctop(mod,t->c);
-    }
-    NEXT(m) = 0;
+  if ( !p ) return 0;
+  m0 = 0;
+  for ( t = BDY(p); t; t = NEXT(t) ) {
+    NEXTMP(m0,m);
+    m->dl = ndltodl(nd_nvar,DL(t));
+    m->c = (Obj)ndctop(mod,t->c);
+  }
+  NEXT(m) = 0;
   MKDP(nd_nvar,m0,d);
-    SG(d) = SG(p);
-    return d;
+  SG(d) = SG(p);
+  return d;
 }
 
 void ndv_print(NDV p)
@@ -5481,7 +7580,7 @@ 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");
@@ -5498,7 +7597,7 @@ void ndv_print_q(NDV p)
         len = LEN(p);
         for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
             printf("+");
-            printexpr(CO,(Obj)CQ(m));
+            printexpr(CO,(Obj)CZ(m));
             printf("*");
             ndl_print(DL(m));
         }
@@ -5512,6 +7611,7 @@ 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) ) {
@@ -5537,12 +7637,15 @@ 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;
@@ -5606,40 +7709,73 @@ 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;
 }
@@ -5675,7 +7811,7 @@ 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;
@@ -5731,7 +7867,6 @@ void nd_nf_p(Obj f,LIST g,LIST v,int m,struct order_sp
     NDV ndvf;
     VL vv,tv;
     int stat,nvar,max,mrank;
-    union oNDC dn;
     Q cont;
     P pp;
     LIST ppl;
@@ -5778,9 +7913,9 @@ 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,1,0,&nf);
+    stat = nd_nf(m,0,ndf,nd_ps,1,&nf);
     if ( !stat )
         error("nd_nf_p : exponent too large");
     if ( nd_module ) *rp = (Obj)ndvtopl(m,CO,vv,ndtondv(m,nf),mrank);
@@ -5803,27 +7938,6 @@ int nd_to_vect(int mod,UINT *s0,int n,ND d,UINT *r)
     return i;
 }
 
-#if defined(__GNUC__) && SIZEOF_LONG==8
-
-#define MOD128(a,c,m) ((a)=(((c)!=0||((a)>=(m)))?(((((U128)(c))<<64)+(a))%(m)):(a)))
-
-int nd_to_vect64(int mod,UINT *s0,int n,ND d,U64 *r)
-{
-    NM m;
-    UINT *t,*s;
-    int i;
-
-    for ( i = 0; i < n; i++ ) r[i] = 0;
-    for ( i = 0, s = s0, m = BDY(d); m; m = NEXT(m) ) {
-        t = DL(m);
-        for ( ; !ndl_equal(t,s); s += nd_wpd, i++ );
-        r[i] = (U64)CM(m);
-    }
-    for ( i = 0; !r[i]; i++ );
-    return i;
-}
-#endif
-
 int nd_to_vect_q(UINT *s0,int n,ND d,Z *r)
 {
     NM m;
@@ -5834,7 +7948,7 @@ int nd_to_vect_q(UINT *s0,int n,ND d,Z *r)
     for ( i = 0, s = s0, m = BDY(d); m; m = NEXT(m) ) {
         t = DL(m);
         for ( ; !ndl_equal(t,s); s += nd_wpd, i++ );
-        dupz(CQ(m),&r[i]);
+        r[i] = CZ(m);
     }
     for ( i = 0; !r[i]; i++ );
     return i;
@@ -5912,23 +8026,22 @@ Z *nm_ind_pair_to_vect(int mod,UINT *s0,int n,NM_ind_p
     for ( i = j = 0, s = s0, mr = BDY(p); j < len; j++, NMV_ADV(mr) ) {
         ndl_add(d,DL(mr),t);    
         for ( ; !ndl_equal(t,s); s += nd_wpd, i++ );
-        r[i] = CQ(mr);
+        r[i] = CZ(mr);
     }
     return r;
 }
 
-IndArray nm_ind_pair_to_vect_compress(int trace,UINT *s0,int n,int *s0hash,NM_ind_pair pair)
+IndArray nm_ind_pair_to_vect_compress(int trace,UINT *s0,int n,NM_ind_pair pair,int start)
 {
     NM m;
     NMV mr;
-    UINT *d,*t,*s;
+    UINT *d,*t,*u;
     NDV p;
     unsigned char *ivc;
     unsigned short *ivs;
-    UINT *v,*ivi,*s0v;
-    int i,j,len,prev,diff,cdiff,h;
+    UINT *v,*ivi;
+    int i,j,len,prev,diff,cdiff,st,ed,md,c;
     IndArray r;
-struct oEGT eg0,eg1;
 
     m = pair->mul;
     d = DL(m);
@@ -5940,14 +8053,20 @@ struct oEGT eg0,eg1;
     len = LEN(p);
     t = (UINT *)MALLOC(nd_wpd*sizeof(UINT));
     v = (unsigned int *)MALLOC(len*sizeof(unsigned int));
-get_eg(&eg0);
-    for ( i = j = 0, s = s0, mr = BDY(p); j < len; j++, NMV_ADV(mr) ) {
-        ndl_add(d,DL(mr),t);    
-    h = ndl_hash_value(t);
-        for ( ; h != s0hash[i] || !ndl_equal(t,s); s += nd_wpd, i++ );
-        v[j] = i;
+    for ( prev = start, mr = BDY(p), j = 0; j < len; j++, NMV_ADV(mr) ) {
+      ndl_add(d,DL(mr),t);    
+      st = prev;
+      ed = n;
+      while ( ed > st ) {
+        md = (st+ed)/2;
+        u = s0+md*nd_wpd;
+        c = DL_COMPARE(u,t);
+        if ( c == 0 ) break;
+        else if ( c > 0 ) st = md;
+        else ed = md;
+      }
+      prev = v[j] = md;
     }
-get_eg(&eg1); add_eg(&eg_search,&eg0,&eg1);
     r = (IndArray)MALLOC(sizeof(struct oIndArray));
     r->head = v[0];
     diff = 0;
@@ -5990,7 +8109,7 @@ void expand_array(Z *svect,Z *cvect,int n)
         if ( svect[i] ) svect[i] = cvect[j++];
 }
 
-#if 1
+#if 0
 int ndv_reduce_vect_q(Z *svect,int trace,int col,IndArray *imat,NM_ind_pair *rp0,int nred)
 {
     int i,j,k,len,pos,prev,nz;
@@ -6020,7 +8139,7 @@ int ndv_reduce_vect_q(Z *svect,int trace,int col,IndAr
             redv = nd_demand?ndv_load(rp0[i]->index)
                      :(trace?nd_ps_trace[rp0[i]->index]:nd_ps[rp0[i]->index]);
             len = LEN(redv); mr = BDY(redv);
-            igcd_cofactor(svect[k],CQ(mr),&gcd,&cs,&cr);
+            igcd_cofactor(svect[k],CZ(mr),&gcd,&cs,&cr);
             chsgnz(cs,&mcs);
             if ( !UNIQ(cr) ) {
                 for ( j = 0; j < col; j++ ) {
@@ -6033,21 +8152,21 @@ int ndv_reduce_vect_q(Z *svect,int trace,int col,IndAr
                     ivc = ivect->index.c;
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivc[j]; prev = pos;
-                        muladdtoz(CQ(mr),mcs,&svect[pos]);
+                        muladdtoz(CZ(mr),mcs,&svect[pos]);
                     }
                     break;
                 case 2:
                     ivs = ivect->index.s; 
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivs[j]; prev = pos;
-                        muladdtoz(CQ(mr),mcs,&svect[pos]);
+                        muladdtoz(CZ(mr),mcs,&svect[pos]);
                     }
                     break;
                 case 4:
                     ivi = ivect->index.i;
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivi[j]; prev = pos;
-                        muladdtoz(CQ(mr),mcs,&svect[pos]);
+                        muladdtoz(CZ(mr),mcs,&svect[pos]);
                     }
                     break;
             }
@@ -6070,11 +8189,11 @@ int ndv_reduce_vect_q(Z *svect,int trace,int col,IndAr
     return maxrs;
 }
 #else
+
 /* direct mpz version */
 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;
@@ -6082,16 +8201,19 @@ int ndv_reduce_vect_q(Z *svect0,int trace,int col,IndA
     unsigned int *ivi;
     NDV redv;
     NMV mr;
-    NODE rp;
     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] )
@@ -6108,12 +8230,16 @@ int ndv_reduce_vect_q(Z *svect0,int trace,int col,IndA
             redv = nd_demand?ndv_load(rp0[i]->index)
                      :(trace?nd_ps_trace[rp0[i]->index]:nd_ps[rp0[i]->index]);
             len = LEN(redv); mr = BDY(redv);
-            mpz_gcd(gcd,svect[k],BDY(CQ(mr)));
+            mpz_gcd(gcd,svect[k],BDY(CZ(mr)));
             mpz_div(cs,svect[k],gcd);
-            mpz_div(cr,BDY(CQ(mr)),gcd);
+            mpz_div(cr,BDY(CZ(mr)),gcd);
             mpz_neg(cs,cs);
-            for ( j = 0; j < col; j++ )
-              mpz_mul(svect[j],svect[j],cr);
+            if ( MUNIMPZ(cr) )
+              for ( j = 0; j < col; j++ ) mpz_neg(svect[j],svect[j]); 
+            else if ( !UNIMPZ(cr) )
+              for ( j = 0; j < col; j++ ) {
+                if ( mpz_sgn(svect[j]) ) mpz_mul(svect[j],svect[j],cr);
+              }
             mpz_set_ui(svect[k],0);
             prev = k;
             switch ( ivect->width ) {
@@ -6121,21 +8247,21 @@ int ndv_reduce_vect_q(Z *svect0,int trace,int col,IndA
                     ivc = ivect->index.c;
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivc[j]; prev = pos;
-                        mpz_addmul(svect[pos],BDY(CQ(mr)),cs);
+                        mpz_addmul(svect[pos],BDY(CZ(mr)),cs);
                     }
                     break;
                 case 2:
                     ivs = ivect->index.s; 
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivs[j]; prev = pos;
-                        mpz_addmul(svect[pos],BDY(CQ(mr)),cs);
+                        mpz_addmul(svect[pos],BDY(CZ(mr)),cs);
                     }
                     break;
                 case 4:
                     ivi = ivect->index.i;
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivi[j]; prev = pos;
-                        mpz_addmul(svect[pos],BDY(CQ(mr)),cs);
+                        mpz_addmul(svect[pos],BDY(CZ(mr)),cs);
                     }
                     break;
             }
@@ -6158,7 +8284,7 @@ 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;
@@ -6168,14 +8294,13 @@ int ndv_reduce_vect(int m,UINT *svect,int col,IndArray
     unsigned int *ivi;
     NDV redv;
     NMV mr;
-    NODE rp;
     int maxrs;
 
     maxrs = 0;
     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);
@@ -6185,12 +8310,12 @@ 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:
@@ -6198,12 +8323,12 @@ 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:
@@ -6211,12 +8336,12 @@ 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;
             }
@@ -6227,89 +8352,16 @@ int ndv_reduce_vect(int m,UINT *svect,int col,IndArray
     return maxrs;
 }
 
