===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2018/engine/nd.c,v
retrieving revision 1.40
retrieving revision 1.66
diff -u -p -r1.40 -r1.66
--- OpenXM_contrib2/asir2018/engine/nd.c	2020/11/02 08:30:55	1.40
+++ OpenXM_contrib2/asir2018/engine/nd.c	2022/04/03 06:45:47	1.66
@@ -1,8 +1,11 @@
-/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.39 2020/10/29 01:50:35 noro Exp $ */
+/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.65 2022/04/03 00:39:12 noro Exp $ */
 
 #include "nd.h"
 
-int Nnd_add,Nf4_red;
+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;
@@ -65,9 +68,9 @@ 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_f4_td,nd_sba_f4step,nd_sba_pot,nd_sba_largelcm,nd_sba_dontsort;
-static int nd_top;
+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;
@@ -76,6 +79,21 @@ 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);
@@ -93,15 +111,19 @@ 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 *);
@@ -156,7 +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));
@@ -361,7 +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");
@@ -459,7 +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]; 
@@ -499,7 +520,7 @@ 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);
@@ -557,7 +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;
@@ -726,7 +747,7 @@ int ndl_module_glex_compare(UINT *d1,UINT *d2)
       break;
 
     case 1:
-      if ( nd_pot_nelim && MPOS(d1)>=nd_pot_nelim+1 && MPOS(d2) >= nd_pot_nelim+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;
@@ -794,13 +815,16 @@ int _eqdl(int n,DL d1,DL d2);
 
 int ndl_module_schreyer_compare(UINT *m1,UINT *m2)
 {
-  int pos1,pos2,t,j;
+  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 ( 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 ) {
@@ -817,8 +841,8 @@ int ndl_module_schreyer_compare(UINT *m1,UINT *m2)
     _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;
+      if ( pos1 < pos2 ) return retpot;
+      else if ( pos1 > pos2 ) return -retpot;
       else return 0;
     }
     pos1 = in[pos1]->pos;
@@ -826,25 +850,24 @@ int ndl_module_schreyer_compare(UINT *m1,UINT *m2)
     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 if ( pos1 < pos2 ) return retpot;
+      else if ( pos1 > pos2 ) return -retpot;
       else return 0;
       break;
     case 1:
-      if ( pos1 < pos2 ) return 1;
-      else if ( pos1 > pos2 ) return -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 1;
-      else if ( pos1 > pos2 ) 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:
@@ -970,7 +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;
@@ -1207,6 +1230,18 @@ 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
@@ -1226,6 +1261,13 @@ void print_sig(SIG s)
   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)
@@ -1257,7 +1299,9 @@ INLINE int ndl_find_reducer_s(UINT *dg,SIG sig)
       _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; }
     }
@@ -1270,16 +1314,15 @@ INLINE int ndl_find_reducer_s(UINT *dg,SIG sig)
 
 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:
@@ -1312,9 +1355,8 @@ 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++;
@@ -1325,7 +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:
@@ -1386,8 +1428,7 @@ 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;
 
@@ -1395,7 +1436,7 @@ ND nd_add_q(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:
@@ -1437,8 +1478,7 @@ 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;
 
@@ -1446,7 +1486,7 @@ 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:
@@ -1528,20 +1568,17 @@ 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,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;
 
@@ -1551,7 +1588,7 @@ int nd_nf(int mod,ND d,ND g,NDV *ps,int full,ND *rp)
     }
     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 )
@@ -1574,7 +1611,7 @@ int nd_nf(int mod,ND d,ND g,NDV *ps,int full,ND *rp)
                 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);
@@ -1616,22 +1653,18 @@ int nd_nf(int mod,ND d,ND g,NDV *ps,int full,ND *rp)
 
 int nd_nf_s(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;
-    union oNDC hg;
-    P cont;
+    Obj div;
+//    union oNDC hg;
     SIG sig;
 
     if ( !g ) {
@@ -1640,7 +1673,7 @@ int nd_nf_s(int mod,ND d,ND g,NDV *ps,int full,ND *rp)
     }
     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 )
@@ -1659,12 +1692,20 @@ int nd_nf_s(int mod,ND d,ND g,NDV *ps,int full,ND *rp)
             p = ps[index];
             /* d+g -> div*(d+g)+mul*p */
             g = nd_reduce2(mod,d,g,p,mul,0,&div);
-            sugar = MAX(sugar,SG(p)+TD(DL(mul)));
+            sugar = MAX(sugar,(int)(SG(p)+TD(DL(mul))));
             if ( !mod && g && ((double)(p_mag(HCP(g))) > hmag) ) {
-                hg = HCU(g);
+//                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;
@@ -1698,13 +1739,12 @@ 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;
@@ -1810,13 +1850,12 @@ int nd_nf_pbucket_s(int mod,ND g,NDV *ps,int full,ND *
 {
   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;
@@ -1936,16 +1975,15 @@ int nd_nf_pbucket_s(int mod,ND g,NDV *ps,int full,ND *
 
 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?1:0,1,0);
-    n = length(cand);
+//    n = length(cand);
 
   if ( nd_gentrace ) { nd_alltracelist = 0; nd_tracelist = 0; }
     /* membercheck : list is a subset of Id(cand) ? */
@@ -2052,7 +2090,7 @@ void add_pbucket_symbolic(PGeoBucket g,ND d)
 #else
 void add_pbucket_symbolic(PGeoBucket g,ND d)
 {
-  int l,i,k,m,m0;
+  int l,k,m,m0;
 
   if ( !d )
     return;
@@ -2095,7 +2133,7 @@ void add_pbucket(int mod,PGeoBucket g,ND d)
 #else
 void add_pbucket(int mod,PGeoBucket g,ND d)
 {
-  int l,i,k,m,m0;
+  int l,k,m,m0;
 
   m0 = g->m;
   while ( d != 0 ) {
@@ -2157,8 +2195,8 @@ 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;
@@ -2203,7 +2241,7 @@ 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;
 
