===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2018/engine/nd.c,v
retrieving revision 1.46
retrieving revision 1.60
diff -u -p -r1.46 -r1.60
--- OpenXM_contrib2/asir2018/engine/nd.c	2021/01/25 00:39:52	1.46
+++ OpenXM_contrib2/asir2018/engine/nd.c	2021/12/17 23:53:13	1.60
@@ -1,10 +1,11 @@
-/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.45 2021/01/11 08:37:44 noro Exp $ */
+/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.59 2021/12/14 01:02:40 noro Exp $ */
 
 #include "nd.h"
 
 void print_siglist(NODE l);
 
-int Nnd_add,Nf4_red,NcriB,NcriMF,Ncri2,Npairs;
+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;
@@ -92,6 +93,7 @@ struct comp_sig_spec {
 
 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);
@@ -1299,6 +1301,7 @@ 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 ) { /* fprintf(asir_out,"s"); fflush(asir_out); */ singular = 1; }
@@ -1707,6 +1710,14 @@ int nd_nf_s(int mod,ND d,ND g,NDV *ps,int full,ND *rp)
                 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;
@@ -2467,6 +2478,129 @@ 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,wlen;
+  DL *p;
+  VECT b,x;
+  DL dl;
+  LIST weight;
+  LIST ret;
+  int *w;
+  NODE nd;
+
+  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,nd,t;
+  DL new,dl;
+  int len,i,n;
+  Z dz;
+  DL *p;
+  VECT b,head;
+  P tv,td,s,hn,hpoly;
+  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;
+
+  root.next = d;
+  prev = &root; cur = d;
+  while ( cur ) {
+    if ( SG(cur) == sugar )
+      prev->next = cur->next;
+    else
+      prev = cur;
+    cur = cur->next;
+  }
+  return root.next;
+}
+
 /* return value = 0 => input is not a GB */
 
 NODE nd_gb(int m,int ishomo,int checkonly,int gensyz,int **indp)
@@ -2483,6 +2617,9 @@ NODE nd_gb(int m,int ishomo,int checkonly,int gensyz,i
   int Nnfnz = 0,Nnfz = 0;
   P cont;
   LIST list;
+  struct oHPDATA current_hpdata,final_hpdata;
+  int final_hpvalue;
+
 struct oEGT eg1,eg2,eg_update;
 
 init_eg(&eg_update);
@@ -2493,6 +2630,10 @@ 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);
@@ -2566,6 +2707,22 @@ get_eg(&eg1);
 get_eg(&eg2); add_eg(&eg_update,&eg1,&eg2);
       g = update_base(g,nh);
       FREENDP(l);
+      if ( nd_hpdata ) {
+        int dg,sugar0;
+
+        update_hpdata(&current_hpdata,nh); 
+        dg = comp_hn(final_hpdata.hn,current_hpdata.hn);
+        if ( dg < 0 ) {
+           fprintf(asir_out,"We found a gb\n");
+           d = 0;
+        }
+        sugar0 = sugar;
+        while ( d && dg > sugar0 ) {
+          if ( DP_Print ) { fprintf(asir_out,"[%d]",sugar0); fflush(asir_out); }
+          d = nd_remove_same_sugar(d,sugar0);
+          sugar0++;
+        }
+      }
     } else {
       Nnfz++;
       if ( nd_gentrace && gensyz ) {
@@ -2575,14 +2732,14 @@ get_eg(&eg2); add_eg(&eg_update,&eg1,&eg2);
         MKNODE(t,list,nd_alltracelist); 
         nd_alltracelist = t; nd_tracelist = 0;
       }
-      if ( DP_Print ) { printf("."); fflush(stdout); }
+      if ( DP_Print ) { fprintf(asir_out,"."); fflush(asir_out); }
         FREENDP(l);
     }
   }
   conv_ilist(nd_demand,0,g,indp);
   if ( !checkonly && DP_Print ) { 
-    printf("\nnd_gb done. Nnd_add=%d,Npairs=%d, Nnfnz=%d,Nnfz=%d,",Nnd_add,Npairs,Nnfnz,Nnfz);
-    printf("Nremoved=%d\n",NcriB+NcriMF+Ncri2);
+    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 ) {
@@ -2592,7 +2749,9 @@ get_eg(&eg2); add_eg(&eg_update,&eg1,&eg2);
 }
 
