===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2018/engine/nd.c,v
retrieving revision 1.6
retrieving revision 1.21
diff -u -p -r1.6 -r1.21
--- OpenXM_contrib2/asir2018/engine/nd.c	2018/09/28 08:20:28	1.6
+++ OpenXM_contrib2/asir2018/engine/nd.c	2019/09/19 06:29:48	1.21
@@ -1,12 +1,17 @@
-/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.5 2018/09/27 02:39:37 noro Exp $ */
+/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.20 2019/09/15 08:46:12 noro Exp $ */
 
 #include "nd.h"
 
-struct oEGT eg_search;
+int Nnd_add,Nf4_red;
+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;
@@ -54,7 +59,7 @@ static int nd_worb_len;
 static int nd_found,nd_create,nd_notfirst;
 static int nmv_adv;
 static int nd_demand;
-static int nd_module,nd_ispot,nd_mpos,nd_pot_nelim;
+static int nd_module,nd_module_ordtype,nd_mpos,nd_pot_nelim;
 static int nd_module_rank,nd_poly_weight_len;
 static int *nd_poly_weight,*nd_module_weight;
 static NODE nd_tracelist;
@@ -77,6 +82,7 @@ NDV pltondv(VL vl,VL dvl,LIST p);
 void pltozpl(LIST l,Q *cont,LIST *pp);
 void ndl_max(UINT *d1,unsigned *d2,UINT *d);
 void nmtodp(int mod,NM m,DP *r);
+void ndltodp(UINT *d,DP *r);
 NODE reverse_node(NODE n);
 P ndc_div(int mod,union oNDC a,union oNDC b);
 P ndctop(int mod,union oNDC c);
@@ -86,6 +92,11 @@ void parse_nd_option(NODE opt);
 void dltondl(int n,DL dl,UINT *r);
 DP ndvtodp(int mod,NDV p);
 DP ndtodp(int mod,ND p);
+DPM ndvtodpm(int mod,NDV p);
+NDV dpmtondv(int mod,DPM p);
+int dpm_getdeg(DPM p,int *rank);
+void dpm_ptozp(DPM p,Z *cont,DPM *r);
+int compdmm(int nv,DMM a,DMM b);
 
 void Pdp_set_weight(NODE,VECT *);
 void Pox_cmo_rpc(NODE,Obj *);
@@ -469,8 +480,11 @@ 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;
 }
 
@@ -485,8 +499,8 @@ int ndl_weight2(UINT *d)
         u = GET_EXP(d,i);
         t += nd_sugarweight[i]*u;
     }
-    if ( nd_module && current_module_weight_vector && MPOS(d) )
-        t += current_module_weight_vector[MPOS(d)];
+    if ( nd_module && nd_module_rank && MPOS(d) )
+        t += nd_module_weight[MPOS(d)-1];
     return t;
 }
 
@@ -514,6 +528,13 @@ 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;
@@ -683,135 +704,143 @@ int ndl_ww_lex_compare(UINT *d1,UINT *d2)
     return ndl_lex_compare(d1,d2);
 }
 
-int ndl_module_weight_compare(UINT *d1,UINT *d2)
+// common function for module glex and grlex comparison
+int ndl_module_glex_compare(UINT *d1,UINT *d2)
 {
-  int s,j;
+  int c;
 
-  if ( nd_nvar != nd_poly_weight_len )
-    error("invalid module weight : the length of polynomial weight != the number of variables");
-  s = 0;
-  for ( j = 0; j < nd_nvar; j++ )
-     s += (GET_EXP(d1,j)-GET_EXP(d2,j))*nd_poly_weight[j];
-  if ( MPOS(d1) >= 1 && MPOS(d2) >= 1 ) {
-    s += nd_module_weight[MPOS(d1)-1]-nd_module_weight[MPOS(d2)-1];
-  }
-  if ( s > 0 ) return 1;
-  else if ( s < 0 ) return -1;
-  else return 0;
-}
+  switch ( nd_module_ordtype ) {
+    case 0:
+      if ( TD(d1) > TD(d2) ) return 1;
+      else if ( TD(d1) < TD(d2) ) return -1;
+      else if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c;
+      else if ( MPOS(d1) < MPOS(d2) ) return 1;
+      else if ( MPOS(d1) > MPOS(d2) ) return -1;
+      else return 0;
+      break;
 