@@ -2217,7 +2255,7 @@ int head_pbucket_q(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;
@@ -2243,7 +2281,7 @@ 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;
 
@@ -2257,7 +2295,7 @@ 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;
@@ -2284,7 +2322,7 @@ 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++ ) {
@@ -2325,7 +2363,6 @@ void register_hcf(NDV p)
 #else
 void register_hcf(NDV p)
 {
-    DCP dc,t;
     P hc,h,q;
     Q dmy;
     int c;
@@ -2359,17 +2396,16 @@ 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;
+  int i,stat;
+  ND nf,s,head;
   NDV nfv;
-  Q q;
-  P nm,nmp,dn,mnp,dnp,cont,cont1;
+  P cont;
   union oNDC hc;
   NODE node;
   LIST l;
   Z iq;
 
+  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] */
@@ -2425,21 +2461,149 @@ 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;
+  NODE g,t;
   ND_pairs d;
   ND_pairs l;
-  ND h,nf,s,head,nf1;
+  ND h,nf;
   NDV nfv;
   Z q;
-  union oNDC dn,hc;
+  union oNDC hc;
   int diag_count = 0;
+  int Nnfnz = 0,Nnfz = 0;
   P cont;
   LIST list;
+  struct oHPDATA current_hpdata,final_hpdata;
+
 struct oEGT eg1,eg2,eg_update;
 
 init_eg(&eg_update);
@@ -2450,6 +2614,10 @@ init_eg(&eg_update);
     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);
@@ -2484,6 +2652,7 @@ again:
       d = nd_reconstruct(0,d);
       goto again;
     } else if ( nf ) {
+      Nnfnz++;
       if ( checkonly || gensyz ) return 0;
       if ( nd_newelim ) {
         if ( nd_module ) {
@@ -2522,28 +2691,51 @@ get_eg(&eg1);
 get_eg(&eg2); add_eg(&eg_update,&eg1,&eg2);
       g = update_base(g,nh);
       FREENDP(l);
-   } else {
-     if ( nd_gentrace && gensyz ) {
-       nd_tracelist = reverse_node(nd_tracelist); 
-       MKLIST(list,nd_tracelist);
-       STOZ(-1,q); t = mknode(2,q,list); MKLIST(list,t);
-       MKNODE(t,list,nd_alltracelist); 
-       nd_alltracelist = t; nd_tracelist = 0;
-     }
-     if ( DP_Print ) { printf("."); fflush(stdout); }
-       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);
+        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 ) { fprintf(asir_out,"."); fflush(asir_out); }
+        FREENDP(l);
+    }
   }
   conv_ilist(nd_demand,0,g,indp);
-  if ( !checkonly && DP_Print ) { printf("nd_gb done. Number of nd_add=%d\n",Nnd_add); fflush(stdout); }
- 
-  if ( DP_Print )
-    print_eg("update",&eg_update);
+  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);
@@ -2551,7 +2743,38 @@ 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;
@@ -2570,6 +2793,8 @@ NODE insert_sig(NODE l,SIG s)
       else if ( _dl_redble(sig,DL(t),nd_nvar) )
         // remove p
         prev->next = p->next;
+      else
+        prev = p;
     } else
       prev = p;
   }
@@ -2602,15 +2827,13 @@ ND_pairs remove_spair_s(ND_pairs d,SIG sig)
   return (ND_pairs)root.next;
 }
 
-int _dl_redble_ext(DL,DL,DL,int);
-
 int small_lcm(ND_pairs l)
 {
   SIG sig;
   int i;
   NODE t;
   static DL lcm,mul,quo;
-  static int nvar;
+  static int nvar = 0;
 
   if ( nd_sba_largelcm ) return 0;
   if ( nvar < nd_nvar ) {
@@ -2645,6 +2868,64 @@ int small_lcm(ND_pairs l)
 #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;
@@ -2653,10 +2934,17 @@ ND_pairs remove_large_lcm(ND_pairs d)
   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;
   }
@@ -2667,127 +2955,278 @@ struct oEGT eg_create,eg_newpairs,eg_merge;
 
 NODE conv_ilist_s(int demand,int trace,int **indp);
 