 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);
@@ -2600,7 +2759,38 @@ 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;
@@ -2653,8 +2843,6 @@ 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;
@@ -2703,12 +2891,12 @@ ND_pairs find_smallest_lcm(ND_pairs l)
   NODE t;
   ND_pairs r;
   struct oSIG sig1;
-  static DL mul,quo,minlm;
+  static DL mul,quo,quo2,minlm;
   static int nvar = 0;
 
   if ( nvar < nd_nvar ) {
     nvar = nd_nvar; 
-    NEWDL(quo,nvar); NEWDL(mul,nvar);
+    NEWDL(quo,nvar); NEWDL(quo2,nvar); NEWDL(mul,nvar);
     NEWDL(minlm,nvar);
   }
   sig = l->sig;
@@ -2721,12 +2909,14 @@ ND_pairs find_smallest_lcm(ND_pairs l)
       _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);
@@ -2734,6 +2924,8 @@ ND_pairs find_smallest_lcm(ND_pairs l)
       _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);
@@ -2792,27 +2984,56 @@ SIG trivial_sig(int i,int j)
 
   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 *d;
   ND_pairs l,l1;
   ND h,nf,s,head,nf1;
   NDV nfv;
@@ -2822,70 +3043,68 @@ NODE nd_sba_buch(int m,int ishomo,int **indp,NODE *syz
   LIST list;
   SIG sig;
   NODE *syzlist;
-  int ngen;
+  int ngen,ind;
   int Nnominimal,Nredundant;
   DL lcm,quo,mul;
-  struct oEGT eg1,eg2,eg_update,eg_remove,eg_large,eg_nf,eg_nfzero;
-  int Nnfs=0,Nnfz=0,Nnfnz=0;
+  struct oHPDATA final_hpdata,current_hpdata;
+  struct oEGT eg1,eg2,eg3,eg4,eg_update,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;
-  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);
+  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);
   }
   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 0
-    if ( small_lcm(l) ) {
-      if ( DP_Print ) fprintf(asir_out,"M");
-      Nnominimal++;
-      continue;
-    }
-    if ( SG(l) != sugar ) {
-      sugar = SG(l);
-      if ( DP_Print ) fprintf(asir_out,"%d",sugar);
-    }
-    sig = l->sig;
-    if ( DP_Print && nd_sba_pot ) {
-      if ( sig->pos != pos ) {
-        fprintf(asir_out,"[%d]",sig->pos);
-        pos = sig->pos;
-      }
-    }
-    stat = nd_sp(m,0,l,&h);
-#else
-//    if ( l->sig->dl->td == 0 )
-//      if ( DP_Print ) print_sig(l->sig); 
+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 ) {
-      if ( DP_Print ) fprintf(asir_out,"M");
+      d[ind] = d[ind]->next; dlen--;
+//      if ( DP_Print && !nd_hpdata ) fprintf(asir_out,"M");
       Nnominimal++;
       continue;
     }
@@ -2900,29 +3119,29 @@ again:
         pos = sig->pos;
       }
     }
+get_eg(&eg1);
     stat = nd_sp(m,0,l1,&h);
-#endif
+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 ) {
+      d[ind] = d[ind]->next; dlen--;
       Nnfnz++;
       if ( DP_Print ) { 
         if ( nd_sba_redundant_check ) {
@@ -2937,41 +3156,70 @@ get_eg(&eg2); 
       }
       add_eg(&eg_nf,&eg1,&eg2);
       hc = HCU(nf);
-      nd_removecont(m,nf);
-      nfv = ndtondv(m,nf); nd_free(nf);
-      nh = ndv_newps(m,nfv,0);
-
-      d = update_pairs_s(d,nh,syzlist);
-      nd_sba_pos[sig->pos] = append_one(nd_sba_pos[sig->pos],nh);
-      FREENDP(l);
+       get_eg(&eg1);
+       nd_removecont(m,nf);
+       get_eg(&eg2); add_eg(&eg_removecont,&eg1,&eg2);
+       nfv = ndtondv(m,nf); nd_free(nf);