-#if defined(__GNUC__) && SIZEOF_LONG==8
-
-int ndv_reduce_vect64(int m,U64 *svect,U64 *cvect,int col,IndArray *imat,NM_ind_pair *rp0,int nred)
-{
-    int i,j,k,len,pos,prev;
-    U64 a,c,c1,c2;
-    IndArray ivect;
-    unsigned char *ivc;
-    unsigned short *ivs;
-    unsigned int *ivi;
-    NDV redv;
-    NMV mr;
-    NODE rp;
-    int maxrs;
-
-    for ( i = 0; i < col; i++ ) cvect[i] = 0;
-    maxrs = 0;
-    for ( i = 0; i < nred; i++ ) {
-        ivect = imat[i];
-        k = ivect->head; 
-        a = svect[k]; c = cvect[k];
-        MOD128(a,c,m);
-        svect[k] = a; cvect[k] = 0;
-        if ( (c = svect[k]) != 0 ) {
-            maxrs = MAX(maxrs,rp0[i]->sugar);
-            c = m-c; redv = nd_ps[rp0[i]->index];
-            len = LEN(redv); mr = BDY(redv);
-            svect[k] = 0; prev = k;
-            switch ( ivect->width ) {
-                case 1:
-                    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;
-                        }
-                    }
-                    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;
-                        }
-                    }
-                    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;
-                        }
-                    }
-                    break;
-            }
-        }
-    }
-    for ( i = 0; i < col; i++ ) {
-      a = svect[i]; c = cvect[i]; MOD128(a,c,m); svect[i] = a;
-    }
-    return maxrs;
-}
-#endif
-
 int ndv_reduce_vect_sf(int m,UINT *svect,int col,IndArray *imat,NM_ind_pair *rp0,int nred)
 {
     int i,j,k,len,pos,prev;
-    UINT c,c1,c2,c3,up,lo,dmy;
+    UINT c;
     IndArray ivect;
     unsigned char *ivc;
     unsigned short *ivs;
     unsigned int *ivi;
     NDV redv;
     NMV mr;
-    NODE rp;
     int maxrs;
 
     maxrs = 0;
@@ -6351,8 +8403,7 @@ int ndv_reduce_vect_sf(int m,UINT *svect,int col,IndAr
 
 ND nd_add_lf(ND p1,ND p2)
 {
-    int n,c,can;
-    ND r;
+    int c,can;
     NM m1,m2,mr0,mr,s;
     Z t;
 
@@ -6360,7 +8411,7 @@ ND nd_add_lf(ND p1,ND p2)
     else if ( !p2 ) return p1;
     else {
         can = 0;
-        for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
+        for (  m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
             c = DL_COMPARE(DL(m1),DL(m2));
             switch ( c ) {
                 case 0:
@@ -6399,14 +8450,12 @@ ND nd_add_lf(ND p1,ND p2)
 int ndv_reduce_vect_lf(mpz_t *svect,int trace,int col,IndArray *imat,NM_ind_pair *rp0,int nred)
 {
     int i,j,k,len,pos,prev;
-    mpz_t c,mc,c1;
     IndArray ivect;
     unsigned char *ivc;
     unsigned short *ivs;
     unsigned int *ivi;
     NDV redv;
     NMV mr;
-    NODE rp;
     int maxrs;
 
     maxrs = 0;
@@ -6457,16 +8506,13 @@ int ndv_reduce_vect_lf(mpz_t *svect,int trace,int col,
 int nd_gauss_elim_lf(mpz_t **mat0,int *sugar,int row,int col,int *colstat)
 {
     int i,j,k,l,rank,s;
-    mpz_t a,a1,inv;
+    mpz_t a,inv;
     mpz_t *t,*pivot,*pk;
     mpz_t **mat;
-    struct oEGT eg0,eg1,eg_forward,eg_mod,eg_back;
-    int size,size1;
 
     mpz_init(inv); 
     mpz_init(a);
     mat = (mpz_t **)mat0;
-        size = 0;
     for ( rank = 0, j = 0; j < col; j++ ) {
         for ( i = rank; i < row; i++ ) {
             mpz_mod(mat[i][j],mat[i][j],BDY(current_mod_lf));
@@ -6556,8 +8602,7 @@ NDV vect_to_ndv(UINT *vect,int spcol,int col,int *rhea
     }
 }
 
-#if defined(__GNUC__) && SIZEOF_LONG==8
-NDV vect64_to_ndv(U64 *vect,int spcol,int col,int *rhead,UINT *s0vect)
+NDV vect_to_ndv_s(UINT *vect,int col,UINT *s0vect)
 {
     int j,k,len;
     UINT *p;
@@ -6565,30 +8610,24 @@ NDV vect64_to_ndv(U64 *vect,int spcol,int col,int *rhe
     NDV r;
     NMV mr0,mr;
 
-    for ( j = 0, len = 0; j < spcol; j++ ) if ( vect[j] ) len++;
+    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);
-#if 0
-        ndv_alloc += nmv_adv*len;
-#endif
         mr = mr0; 
         p = s0vect;
         for ( j = k = 0; j < col; j++, p += nd_wpd )
-            if ( !rhead[j] ) {
-                if ( (c = (UINT)vect[k++]) != 0 ) {
-                    ndl_copy(p,DL(mr)); CM(mr) = c; NMV_ADV(mr);
-                }
-            }
+          if ( (c = vect[k++]) != 0 ) {
+            ndl_copy(p,DL(mr)); CM(mr) = c; NMV_ADV(mr);
+          }
         MKNDV(nd_nvar,mr0,len,r);
         return r;
     }
 }
-#endif
 
 NDV vect_to_ndv_2(unsigned long *vect,int col,UINT *s0vect)
 {
-    int j,k,len;
+    int j,len;
     UINT *p;
     NDV r;
     NMV mr0,mr;
@@ -6612,32 +8651,33 @@ NDV vect_to_ndv_2(unsigned long *vect,int col,UINT *s0
 
 NDV vect_to_ndv_q(Z *vect,int spcol,int col,int *rhead,UINT *s0vect)
 {
-    int j,k,len;
-    UINT *p;
-    Z c;
-    NDV r;
-    NMV mr0,mr;
+  int j,k,len;
+  UINT *p;
+  Z c;
+  NDV r;
+  NMV mr0,mr;
 
-    for ( j = 0, len = 0; j < spcol; j++ ) if ( vect[j] ) len++;
-    if ( !len ) return 0;
-    else {
-        mr0 = (NMV)MALLOC(nmv_adv*len);
+  for ( j = 0, len = 0; j < spcol; j++ ) if ( vect[j] ) len++;
+  if ( !len ) return 0;
+  else {
+    mr0 = (NMV)MALLOC(nmv_adv*len);
 #if 0
-        ndv_alloc += nmv_adv*len;
+    ndv_alloc += nmv_adv*len;
 #endif
-        mr = mr0; 
-        p = s0vect;
-        for ( j = k = 0; j < col; j++, p += nd_wpd )
-            if ( !rhead[j] ) {
-                if ( (c = vect[k++]) != 0 ) {
-                    if ( !INT(c) )
-                        error("afo");
-                    ndl_copy(p,DL(mr)); CQ(mr) = c; NMV_ADV(mr);
-                }
-            }
-        MKNDV(nd_nvar,mr0,len,r);
-        return r;
+    mr = mr0; 
+    p = s0vect;
+    for ( j = k = 0; j < col; j++, p += nd_wpd ) {
+      if ( !rhead[j] ) {
+        if ( (c = vect[k++]) != 0 ) {
+          if ( !INT(c) )
+            error("vect_to_ndv_q : components must be integers");
+          ndl_copy(p,DL(mr)); CZ(mr) = c; NMV_ADV(mr);
+        }
+      }
     }
+    MKNDV(nd_nvar,mr0,len,r);
+    return r;
+  }
 }
 
 NDV vect_to_ndv_lf(mpz_t *vect,int spcol,int col,int *rhead,UINT *s0vect)
@@ -6691,8 +8731,8 @@ NDV plain_vect_to_ndv_q(Z *vect,int col,UINT *s0vect)
         for ( j = k = 0; j < col; j++, p += nd_wpd, k++ )
             if ( (c = vect[k]) != 0 ) {
                 if ( !INT(c) )
-                    error("afo");
-                ndl_copy(p,DL(mr)); CQ(mr) = c; NMV_ADV(mr);
+                    error("plain_vect_to_ndv_q : components must be integers");
+                ndl_copy(p,DL(mr)); CZ(mr) = c; NMV_ADV(mr);
             }
         MKNDV(nd_nvar,mr0,len,r);
         return r;
@@ -6702,7 +8742,6 @@ NDV plain_vect_to_ndv_q(Z *vect,int col,UINT *s0vect)
 int nd_sp_f4(int m,int trace,ND_pairs l,PGeoBucket bucket)
 {
     ND_pairs t;
-    NODE sp0,sp;
     int stat;
     ND spol;
 
@@ -6726,7 +8765,6 @@ int nd_symbolic_preproc(PGeoBucket bucket,int trace,UI
     NM_ind_pair pair;
     ND red;
     NDV *ps;
-    static int afo;
 
     s0 = 0; rp0 = 0; col = 0;
   if ( nd_demand )
@@ -6747,7 +8785,7 @@ 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;
@@ -6775,140 +8813,133 @@ void print_ndp(ND_pairs l)
 