-NODE nd_sba_buch(int m,int ishomo,int **indp)
+// 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 r,t,g;
-  ND_pairs d;
-  ND_pairs l;
-  ND h,nf,s,head,nf1;
+  NODE g;
+  ND_pairs *d;
+  ND_pairs l,l1;
+  ND h,nf;
   NDV nfv;
-  Z q;
-  union oNDC dn,hc;
-  P cont;
-  LIST list;
+//  union oNDC hc;
   SIG sig;
   NODE *syzlist;
-  int Nredundant;
+  int ngen,ind;
+  int Nnominimal,Nredundant;
   DL lcm,quo,mul;
-  struct oEGT eg1,eg2,eg_update,eg_remove,eg_large,eg_nf,eg_nfzero;
+  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;
-  d = 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++ ) {
-    d = update_pairs_s(d,i,syzlist);
+    dlen += update_pairs_array_s(d,i,syzlist);
   }
-  for ( i = 0; i < nd_psn; i++ )
-    for ( j = i+1; j < nd_psn; j++ ) {
-      NEWSIG(sig); sig->pos = j;
-      _copydl(nd_nvar,nd_sba_hm[i],sig->dl);
-      syzlist[sig->pos] = insert_sig(syzlist[sig->pos],sig);
-    }
   sugar = 0;
   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);
-  while ( d ) {
-again:
-    if ( DP_Print ) {
-      int len;
-      ND_pairs td;
-      for ( td = d, len=0; td; td = td->next, len++)
-        ;
-       if ( !(len%100) ) fprintf(asir_out,"(%d)",len);
-      }
-    l = d; d = d->next;
-    if ( small_lcm(l) ) {
-      if ( DP_Print ) fprintf(asir_out,"M");
-      Nredundant++;
+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(l) != sugar ) {
-      sugar = SG(l);
+    if ( SG(l1) != sugar ) {
+      sugar = SG(l1);
       if ( DP_Print ) fprintf(asir_out,"%d",sugar);
     }
-    sig = l->sig;
+    sig = l1->sig;
     if ( DP_Print && nd_sba_pot ) {
       if ( sig->pos != pos ) {
         fprintf(asir_out,"[%d]",sig->pos);
         pos = sig->pos;
       }
     }
-    stat = nd_sp(m,0,l,&h);
+get_eg(&eg1);
+    stat = nd_sp(m,0,l1,&h);
+get_eg(&eg2); add_eg(&eg_sp,&eg1,&eg2);
     if ( !stat ) {
-      NEXT(l) = d; d = l;
-      d = nd_reconstruct(0,d);
+      nd_reconstruct_s(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);
+    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 ) {
-      NEXT(l) = d; d = l;
-      d = nd_reconstruct(0,d);
+      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); }
-      FREENDP(l);
     } else if ( nf ) {
-      if ( DP_Print ) { printf("+"); fflush(stdout); }
+      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);
+//      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);
-
-      d = update_pairs_s(d,nh,syzlist);
+  
+      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);
-      FREENDP(l);
-   } else {
+      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
+    // syzygy
 get_eg(&eg1);
-     d = remove_spair_s(d,sig);
+      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); }
-     FREENDP(l);
-   }
- }
- g = conv_ilist_s(nd_demand,0,indp);
- if ( DP_Print ) { 
-   printf("\nnd_sba done. nd_add=%d,Nsyz=%d,Nsamesig=%d,Nredundant=%d\n",Nnd_add,Nsyz,Nsamesig,Nredundant);
-   fflush(stdout); 
-   print_eg("create",&eg_create);
-   print_eg("merge",&eg_merge);
-   print_eg("remove",&eg_remove);
-   print_eg("nf",&eg_nf);
-   print_eg("nfzero",&eg_nfzero);
-   printf("\n");
- }
- return g;
+      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],...] */
@@ -2802,7 +3241,7 @@ 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 = ZTOS((Q)ARG0(p)); r->i2 = ZTOS((Q)ARG1(p));
+    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 */
   }
@@ -2840,7 +3279,7 @@ int check_splist_f4(int m,NODE splist)
   for ( d = 0, t = splist; t; t = NEXT(t) ) {
     p = BDY((LIST)BDY(t));
     NEXTND_pairs(d,r);
-    r->i1 = ZTOS((Q)ARG0(p)); r->i2 = ZTOS((Q)ARG1(p));
+    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 */
   }
@@ -2871,17 +3310,16 @@ int check_splist_f4(int m,NODE splist)
 
 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;
+  int i,stat;
+  ND nf,s,head;
+  NDV nfv;
   union oNDC hc;
   NODE node;
   LIST l;
   Z iq;
-  P cont,cont1;
+  P cont;
 
+  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] */
@@ -2942,18 +3380,19 @@ 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;
+  NODE g,t;
   ND_pairs d;
   ND_pairs l;
-  ND h,nf,nfq,s,head;
+  ND h,nf,nfq;
   NDV nfv,nfqv;
-  Z q,den,num;
+  Z q;
   P hc;
-  union oNDC dn,hnfq;
+  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);
@@ -2964,6 +3403,11 @@ NODE nd_gb_trace(int m,int ishomo,int **indp)
     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);
@@ -3057,11 +3501,27 @@ again:
         }
         d = update_pairs(d,g,nh,0);
         g = update_base(g,nh);
+        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 {
-        if ( DP_Print ) { printf("*"); fflush(stdout); }
+        if ( DP_Print ) { fprintf(asir_out,"*"); fflush(asir_out); }
       }
     } else {
-      if ( DP_Print ) { printf("."); fflush(stdout); }
+      if ( DP_Print ) { fprintf(asir_out,"."); fflush(asir_out); }
     }
     FREENDP(l);
   }
@@ -3073,7 +3533,7 @@ again:
     }
   }
   conv_ilist(nd_demand,1,g,indp);
-  if ( DP_Print ) { printf("nd_gb_trace done.\n"); fflush(stdout); }
+  if ( DP_Print ) { fprintf(asir_out,"\nnd_gb_trace done. Nbase=%d\n",nd_psn); fflush(asir_out); }
   return g;
 }
 