+       nh = ndv_newps(m,nfv,0);
+  
+       get_eg(&eg1);
+       dlen += update_pairs_array_s(d,nh,syzlist);
+       get_eg(&eg2); add_eg(&eg_updatepairs,&eg1,&eg2);
+       nd_sba_pos[sig->pos] = append_one(nd_sba_pos[sig->pos],nh);
+       if ( nd_hpdata ) {
+         get_eg(&eg1);
+         update_hpdata(&current_hpdata,nh);
+         get_eg(&eg2); add_eg(&eg_hpdata,&eg1,&eg2);
+         if ( !compp(CO,final_hpdata.hn,current_hpdata.hn) ) {
+           if ( DP_Print ) { printf("\nWe found a gb.\n"); }
+             break;
+         }
+      }
    } else {
+      d[ind] = d[ind]->next; dlen--;
       Nnfz++;
       add_eg(&eg_nfzero,&eg1,&eg2);
      // 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);
    }
  }
+ get_eg(&eg4); add_eg(&eg_sbabuch,&eg3,&eg4);
  g = conv_ilist_s(nd_demand,0,indp);
  if ( DP_Print ) { 
-   printf("\nnd_sba done. nd_add=%d,Nsyz=%d,Nsamesig=%d,Nnominimal=%d\n",Nnd_add,Nsyz,Nsamesig,Nnominimal);
-   printf("Nnfnz=%d,Nnfz=%d,Nnfsingular=%d\n",Nnfnz,Nnfz,Nnfs);
-   fflush(stdout); 
+   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",Nnfnz,Nnfz,Nnfs,nd_psn);
+   fflush(stdout);
    if ( nd_sba_redundant_check )
    printf("Nredundant=%d\n",Nredundant);
-   fflush(stdout); 
+   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;
@@ -3152,6 +3400,8 @@ NODE nd_gb_trace(int m,int ishomo,int **indp)
   int diag_count = 0;
   P cont;
   LIST list;
+  struct oHPDATA current_hpdata,final_hpdata;
+  int final_hpvalue;
 
   init_eg(&eg_monic);
   init_eg(&eg_invdalg);
@@ -3162,6 +3412,11 @@ 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);
@@ -3255,11 +3510,27 @@ 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 ) {
+             fprintf(asir_out,"We found a gb\n");
+             d = 0;
+          }
+          sugar0 = sugar;
+          while ( d && dg > sugar0 ) {
+            if ( DP_Print ) { fprintf(asir_out,"[%d]",sugar0); fflush(asir_out); }
+            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);
   }
@@ -3271,7 +3542,7 @@ again:
     }
   }
   conv_ilist(nd_demand,1,g,indp);
-  if ( DP_Print ) { printf("\nnd_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;
 }
 
@@ -3431,6 +3702,23 @@ 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;
@@ -3640,7 +3928,9 @@ int comp_sig_monomial(int n,DL d1,DL d2)
   }
   if ( !nd_sba_modord )
     return (*cmpdl)(n,d1,d2);
-  else {
+  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 ) {
@@ -3666,7 +3956,7 @@ int comp_sig(SIG s1,SIG s2)
   if ( nd_sba_pot ) {
     if ( s1->pos > s2->pos ) return 1;
     else if ( s1->pos < s2->pos ) return -1;
-    else return comp_sig_monomial(nd_nvar,s1->dl,s2->dl);
+    else return comp_sig_monomial(nd_nvar,DL(s1),DL(s2));
   } else {
     static DL m1,m2;
     static int nvar = 0;
@@ -3675,9 +3965,10 @@ int comp_sig(SIG s1,SIG s2)
     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 = comp_sig_monomial(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;
@@ -3697,9 +3988,11 @@ 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;
@@ -3712,6 +4005,7 @@ 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)
@@ -3720,11 +4014,17 @@ 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;
 }
 
