===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2018/engine/nd.c,v
retrieving revision 1.46
retrieving revision 1.50
diff -u -p -r1.46 -r1.50
--- OpenXM_contrib2/asir2018/engine/nd.c	2021/01/25 00:39:52	1.46
+++ OpenXM_contrib2/asir2018/engine/nd.c	2021/03/09 05:20:35	1.50
@@ -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 1.49 2021/02/28 02:33:16 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);
@@ -2467,6 +2469,130 @@ LIST compute_splist()
   return l0;
 }
 
+typedef struct oHPDATA {
+  P hn; // HP(t)=hn(t)/(1-t)^n
+  int len;
+  P *head; // hp(i)=head[i] (i=0,...,len-1)
+  P hp; // dim Hm(i)=hp(i) (i >= len)
+  VECT x; // BDY(x)[i] = <<0,...,1,...,0>>
+  P *plist; // plist[i]=(1-t)^i
+} *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);
+void mhp_to_hf(VL vl,P hp,int n,P *plist,VECT *head,P *hf);
+DL monomial_colon(DL a,DL b,int n);
+LIST dp_monomial_hilbert_poincare(VECT b,VECT x,P *plist);
+
+int hpvalue(HPDATA data,int d)
+{
+  P *head;
+  int len;
+  P hp,val;
+  Z dz;
+
+  head = data->head;
+  len = data->len;
+  hp = data->hp;
+  if ( d < len )
+    return ZTOS((Z)head[d]);
+  else {
+    STOZ(d,dz);
+    substp(CO,hp,hp->v,(P)dz,&val);
+    return ZTOS((Z)val);
+  }
+}
+
+void setup_hpdata(HPDATA final,HPDATA current)
+{
+  int n,i;
+  P *r;
+  DL *p;
+  P tv;
+  VECT b,x,head;
+  DL dl;
+
+  n = nd_nvar;
+  final->hn = (P)ARG0(nd_hpdata);
+  head = (VECT)ARG2(nd_hpdata);
+  final->len = head->len;
+  final->head = (P *)BDY(head);
+  final->hp = (P)ARG3(nd_hpdata);
+  final->plist = (P *)BDY((VECT)ARG4(nd_hpdata));
+  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;
+
+  r = (P *)CALLOC(n+1,sizeof(P));
+  MKVECT(b,nd_psn); p = (DL *)BDY(b);
+  for ( i = 0; i < nd_psn; i++ ) {
+    p[i] = ndltodl(n,nd_psh[i]->dl);
+  }
+  make_reduced(b,n);
+  makevar("t",&tv);
+  mhp_rec(b,x,tv,r);
+  current->hn = mhp_ctop(r,final->plist,n);
+  mhp_to_hf(CO,current->hn,n,final->plist,&head,&current->hp);
+  current->head = (P *)BDY(head);
+  current->len = head->len;
+  current->x = x;
+  current->plist = final->plist;
+}
+
+void update_hpdata(HPDATA current,int nh,int do_hf)
+{
+  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)
+  list1 = dp_monomial_hilbert_poincare(b,current->x,current->plist);
+  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;
+  if ( do_hf ) {
+    mhp_to_hf(CO,hn,n,current->plist,&head,&hpoly);
+    current->head = (P *)BDY(head);
+    current->len = head->len;
+    current->hp = hpoly;
+  }
+}
+
+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 +2609,9 @@ 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 +2622,9 @@ init_eg(&eg_update);
     g = update_base(g,i);
   }
   sugar = 0;
+  if ( nd_hpdata ) {
+    setup_hpdata(&final_hpdata,&current_hpdata);
+  }
   while ( d ) {
 again:
     l = nd_minp(d,&d);
@@ -2509,6 +2641,18 @@ again:
       }
       sugar = SG(l);
       if ( DP_Print ) fprintf(asir_out,"%d",sugar);
+      if ( nd_hpdata ) {
+        if ( !compp(CO,final_hpdata.hn,current_hpdata.hn) )
+          break;
+        else {
+          final_hpvalue = hpvalue(&final_hpdata,sugar);
+          if ( final_hpvalue == hpvalue(&current_hpdata,sugar) ) {
+            if ( DP_Print ) fprintf(asir_out,"sugar=%d done.\n",sugar);
+            d = nd_remove_same_sugar(d,sugar);
+            continue;
+          }
+        }
+      }
     }
     stat = nd_sp(m,0,l,&h);
     if ( !stat ) {
@@ -2566,6 +2710,13 @@ get_eg(&eg1);
 get_eg(&eg2); add_eg(&eg_update,&eg1,&eg2);
       g = update_base(g,nh);
       FREENDP(l);
+      if ( nd_hpdata ) {
+        update_hpdata(&current_hpdata,nh,1);
+        if ( final_hpvalue == hpvalue(&current_hpdata,sugar) ) {
+          if ( DP_Print ) fprintf(asir_out,"sugar=%d done.\n",sugar);
+          d = nd_remove_same_sugar(d,sugar);
+        }
+      }
     } else {
       Nnfz++;
       if ( nd_gentrace && gensyz ) {
@@ -2592,7 +2743,9 @@ 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);
@@ -2721,12 +2874,14 @@ 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);
@@ -2808,11 +2963,35 @@ SIG trivial_sig(int i,int j)
   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 +3001,68 @@ 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 ) {
+    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 && dlen%100 == 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;
     }
@@ -2900,11 +3077,11 @@ 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);
@@ -2915,14 +3092,14 @@ get_eg(&eg1);
 #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 +3114,70 @@ get_eg(&eg2); 
       }
       add_eg(&eg_nf,&eg1,&eg2);
       hc = HCU(nf);
+      get_eg(&eg1);
       nd_removecont(m,nf);
+      get_eg(&eg2); add_eg(&eg_removecont,&eg1,&eg2);
       nfv = ndtondv(m,nf); nd_free(nf);
       nh = ndv_newps(m,nfv,0);
 