@@ -3102,14 +3562,12 @@ 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);
@@ -3117,7 +3575,7 @@ NODE ndv_reduceall(int m,NODE f)
   perm = (int *)MALLOC(n*sizeof(int));
   if ( nd_gentrace ) {
     for ( t = nd_tracelist, i = 0; i < n; i++, t = NEXT(t) )
-      perm[i] = ZTOS((Q)ARG1(BDY((LIST)BDY(t))));
+      perm[i] = (int)ZTOS((Q)ARG1(BDY((LIST)BDY(t))));
   }
   for ( i = 0; i < n; ) {
     if ( nd_gentrace ) {
@@ -3136,7 +3594,7 @@ 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 = ZTOS(jq);
+          jq = ARG1(BDY((LIST)BDY(t))); j = (int)ZTOS(jq);
           STOZ(perm[j],jq); ARG1(BDY((LIST)BDY(t))) = jq;
         }
         /* exact division */
@@ -3161,9 +3619,17 @@ 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 */
@@ -3180,8 +3646,10 @@ 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 {
@@ -3191,7 +3659,7 @@ 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);
       }
@@ -3223,6 +3691,23 @@ 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;
@@ -3232,7 +3717,7 @@ 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) > nd_intersect) ) 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;
@@ -3246,7 +3731,7 @@ 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);
@@ -3260,23 +3745,218 @@ 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 (*cmpdl)(nd_nvar,s1->dl,s2->dl);
+    else return comp_sig_monomial(nd_nvar,DL(s1),DL(s2));
   } else {
     static DL m1,m2;
-    static int nvar;
+    static int nvar = 0;
     int ret;
   
     if ( nvar != nd_nvar ) {
       nvar = nd_nvar; NEWDL(m1,nvar); NEWDL(m2,nvar);
     }
-    _adddl(nd_nvar,s1->dl,nd_sba_hm[s1->pos],m1);
-    _adddl(nd_nvar,s2->dl,nd_sba_hm[s2->pos],m2);
-    ret = (*cmpdl)(nd_nvar,m1,m2);
+    if ( !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;
@@ -3296,9 +3976,11 @@ int _create_spair_s(int i1,int i2,ND_pairs sp,SIG sig1
   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;
@@ -3311,6 +3993,7 @@ int _create_spair_s(int i1,int i2,ND_pairs sp,SIG sig1
   _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)
@@ -3319,11 +4002,17 @@ int _create_spair_s(int i1,int i2,ND_pairs sp,SIG sig1
   _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;
 }
 
@@ -3335,6 +4024,7 @@ SIG dup_sig(SIG sig)
   else {
     NEWSIG(r);
     _copydl(nd_nvar,DL(sig),DL(r));
+    _copydl(nd_nvar,DL2(sig),DL2(r));
     r->pos = sig->pos;
     return r;
   }
@@ -3353,7 +4043,7 @@ void dup_ND_pairs(ND_pairs to,ND_pairs from)
 ND_pairs merge_pairs_s(ND_pairs p1,ND_pairs p2)
 {
   struct oND_pairs root;
-  ND_pairs q1,q2,r0,r;
+  ND_pairs q1,q2,r;
   int ret;
 
   r = &root;
@@ -3364,6 +4054,7 @@ ND_pairs merge_pairs_s(ND_pairs p1,ND_pairs p2)
     } 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 ) {
@@ -3386,7 +4077,7 @@ ND_pairs merge_pairs_s(ND_pairs p1,ND_pairs p2)
 ND_pairs insert_pair_s(ND_pairs l,ND_pairs s)
 {
   ND_pairs p,prev;
-  int ret;
+  int ret=1;
 
   for ( p = l, prev = 0; p != 0; prev = p, p = p->next ) {
     if ( (ret = comp_sig(s->sig,p->sig)) <= 0 )
@@ -3407,6 +4098,7 @@ ND_pairs insert_pair_s(ND_pairs l,ND_pairs s)
       return l;
   } else {
     // insert s between prev and p
+    Nnewpair++;
     s->next = p;
     if ( prev == 0 ) {
       return s;
@@ -3434,14 +4126,12 @@ INLINE int __dl_redble(DL d1,DL d2,int nvar)
 
 ND_pairs nd_newpairs_s(int t, NODE *syz)
 {
-  NODE h,s;
-  UINT *dl;
-  int ts,ret,i;
-  ND_pairs r,r0,_sp,sp;
+  NODE s;
+  int ret,i;
+  ND_pairs r0,_sp,sp;
   SIG spsig,tsig;
-  static int nvar;
+  static int nvar = 0;
   static SIG _sig1,_sig2;
-  struct oEGT eg1,eg2,eg3,eg4;
 
   NEWND_pairs(_sp);
   if ( !_sig1 || nvar != nd_nvar ) {
@@ -3468,6 +4158,42 @@ ND_pairs nd_newpairs_s(int t, NODE *syz)
   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)
 {
@@ -3478,8 +4204,8 @@ 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 = ZTOS((Q)ARG0(tn));
-    r->i2 = ZTOS((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]));
@@ -3498,7 +4224,6 @@ 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]);
@@ -3518,7 +4243,7 @@ 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);
         }
@@ -3664,8 +4389,7 @@ 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;
@@ -3765,15 +4489,13 @@ 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 len;
     RHist r;
-    NDV b;
     NODE tn;
     LIST l;
     Z iq;
@@ -3838,20 +4560,36 @@ int ndv_newps(int m,NDV a,NDV aq)
     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 sba)
 {
-  int i,j,td,len,max;
-  NODE s,s0,f0,tn;
-  UINT *d;
+  int i,j;
+  NODE s,tn;
   RHist r;
   NDVI w;
   NDV a,am;
   union oNDC hc;
   NODE node;
-  P hcp;
   Z iq,jq;
   LIST l;
 