-int ndl_module_grlex_compare(UINT *d1,UINT *d2)
-{
-    int i,c;
+    case 1:
+      if ( nd_pot_nelim && MPOS(d1)>=nd_pot_nelim+1 && MPOS(d2) >= nd_pot_nelim+1 ) {
+         if ( TD(d1) > TD(d2) ) return 1;
+         else if ( TD(d1) < TD(d2) ) return -1;
+         if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c;
+         if ( MPOS(d1) < MPOS(d2) ) return 1;
+         else if ( MPOS(d1) > MPOS(d2) ) return -1;
+      }
+      if ( MPOS(d1) < MPOS(d2) ) return 1;
+      else if ( MPOS(d1) > MPOS(d2) ) return -1;
+      else if ( TD(d1) > TD(d2) ) return 1;
+      else if ( TD(d1) < TD(d2) ) return -1;
+      else return ndl_lex_compare(d1,d2);
+      break;
 
-    if ( nd_module_rank && (c = ndl_module_weight_compare(d1,d2)) ) return c;
-    if ( nd_ispot ) {
-    if ( nd_pot_nelim && MPOS(d1)>=nd_pot_nelim+1 && MPOS(d2) >= nd_pot_nelim+1 ) {
-            if ( TD(d1) > TD(d2) ) return 1;
-            else if ( TD(d1) < TD(d2) ) return -1;
-            if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c;
-            if ( MPOS(d1) < MPOS(d2) ) return 1;
-            else if ( MPOS(d1) > MPOS(d2) ) return -1;
-            return 0;
-    }
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    if ( TD(d1) > TD(d2) ) return 1;
-    else if ( TD(d1) < TD(d2) ) return -1;
-    if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c;
-    if ( !nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    return 0;
-}
+    case 2: // weight -> POT
+      if ( TD(d1) > TD(d2) ) return 1;
+      else if ( TD(d1) < TD(d2) ) return -1;
+      else if ( MPOS(d1) < MPOS(d2) ) return 1;
+      else if ( MPOS(d1) > MPOS(d2) ) return -1;
+      else return ndl_lex_compare(d1,d2);
+      break;
 
-int ndl_module_glex_compare(UINT *d1,UINT *d2)
-{
-    int i,c;
-
-    if ( nd_module_rank && (c = ndl_module_weight_compare(d1,d2)) ) return c;
-    if ( nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    if ( TD(d1) > TD(d2) ) return 1;
-    else if ( TD(d1) < TD(d2) ) return -1;
-    if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c;
-    if ( !nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    return 0;
+    default:    
+      error("ndl_module_glex_compare : invalid module_ordtype");
+  }
 }
 
-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_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_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");
+  }
 }
 
-int ndl_module_composite_compare(UINT *d1,UINT *d2)
+extern DMMstack dmm_stack;
+void _addtodl(int n,DL d1,DL d2);
+int _eqdl(int n,DL d1,DL d2);
+
+int ndl_module_schreyer_compare(UINT *m1,UINT *m2)
 {
-    int i,c;
+  int pos1,pos2,t,j;
+  DMM *in;
+  DMMstack s;
+  static DL d1=0;
+  static DL d2=0;
+  static int dlen=0;
 