 NODE nd_f4(int m,int checkonly,int **indp)
 {
-    int i,nh,stat,index,f4red;
-    NODE r,g,tn0,tn,node;
-    ND_pairs d,l,t,ll0,ll,lh;
+  int i,nh,stat,f4red;
+  NODE r,g,tn0,tn,node;
+  ND_pairs d,l,t,ll,lh;
   LIST l0,l1;
-    ND spol,red;
-    NDV nf,redv;
-    NM s0,s;
-    NODE rp0,srp0,nflist,nzlist,nzlist_t;
-    int nsp,nred,col,rank,len,k,j,a,i1s,i2s;
-    UINT c;
-    UINT **spmat;
-    UINT *s0vect,*svect,*p,*v;
-    int *colstat;
-    IndArray *imat;
-    int *rhead;
-    int spcol,sprow;
-    int sugar,sugarh;
-    PGeoBucket bucket;
-    struct oEGT eg0,eg1,eg_f4;
-    Z i1,i2,sugarq;
+  NDV nf;
+  NODE rp0,nflist,nzlist,nzlist_t;
+  int col;
+  UINT *s0vect;
+  int sugar;
+  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;
+  ndv_alloc = 0;
 #endif
-    g = 0; d = 0;
-    for ( i = 0; i < nd_psn; i++ ) {
-        d = update_pairs(d,g,i,0);
-        g = update_base(g,i);
-    }
+  Nf4_red=0;
+  g = 0; d = 0;
+  for ( i = 0; i < nd_psn; i++ ) {
+    d = update_pairs(d,g,i,0);
+    g = update_base(g,i);
+  }
   nzlist = 0;
-    nzlist_t = nd_nzlist;
-    f4red = 1;
-    nd_last_nonzero = 0;
-    while ( d ) {
-        get_eg(&eg0);
-        l = nd_minsugarp(d,&d);
-        sugar = nd_sugarweight?l->sugar2:SG(l);
-        if ( MaxDeg > 0 && sugar > MaxDeg ) break;
-        if ( nzlist_t ) {
-            node = BDY((LIST)BDY(nzlist_t));
-            sugarh = QTOS((Q)ARG0(node));
-            tn = BDY((LIST)ARG1(node));
-            if ( !tn ) {
-              nzlist_t = NEXT(nzlist_t);
-              continue;
-            }
-            /* tn = [[i1,i2],...] */
-            lh = nd_ipairtospair(tn);
-        }
-        bucket = create_pbucket();
-        stat = nd_sp_f4(m,0,l,bucket);
-        if ( !stat ) {
-            for ( t = l; NEXT(t); t = NEXT(t) );
-            NEXT(t) = d; d = l;
-            d = nd_reconstruct(0,d);
-            continue;
-        }
-        if ( bucket->m < 0 ) continue;
-        col = nd_symbolic_preproc(bucket,0,&s0vect,&rp0);
-        if ( !col ) {
-            for ( t = l; NEXT(t); t = NEXT(t) );
-            NEXT(t) = d; d = l;
-            d = nd_reconstruct(0,d);
-            continue;
-        }
-        get_eg(&eg1); init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg1);
-        if ( DP_Print )
-            fprintf(asir_out,"\nsugar=%d,symb=%.3fsec,",
-                sugar,eg_f4.exectime);
-        nflist = nd_f4_red(m,nd_nzlist?lh:l,0,s0vect,col,rp0,nd_gentrace?&ll:0);
-        if ( checkonly && nflist ) return 0;
-        /* adding new bases */
-        if ( nflist ) nd_last_nonzero = f4red;
-        for ( r = nflist; r; r = NEXT(r) ) {
-            nf = (NDV)BDY(r);
-            ndv_removecont(m,nf);
-            if ( !m && nd_nalg ) {
-                ND nf1;
+  nzlist_t = nd_nzlist;
+  f4red = 1;
+  nd_last_nonzero = 0;
+  while ( d ) {
+    get_eg(&eg0);
+    l = nd_minsugarp(d,&d);
+    sugar = nd_sugarweight?l->sugar2:SG(l);
+    if ( MaxDeg > 0 && sugar > MaxDeg ) break;
+    if ( nzlist_t ) {
+      node = BDY((LIST)BDY(nzlist_t));
+//      sugarh = (int)ZTOS((Q)ARG0(node));
+      tn = BDY((LIST)ARG1(node));
+      if ( !tn ) {
+        nzlist_t = NEXT(nzlist_t);
+        continue;
+      }
+      /* tn = [[i1,i2],...] */
+          lh = nd_ipairtospair(tn);
+    }
+    bucket = create_pbucket();
+    stat = nd_sp_f4(m,0,l,bucket);
+    if ( !stat ) {
+      for ( t = l; NEXT(t); t = NEXT(t) );
+      NEXT(t) = d; d = l;
+      d = nd_reconstruct(0,d);
+      continue;
+    }
+    if ( bucket->m < 0 ) continue;
+    col = nd_symbolic_preproc(bucket,0,&s0vect,&rp0);
+    if ( !col ) {
+      for ( t = l; NEXT(t); t = NEXT(t) );
+      NEXT(t) = d; d = l;
+      d = nd_reconstruct(0,d);
+      continue;
+    }
+    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);
+    nflist = nd_f4_red(m,nd_nzlist?lh:l,0,s0vect,col,rp0,nd_gentrace?&ll:0);
+    if ( checkonly && nflist ) return 0;
+    /* adding new bases */
+    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;
 
-                nf1 = ndvtond(m,nf);
-                nd_monic(0,&nf1);
-                nd_removecont(m,nf1);
-                nf = ndtondv(m,nf1);
-            }
-            nh = ndv_newps(m,nf,0,1);
-            d = update_pairs(d,g,nh,0);
-            g = update_base(g,nh);
-        }
-        if ( DP_Print ) { 
-          fprintf(asir_out,"f4red=%d,gblen=%d\n",f4red,length(g)); fflush(asir_out);
-        }
-        if ( nd_gentrace ) {
+        nf1 = ndvtond(m,nf);
+        nd_monic(0,&nf1);
+        nd_removecont(m,nf1);
+        nf = ndtondv(m,nf1);
+      }
+      nh = ndv_newps(m,nf,0);
+      d = update_pairs(d,g,nh,0);
+      g = update_base(g,nh);
+    }
+    if ( DP_Print ) { 
+      fprintf(asir_out,"f4red=%d,gblen=%d\n",f4red,length(g)); fflush(asir_out);
+    }
+    if ( nd_gentrace ) {
       for ( t = ll, tn0 = 0; t; t = NEXT(t) ) {
         NEXTNODE(tn0,tn);
-                STOQ(t->i1,i1); STOQ(t->i2,i2);
-                node = mknode(2,i1,i2); MKLIST(l0,node);
+        STOZ(t->i1,i1); STOZ(t->i2,i2);
+        node = mknode(2,i1,i2); MKLIST(l0,node);
         BDY(tn) = l0;
       }
       if ( tn0 ) NEXT(tn) = 0; MKLIST(l0,tn0);
-            STOQ(sugar,sugarq); node = mknode(2,sugarq,l0); MKLIST(l1,node);
-            MKNODE(node,l1,nzlist); nzlist = node;
-        }
-        if ( nd_nzlist ) nzlist_t = NEXT(nzlist_t);
-        f4red++;
-        if ( nd_f4red && f4red > nd_f4red ) break;
-        if ( nd_rank0 && !nflist ) break;
+        STOZ(sugar,sugarq); node = mknode(2,sugarq,l0); MKLIST(l1,node);
+        MKNODE(node,l1,nzlist); nzlist = node;
     }
-    if ( nd_gentrace ) {
-    MKLIST(l0,reverse_node(nzlist));
-        MKNODE(nd_alltracelist,l0,0);
-    }
+    if ( nd_nzlist ) nzlist_t = NEXT(nzlist_t);
+    f4red++;
+    if ( nd_f4red && f4red > nd_f4red ) break;
+    if ( nd_rank0 && !nflist ) break;
+  }
+  if ( nd_gentrace ) {
+  MKLIST(l0,reverse_node(nzlist));
+      MKNODE(nd_alltracelist,l0,0);
+  }
 #if 0
-    fprintf(asir_out,"ndv_alloc=%d\n",ndv_alloc);
+  fprintf(asir_out,"ndv_alloc=%d\n",ndv_alloc);
 #endif
+  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;
+  return g;
 }
 
 NODE nd_f4_trace(int m,int **indp)
 {
-    int i,nh,stat,index;
+    int i,nh,stat;
     NODE r,g;
     ND_pairs d,l,l0,t;
-    ND spol,red;
-    NDV nf,redv,nfqv,nfv;
-    NM s0,s;
-    NODE rp0,srp0,nflist;
-    int nsp,nred,col,rank,len,k,j,a;
-    UINT c;
-    UINT **spmat;
-    UINT *s0vect,*svect,*p,*v;
-    int *colstat;
-    IndArray *imat;
-    int *rhead;
-    int spcol,sprow;
+    NDV nfqv,nfv;
+    NODE rp0,nflist;
+    int col;
+    UINT *s0vect;
     int sugar;
     PGeoBucket bucket;
     struct oEGT eg0,eg1,eg_f4;
@@ -6969,7 +9000,7 @@ NODE nd_f4_trace(int m,int **indp)
         for ( r = nflist; r; r = NEXT(r) ) {
             nfqv = (NDV)BDY(r);
             ndv_removecont(0,nfqv);
-            if ( !remqi((Q)HCQ(nfqv),m) ) return 0;
+            if ( !remqi((Q)HCZ(nfqv),m) ) return 0;
             if ( nd_nalg ) {
                 ND nf1;
 
@@ -6981,7 +9012,7 @@ 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);
         }
@@ -7095,29 +9126,27 @@ void red_by_vect_2(matrix mat,int *sugar,unsigned long
 
 NODE nd_f4_red_2(ND_pairs sp0,UINT *s0vect,int col,NODE rp0,ND_pairs *nz)
 {
-    int nsp,nred,i,i0,k,rank,row;
-    NODE r0,rp;
-    ND_pairs sp;
+  int nsp,i,rank;
+  NODE r0,rp;
+  ND_pairs sp;
   ND spol;
   NM_ind_pair rt;
-    int *s0hash;
+  int *s0hash;
   UINT *s;
-  int *pivot,*sugar,*head;
+  int *sugar;
   matrix mat;
-    NM m;
-    NODE r;
+  NODE r;
   struct oEGT eg0,eg1,eg2,eg_elim1,eg_elim2;
   int rhead,rsugar,size;
-    unsigned long *v;
+  unsigned long *v;
 
-    get_eg(&eg0);
-init_eg(&eg_search);
-    for ( sp = sp0, nsp = 0; sp; sp = NEXT(sp), nsp++ );
-    nred = length(rp0);
-    mat = alloc_matrix(nsp,col);
-    s0hash = (int *)MALLOC(col*sizeof(int));
-    for ( i = 0, s = s0vect; i < col; i++, s += nd_wpd )
-        s0hash[i] = ndl_hash_value(s);
+  get_eg(&eg0);
+  for ( sp = sp0, nsp = 0; sp; sp = NEXT(sp), nsp++ );
+//  nred = length(rp0);
+  mat = alloc_matrix(nsp,col);
+  s0hash = (int *)MALLOC(col*sizeof(int));
+  for ( i = 0, s = s0vect; i < col; i++, s += nd_wpd )
+    s0hash[i] = ndl_hash_value(s);
 
   sugar = (int *)MALLOC(nsp*sizeof(int));
   for ( i = 0, sp = sp0; sp; sp = NEXT(sp) ) {
@@ -7166,18 +9195,16 @@ init_eg(&eg_search);
 NODE nd_f4_red(int m,ND_pairs sp0,int trace,UINT *s0vect,int col,NODE rp0,ND_pairs *nz)
 {
     IndArray *imat;
-    int nsp,nred,i;
+    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;
 
     if ( m == 2 && nd_rref2 )
      return nd_f4_red_2(sp0,s0vect,col,rp0,nz);
 