@@ -3900,8 +4638,7 @@ int ndv_setup(int mod,int trace,NODE f,int dont_sort,i
         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;
+        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);
@@ -3909,8 +4646,7 @@ int ndv_setup(int mod,int trace,NODE f,int dont_sort,i
         register_hcf(a);
         am = nd_ps[i] = ndv_dup(mod,a);
         ndv_mod(mod,am);
-      if ( DL_COMPARE(HDL(am),HDL(a)) ) 
-        return 0;
+        if ( DL_COMPARE(HDL(am),HDL(a)) ) return 0;
         ndv_removecont(mod,am);
       }
     } else {
@@ -3956,7 +4692,11 @@ int ndv_setup(int mod,int trace,NODE f,int dont_sort,i
         if ( nd_demand ) nd_ps_trace_sym[i]->sig = sig;
       }
       NEWDL(nd_sba_hm[i],nd_nvar);
-      _ndltodl(DL(nd_psh[i]),nd_sba_hm[i]);
+      if ( nd_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++ ) {
@@ -3977,7 +4717,7 @@ 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;
@@ -3986,8 +4726,7 @@ 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;
 
@@ -4076,156 +4815,167 @@ 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;
-    VECT hvect;
+  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);
-                  }
-                }
-            } 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) ) {
+    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 ) {
-          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);
+          e = dpm_getdeg((DPM)BDY(t),&trank);
+          max = MAX(e,max);
+          mrank = MAX(mrank,trank);
         } else {
-          if ( !m && !nd_gentrace ) pltozpl((LIST)BDY(t),&dmy,&zpl);
-          else zpl = (LIST)BDY(t);
-          b = (pointer)pltondv(CO,vv,zpl);
+          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 {
+        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 ) {
+      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 ( 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)?1:0,0,0);
-    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]);
+      ndltodp(nd_psh[i]->dl,(DP *)&BDY(hvect)[i]);
   }
   if ( !ishomo && homo ) {
        /* dehomogenization */
@@ -4233,45 +4983,45 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     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])) > nd_intersect ) { 
+      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 ) {
-        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 )
+  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 )
         r0 = postprocess_algcoef(av,alist,r0);
-    MKLIST(*rp,r0);
-    if ( nd_gentrace ) {
+  MKLIST(*rp,r0);
+  if ( nd_gentrace ) {
   if ( f4 ) {
             STOZ(16,bpe);
             STOZ(nd_last_nonzero,last_nonzero);
@@ -4307,28 +5057,29 @@ NODE nd_sba_f4(int m,int **indp);
 
 void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int f4,struct order_spec *ord,LIST *rp)
 {
-  VL tv,fv,vv,vc,av;
-  NODE fd,fd0,r,r0,t,x,s,xx;
+  VL tv,fv,vv;
+  NODE fd,fd0,r,r0,t,x,nd,nd1,syz;
   int e,max,nvar,i;
   NDV b;
-  int ishomo,nalg,wmax,len;
+  int ishomo,wmax,len;
   NMV a;
-  P p,zp;
+  P zp;
   Q dmy;
   struct order_spec *ord1;
-  int j;
   int *perm;
   EPOS oepos;
-  int obpe,oadv,ompos,cbpe;
-  struct oEGT eg0,eg1,egconv;
+  int obpe,oadv,ompos;
+  struct oEGT eg0,eg1,egconv,egintred;
+  LIST l1,redind;
+  Z z;
 
   nd_module = 0;
   nd_demand = 0;
-  parse_nd_option(current_option);
   Nsamesig = 0;
   if ( DP_Multiple )
     nd_scale = ((double)DP_Multiple)/(double)(Denominator?Denominator:1);
   get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+  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++ );
@@ -4336,9 +5087,9 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int
     case 1:
       if ( ord->nv != nvar )
         error("nd_sba : invalid order specification");
-        break;
-      default:
-        break;
+      break;
+    default:
+      break;
   }
   nd_nalg = 0;
   nd_init_ord(ord);
@@ -4346,17 +5097,30 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int
   initd(ord);
   for ( t = BDY(f), max = 1; t; t = NEXT(t) ) {
     for ( tv = vv; tv; tv = NEXT(tv) ) {
-      e = getdeg(tv->v,(P)BDY(t));
-      max = MAX(e,max);
+      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 ( !m ) ptozp((P)BDY(t),1,&dmy,&zp);
-    else zp = (P)BDY(t);
-    b = (pointer)ptondv(CO,vv,zp);
+    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);
@@ -4368,17 +5132,22 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int
     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);
+      // 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);
-  x = f4 ? nd_sba_f4(m,&perm) : nd_sba_buch(m,ishomo || homo,&perm);
+  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;
   }
@@ -4386,11 +5155,19 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int
        /* 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) ) {
@@ -4399,29 +5176,42 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int
     else BDY(r) = ndvtop(m,CO,vv,BDY(t));
   }
   if ( r0 ) NEXT(r) = 0;
-  MKLIST(*rp,r0);
+  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:
@@ -4552,46 +5342,40 @@ 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 = ZTOS((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))); 
@@ -4600,7 +5384,7 @@ 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 = ZTOS((Q)ARG0(BDY((LIST)BDY(t))));
+    j = (int)ZTOS((Q)ARG0(BDY((LIST)BDY(t))));
     if ( j > i ) i = j;
   }
   n = i+1;
@@ -4622,42 +5406,38 @@ void nd_gr_recompute_trace(LIST f,LIST v,int m,struct 
     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); 
+  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));
+    ndv_mul_c(m,b,invm(HCM(b),m));
 #if 0
-        BDY(r) = ndvtop(m,CO,vv,pb[ZTOS((Q)BDY(t))]);
+    BDY(r) = ndvtop(m,CO,vv,pb[ZTOS((Q)BDY(t))]);
 #else
-        BDY(r) = ndvtodp(m,pb[ZTOS((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 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;
@@ -4665,9 +5445,11 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     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);
@@ -4678,7 +5460,6 @@ 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:
@@ -4732,8 +5513,13 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
                 }
               }
             } 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);
@@ -4754,9 +5540,17 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
             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 ( 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);
@@ -4771,7 +5565,7 @@ 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);
@@ -4781,7 +5575,8 @@ 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?1:0,0,0);
@@ -4807,10 +5602,13 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
             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);
@@ -4821,7 +5619,7 @@ 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;
@@ -4848,7 +5646,8 @@ 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\n",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);
@@ -5098,7 +5897,7 @@ 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;
 