-    if ( nd_module_rank && (c = ndl_module_weight_compare(d1,d2)) ) return c;
-    if ( nd_ispot ) {
-        if ( MPOS(d1) > MPOS(d2) ) return 1;
-        else if ( MPOS(d1) < MPOS(d2) ) return -1;
+  pos1 = MPOS(m1); pos2 = MPOS(m2);
+  if ( pos1 == pos2 ) return (*ndl_base_compare_function)(m1,m2);
+  if ( nd_nvar > dlen ) {
+    NEWDL(d1,nd_nvar);
+    NEWDL(d2,nd_nvar);
+    dlen = nd_nvar;
+  }
+  d1->td = TD(m1);
+  for ( j = 0; j < nd_nvar; j++ ) d1->d[j] = GET_EXP(m1,j);
+  d2->td = TD(m2);
+  for ( j = 0; j < nd_nvar; j++ ) d2->d[j] = GET_EXP(m2,j);
+  for ( s = dmm_stack; s; s = NEXT(s) ) {
+    in = s->in;
+    _addtodl(nd_nvar,in[pos1]->dl,d1);
+    _addtodl(nd_nvar,in[pos2]->dl,d2);
+    if ( in[pos1]->pos == in[pos2]->pos && _eqdl(nd_nvar,d1,d2)) {
+      if ( pos1 < pos2 ) return 1;
+      else if ( pos1 > pos2 ) return -1;
+      else return 0;
     }
-    if ( (c = ndl_composite_compare(d1,d2)) != 0 ) return c;
-    if ( !nd_ispot ) {
-        if ( MPOS(d1) > MPOS(d2) ) return 1;
-        else if ( MPOS(d1) < MPOS(d2) ) return -1;
-    }
-    return 0;
+    pos1 = in[pos1]->pos;
+    pos2 = in[pos2]->pos;
+    if ( pos1 == pos2 ) return (*dl_base_compare_function)(nd_nvar,d1,d2);
+  }
+  // comparison by the bottom order
+LAST:
+  switch ( nd_base_ordtype ) {
+    case 0:
+      t = (*dl_base_compare_function)(nd_nvar,d1,d2);
+      if ( t ) return t;
+      else if ( pos1 < pos2 ) return 1;
+      else if ( pos1 > pos2 ) return -1;
+      else return 0;
+      break;
+    case 1:
+      if ( pos1 < pos2 ) return 1;
+      else if ( pos1 > pos2 ) return -1;
+      else return (*dl_base_compare_function)(nd_nvar,d1,d2);
+      break;
+    case 2:
+      if ( d1->td > d2->td  ) return 1;
+      else if ( d1->td < d2->td ) return -1;
+      else if ( pos1 < pos2 ) return 1;
+      else if ( pos1 > pos2 ) return -1;
+      else return (*dl_base_compare_function)(nd_nvar,d1,d2);
+      break;
+    default:
+      error("ndl_schreyer_compare : invalid base ordtype");
+  }
 }
 
 INLINE int ndl_equal(UINT *d1,UINT *d2)
@@ -1125,11 +1154,12 @@ 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;
 }
 
@@ -1216,6 +1246,7 @@ ND nd_add(int mod,ND p1,ND p2)
     ND r;
     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);
@@ -2081,6 +2112,7 @@ NODE nd_gb(int m,int ishomo,int checkonly,int gensyz,i
   P cont;
   LIST list;
 
+  Nnd_add = 0;
   g = 0; d = 0;
   for ( i = 0; i < nd_psn; i++ ) {
     d = update_pairs(d,g,i,gensyz);
@@ -2170,7 +2202,7 @@ again:
    }
  }
  conv_ilist(nd_demand,0,g,indp);
-    if ( !checkonly && DP_Print ) { printf("nd_gb done.\n"); fflush(stdout); }
+    if ( !checkonly && DP_Print ) { printf("nd_gb done. Number of nd_add=%d\n",Nnd_add); fflush(stdout); }
     return g;
 }
 
@@ -2601,7 +2633,7 @@ ND_pairs nd_newpairs( NODE g, int t )
 
   dl = DL(nd_psh[t]);
   ts = SG(nd_psh[t]) - TD(dl);
-  if ( nd_module && nd_intersect && (MPOS(dl) > 1) ) return 0;
+  if ( nd_module && nd_intersect && (MPOS(dl) > nd_intersect) ) return 0;
   for ( r0 = 0, h = g; h; h = NEXT(h) ) {
     if ( nd_module && (MPOS(DL(nd_psh[(long)BDY(h)])) != MPOS(dl)) )
       continue;
@@ -3220,6 +3252,7 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     int *perm;
     EPOS oepos;
     int obpe,oadv,ompos,cbpe;
+    VECT hvect;
 