-init_eg(&eg_search);
     for ( sp = sp0, nsp = 0; sp; sp = NEXT(sp), nsp++ );
     nred = length(rp0);
     imat = (IndArray *)MALLOC(nred*sizeof(IndArray));
@@ -7185,20 +9212,25 @@ init_eg(&eg_search);
     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);
+      fprintf(asir_out,"%dx%d,",nsp+nred,col);
+      fflush(asir_out);
     }
     rvect = (NM_ind_pair *)MALLOC(nred*sizeof(NM_ind_pair));
-    s0hash = (int *)MALLOC(col*sizeof(int));
-    for ( i = 0, s = s0vect; i < col; i++, s += nd_wpd )
-        s0hash[i] = ndl_hash_value(s);
-    for ( rp = rp0, i = 0; rp; i++, rp = NEXT(rp) ) {
+    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,s0hash,rvect[i]);
+        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 defined(__GNUC__) && SIZEOF_LONG==8
+#if SIZEOF_LONG==8
         r0 = nd_f4_red_mod64_main(m,sp0,nsp,s0vect,col,rvect,rhead,imat,nred,nz);
 #else
         r0 = nd_f4_red_main(m,sp0,nsp,s0vect,col,rvect,rhead,imat,nred,nz);
@@ -7209,9 +9241,6 @@ init_eg(&eg_search);
         r0 = nd_f4_red_lf_main(m,sp0,nsp,trace,s0vect,col,rvect,rhead,imat,nred);
     else
         r0 = nd_f4_red_q_main(sp0,nsp,trace,s0vect,col,rvect,rhead,imat,nred);
-#if 0
-    if ( DP_Print ) print_eg("search",&eg_search);
-#endif
     return r0;
 }
 
@@ -7221,7 +9250,7 @@ NODE nd_f4_red_main(int m,ND_pairs sp0,int nsp,UINT *s
         NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred,ND_pairs *nz)
 {
     int spcol,sprow,a;
-    int i,j,k,l,rank;
+    int i,j,k,rank;
     NODE r0,r;
     ND_pairs sp;
     ND spol;
@@ -7247,7 +9276,7 @@ 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));
@@ -7303,52 +9332,48 @@ NODE nd_f4_red_main(int m,ND_pairs sp0,int nsp,UINT *s
     return r0;
 }
 
-#if defined(__GNUC__) && SIZEOF_LONG==8
-/* for Fp, 2^15=<p<2^29 */
-
-NODE nd_f4_red_mod64_main(int m,ND_pairs sp0,int nsp,UINT *s0vect,int col,
-        NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred,ND_pairs *nz)
+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;
+    int sprow,a;
+    int i,rank;
     NODE r0,r;
     ND_pairs sp;
     ND spol;
-    U64 **spmat;
-    U64 *svect,*cvect;
-    U64 *v;
+    UINT **spmat;
+    UINT *svect;
     int *colstat;
     struct oEGT eg0,eg1,eg2,eg_f4,eg_f4_1,eg_f4_2;
     int maxrs;
     int *spsugar;
-    ND_pairs *spactive;
+    SIG *spsig;
 
-    spcol = col-nred;
     get_eg(&eg0);
     /* elimination (1st step) */
-    spmat = (U64 **)MALLOC(nsp*sizeof(U64 *));
-    svect = (U64 *)MALLOC(col*sizeof(U64));
-    cvect = (U64 *)MALLOC(col*sizeof(U64));
+    spmat = (UINT **)MALLOC(nsp*sizeof(UINT *));
     spsugar = (int *)MALLOC(nsp*sizeof(int));
-    spactive = !nz?0:(ND_pairs *)MALLOC(nsp*sizeof(ND_pairs));
+    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 ) continue;
-        nd_to_vect64(m,s0vect,col,spol,svect);
-        maxrs = ndv_reduce_vect64(m,svect,cvect,col,imat,rvect,nred);
+        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] = v = (U64 *)MALLOC_ATOMIC(spcol*sizeof(U64));
-            for ( j = k = 0; j < col; j++ )
-                if ( !rhead[j] ) v[k++] = (UINT)svect[j];
+            spmat[sprow] = svect;
             spsugar[sprow] = MAX(maxrs,SG(spol));
-            if ( nz )
-            spactive[sprow] = sp;
+            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);
+    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);
@@ -7357,45 +9382,39 @@ NODE nd_f4_red_mod64_main(int m,ND_pairs sp0,int nsp,U
     for ( i = 0; i < nred; i++ ) GCFREE(imat[i]->index.c);
 
     /* elimination (2nd step) */
-    colstat = (int *)MALLOC(spcol*sizeof(int));
-    rank = nd_gauss_elim_mod64(spmat,spsugar,spactive,sprow,spcol,m,colstat);
+    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 < rank; i++ ) {
-        NEXTNODE(r0,r); BDY(r) = 
-          (pointer)vect64_to_ndv(spmat[i],spcol,col,rhead,s0vect);
-        SG((NDV)BDY(r)) = spsugar[i];
+    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;
-
-    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);
         fprintf(asir_out,"nsp=%d,nred=%d,spmat=(%d,%d),rank=%d ",
-            nsp,nred,sprow,spcol,rank);
+            nsp,nred,sprow,col,rank);
         fprintf(asir_out,"%.3fsec,",eg_f4.exectime);
     }
-    if ( nz ) {
-        for ( i = 0; i < rank-1; i++ ) NEXT(spactive[i]) = spactive[i+1];
-        if ( rank > 0 ) {
-            NEXT(spactive[rank-1]) = 0;
-            *nz = spactive[0];
-        } else
-            *nz = 0;
-    }
     return r0;
 }
-#endif
 
+
 /* for small finite fields */
 
 NODE nd_f4_red_sf_main(int m,ND_pairs sp0,int nsp,UINT *s0vect,int col,
         NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred,ND_pairs *nz)
 {
     int spcol,sprow,a;
-    int i,j,k,l,rank;
+    int i,j,k,rank;
     NODE r0,r;
     ND_pairs sp;
     ND spol;
@@ -7475,7 +9494,7 @@ NODE nd_f4_red_lf_main(int m,ND_pairs sp0,int nsp,int 
         NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred)
 {
     int spcol,sprow,a;
-    int i,j,k,l,rank;
+    int i,j,k,rank;
     NODE r0,r;
     ND_pairs sp;
     ND spol;
@@ -7557,7 +9576,7 @@ NODE nd_f4_red_q_main(ND_pairs sp0,int nsp,int trace,U
         NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred)
 {
     int spcol,sprow,a;
-    int i,j,k,l,rank;
+    int i,j,k,rank;
     NODE r0,r;
     ND_pairs sp;
     ND spol;
@@ -7711,7 +9730,7 @@ NDV nd_recv_ndv()
 
 int nd_gauss_elim_q(Z **mat0,int *sugar,int row,int col,int *colstat)
 {
-    int i,j,t,c,rank,inv;
+    int i,j,c,rank;
     int *ci,*ri;
     Z dn;
     MAT m,nm;
@@ -7800,85 +9819,53 @@ int nd_gauss_elim_mod(UINT **mat0,int *sugar,ND_pairs 
     return rank;
 }
 
-#if defined(__GNUC__) && SIZEOF_LONG==8
-
-int nd_gauss_elim_mod64(U64 **mat,int *sugar,ND_pairs *spactive,int row,int col,int md,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)
 {
-  int i,j,k,l,rank,s;
-  U64 inv;
-  U64 a;
-  UINT c;
-  U64 *t,*pivot,*pk;
-  UINT *ck;
-  UINT **cmat;
-  UINT *ct;
-  ND_pairs pair;
+  int i,j,k,rank,s;
+  UINT inv;
+  UINT a;
+  UINT *pk;
+  int *used;
 
-  cmat = (UINT **)MALLOC(row*sizeof(UINT *));
-  for ( i = 0; i < row; i++ ) {
-    cmat[i] = MALLOC_ATOMIC(col*sizeof(UINT));
-    bzero(cmat[i],col*sizeof(UINT));
-  }
-
-  for ( rank = 0, j = 0; j < col; j++ ) {
-    for ( i = rank; i < row; i++ ) {
-      a = mat[i][j]; c = cmat[i][j];
-      MOD128(a,c,md);
-      mat[i][j] = a; cmat[i][j] = 0;
-    }
-    for ( i = rank; i < row; i++ )
-      if ( mat[i][j] )
-        break;
+  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
+    } else {
       colstat[j] = 1;
-    if ( i != rank ) {
-      t = mat[i]; mat[i] = mat[rank]; mat[rank] = t;
-      ct = cmat[i]; cmat[i] = cmat[rank]; cmat[rank] = ct;
-      s = sugar[i]; sugar[i] = sugar[rank]; sugar[rank] = s;
-      if ( spactive ) {
-        pair = spactive[i]; spactive[i] = spactive[rank]; 
-        spactive[rank] = pair;
-      }
+      used[i] = 1;
     }
     /* column j is normalized */
-    s = sugar[rank];
-    inv = invm((UINT)mat[rank][j],md);
+    s = sugar[i];
+    inv = invm(mat[i][j],md);
     /* normalize pivot row */
-    for ( k = j, pk = mat[rank]+j, ck = cmat[rank]+j; k < col; k++, pk++, ck++ ) {
-      a = *pk; c = *ck; MOD128(a,c,md); *pk = (a*inv)%md; *ck = 0;
+    for ( k = j, pk = mat[i]+j; k < col; k++, pk++ ) {
+      DMAR(*pk,inv,0,md,*pk);
     }
-    for ( i = rank+1; i < row; i++ ) {
-      if ( (a = mat[i][j]) != 0 ) {
-        sugar[i] = MAX(sugar[i],s);
-        red_by_vect64(md,mat[i]+j,cmat[i]+j,mat[rank]+j,(int)(md-a),col-j);
+    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++;
   }
-  for ( j = col-1, l = rank-1; j >= 0; j-- )
-    if ( colstat[j] ) {
-      for ( k = j, pk = mat[l]+j, ck = cmat[l]+j; k < col; k++, pk++, ck++ ) {
-        a = *pk; c = *ck; MOD128(a,c,md); *pk = a; *ck = 0;
-      }
-      s = sugar[l];
-      for ( i = 0; i < l; i++ ) {
-        a = mat[i][j]; c = cmat[i][j]; MOD128(a,c,md); mat[i][j] = a; cmat[i][j] = 0;
-        if ( a ) {
-          sugar[i] = MAX(sugar[i],s);
-          red_by_vect64(md,mat[i]+j,cmat[i]+j,mat[l]+j,(int)(md-a),col-j);
-        }
-      }
-      l--;
-    }
-  for ( i = 0; i < row; i++ ) GCFREE(cmat[i]);
-  GCFREE(cmat);
+  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;
 }
-#endif
 