@@ -5143,7 +5942,7 @@ void ndv_homogenize(NDV p,int obpe,int oadv,EPOS oepos
 
     len = p->len;
     for ( m = BDY(p), i = 0, max = 0; i < len; NMV_OADV(m), i++ )
-        max = MAX(max,TD(DL(m)));
+        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);
@@ -5161,8 +5960,6 @@ 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;
@@ -5222,7 +6019,7 @@ 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;
@@ -5251,7 +6048,7 @@ 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));
@@ -5395,7 +6192,7 @@ void ndv_free(NDV p)
 
 void nd_append_red(UINT *d,int i)
 {
-    RHist m,m0;
+    RHist m;
     int h;
 
     NEWRHist(m);
@@ -5439,14 +6236,13 @@ 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);
@@ -5490,10 +6286,11 @@ 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;
@@ -5510,20 +6307,20 @@ 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++ );
@@ -5567,7 +6364,7 @@ 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;
@@ -5649,7 +6446,7 @@ void nd_reconstruct_s(int trace,ND_pairs *d)
     int i,obpe,oadv,h;
     static NM prev_nm_free_list;
     static ND_pairs prev_ndp_free_list;
-    RHist mr0,mr;
+    RHist mr;
     RHist r;
     RHist *old_red;
     ND_pairs s0,s,t;
@@ -5694,6 +6491,7 @@ void nd_reconstruct_s(int trace,ND_pairs *d)
           SG(s) = SG(t);
           ndl_reconstruct(LCM(t),LCM(s),obpe,oepos);
       }
+      if ( s0 ) NEXT(s) = 0;
       d[i] = s0;
     }
     
@@ -5731,11 +6529,11 @@ void nd_reconstruct_s(int trace,ND_pairs *d)
 
 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;
@@ -5763,7 +6561,6 @@ 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 )
@@ -5790,7 +6587,6 @@ 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;
@@ -6043,19 +6839,16 @@ 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;
@@ -6072,8 +6865,8 @@ 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;
 
@@ -6085,11 +6878,10 @@ 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) ) {
@@ -6133,8 +6925,7 @@ 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;
@@ -6281,7 +7072,7 @@ 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;
@@ -6393,14 +7184,13 @@ 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;
 
@@ -6409,7 +7199,7 @@ 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");
         CZ(m) = (Z)p;
         NEXT(m) = 0;
@@ -6432,7 +7222,7 @@ 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 = ZTOS(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;
@@ -6492,7 +7282,7 @@ 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;
@@ -6623,6 +7413,31 @@ int nmv_comp(NMV a,NMV b)
   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;
@@ -6699,6 +7514,21 @@ 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;
@@ -6724,23 +7554,21 @@ DPM ndvtodpm(int mod,NDV p)
 
 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)
@@ -6784,6 +7612,7 @@ 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) ) {
@@ -7039,7 +7868,6 @@ 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;
@@ -7208,12 +8036,12 @@ IndArray nm_ind_pair_to_vect_compress(int trace,UINT *
 {
     NM m;
     NMV mr;
-    UINT *d,*t,*s,*u;
+    UINT *d,*t,*u;
     NDV p;
     unsigned char *ivc;
     unsigned short *ivs;
-    UINT *v,*ivi,*s0v;
-    int i,j,len,prev,diff,cdiff,h,st,ed,md,c;
+    UINT *v,*ivi;
+    int i,j,len,prev,diff,cdiff,st,ed,md,c;
     IndArray r;
 
     m = pair->mul;
@@ -7374,10 +8202,8 @@ 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;
 
@@ -7469,7 +8295,6 @@ int ndv_reduce_vect(int m,UINT *svect,int col,IndArray
     unsigned int *ivi;
     NDV redv;
     NMV mr;
-    NODE rp;
     int maxrs;
 
     maxrs = 0;
@@ -7531,14 +8356,13 @@ int ndv_reduce_vect(int m,UINT *svect,int col,IndArray
 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;
@@ -7580,8 +8404,7 @@ 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;
 
@@ -7589,7 +8412,7 @@ 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:
@@ -7628,14 +8451,12 @@ 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;
@@ -7686,16 +8507,13 @@ 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));
@@ -7810,7 +8628,7 @@ NDV vect_to_ndv_s(UINT *vect,int col,UINT *s0vect)
 
 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;
@@ -7854,7 +8672,7 @@ NDV vect_to_ndv_q(Z *vect,int spcol,int col,int *rhead
         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);
+          ndl_copy(p,DL(mr)); CZ(mr) = c; NMV_ADV(mr);
         }
       }
     }
@@ -7925,7 +8743,6 @@ 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;
 