     nd_module = 0;
     if ( !m && Demand ) nd_demand = 1;
@@ -3263,12 +3296,18 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     for ( t = BDY(f), max = 1; t; t = NEXT(t) )
         for ( tv = vv; tv; tv = NEXT(tv) ) {
             if ( nd_module ) {
-                s = BDY((LIST)BDY(t));
-                trank = length(s);
-                mrank = MAX(mrank,trank);
-                for ( ; s; s = NEXT(s) ) {
-                    e = getdeg(tv->v,(P)BDY(s));
-                    max = MAX(e,max);
+                if ( OID(BDY(t)) == O_DPM ) {
+                  e = dpm_getdeg((DPM)BDY(t),&trank);
+                  max = MAX(e,max);
+                  mrank = MAX(mrank,trank);
+                } else {
+                  s = BDY((LIST)BDY(t));
+                  trank = length(s);
+                  mrank = MAX(mrank,trank);
+                  for ( ; s; s = NEXT(s) ) {
+                      e = getdeg(tv->v,(P)BDY(s));
+                      max = MAX(e,max);
+                  }
                 }
             } else {
                 e = getdeg(tv->v,(P)BDY(t));
@@ -3280,9 +3319,18 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     ishomo = 1;
     for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
       if ( nd_module ) {
-        if ( !m && !nd_gentrace ) pltozpl((LIST)BDY(t),&dmy,&zpl);
-        else zpl = (LIST)BDY(t);
+        if ( OID(BDY(t)) == O_DPM ) {
+          Z cont;
+          DPM zdpm;
+
+          if ( !m && !nd_gentrace ) dpm_ptozp((DPM)BDY(t),&cont,&zdpm);
+          else zdpm = (DPM)BDY(t);
+          b = (pointer)dpmtondv(m,zdpm);
+        } else {
+          if ( !m && !nd_gentrace ) pltozpl((LIST)BDY(t),&dmy,&zpl);
+          else zpl = (LIST)BDY(t);
           b = (pointer)pltondv(CO,vv,zpl);
+        }
       } else {
         if ( !m && !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp);
         else zp = (P)BDY(t);
@@ -3330,6 +3378,11 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
   if ( !x ) {
     *rp = 0; return;
   }
+  if ( nd_gentrace ) {
+    MKVECT(hvect,nd_psn);
+    for ( i = 0; i < nd_psn; i++ )
+       ndltodp(nd_psh[i]->dl,(DP *)&BDY(hvect)[i]);
+  }
   if ( !ishomo && homo ) {
        /* dehomogenization */
     for ( t = x; t; t = NEXT(t) ) ndv_dehomogenize((NDV)BDY(t),ord);
@@ -3339,7 +3392,7 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     nd_demand = 0;
   if ( nd_module && nd_intersect ) {
     for ( j = nd_psn-1, x = 0; j >= 0; j-- )
-      if ( MPOS(DL(nd_psh[j])) > 1 ) { 
+      if ( MPOS(DL(nd_psh[j])) > nd_intersect ) { 
         MKNODE(xx,(pointer)((unsigned long)j),x); x = xx; 
       }
     conv_ilist(nd_demand,0,x,0);
@@ -3363,10 +3416,12 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     nd_setup_parameters(nd_nvar,0);
 FINAL:
     for ( r0 = 0, t = x; t; t = NEXT(t) ) {
-        NEXTNODE(r0,r); 
-        if ( nd_module ) BDY(r) = ndvtopl(m,CO,vv,BDY(t),mrank);
-        else if ( retdp ) BDY(r) = ndvtodp(m,BDY(t));
-    else BDY(r) = ndvtop(m,CO,vv,BDY(t));
+      NEXTNODE(r0,r); 
+      if ( nd_module ) {
+        if ( retdp ) BDY(r) = ndvtodpm(m,BDY(t));
+        else BDY(r) = ndvtopl(m,CO,vv,BDY(t),mrank);
+      } else if ( retdp ) BDY(r) = ndvtodp(m,BDY(t));
+      else BDY(r) = ndvtop(m,CO,vv,BDY(t));
     }
     if ( r0 ) NEXT(r) = 0;
     if ( !m && nd_nalg )
@@ -3376,8 +3431,7 @@ FINAL:
   if ( f4 ) {
             STOZ(16,bpe);
             STOZ(nd_last_nonzero,last_nonzero);
-            tr = mknode(5,*rp,(!ishomo&&homo)?ONE:0,BDY(nzlist),bpe,last_nonzero); MKLIST(*rp,tr);
-            
+            tr = mknode(6,*rp,(!ishomo&&homo)?ONE:0,BDY(nzlist),bpe,last_nonzero,hvect); MKLIST(*rp,tr);
         } else {
             tl1 = reverse_node(tl1); tl2 = reverse_node(tl2);
             tl3 = reverse_node(tl3);
@@ -3397,7 +3451,7 @@ FINAL:
             MKLIST(l1,tl1); MKLIST(l2,tl2); MKLIST(l3,t); MKLIST(l4,tl3);
             MKLIST(l5,tl4);
             STOZ(nd_bpe,bpe);
-            tr = mknode(8,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe); MKLIST(*rp,tr);
+            tr = mknode(9,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe,hvect); MKLIST(*rp,tr);
         }
     }
 #if 0
@@ -3641,7 +3695,7 @@ void nd_gr_recompute_trace(LIST f,LIST v,int m,struct 
     if ( DP_Print ) fprintf(asir_out,"\n");
 }
 