+
 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;
@@ -7941,7 +9928,9 @@ 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;
 }
 
@@ -7950,7 +9939,7 @@ void ndv_save(NDV p,int index)
     FILE *s;
     char name[BUFSIZ];
     short id;
-    int nv,sugar,len,n,i,td,e,j;
+    int nv,sugar,len,i,td,e,j;
     NMV m;
     unsigned int *dl;
     int mpos;
@@ -7970,7 +9959,7 @@ void ndv_save(NDV p,int index)
     write_int(s,(unsigned int *)&len);
 
     for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
-        saveobj(s,(Obj)CQ(m));
+        saveobj(s,(Obj)CZ(m));
         dl = DL(m);
         td = TD(dl);
         write_int(s,(unsigned int *)&td);
@@ -8016,7 +10005,7 @@ NDV ndv_load(int index)
     FILE *s;
     char name[BUFSIZ];
     short id;
-    int nv,sugar,len,n,i,td,e,j;
+    int nv,sugar,len,i,td,e,j;
     NDV d;
     NMV m0,m;
     unsigned int *dl;
@@ -8036,7 +10025,7 @@ NDV ndv_load(int index)
 
     m0 = m = MALLOC(len*nmv_adv);
     for ( i = 0; i < len; i++, NMV_ADV(m) ) {
-        loadobj(s,&obj); CQ(m) = (Z)obj;
+        loadobj(s,&obj); CZ(m) = (Z)obj;
         dl = DL(m);
         ndl_zero(dl);
         read_int(s,(unsigned int *)&td); TD(dl) = td;
@@ -8135,7 +10124,7 @@ void nd_det(int mod,MAT f,P *rp)
             for ( j = 0; j < n; j++ ) {
                 if ( !m[i][j] ) continue;
                 lgp(m[i][j],&nm,&dn);
-                gcdz(dn0,dn,&gn); divz(dn0,gn,&qn); mulz(qn,dn,&dn0);
+                gcdz(dn0,dn,&gn); divsz(dn0,gn,&qn); mulz(qn,dn,&dn0);
             }
             if ( !UNIZ(dn0) ) {
                 ds = dn0;
@@ -8249,16 +10238,15 @@ ND ndv_mul_nmv_trunc(int mod,NMV m0,NDV p,UINT *d)
     NM mr,mr0;
     NM tnm;
     NMV m;
-    UINT *d0,*dt,*dm;
-    int c,n,td,i,c1,c2,len;
+    UINT *d0;
+    int c,i,c1,c2,len;
     Z q;
     ND r;
 
     if ( !p ) return 0;
     else {
-        n = NV(p); m = BDY(p); len = LEN(p);
+        m = BDY(p); len = LEN(p);
         d0 = DL(m0);
-        td = TD(d);
         mr0 = 0;
         NEWNM(tnm);
         if ( mod ) {
@@ -8272,12 +10260,12 @@ ND ndv_mul_nmv_trunc(int mod,NMV m0,NDV p,UINT *d)
                 }
             }
         } else {
-            q = CQ(m0);
+            q = CZ(m0);
             for ( i = 0; i < len; i++, NMV_ADV(m) ) {
                 ndl_add(DL(m),d0,DL(tnm));
                 if ( ndl_reducible(DL(tnm),d) ) {
                     NEXTNM(mr0,mr);
-                    mulz(CQ(m),q,&CQ(mr));
+                    mulz(CZ(m),q,&CZ(mr));
                     ndl_copy(DL(tnm),DL(mr));
                 }
             }
@@ -8296,7 +10284,7 @@ ND ndv_mul_nmv_trunc(int mod,NMV m0,NDV p,UINT *d)
 
 void nd_det_reconstruct(NDV **dm,int n,int j,NDV d)
 {
-    int i,obpe,oadv,h,k,l;
+    int obpe,oadv,k,l;
     static NM prev_nm_free_list;
     EPOS oepos;
 
@@ -8331,7 +10319,7 @@ void nd_det_reconstruct(NDV **dm,int n,int j,NDV d)
 
 UINT *nd_det_compute_bound(NDV **dm,int n,int j)
 {
-    UINT *d0,*d1,*d,*t,*r;
+    UINT *d0,*d;
     int k,l,i;
 
     d0 = (UINT *)MALLOC(nd_nvar*sizeof(UINT));
@@ -8348,7 +10336,7 @@ UINT *nd_det_compute_bound(NDV **dm,int n,int j)
 
 DL nd_separate_d(UINT *d,UINT *trans)
 {
-    int n,td,i,e,j;
+    int td,i,e,j;
     DL a;
 
     ndl_zero(trans);
@@ -8381,19 +10369,16 @@ DL nd_separate_d(UINT *d,UINT *trans)
 
 int nd_monic(int mod,ND *p)
 {
-    UINT *trans,*t;
     DL alg;
     MP mp0,mp;
-    NM m,m0,m1,ma0,ma,mb,mr0,mr;
+    NM m,ma0,ma,mb,mr0,mr;
     ND r;
     DL dl;
     DP nm;
-    NDV ndv;
     DAlg inv,cd;
-    ND s,c;
     Z l,mul;
     Z ln;
-    int n,ntrans,i,e,td,is_lc,len;
+    int i,e,td,is_lc,len;
     NumberField nf;
     struct oEGT eg0,eg1;
 
@@ -8406,14 +10391,14 @@ int nd_monic(int mod,ND *p)
     is_lc = 1;
     while ( 1 ) {
         NEWMP(mp0); mp = mp0;
-        mp->c = (Obj)CQ(m);
+        mp->c = (Obj)CZ(m);
         mp->dl = nd_separate_d(DL(m),DL(ma));
         NEWNM(mb);
         for ( m = NEXT(m); m; m = NEXT(m) ) {
             alg = nd_separate_d(DL(m),DL(mb));
             if ( !ndl_equal(DL(ma),DL(mb)) )
                 break;
-            NEXTMP(mp0,mp); mp->c = (Obj)CQ(m); mp->dl = alg;
+            NEXTMP(mp0,mp); mp->c = (Obj)CZ(m); mp->dl = alg;
         }
         NEXT(mp) = 0;
         MKDP(nd_nalg,mp0,nm);
@@ -8446,10 +10431,10 @@ int nd_monic(int mod,ND *p)
     /* l = lcm(denoms) */
     l = ln;
     for ( mr0 = 0, m = ma0; m; m = NEXT(m) ) {
-        divz(l,CA(m)->dn,&mul);
+        divsz(l,CA(m)->dn,&mul);
         for ( mp = BDY(CA(m)->nm); mp; mp = NEXT(mp) ) {
             NEXTNM(mr0,mr);
-            mulz((Z)mp->c,mul,&CQ(mr));
+            mulz((Z)mp->c,mul,&CZ(mr));
             dl = mp->dl;
             td = TD(DL(m));
             ndl_copy(DL(m),DL(mr));
@@ -8489,7 +10474,7 @@ P ndc_div(int mod,union oNDC a,union oNDC b)
     int inv,t;
 
     if ( mod == -1 ) c.m = _mulsf(a.m,_invsf(b.m));
-    else if ( mod == -2 ) divlf(a.gz,b.gz,&c.gz);
+    else if ( mod == -2 ) divlf(a.z,b.z,&c.z);
     else if ( mod ) {
         inv = invm(b.m,mod);
         DMAR(a.m,inv,0,mod,t); c.m = t;
@@ -8509,9 +10494,9 @@ P ndctop(int mod,union oNDC c)
     if ( mod == -1 ) {
         e = IFTOF(c.m); MKGFS(e,gfs); return (P)gfs;
     } else if ( mod == -2 ) {
-       q = c.gz; return (P)q;
+       q = c.z; return (P)q;
     } else if ( mod > 0 ) {
-        STOQ(c.m,q); return (P)q;
+        STOZ(c.m,q); return (P)q;
     } else
         return (P)c.p;
 }
@@ -8529,7 +10514,7 @@ void finalize_tracelist(int i,P cont)
     MKLIST(l,node); MKNODE(node,l,nd_tracelist);
     nd_tracelist = node;
   }
-  STOQ(i,iq);
+  STOZ(i,iq);
   nd_tracelist = reverse_node(nd_tracelist);
   MKLIST(l,nd_tracelist);
   node = mknode(2,iq,l); MKLIST(l,node);
@@ -8552,69 +10537,131 @@ void conv_ilist(int demand,int trace,NODE g,int **indp
   if ( indp ) *indp = ind;
 }
 
-void parse_nd_option(NODE opt)
+NODE conv_ilist_s(int demand,int trace,int **indp)
 {
-    NODE t,p,u;
+  int n,i;
+  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(VL vl,NODE opt)
+{
+  NODE t,p,u;
   int i,s,n;
-    char *key;
-    Obj value;
+  char *key;
+  Obj value;
+  VL oldvl;
 