-      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);
+      if ( nd_hpdata ) {
+        get_eg(&eg1);
+        update_hpdata(&current_hpdata,nh,0);
+        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("\ndlen=%d,nd_sba done. nd_add=%d,Nsyz=%d,Nsamesig=%d,Nnominimal=%d\n",dlen,Nnd_add,Nsyz,Nsamesig,Nnominimal);
    printf("Nnfnz=%d,Nnfz=%d,Nnfsingular=%d\n",Nnfnz,Nnfz,Nnfs);
-   fflush(stdout); 
+   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 +3358,8 @@ 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 +3370,10 @@ NODE nd_gb_trace(int m,int ishomo,int **indp)
     g = update_base(g,i);
   }
   sugar = 0;
+  if ( nd_hpdata ) {
+    setup_hpdata(&final_hpdata,&current_hpdata);
+  }
+
   while ( d ) {
 again:
     l = nd_minp(d,&d);
@@ -3182,6 +3394,18 @@ again:
 #endif
       sugar = SG(l);
       if ( DP_Print ) fprintf(asir_out,"%d",sugar);
+      if ( nd_hpdata ) {
+        if ( !compp(CO,final_hpdata.hn,current_hpdata.hn) )
+          break;
+        else {
+          final_hpvalue = hpvalue(&final_hpdata,sugar);
+          if ( final_hpvalue == hpvalue(&current_hpdata,sugar) ) {
+            if ( DP_Print ) fprintf(asir_out,"sugar=%d done.\n",sugar);
+            d = nd_remove_same_sugar(d,sugar);
+            continue;
+          }
+        }
+      }
     }
     stat = nd_sp(m,0,l,&h);
     if ( !stat ) {
@@ -3255,6 +3479,13 @@ again:
         }
         d = update_pairs(d,g,nh,0);
         g = update_base(g,nh);
+        if ( nd_hpdata ) {
+          update_hpdata(&current_hpdata,nh,1);
+          if ( final_hpvalue == hpvalue(&current_hpdata,sugar) ) {
+            if ( DP_Print ) fprintf(asir_out,"sugar=%d done.\n",sugar);
+            d = nd_remove_same_sugar(d,sugar);
+          }
+        }
       } else {
         if ( DP_Print ) { printf("*"); fflush(stdout); }
       }
@@ -3431,6 +3662,23 @@ 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;
@@ -3677,7 +3925,10 @@ int comp_sig(SIG s1,SIG s2)
     }
     _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,m1,m2);
+    else
+      ret = comp_sig_monomial(nd_nvar,m1,m2);
     if ( ret != 0 ) return ret;
     else if ( s1->pos > s2->pos ) return 1;
     else if ( s1->pos < s2->pos ) return -1;
@@ -3697,9 +3948,11 @@ 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;
@@ -3725,6 +3978,11 @@ int _create_spair_s(int i1,int i2,ND_pairs sp,SIG sig1
   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;
 }
 
@@ -3765,6 +4023,7 @@ 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 +4046,7 @@ 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 +4067,7 @@ 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 +4129,44 @@ 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)
 {
@@ -6172,6 +6470,7 @@ 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 +7186,7 @@ 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 +10604,7 @@ 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 +10652,9 @@ 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);