-void nd_gr_trace(LIST f,LIST v,int trace,int homo,int f4,struct order_spec *ord,LIST *rp)
+void nd_gr_trace(LIST f,LIST v,int trace,int homo,int retdp,int f4,struct order_spec *ord,LIST *rp)
 {
     VL tv,fv,vv,vc,av;
     NODE fd,fd0,in0,in,r,r0,t,s,cand,alist;
@@ -3664,6 +3718,7 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     int *perm;
     int j,ret;
     Z jq,bpe;
+    VECT hvect;
 
     nd_module = 0;
     nd_lf = 0;
@@ -3718,6 +3773,11 @@ 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);
@@ -3725,6 +3785,7 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
                     e = getdeg(tv->v,(P)BDY(s));
                     max = MAX(e,max);
                 }
+              }
             } else {
                 e = getdeg(tv->v,(P)BDY(t));
                 max = MAX(e,max);
@@ -3735,13 +3796,22 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     ishomo = 1;
     for ( in0 = 0, fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
         if ( nd_module ) {
-      if ( !nd_gentrace ) pltozpl((LIST)BDY(t),&dmy,&zpl);
-      else zpl = (LIST)BDY(t);
+          if ( OID(BDY(t)) == O_DPM ) {
+            Z cont;
+            DPM zdpm;
+
+            if ( !nd_gentrace ) dpm_ptozp((DPM)BDY(t),&cont,&zdpm);
+            else zdpm = (DPM)BDY(t);
+            c = (pointer)dpmtondv(m,zdpm);
+          } else {
+            if ( !nd_gentrace ) pltozpl((LIST)BDY(t),&dmy,&zpl);
+            else zpl = (LIST)BDY(t);
             c = (pointer)pltondv(CO,vv,zpl);
+          }
         } else {
-      if ( !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp);
-      else zp = (P)BDY(t);
-            c = (pointer)ptondv(CO,vv,zp);
+          if ( !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp);
+          else zp = (P)BDY(t);
+          c = (pointer)ptondv(CO,vv,zp);
         }
         if ( ishomo )
             ishomo = ishomo && ndv_ishomo(c);
@@ -3781,6 +3851,11 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
             else m = get_lprime(++mindex);
             continue;
         }
+        if ( nd_gentrace ) {
+          MKVECT(hvect,nd_psn);
+          for ( i = 0; i < nd_psn; i++ )
+             ndltodp(nd_psh[i]->dl,(DP *)&BDY(hvect)[i]);
+        }
         if ( !ishomo && homo ) {
             /* dehomogenization */
             for ( t = cand; t; t = NEXT(t) ) ndv_dehomogenize((NDV)BDY(t),ord);
@@ -3833,8 +3908,11 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     nd_bpe = cbpe;
     nd_setup_parameters(nd_nvar,0);
     for ( r = cand; r; r = NEXT(r) ) {
-    if ( nd_module ) BDY(r) = ndvtopl(0,CO,vv,BDY(r),mrank);
-        else BDY(r) = (pointer)ndvtop(0,CO,vv,BDY(r));
+      if ( nd_module ) {
+        if ( retdp ) BDY(r) = ndvtodpm(0,BDY(r));
+        else BDY(r) = ndvtopl(0,CO,vv,BDY(r),mrank);
+      } else if ( retdp ) BDY(r) = ndvtodp(0,BDY(r));
+      else BDY(r) = (pointer)ndvtop(0,CO,vv,BDY(r));
     }
     if ( nd_nalg )
         cand = postprocess_algcoef(av,alist,cand);
@@ -3858,7 +3936,7 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
         MKLIST(l1,tl1); MKLIST(l2,tl2); MKLIST(l3,t); MKLIST(l4,tl3);
     MKLIST(l5,tl4);
       STOZ(nd_bpe,bpe);
-        tr = mknode(8,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe); MKLIST(*rp,tr);
+        tr = mknode(9,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe,hvect); MKLIST(*rp,tr);
     }
 }
 