@@ -7997,149 +8814,133 @@ 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);
+  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
-    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);
-    }
+  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 = 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;
+  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);
-            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);
-                STOZ(t->i1,i1); STOZ(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);
-            STOZ(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 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;
@@ -8326,28 +9127,27 @@ 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);
-    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) ) {
@@ -8401,8 +9201,6 @@ NODE nd_f4_red(int m,ND_pairs sp0,int trace,UINT *s0ve
     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 )
@@ -8453,7 +9251,7 @@ 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;
@@ -8538,19 +9336,17 @@ NODE nd_f4_red_main(int m,ND_pairs sp0,int nsp,UINT *s
 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;
     UINT **spmat;
-    UINT *svect,*cvect;
-    UINT *v;
+    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;
 
     get_eg(&eg0);
@@ -8619,7 +9415,7 @@ NODE nd_f4_red_sf_main(int m,ND_pairs sp0,int nsp,UINT
         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;
@@ -8699,7 +9495,7 @@ 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;
@@ -8781,7 +9577,7 @@ 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;
@@ -8935,7 +9731,7 @@ 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;
@@ -9026,14 +9822,10 @@ int nd_gauss_elim_mod(UINT **mat0,int *sugar,ND_pairs 
 
 int nd_gauss_elim_mod_s(UINT **mat,int *sugar,ND_pairs *spactive,int row,int col,int md,int *colstat,SIG *sig)
 {
-  int i,j,k,l,rank,s,imin;
+  int i,j,k,rank,s;
   UINT inv;
   UINT a;
-  UINT *t,*pivot,*pk;
-  UINT *ck;
-  UINT *ct;
-  ND_pairs pair;
-  SIG sg;
+  UINT *pk;
   int *used;
 
   used = (int *)MALLOC(row*sizeof(int));
@@ -9053,7 +9845,7 @@ int nd_gauss_elim_mod_s(UINT **mat,int *sugar,ND_pairs
     s = sugar[i];
     inv = invm(mat[i][j],md);
     /* normalize pivot row */
-    for ( k = j, pk = mat[i]+j; k < col; k++, pk++, ck++ ) {
+    for ( k = j, pk = mat[i]+j; k < col; k++, pk++ ) {
       DMAR(*pk,inv,0,md,*pk);
     }
     for ( k = i+1; k < row; k++ ) {
@@ -9148,7 +9940,7 @@ 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;
@@ -9214,7 +10006,7 @@ 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;
@@ -9447,16 +10239,15 @@ 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 ) {
@@ -9494,7 +10285,7 @@ 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;
 
@@ -9529,7 +10320,7 @@ 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));
@@ -9546,7 +10337,7 @@ 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);
@@ -9579,19 +10370,16 @@ 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;
 
@@ -9752,7 +10540,7 @@ void conv_ilist(int demand,int trace,NODE g,int **indp
 
 NODE conv_ilist_s(int demand,int trace,int **indp)
 {
-  int n,i,j;
+  int n,i;
   int *ind;
   NODE g0,g;
 
@@ -9769,19 +10557,22 @@ NODE conv_ilist_s(int demand,int trace,int **indp)
   return g0;
 }
 
-void parse_nd_option(NODE opt)
+void parse_nd_option(VL vl,NODE opt)
 {
   NODE t,p,u;
   int i,s,n;
   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;
   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_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));
@@ -9793,14 +10584,16 @@ void parse_nd_option(NODE opt)
       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));
         for ( i = 0; u; u = NEXT(u) ) {
           p = BDY((LIST)BDY(u));
-          s = nd_gbblock[i++] = ZTOS((Q)BDY(p));
-          nd_gbblock[i++] = s+ZTOS((Q)BDY(NEXT(p)))-1;
+          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
@@ -9810,43 +10603,66 @@ void parse_nd_option(NODE opt)
     else if ( !strcmp(key,"intersect") )
             nd_intersect = value?1:0;
     else if ( !strcmp(key,"syzgen") )
-            nd_intersect = ZTOS((Q)value);
+            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 = ZTOS((Q)ARG3(u));
+        nd_bpe = (int)ZTOS((Q)ARG3(u));
       }
     } else if ( !strcmp(key,"f4red") ) {
-      nd_f4red = ZTOS((Q)value);
+      nd_f4red = (int)ZTOS((Q)value);
     } else if ( !strcmp(key,"rank0") ) {
       nd_rank0 = value?1:0;
     } else if ( !strcmp(key,"splist") ) {
       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));
       for ( i = 0; i < n; i++, u = NEXT(u) ) 
-        nd_sugarweight[i] = ZTOS((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?ZTOS((Q)value):0;
+      nd_sba_f4step = value?(int)ZTOS((Q)value):0;
     } else if ( !strcmp(key,"sba_pot") ) {
-      nd_sba_pot = value?1:0;
+      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);
@@ -9899,7 +10715,7 @@ 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;
 