-    nd_gentrace = 0; nd_gensyz = 0; nd_nora = 0; nd_gbblock = 0;
+  nd_gentrace = 0; nd_gensyz = 0; nd_nora = 0; nd_norb = 0; nd_gbblock = 0;
   nd_newelim = 0; nd_intersect = 0; nd_nzlist = 0;
   nd_splist = 0; nd_check_splist = 0;
-    nd_sugarweight = 0;
-    nd_f4red =0;
-    nd_rank0 = 0;
-    for ( t = opt; t; t = NEXT(t) ) {
-        p = BDY((LIST)BDY(t));
-        key = BDY((STRING)BDY(p));
-        value = (Obj)BDY(NEXT(p));
-        if ( !strcmp(key,"gentrace") )
-            nd_gentrace = value?1:0;
-        else if ( !strcmp(key,"gensyz") )
-            nd_gensyz = value?1:0;
-        else if ( !strcmp(key,"nora") )
-            nd_nora = value?1:0;
-        else if ( !strcmp(key,"gbblock") ) {
-            if ( value && OID(value) == O_LIST ) {
+  nd_sugarweight = 0; nd_f4red =0; nd_rank0 = 0;
+  nd_f4_td = 0; nd_sba_f4step = 2; nd_sba_pot = 0; nd_sba_largelcm = 0;
+  nd_sba_dontsort = 0; nd_top = 0; nd_sba_redundant_check = 0;
+  nd_sba_syz = 0; nd_sba_modord = 0; nd_sba_inputisgb = 0;
+  nd_hpdata = 0; nd_sba_heu = 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++] = QTOS((Q)BDY(p));
-          nd_gbblock[i++] = s+QTOS((Q)BDY(NEXT(p)))-1;
+          s = nd_gbblock[i++] = (int)ZTOS((Q)BDY(p));
+          nd_gbblock[i++] = (int)(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 = (int)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 = QTOS((Q)ARG3(u));
-           }
+      if ( value ) {
+        u = BDY((LIST)value);
+        nd_nzlist = BDY((LIST)ARG2(u));
+        nd_bpe = (int)ZTOS((Q)ARG3(u));
+      }
     } else if ( !strcmp(key,"f4red") ) {
-       nd_f4red = QTOS((Q)value);
+      nd_f4red = (int)ZTOS((Q)value);
     } else if ( !strcmp(key,"rank0") ) {
-            nd_rank0 = value?1:0;
+      nd_rank0 = value?1:0;
     } else if ( !strcmp(key,"splist") ) {
-            nd_splist = value?1:0;
+      nd_splist = value?1:0;
     } else if ( !strcmp(key,"check_splist") ) {
       nd_check_splist = BDY((LIST)value);
+    } else if ( !strcmp(key,"hpdata") ) {
+      if ( value )
+        nd_hpdata = BDY((LIST)value);
     } else if ( !strcmp(key,"sugarweight") ) {
       u = BDY((LIST)value);
-            n = length(u);
-            nd_sugarweight = MALLOC(n*sizeof(int));
+      n = length(u);
+      nd_sugarweight = MALLOC(n*sizeof(int));
       for ( i = 0; i < n; i++, u = NEXT(u) ) 
-                nd_sugarweight[i] = QTOS((Q)BDY(u));
+        nd_sugarweight[i] = (int)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?(int)ZTOS((Q)value):0;
+    } else if ( !strcmp(key,"sba_pot") ) {
+      nd_sba_pot = (int)ZTOS((Q)value);
+    } else if ( !strcmp(key,"sba_largelcm") ) {
+      nd_sba_largelcm = value?1:0;
+    } else if ( !strcmp(key,"sba_dontsort") ) {
+      nd_sba_dontsort = value?1:0;
+    } else if ( !strcmp(key,"sba_syz") ) {
+      nd_sba_syz = value?1:0;
+    } else if ( !strcmp(key,"sba_heu") ) {
+      nd_sba_heu = value?1:0;
+    } else if ( !strcmp(key,"sba_modord") ) {
+      // value=[vlist,ordspec,weight]
+      u = BDY((LIST)value);
+      pltovl((LIST)ARG0(u),&oldvl);
+      nd_sba_modord = create_comp_sig_spec(vl,oldvl,(Obj)ARG1(u),argc(u)==3?ARG2(u):0);
+    } else if ( !strcmp(key,"sba_gbinput") ) {
+      nd_sba_inputisgb = value?1:0;
+      if ( nd_sba_inputisgb != 0 ) {
+        // value=[vlist,ordspec,weight]
+        u = BDY((LIST)value);
+        pltovl((LIST)ARG0(u),&oldvl);
+        nd_sba_modord = create_comp_sig_spec(vl,oldvl,(Obj)ARG1(u),argc(u)==3?ARG2(u):0);
+      }
+    } else if ( !strcmp(key,"sba_redundant_check") ) {
+      nd_sba_redundant_check = value?1:0;
+    } else if ( !strcmp(key,"top") ) {
+      nd_top = value?1:0;
     }
-    }
+  }
+  if ( nd_sba_syz ) nd_sba_dontsort = 1;
 }
 
 ND mdptond(DP d);
@@ -8636,7 +10683,7 @@ ND mdptond(DP d)
   else {
     NEWNM(m);
     dltondl(NV(d),BDY(d)->dl,DL(m));
-    CQ(m) = (Z)BDY(d)->c;
+    CZ(m) = (Z)BDY(d)->c;
     NEXT(m) = 0;
     MKND(NV(d),m,1,r);
   }
@@ -8667,7 +10714,7 @@ ND nd_mul_nm(int mod,NM m0,ND p)
 ND nd_mul_nm_lf(NM m0,ND p)
 {
   UINT *d0;
-  Z c0,c1,c;
+  Z c0,c1;
   NM tm,mr,mr0;
   ND r;
 
@@ -8677,7 +10724,7 @@ ND nd_mul_nm_lf(NM m0,ND p)
   mr0 = 0;
   for ( tm = BDY(p); tm; tm = NEXT(tm) ) {
     NEXTNM(mr0,mr);
-    c = CZ(tm); mullf(c0,CZ(tm),&c1); CZ(mr) = c1;
+    mullf(c0,CZ(tm),&c1); CZ(mr) = c1;
     ndl_add(d0,DL(tm),DL(mr));
   }
   NEXT(mr) = 0;
@@ -8701,10 +10748,10 @@ ND *btog(NODE ti,ND **p,int nb,int mod)
   s = BDY((LIST)BDY(t));
     if ( ARG0(s) ) {
     m = mdptond((DP)ARG2(s));
-    ptomp(mod,(P)HCQ(m),&c);
+    ptomp(mod,(P)HCZ(m),&c);
     if ( (ci = ((MQ)c)->cont) != 0 ) {
       HCM(m) = ci;
-      pi = p[QTOS((Q)ARG1(s))];
+      pi = p[ZTOS((Q)ARG1(s))];
       for ( i = 0; i < nb; i++ ) {
       tp = nd_mul_nm(mod,BDY(m),pi[i]);
         add_pbucket(mod,r[i],tp);
@@ -8742,10 +10789,10 @@ ND *btog_lf(NODE ti,ND **p,int nb)
     s = BDY((LIST)BDY(t));
     if ( ARG0(s) ) {
       m = mdptond((DP)ARG2(s));
-      simp_ff((Obj)HCQ(m),(Obj *)&lm);
+      simp_ff((Obj)HCZ(m),(Obj *)&lm);
       if ( lm ) {
         lmtolf(lm,&lf); HCZ(m) = lf;
-        pi = p[QTOS((Q)ARG1(s))];
+        pi = p[ZTOS((Q)ARG1(s))];
         for ( i = 0; i < nb; i++ ) {
           tp = nd_mul_nm_lf(BDY(m),pi[i]);
           add_pbucket(-2,r[i],tp);
@@ -8766,7 +10813,7 @@ ND *btog_lf(NODE ti,ND **p,int nb)
 ND btog_one(NODE ti,ND *p,int nb,int mod)
 {
   PGeoBucket r;
-  int i,ci,j;
+  int ci,j;
   NODE t,s;
   ND m,tp;
   ND pi,rd;
@@ -8777,10 +10824,10 @@ ND btog_one(NODE ti,ND *p,int nb,int mod)
   s = BDY((LIST)BDY(t));
     if ( ARG0(s) ) {
     m = mdptond((DP)ARG2(s));
-    ptomp(mod,(P)HCQ(m),&c);
+    ptomp(mod,(P)HCZ(m),&c);
     if ( (ci = ((MQ)c)->cont) != 0 ) {
       HCM(m) = ci;
-      pi = p[j=QTOS((Q)ARG1(s))];
+      pi = p[j=(int)ZTOS((Q)ARG1(s))];
     if ( !pi ) {
       pi = nd_load_mod(j);
       tp = nd_mul_nm(mod,BDY(m),pi);
@@ -8819,8 +10866,8 @@ MAT nd_btog(LIST f,LIST v,int mod,struct order_spec *o
   if ( mod == -2 )
     return nd_btog_lf(f,v,ord,tlist,rp);
 
-  parse_nd_option(current_option);
   get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+  parse_nd_option(vv,current_option);
   for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
   switch ( ord->id ) {
     case 1:
@@ -8832,7 +10879,7 @@ MAT nd_btog(LIST f,LIST v,int mod,struct order_spec *o
   }
   nd_init_ord(ord);
 #if 0
-  nd_bpe = QTOS((Q)ARG7(BDY(tlist)));
+  nd_bpe = ZTOS((Q)ARG7(BDY(tlist)));
 #else
   nd_bpe = 32;
 #endif
@@ -8842,7 +10889,7 @@ MAT nd_btog(LIST f,LIST v,int mod,struct order_spec *o
   ind = BDY((LIST)ARG4(BDY(tlist)));
   perm = BDY((LIST)BDY(permtrace)); trace =NEXT(permtrace);
   for ( i = length(perm)-1, t = trace; t; t = NEXT(t) ) {
-    j = QTOS((Q)BDY(BDY((LIST)BDY(t))));
+    j = (int)ZTOS((Q)BDY(BDY((LIST)BDY(t))));
   if ( j > i ) i = j;
   }
   n = i+1;
@@ -8850,7 +10897,7 @@ MAT nd_btog(LIST f,LIST v,int mod,struct order_spec *o
   p = (ND **)MALLOC(n*sizeof(ND *));
   for ( t = perm, i = 0; t; t = NEXT(t), i++ ) {
     pi = BDY((LIST)BDY(t)); 
-    pi0 = QTOS((Q)ARG0(pi)); pi1 = QTOS((Q)ARG1(pi));
+    pi0 = (int)ZTOS((Q)ARG0(pi)); pi1 = (int)ZTOS((Q)ARG1(pi));
     p[pi0] = c = (ND *)MALLOC(nb*sizeof(ND));
     ptomp(mod,(P)ARG2(pi),&inv);
     ((MQ)inv)->cont = invm(((MQ)inv)->cont,mod);
@@ -8861,17 +10908,17 @@ MAT nd_btog(LIST f,LIST v,int mod,struct order_spec *o
   for ( t = trace,i=0; t; t = NEXT(t), i++ ) {
     printf("%d ",i); fflush(stdout);
     ti = BDY((LIST)BDY(t));
-    p[j=QTOS((Q)ARG0(ti))] = btog(BDY((LIST)ARG1(ti)),p,nb,mod);
+    p[j=(int)ZTOS((Q)ARG0(ti))] = btog(BDY((LIST)ARG1(ti)),p,nb,mod);
   }
   for ( t = intred, i=0; t; t = NEXT(t), i++ ) {
     printf("%d ",i); fflush(stdout);
     ti = BDY((LIST)BDY(t));
-    p[j=QTOS((Q)ARG0(ti))] = btog(BDY((LIST)ARG1(ti)),p,nb,mod);
+    p[j=(int)ZTOS((Q)ARG0(ti))] = btog(BDY((LIST)ARG1(ti)),p,nb,mod);
   }
   m = length(ind);
   MKMAT(mat,nb,m);
   for ( j = 0, t = ind; j < m; j++, t = NEXT(t) ) 
-    for ( i = 0, c = p[QTOS((Q)BDY(t))]; i < nb; i++ ) 
+    for ( i = 0, c = p[ZTOS((Q)BDY(t))]; i < nb; i++ ) 
       BDY(mat)[i][j] = ndtodp(mod,c[i]);
   return mat;
 }
@@ -8888,8 +10935,8 @@ MAT nd_btog_lf(LIST f,LIST v,struct order_spec *ord,LI
   LM lm;
   Z lf,inv;
 