@@ -3922,6 +4000,18 @@ 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;
@@ -4086,7 +4176,7 @@ void ndv_homogenize(NDV p,int obpe,int oadv,EPOS oepos
     NMV m,mr0,mr,t;
 
     len = p->len;
-    for ( m = BDY(p), i = 0, max = 1; i < len; NMV_OADV(m), i++ )
+    for ( m = BDY(p), i = 0, max = 0; i < len; NMV_OADV(m), i++ )
         max = MAX(max,TD(DL(m)));
     mr0 = nmv_adv>oadv?(NMV)REALLOC(BDY(p),len*nmv_adv):BDY(p);
     m = (NMV)((char *)mr0+(len-1)*oadv);
@@ -4231,14 +4321,18 @@ 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);
@@ -4410,7 +4504,7 @@ 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 */
@@ -5188,31 +5282,32 @@ 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) */
@@ -5401,6 +5496,108 @@ NDV ndtondv(int mod,ND p)
     return d;
 }
 
+static int dmm_comp_nv;
+
+int dmm_comp(DMM *a,DMM *b)
+{
+   return -compdmm(dmm_comp_nv,*a,*b);
+}
+
+void dmm_sort_by_ord(DMM *a,int len,int nv)
+{
+  dmm_comp_nv = nv;
+  qsort(a,len,sizeof(DMM),(int (*)(const void *,const void *))dmm_comp);
+}
+
+void dpm_sort(DPM p,DPM *rp)
+{
+  DMM t,t1;
+  int len,i,n;
+  DMM *a;
+  DPM d;
+ 
+  if ( !p ) *rp = 0;
+  for ( t = BDY(p), len = 0; t; t = NEXT(t), len++ );
+  a = (DMM *)MALLOC(len*sizeof(DMM));
+  for ( i = 0, t = BDY(p); i < len; i++, t = NEXT(t) ) a[i] = t;
+  n = p->nv;
+  dmm_sort_by_ord(a,len,n);  
+  t = 0;
+  for ( i = len-1; i >= 0; i-- ) {
+    NEWDMM(t1); 
+    t1->c = a[i]->c;
+    t1->dl = a[i]->dl;
+    t1->pos = a[i]->pos;
+    t1->next = t;
+    t = t1;
+  }
+  MKDPM(n,t,d);
+  SG(d) = SG(p);
+  *rp = d;
+}
+
+int dpm_comp(DPM *a,DPM *b)
+{
+  return compdpm(CO,*a,*b);
+}
+
+NODE dpm_sort_list(NODE l)
+{
+  int i,len;
+  NODE t,t1;
+  DPM *a;
+  
+  len = length(l);
+  a = (DPM *)MALLOC(len*sizeof(DPM));
+  for ( t = l, i = 0; i < len; i++, t = NEXT(t) ) a[i] = (DPM)BDY(t);
+  qsort(a,len,sizeof(DPM),(int (*)(const void *,const void *))dpm_comp);
+  t = 0;
+  for ( i = len-1; i >= 0; i-- ) {
+    MKNODE(t1,(pointer)a[i],t); t = t1;
+  }
+  return t;
+}
+
+int nmv_comp(NMV a,NMV b)
+{
+  int t;
+  t = DL_COMPARE(a->dl,b->dl);
+  return -t;
+}
+
+NDV dpmtondv(int mod,DPM p)
+{
+  NDV d;
+  NMV m,m0;
+  DMM t;
+  DMM *a;
+  int i,len,n;
+
+  if ( !p ) return 0;
+  for ( t = BDY(p), len = 0; t; t = NEXT(t), len++ );
+  a = (DMM *)MALLOC(len*sizeof(DMM));
+  for ( i = 0, t = BDY(p); i < len; i++, t = NEXT(t) ) a[i] = t;
+  n = p->nv;
+  dmm_sort_by_ord(a,len,n);  
+  if ( mod > 0 || mod == -1 )
+    m0 = m = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(len*nmv_adv);
+  else
+    m0 = m = MALLOC(len*nmv_adv);
+#if 0
+  ndv_alloc += nmv_adv*len;
+#endif
+  for ( i = 0; i < len; i++, NMV_ADV(m) ) {
+    dltondl(n,a[i]->dl,DL(m));
+    MPOS(DL(m)) = a[i]->pos;
+    TD(DL(m)) = ndl_weight(DL(m));
+    CZ(m) = (Z)a[i]->c;
+  }
+  qsort(m0,len,nmv_adv,(int (*)(const void *,const void *))nmv_comp);
+  MKNDV(NV(p),m0,len,d);
+  SG(d) = SG(p);
+  return d;
+}
+
 ND ndvtond(int mod,NDV p)
 {
     ND d;
@@ -5443,6 +5640,29 @@ DP ndvtodp(int mod,NDV p)
     return d;
 }
 