@@ -3736,6 +4036,7 @@ 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;
   }
@@ -3765,6 +4066,7 @@ 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 ) {
@@ -3787,7 +4089,7 @@ 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 )
@@ -3808,6 +4110,7 @@ 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;
@@ -3869,6 +4172,44 @@ ND_pairs nd_newpairs_s(int t, NODE *syz)
   return r0;
 }
 
+ND_pairs *nd_newpairs_array_s(int t, NODE *syz)
+{
+  NODE h,s;
+  UINT *dl;
+  int ts,ret,i;
+  ND_pairs r,r0,_sp,sp;
+  ND_pairs *d;
+  SIG spsig,tsig;
+  static int nvar = 0;
+  static SIG _sig1,_sig2;
+  struct oEGT eg1,eg2,eg3,eg4;
+
+  NEWND_pairs(_sp);
+  if ( !_sig1 || nvar != nd_nvar ) {
+    nvar = nd_nvar; NEWSIG(_sig1); NEWSIG(_sig2);
+  }
+  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)
 {
@@ -4379,6 +4720,7 @@ int ndv_setup(int mod,int trace,NODE f,int dont_sort,i
         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++ ) {
@@ -4744,7 +5086,7 @@ 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,nd,syz;
+  NODE fd,fd0,r,r0,t,x,s,xx,nd,nd1,syz;
   int e,max,nvar,i;
   NDV b;
   int ishomo,nalg,wmax,len;
@@ -4756,7 +5098,9 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int
   int *perm;
   EPOS oepos;
   int obpe,oadv,ompos,cbpe;
-  struct oEGT eg0,eg1,egconv;
+  struct oEGT eg0,eg1,egconv,egintred;
+  LIST l1,redind;
+  Z z;
 
   nd_module = 0;
   nd_demand = 0;
@@ -4829,6 +5173,9 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int
   }
 
   ndv_setup(m,0,fd0,nd_sba_dontsort,0,1);
+  if ( nd_gentrace ) {
+    MKLIST(l1,nd_tracelist); MKNODE(nd_alltracelist,l1,0);
+  }
   x = f4 ? nd_sba_f4(m,&perm) : nd_sba_buch(m,ishomo || homo,&perm,&syz);
   if ( !x ) {
     *rp = 0; return;
@@ -4842,8 +5189,14 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int
     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) ) {
@@ -4854,15 +5207,22 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int
   if ( r0 ) NEXT(r) = 0;
   if ( nd_sba_syz ) {
     LIST gb,hsyz;
-    NODE nd;
 
     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");
 }
 
@@ -5297,7 +5657,7 @@ 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;
@@ -6172,6 +6532,7 @@ 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;
     }
     
@@ -6887,7 +7248,7 @@ 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;
@@ -10305,6 +10666,7 @@ void parse_nd_option(VL vl,NODE opt)
   nd_f4_td = 0; nd_sba_f4step = 2; nd_sba_pot = 0; nd_sba_largelcm = 0;
   nd_sba_dontsort = 0; nd_top = 0; nd_sba_redundant_check = 0;
   nd_sba_syz = 0; nd_sba_modord = 0; nd_sba_inputisgb = 0;
+  nd_hpdata = 0;
 
   for ( t = opt; t; t = NEXT(t) ) {
     p = BDY((LIST)BDY(t));
@@ -10352,6 +10714,9 @@ void parse_nd_option(VL vl,NODE opt)
       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);
@@ -11575,6 +11940,7 @@ 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;
@@ -11625,6 +11991,7 @@ 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));