-  parse_nd_option(current_option);
   get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+  parse_nd_option(vv,current_option);
   for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
   switch ( ord->id ) {
     case 1:
@@ -8901,7 +10948,7 @@ MAT nd_btog_lf(LIST f,LIST v,struct order_spec *ord,LI
   }
   nd_init_ord(ord);
 #if 0
-  nd_bpe = QTOS((Q)ARG7(BDY(tlist)));
+  nd_bpe = ZTOS((Q)ARG7(BDY(tlist)));
 #else
   nd_bpe = 32;
 #endif
@@ -8911,7 +10958,7 @@ MAT nd_btog_lf(LIST f,LIST v,struct order_spec *ord,LI
   ind = BDY((LIST)ARG4(BDY(tlist)));
   perm = BDY((LIST)BDY(permtrace)); trace =NEXT(permtrace);
   for ( i = length(perm)-1, t = trace; t; t = NEXT(t) ) {
-    j = QTOS((Q)BDY(BDY((LIST)BDY(t))));
+    j = (int)ZTOS((Q)BDY(BDY((LIST)BDY(t))));
   if ( j > i ) i = j;
   }
   n = i+1;
@@ -8919,7 +10966,7 @@ MAT nd_btog_lf(LIST f,LIST v,struct order_spec *ord,LI
   p = (ND **)MALLOC(n*sizeof(ND *));
   for ( t = perm, i = 0; t; t = NEXT(t), i++ ) {
     pi = BDY((LIST)BDY(t)); 
-    pi0 = QTOS((Q)ARG0(pi)); pi1 = QTOS((Q)ARG1(pi));
+    pi0 = (int)ZTOS((Q)ARG0(pi)); pi1 = (int)ZTOS((Q)ARG1(pi));
     p[pi0] = c = (ND *)MALLOC(nb*sizeof(ND));
     simp_ff((Obj)ARG2(pi),(Obj *)&lm); lmtolf(lm,&lf); invz(lf,current_mod_lf,&inv);
     u = ptond(CO,vv,(P)ONE);
@@ -8929,17 +10976,17 @@ MAT nd_btog_lf(LIST f,LIST v,struct order_spec *ord,LI
   for ( t = trace,i=0; t; t = NEXT(t), i++ ) {
     printf("%d ",i); fflush(stdout);
     ti = BDY((LIST)BDY(t));
-    p[j=QTOS((Q)ARG0(ti))] = btog_lf(BDY((LIST)ARG1(ti)),p,nb);
+    p[j=(int)ZTOS((Q)ARG0(ti))] = btog_lf(BDY((LIST)ARG1(ti)),p,nb);
   }
   for ( t = intred, i=0; t; t = NEXT(t), i++ ) {
     printf("%d ",i); fflush(stdout);
     ti = BDY((LIST)BDY(t));
-    p[j=QTOS((Q)ARG0(ti))] = btog_lf(BDY((LIST)ARG1(ti)),p,nb);
+    p[j=(int)ZTOS((Q)ARG0(ti))] = btog_lf(BDY((LIST)ARG1(ti)),p,nb);
   }
   m = length(ind);
   MKMAT(mat,nb,m);
   for ( j = 0, t = ind; j < m; j++, t = NEXT(t) ) 
-    for ( i = 0, c = p[QTOS((Q)BDY(t))]; i < nb; i++ ) 
+    for ( i = 0, c = p[ZTOS((Q)BDY(t))]; i < nb; i++ ) 
       BDY(mat)[i][j] = ndtodp(-2,c[i]);
   return mat;
 }
@@ -8951,7 +10998,6 @@ VECT nd_btog_one(LIST f,LIST v,int mod,struct order_sp
   VL fv,tv,vv;
   NODE permtrace,perm,trace,intred,ind,t,pi,ti;
   ND *p;
-  ND *c;
   ND u;
   P inv;
   VECT vect;
@@ -8959,8 +11005,8 @@ VECT nd_btog_one(LIST f,LIST v,int mod,struct order_sp
   if ( mod == -2 )
     error("nd_btog_one : not implemented yet for a large finite field");
 
-  parse_nd_option(current_option);
   get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+  parse_nd_option(vv,current_option);
   for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
   switch ( ord->id ) {
     case 1:
@@ -8972,7 +11018,7 @@ VECT nd_btog_one(LIST f,LIST v,int mod,struct order_sp
   }
   nd_init_ord(ord);
 #if 0
-  nd_bpe = QTOS((Q)ARG7(BDY(tlist)));
+  nd_bpe = ZTOS((Q)ARG7(BDY(tlist)));
 #else
   nd_bpe = 32;
 #endif
@@ -8982,7 +11028,7 @@ VECT nd_btog_one(LIST f,LIST v,int mod,struct order_sp
   ind = BDY((LIST)ARG4(BDY(tlist)));
   perm = BDY((LIST)BDY(permtrace)); trace =NEXT(permtrace);
   for ( i = length(perm)-1, t = trace; t; t = NEXT(t) ) {
-    j = QTOS((Q)BDY(BDY((LIST)BDY(t))));
+    j = (int)ZTOS((Q)BDY(BDY((LIST)BDY(t))));
   if ( j > i ) i = j;
   }
   n = i+1;
@@ -8990,7 +11036,7 @@ VECT nd_btog_one(LIST f,LIST v,int mod,struct order_sp
   p = (ND *)MALLOC(n*sizeof(ND *));
   for ( t = perm, i = 0; t; t = NEXT(t), i++ ) {
     pi = BDY((LIST)BDY(t)); 
-  pi0 = QTOS((Q)ARG0(pi)); pi1 = QTOS((Q)ARG1(pi));
+  pi0 = (int)ZTOS((Q)ARG0(pi)); pi1 = (int)ZTOS((Q)ARG1(pi));
   if ( pi1 == pos ) {
     ptomp(mod,(P)ARG2(pi),&inv); 
     ((MQ)inv)->cont = invm(((MQ)inv)->cont,mod);
@@ -9002,7 +11048,7 @@ VECT nd_btog_one(LIST f,LIST v,int mod,struct order_sp
   for ( t = trace,i=0; t; t = NEXT(t), i++ ) {
   printf("%d ",i); fflush(stdout);
     ti = BDY((LIST)BDY(t));
-    p[j=QTOS((Q)ARG0(ti))] = btog_one(BDY((LIST)ARG1(ti)),p,nb,mod);
+    p[j=(int)ZTOS((Q)ARG0(ti))] = btog_one(BDY((LIST)ARG1(ti)),p,nb,mod);
     if ( Demand ) {
         nd_save_mod(p[j],j); nd_free(p[j]); p[j] = 0;
   }
@@ -9010,7 +11056,7 @@ VECT nd_btog_one(LIST f,LIST v,int mod,struct order_sp
   for ( t = intred, i=0; t; t = NEXT(t), i++ ) {
   printf("%d ",i); fflush(stdout);
     ti = BDY((LIST)BDY(t));
-    p[j=QTOS((Q)ARG0(ti))] = btog_one(BDY((LIST)ARG1(ti)),p,nb,mod);
+    p[j=(int)ZTOS((Q)ARG0(ti))] = btog_one(BDY((LIST)ARG1(ti)),p,nb,mod);
     if ( Demand ) {
         nd_save_mod(p[j],j); nd_free(p[j]); p[j] = 0;
   }
@@ -9018,9 +11064,9 @@ VECT nd_btog_one(LIST f,LIST v,int mod,struct order_sp
   m = length(ind);
   MKVECT(vect,m);
   for ( j = 0, t = ind; j < m; j++, t = NEXT(t) ) {
-  u = p[QTOS((Q)BDY(t))];
+  u = p[ZTOS((Q)BDY(t))];
   if ( !u ) {
-    u = nd_load_mod(QTOS((Q)BDY(t)));
+    u = nd_load_mod((int)ZTOS((Q)BDY(t)));
     BDY(vect)[j] = ndtodp(mod,u);
     nd_free(u);
   } else
@@ -9049,32 +11095,22 @@ void ndv_print_lf(NDV p)
 
 void nd_f4_lf_trace(LIST f,LIST v,int trace,int homo,struct order_spec *ord,LIST *rp)
 {
-    VL tv,fv,vv,vc,av;
-    NODE fd,fd0,in0,in,r,r0,t,s,cand,alist;
-    int m,nocheck,nvar,mindex,e,max;
+    VL tv,fv,vv;
+    NODE fd,fd0,in0,in,r,t,s,cand;
+    int m,nvar,mindex,e,max;
     NDV c;
     NMV a;
-    P p,zp;
-    Q dmy;
     EPOS oepos;
-    int obpe,oadv,wmax,i,len,cbpe,ishomo,nalg,mrank,trank,ompos;
-    Alg alpha,dp;
-    P poly;
-    LIST f1,f2,zpl;
-    Obj obj;
-    NumberField nf;
+    int obpe,oadv,wmax,i,len,cbpe,ishomo,mrank,trank,ompos;
     struct order_spec *ord1;
     struct oEGT eg_check,eg0,eg1;
-    NODE tr,tl1,tl2,tl3,tl4;
-    LIST l1,l2,l3,l4,l5;
     int *perm;
-    int j,ret;
+    int ret;
     NODE retn;
-    Q jq,bpe;
 
     nd_module = 0;
-    parse_nd_option(current_option);
     get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+    parse_nd_option(vv,current_option);
     if ( nd_vc )
       error("nd_f4_lf_trace : computation over a rational function field is not implemented");
     for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
@@ -9090,7 +11126,7 @@ void nd_f4_lf_trace(LIST f,LIST v,int trace,int homo,s
     nd_ntrans = nvar;
     nd_nalg = 0;
 
-    nocheck = 0;
+//    nocheck = 0;
     mindex = 0;
 
     /* do not use on-demand load/save */
@@ -9137,7 +11173,7 @@ void nd_f4_lf_trace(LIST f,LIST v,int trace,int homo,s
         for ( t = in0, wmax = max; t; t = NEXT(t) ) {
             c = (NDV)BDY(t); len = LEN(c);
             for ( a = BDY(c), i = 0; i < len; i++, NMV_ADV(a) )
-                wmax = MAX(TD(DL(a)),wmax);
+                wmax = MAX((int)TD(DL(a)),wmax);
         }
         homogenize_order(ord,nvar,&ord1);
         nd_init_ord(ord1);
@@ -9145,8 +11181,8 @@ void nd_f4_lf_trace(LIST f,LIST v,int trace,int homo,s
         for ( t = fd0; t; t = NEXT(t) )
             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);
+//    if ( MaxDeg > 0 ) nocheck = 1;
+    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 ) {
@@ -9165,11 +11201,11 @@ void nd_f4_lf_trace(LIST f,LIST v,int trace,int homo,s
     if ( (ret = ndv_check_membership(-2,in0,obpe,oadv,oepos,cand)) != 0 ) {
       /* gbcheck : cand is a GB of Id(cand) ? */
       retn = nd_f4(-2,0,0);
+      if ( !retn ) {
+        /* failure */
+        *rp = 0; return;    
+      }   
     }
-  if ( !retn ) {
-      /* failure */
-      *rp = 0; return;    
-    } 
     get_eg(&eg1); init_eg(&eg_check); add_eg(&eg_check,&eg0,&eg1);
     if ( DP_Print )
         fprintf(asir_out,"check=%.3fsec\n",eg_check.exectime);
@@ -9185,21 +11221,13 @@ void nd_f4_lf_trace(LIST f,LIST v,int trace,int homo,s
 