+DPM ndvtodpm(int mod,NDV p)
+{
+  DMM m,m0;
+  DPM d;
+  NMV t;
+  int i,len;
+
+  if ( !p ) return 0;
+  m0 = 0;
+  len = p->len;
+  for ( t = BDY(p), i = 0; i < len; NMV_ADV(t), i++ ) {
+    NEXTDMM(m0,m);
+    m->dl = ndltodl(nd_nvar,DL(t));
+    m->c = (Obj)ndctop(mod,t->c);
+    m->pos = MPOS(DL(t));
+  }
+  NEXT(m) = 0;
+  MKDPM(nd_nvar,m0,d);
+  SG(d) = SG(p);
+  return d;
+}
+
+
 DP ndtodp(int mod,ND p)
 {
     MP m,m0;
@@ -5530,12 +5750,15 @@ 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;
@@ -5599,40 +5822,73 @@ 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;
 }
@@ -5668,7 +5924,7 @@ 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;
@@ -5796,27 +6052,6 @@ 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;
@@ -5910,18 +6145,17 @@ Z *nm_ind_pair_to_vect(int mod,UINT *s0,int n,NM_ind_p
     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,*s,*u;
     NDV p;
     unsigned char *ivc;
     unsigned short *ivs;
     UINT *v,*ivi,*s0v;
-    int i,j,len,prev,diff,cdiff,h;
+    int i,j,len,prev,diff,cdiff,h,st,ed,md,c;
     IndArray r;
-struct oEGT eg0,eg1;
 
     m = pair->mul;
     d = DL(m);
@@ -5933,14 +6167,20 @@ 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;
@@ -5983,7 +6223,7 @@ 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;
@@ -6063,11 +6303,11 @@ 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;
@@ -6079,12 +6319,17 @@ int ndv_reduce_vect_q(Z *svect0,int trace,int col,IndA
     int maxrs;
     double hmag;
     int l;
+    static mpz_t *svect;
+    static int svect_len=0;
 