@@ -9909,7 +10725,7 @@ 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;
@@ -9998,7 +10814,7 @@ 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;
@@ -10012,7 +10828,7 @@ ND btog_one(NODE ti,ND *p,int nb,int mod)
     ptomp(mod,(P)HCZ(m),&c);
     if ( (ci = ((MQ)c)->cont) != 0 ) {
       HCM(m) = ci;
-      pi = p[j=ZTOS((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);
@@ -10051,8 +10867,8 @@ 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:
@@ -10074,7 +10890,7 @@ 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 = ZTOS((Q)BDY(BDY((LIST)BDY(t))));
+    j = (int)ZTOS((Q)BDY(BDY((LIST)BDY(t))));
   if ( j > i ) i = j;
   }
   n = i+1;
@@ -10082,7 +10898,7 @@ 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 = ZTOS((Q)ARG0(pi)); pi1 = ZTOS((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);
@@ -10093,12 +10909,12 @@ 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=ZTOS((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=ZTOS((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);
@@ -10120,8 +10936,8 @@ 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:
@@ -10143,7 +10959,7 @@ 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 = ZTOS((Q)BDY(BDY((LIST)BDY(t))));
+    j = (int)ZTOS((Q)BDY(BDY((LIST)BDY(t))));
   if ( j > i ) i = j;
   }
   n = i+1;
@@ -10151,7 +10967,7 @@ 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 = ZTOS((Q)ARG0(pi)); pi1 = ZTOS((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);
@@ -10161,12 +10977,12 @@ 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=ZTOS((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=ZTOS((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);
@@ -10183,7 +10999,6 @@ 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;
@@ -10191,8 +11006,8 @@ 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:
@@ -10214,7 +11029,7 @@ 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 = ZTOS((Q)BDY(BDY((LIST)BDY(t))));
+    j = (int)ZTOS((Q)BDY(BDY((LIST)BDY(t))));
   if ( j > i ) i = j;
   }
   n = i+1;
@@ -10222,7 +11037,7 @@ 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 = ZTOS((Q)ARG0(pi)); pi1 = ZTOS((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);
@@ -10234,7 +11049,7 @@ 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=ZTOS((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;
   }
@@ -10242,7 +11057,7 @@ 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=ZTOS((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;
   }
@@ -10252,7 +11067,7 @@ VECT nd_btog_one(LIST f,LIST v,int mod,struct order_sp
   for ( j = 0, t = ind; j < m; j++, t = NEXT(t) ) {
   u = p[ZTOS((Q)BDY(t))];
   if ( !u ) {
-    u = nd_load_mod(ZTOS((Q)BDY(t)));
+    u = nd_load_mod((int)ZTOS((Q)BDY(t)));
     BDY(vect)[j] = ndtodp(mod,u);
     nd_free(u);
   } else
@@ -10281,32 +11096,22 @@ 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++ );
@@ -10322,7 +11127,7 @@ 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 */
@@ -10369,7 +11174,7 @@ 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);
@@ -10377,7 +11182,7 @@ 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;
+//    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);
@@ -10397,11 +11202,11 @@ 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);
@@ -10417,21 +11222,13 @@ 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;
@@ -10962,8 +11759,6 @@ NODE nd_f4_red_s(int m,ND_pairs sp0,int trace,UINT *s0
   NODE r0,rp;
   ND_pairs sp;
   NM_ind_pair *rvect;
-  UINT *s;
-  int *s0hash;
   struct oEGT eg0,eg1,eg_conv;
 
   for ( sp = sp0, nsp = 0; sp; sp = NEXT(sp), nsp++ );
@@ -10996,16 +11791,18 @@ NODE nd_f4_red_s(int m,ND_pairs sp0,int trace,UINT *s0
 #else
     r0 = nd_f4_red_main_s(m,sp0,nsp,s0vect,col,rvect,rhead,imat,nred,syzlistp);
 #endif
-  else
+  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,singular,ret,d,k,imin;
+  int i,imin;
   SIG t;
   static int wpd,nvar;
   static SIG quo,quomin;
@@ -11032,6 +11829,7 @@ INLINE int ndl_find_reducer_minsig(UINT *dg)
       _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;
@@ -11082,6 +11880,7 @@ int nd_symbolic_preproc_s(PGeoBucket bucket,int trace,
       _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));
@@ -11102,20 +11901,19 @@ int nd_symbolic_preproc_s(PGeoBucket bucket,int trace,
 
 NODE nd_sba_f4(int m,int **indp)
 {
-  int i,nh,stat,index,f4red,f4step;
-  int col,rank,len,k,j,a,sugar,nbase,psugar,ms;
+  int i,nh,stat,f4red,f4step;
+  int col,psugar,ms;
   NODE r,g,rp0,nflist;
-  ND_pairs d,l,t;
+  ND_pairs d,l,t,l1;
   ND h,nf;
   NDV nfv;
-  union oNDC hc;
+//  union oNDC hc;
   UINT *s0vect;
-  UINT c;
   PGeoBucket bucket;
   NODE *syzlist;
   SIG sig;
-  struct oEGT eg0,eg1,eg_f4;
-  struct oEGT eg2,eg_update,eg_remove,eg_large,eg_nf,eg_nfzero;
+  struct oEGT eg1;
+  struct oEGT eg2,eg_remove,eg_nf,eg_nfzero;
 
   Nf4_red=0;
   d = 0;
@@ -11133,12 +11931,22 @@ NODE nd_sba_f4(int m,int **indp)
     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);
@@ -11161,7 +11969,7 @@ again:
       } else if ( nf ) {
         if ( DP_Print ) { printf("+"); fflush(stdout); }
         add_eg(&eg_nf,&eg1,&eg2);
-        hc = HCU(nf);
+//        hc = HCU(nf);
         nd_removecont(m,nf);
         nfv = ndtondv(m,nf); nd_free(nf);
         nh = ndv_newps(m,nfv,0);
@@ -11185,7 +11993,7 @@ again:
 again2:
       psugar = ms;
       l = nd_minsugarp_s(d,&d);
-      sugar = nd_sugarweight?d->sugar2:SG(d);
+//      sugar = nd_sugarweight?d->sugar2:SG(d);
       bucket = create_pbucket();
       stat = nd_sp_f4(m,0,l,bucket);
       if ( !stat ) {