 NODE nd_f4_lf_trace_main(int m,int **indp)
 {
-    int i,nh,stat,index;
+    int i,nh,stat;
     NODE r,rm,g;
     ND_pairs d,l,l0,t;
-    ND spol,red;
-    NDV nf,redv,nfqv,nfv;
-    NM s0,s;
-    NODE rp0,srp0,nflist,nflist_lf;
-    int nsp,nred,col,rank,len,k,j,a;
-    UINT c;
-    UINT **spmat;
-    UINT *s0vect,*svect,*p,*v;
-    int *colstat;
-    IndArray *imat;
-    int *rhead;
-    int spcol,sprow;
+    NDV nfqv,nfv;
+    NODE rp0,nflist,nflist_lf;
+    UINT *s0vect;
+    int col;
     int sugar;
     PGeoBucket bucket;
     struct oEGT eg0,eg1,eg_f4;
@@ -9262,7 +11290,7 @@ 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);
         }
@@ -9272,3 +11300,740 @@ NODE nd_f4_lf_trace_main(int m,int **indp)
     return g;
 }
 
+#if SIZEOF_LONG==8
+
+NDV vect64_to_ndv(mp_limb_t *vect,int spcol,int col,int *rhead,UINT *s0vect)
+{
+    int j,k,len;
+    UINT *p;
+    UINT c;
+    NDV r;
+    NMV mr0,mr;
+
+    for ( j = 0, len = 0; j < spcol; j++ ) if ( vect[j] ) len++;
+    if ( !len ) return 0;
+    else {
+        mr0 = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(nmv_adv*len);
+#if 0
+        ndv_alloc += nmv_adv*len;
+#endif
+        mr = mr0; 
+        p = s0vect;
+        for ( j = k = 0; j < col; j++, p += nd_wpd )
+            if ( !rhead[j] ) {
+                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;
+    }
+}
+
+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;
+    UINT *t,*s,*u;
+    int i,st,ed,md,prev,c;
+
+    for ( i = 0; i < n; i++ ) r[i] = 0;
+    prev = 0;
+    for ( i = 0, m = BDY(d); m; m = NEXT(m) ) {
+      t = DL(m);
+      st = prev;
+      ed = n;
+      while ( ed > st ) {
+        md = (st+ed)/2;
+        u = s0+md*nd_wpd;
+        c = DL_COMPARE(u,t);
+        if ( c == 0 ) break;
+        else if ( c > 0 ) st = md;
+        else ed = md;
+      }
+      r[md] = (mp_limb_t)CM(m);
+      prev = md;
+    }
+    for ( i = 0; !r[i]; i++ );
+    return i;
+}
+
+#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,SIG sig)
+{
+    int i,j,k,len,pos,prev;
+    mp_limb_t a,c,c1,c2;
+    IndArray ivect;
+    unsigned char *ivc;
+    unsigned short *ivs;
+    unsigned int *ivi;
+    NDV redv;
+    NMV mr;
+    NODE rp;
+    int maxrs;
+
+    for ( i = 0; i < col; i++ ) cvect[i] = 0;
+    maxrs = 0;
+    for ( i = 0; i < nred; i++ ) {
+        ivect = imat[i];
+        k = ivect->head; 
+        a = svect[k]; c = cvect[k];
+        MOD128(a,c,m);
+        svect[k] = a; cvect[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];
+            len = LEN(redv); mr = BDY(redv);
+            svect[k] = 0; prev = k;
+            switch ( ivect->width ) {
+                case 1:
+                    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;
+                        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;
+                        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;
+                        c2 = svect[pos]+c1*c;
+                        if ( c2 < svect[pos] ) cvect[pos]++;
+                        svect[pos] = c2;
+                    }
+                    break;
+            }
+        }
+    }
+    for ( i = 0; i < col; i++ ) {
+      a = svect[i]; c = cvect[i]; MOD128(a,c,m); svect[i] = a;
+    }
+    return maxrs;
+}
+
+/* for Fp, 2^15=<p<2^29 */
+
+NODE nd_f4_red_mod64_main(int m,ND_pairs sp0,int nsp,UINT *s0vect,int col,
+        NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred,ND_pairs *nz)
+{
+    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;
+
+    spcol = col-nred;
+    get_eg(&eg0);
+    /* elimination (1st step) */
+    spmat = (mp_limb_t **)MALLOC(nsp*sizeof(mp_limb_t *));
+    svect = (mp_limb_t *)MALLOC(col*sizeof(mp_limb_t));
+    cvect = (mp_limb_t *)MALLOC(col*sizeof(mp_limb_t));
+    spsugar = (int *)MALLOC(nsp*sizeof(int));
+    spactive = !nz?0:(ND_pairs *)MALLOC(nsp*sizeof(ND_pairs));
+    for ( a = sprow = 0, sp = sp0; a < nsp; a++, sp = NEXT(sp) ) {
+        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,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));
+            for ( j = k = 0; j < col; j++ )
+                if ( !rhead[j] ) v[k++] = (UINT)svect[j];
+            spsugar[sprow] = MAX(maxrs,SG(spol));
+            if ( nz )
+            spactive[sprow] = sp;
+            sprow++;
+        }
+        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(spcol*sizeof(int));
+    rank = nd_gauss_elim_mod64(spmat,spsugar,spactive,sprow,spcol,m,colstat);
+    r0 = 0;
+    for ( i = 0; i < rank; i++ ) {
+        NEXTNODE(r0,r); BDY(r) = 
+          (pointer)vect64_to_ndv(spmat[i],spcol,col,rhead,s0vect);
+        SG((NDV)BDY(r)) = spsugar[i];
+        GCFREE(spmat[i]);
+    }
+    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); 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,spcol,rank);
+        fprintf(asir_out,"%.3fsec,",eg_f4.exectime);
+    }
+    if ( nz ) {
+        for ( i = 0; i < rank-1; i++ ) NEXT(spactive[i]) = spactive[i+1];
+        if ( rank > 0 ) {
+            NEXT(spactive[rank-1]) = 0;
+            *nz = spactive[0];
+        } else
+            *nz = 0;
+    }
+    return r0;
+}
+
+int nd_gauss_elim_mod64(mp_limb_t **mat,int *sugar,ND_pairs *spactive,int row,int col,int md,int *colstat)
+{
+  int i,j,k,l,rank,s;
+  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;
+
+  cmat = (UINT **)MALLOC(row*sizeof(UINT *));
+  for ( i = 0; i < row; i++ ) {
+    cmat[i] = MALLOC_ATOMIC(col*sizeof(UINT));
+    bzero(cmat[i],col*sizeof(UINT));
+  }
+
+  for ( rank = 0, j = 0; j < col; j++ ) {
+    for ( i = rank; i < row; i++ ) {
+      a = mat[i][j]; c = cmat[i][j];
+      MOD128(a,c,md);
+      mat[i][j] = a; cmat[i][j] = 0;
+    }
+    for ( i = rank; i < row; i++ )
+      if ( mat[i][j] )
+        break;
+    if ( i == row ) {
+      colstat[j] = 0;
+      continue;
+    } else
+      colstat[j] = 1;
+    if ( i != rank ) {
+      t = mat[i]; mat[i] = mat[rank]; mat[rank] = t;
+      ct = cmat[i]; cmat[i] = cmat[rank]; cmat[rank] = ct;
+      s = sugar[i]; sugar[i] = sugar[rank]; sugar[rank] = s;
+      if ( spactive ) {
+        pair = spactive[i]; spactive[i] = spactive[rank]; 
+        spactive[rank] = pair;
+      }
+    }
+    /* column j is normalized */
+    s = sugar[rank];
+    inv = invm((UINT)mat[rank][j],md);
+    /* normalize pivot row */
+    for ( k = j, pk = mat[rank]+j, ck = cmat[rank]+j; k < col; k++, pk++, ck++ ) {
+      a = *pk; c = *ck; MOD128(a,c,md); *pk = (a*inv)%md; *ck = 0;
+    }
+    for ( i = rank+1; i < row; i++ ) {
+      if ( (a = mat[i][j]) != 0 ) {
+        sugar[i] = MAX(sugar[i],s);
+        red_by_vect64(md,mat[i]+j,cmat[i]+j,mat[rank]+j,(int)(md-a),col-j);
+        Nf4_red++;
+      }
+    }
+    rank++;
+  }
+  for ( j = col-1, l = rank-1; j >= 0; j-- )
+    if ( colstat[j] ) {
+      for ( k = j, pk = mat[l]+j, ck = cmat[l]+j; k < col; k++, pk++, ck++ ) {
+        a = *pk; c = *ck; MOD128(a,c,md); *pk = a; *ck = 0;
+      }
+      s = sugar[l];
+      for ( i = 0; i < l; i++ ) {
+        a = mat[i][j]; c = cmat[i][j]; MOD128(a,c,md); mat[i][j] = a; cmat[i][j] = 0;
+        if ( a ) {
+          sugar[i] = MAX(sugar[i],s);
+          red_by_vect64(md,mat[i]+j,cmat[i]+j,mat[l]+j,(int)(md-a),col-j);
+          Nf4_red++;
+        }
+      }
+      l--;
+    }
+  for ( i = 0; i < row; i++ ) GCFREE(cmat[i]);
+  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;
+  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);
+    r0 = 0;
+    error("nd_f4_red_q_main_s : not implemented yet");
+  }
+  return r0;
+}
+
+INLINE int ndl_find_reducer_minsig(UINT *dg)
+{
+  RHist r;
+  int i,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;
+      _adddl(nd_nvar,DL(quo),nd_sba_hm[quo->pos],DL2(quo));
+      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;
+      _adddl(nd_nvar,DL(sig),nd_sba_hm[sig->pos],DL2(sig));
+      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,f4red,f4step;
+  int col,psugar,ms;
+  NODE r,g,rp0,nflist;
+  ND_pairs d,l,t,l1;
+  ND h,nf;
+  NDV nfv;
+//  union oNDC hc;
+  UINT *s0vect;
+  PGeoBucket bucket;
+  NODE *syzlist;
+  SIG sig;
+  struct oEGT eg1;
+  struct oEGT eg2,eg_remove,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;
+}