     maxrs = 0;
     for ( i = 0; i < col && !svect0[i]; i++ );
     if ( i == col ) return maxrs;
     hmag = p_mag((P)svect0[i])*nd_scale;
-    svect = (mpz_t *)MALLOC(col*sizeof(mpz_t));
+    if ( col > svect_len ) {
+      svect = (mpz_t *)MALLOC(col*sizeof(mpz_t));
+      svect_len = col;
+    }
     for ( i = 0; i < col; i++ ) {
       mpz_init(svect[i]);
       if ( svect0[i] )
@@ -6105,8 +6350,12 @@ int ndv_reduce_vect_q(Z *svect0,int trace,int col,IndA
             mpz_div(cs,svect[k],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 ) {
@@ -6220,78 +6469,6 @@ 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;
@@ -6549,36 +6726,6 @@ 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)
-{
-    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;
-    }
-}
-#endif
-
 NDV vect_to_ndv_2(unsigned long *vect,int col,UINT *s0vect)
 {
     int j,k,len;
@@ -6788,9 +6935,12 @@ NODE nd_f4(int m,int checkonly,int **indp)
     PGeoBucket bucket;
     struct oEGT eg0,eg1,eg_f4;
     Z i1,i2,sugarq;
+
+    init_eg(&f4_symb); init_eg(&f4_conv); init_eg(&f4_conv); init_eg(&f4_elim1); init_eg(&f4_elim2);
 #if 0
     ndv_alloc = 0;
 #endif
+    Nf4_red=0;
     g = 0; d = 0;
     for ( i = 0; i < nd_psn; i++ ) {
         d = update_pairs(d,g,i,0);
@@ -6832,7 +6982,7 @@ NODE nd_f4(int m,int checkonly,int **indp)
             d = nd_reconstruct(0,d);
             continue;
         }
-        get_eg(&eg1); init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg1);
+        get_eg(&eg1); init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg1); add_eg(&f4_symb,&eg0,&eg1);
         if ( DP_Print )
             fprintf(asir_out,"sugar=%d,symb=%.3fsec,",
                 sugar,eg_f4.exectime);
@@ -6881,6 +7031,11 @@ NODE nd_f4(int m,int checkonly,int **indp)
 #if 0
     fprintf(asir_out,"ndv_alloc=%d\n",ndv_alloc);
 #endif
+  if ( DP_Print ) {
+    fprintf(asir_out,"number of red=%d,",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);
+  }
   conv_ilist(nd_demand,0,g,indp);
     return g;
 }
@@ -7104,7 +7259,6 @@ NODE nd_f4_red_2(ND_pairs sp0,UINT *s0vect,int col,NOD
     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);
@@ -7159,18 +7313,18 @@ 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));
@@ -7178,20 +7332,25 @@ 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);
@@ -7202,9 +7361,6 @@ 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;
 }
 
@@ -7296,92 +7452,7 @@ 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)
-{
-    int spcol,sprow,a;
-    int i,j,k,l,rank;
-    NODE r0,r;
-    ND_pairs sp;
-    ND spol;
-    U64 **spmat;
-    U64 *svect,*cvect;
-    U64 *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 = (U64 **)MALLOC(nsp*sizeof(U64 *));
-    svect = (U64 *)MALLOC(col*sizeof(U64));
-    cvect = (U64 *)MALLOC(col*sizeof(U64));
-    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);
-        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];
-            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);
-    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);
-    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;
-}
-#endif
-
 /* for small finite fields */
 
 NODE nd_f4_red_sf_main(int m,ND_pairs sp0,int nsp,UINT *s0vect,int col,
@@ -7793,85 +7864,7 @@ 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 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;
-
-  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);
-      }
-    }
-    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);
-  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;
@@ -7934,7 +7927,9 @@ 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;
 }
 
@@ -8482,7 +8477,7 @@ 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;
@@ -8502,7 +8497,7 @@ 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 ) {
         STOZ(c.m,q); return (P)q;
     } else
@@ -8584,6 +8579,8 @@ void parse_nd_option(NODE opt)
             nd_newelim = value?1:0;
     else if ( !strcmp(key,"intersect") )
             nd_intersect = value?1:0;
+    else if ( !strcmp(key,"syzgen") )
+            nd_intersect = ZTOS((Q)value);
     else if ( !strcmp(key,"lf") )
             nd_lf = value?1:0;
     else if ( !strcmp(key,"trace") ) {
@@ -9264,4 +9261,290 @@ NODE nd_f4_lf_trace_main(int m,int **indp)
   conv_ilist(nd_demand,1,g,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;
+    }
+}
+
+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)
+{
+    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 ) {
+            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);
+        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;
+}
+#endif