===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2018/engine/nd.c,v
retrieving revision 1.40
retrieving revision 1.45
diff -u -p -r1.40 -r1.45
--- OpenXM_contrib2/asir2018/engine/nd.c	2020/11/02 08:30:55	1.40
+++ OpenXM_contrib2/asir2018/engine/nd.c	2021/01/11 08:37:44	1.45
@@ -1,8 +1,10 @@
-/* $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 1.44 2020/12/15 07:40:09 noro Exp $ */
 
 #include "nd.h"
 
-int Nnd_add,Nf4_red;
+void print_siglist(NODE l);
+
+int Nnd_add,Nf4_red,NcriB,NcriMF,Ncri2,Npairs;
 struct oEGT eg_search,f4_symb,f4_conv,f4_elim1,f4_elim2;
 
 int diag_period = 6;
@@ -65,9 +67,9 @@ 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_fixord,nd_sba_grevlexgb;
 static int *nd_gbblock;
 static NODE nd_nzlist,nd_check_splist;
 static int nd_splist;
@@ -98,10 +100,14 @@ 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 *);
@@ -794,13 +800,16 @@ 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 +826,8 @@ 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;
@@ -831,20 +840,20 @@ LAST:
     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:
@@ -1207,6 +1216,18 @@ 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 +1247,13 @@ 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)
@@ -2438,6 +2466,7 @@ NODE nd_gb(int m,int ishomo,int checkonly,int gensyz,i
   Z q;
   union oNDC dn,hc;
   int diag_count = 0;
+  int Nnfnz = 0,Nnfz = 0;
   P cont;
   LIST list;
 struct oEGT eg1,eg2,eg_update;
@@ -2484,6 +2513,7 @@ again:
       d = nd_reconstruct(0,d);
       goto again;
     } else if ( nf ) {
+      Nnfnz++;
       if ( checkonly || gensyz ) return 0;
       if ( nd_newelim ) {
         if ( nd_module ) {
@@ -2522,23 +2552,28 @@ 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);
-     }
+    } 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 ) { printf("."); fflush(stdout); }
+        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 ) { 
+    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);
+    fflush(asir_out);
+  }
+  if ( DP_Print ) {
+    print_eg("update",&eg_update); fprintf(asir_out,"\n");
+  }
   return g;
 }
 
@@ -2570,6 +2605,8 @@ 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;
   }
@@ -2610,7 +2647,7 @@ int small_lcm(ND_pairs l)
   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 +2682,60 @@ 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,minlm;
+  static int nvar = 0;
+
+  if ( nvar < nd_nvar ) {
+    nvar = nd_nvar; 
+    NEWDL(quo,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;
+        _copydl(nd_nvar,mul,minlm);
+      }
+    }
+  }
+  // l->lcm is minimal; return l itself
+  if ( minindex < 0 ) return l;
+  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;
+      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 +2744,17 @@ 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;
   }
@@ -2667,12 +2765,41 @@ 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);
+  }
+  if ( nd_sba_grevlexgb != 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);
+    sigj.pos = j; _subdl(nd_nvar,lcm,nd_sba_hm[j],sigj.dl);
+    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);
+    sigj.pos = j; _copydl(nd_nvar,nd_sba_hm[i],sigj.dl);
+    if ( comp_sig(&sigi,&sigj) > 0 ) sig = dup_sig(&sigi);
+    else sig = dup_sig(&sigj);
+  }
+  return sig;
+}
+
+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_pairs l,l1;
   ND h,nf,s,head,nf1;
   NDV nfv;
   Z q;
@@ -2681,25 +2808,28 @@ NODE nd_sba_buch(int m,int ishomo,int **indp)
   LIST list;
   SIG sig;
   NODE *syzlist;
-  int Nredundant;
+  int ngen;
+  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;
 
 init_eg(&eg_remove);
   syzlist = (NODE *)MALLOC(nd_psn*sizeof(NODE));
   Nsyz = 0;
   Nnd_add = 0;
+  Nnominimal = 0;
   Nredundant = 0;
   d = 0;
-  for ( i = 0; i < nd_psn; i++ ) {
-    d = update_pairs_s(d,i,syzlist);
-  }
+  ngen = nd_psn;
   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);
+      sig = trivial_sig(i,j);
       syzlist[sig->pos] = insert_sig(syzlist[sig->pos],sig);
     }
+  for ( i = 0; i < nd_psn; i++ ) {
+    d = update_pairs_s(d,i,syzlist);
+  }
   sugar = 0;
   pos = 0;
   NEWDL(lcm,nd_nvar); NEWDL(quo,nd_nvar); NEWDL(mul,nd_nvar);
@@ -2718,9 +2848,10 @@ again:
        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");
-      Nredundant++;
+      Nnominimal++;
       continue;
     }
     if ( SG(l) != sugar ) {
@@ -2735,6 +2866,26 @@ again:
       }
     }
     stat = nd_sp(m,0,l,&h);
+#else
+    l1 = find_smallest_lcm(l);
+    if ( l1 == 0 ) {
+      if ( DP_Print ) fprintf(asir_out,"M");
+      Nnominimal++;
+      continue;
+    }
+    if ( SG(l1) != sugar ) {
+      sugar = SG(l1);
+      if ( DP_Print ) fprintf(asir_out,"%d",sugar);
+    }
+    sig = l1->sig;
+    if ( DP_Print && nd_sba_pot ) {
+      if ( sig->pos != pos ) {
+        fprintf(asir_out,"[%d]",sig->pos);
+        pos = sig->pos;
+      }
+    }
+    stat = nd_sp(m,0,l1,&h);
+#endif
     if ( !stat ) {
       NEXT(l) = d; d = l;
       d = nd_reconstruct(0,d);
@@ -2752,10 +2903,22 @@ get_eg(&eg2); 
       d = nd_reconstruct(0,d);
       goto again;
     } else if ( stat == -1 ) {
+      Nnfs++;
       if ( DP_Print ) { printf("S"); fflush(stdout); }
       FREENDP(l);
     } else if ( nf ) {
-      if ( DP_Print ) { printf("+"); fflush(stdout); }
+      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);
       nd_removecont(m,nf);
@@ -2766,6 +2929,7 @@ get_eg(&eg2); 
       nd_sba_pos[sig->pos] = append_one(nd_sba_pos[sig->pos],nh);
       FREENDP(l);
    } else {
+      Nnfz++;
       add_eg(&eg_nfzero,&eg1,&eg2);
      // syzygy
 get_eg(&eg1);
@@ -2778,8 +2942,12 @@ get_eg(&eg2); add_eg(&eg_remove,&eg1,&eg2);
  }
  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);
+   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); 
+   if ( nd_sba_redundant_check )
+   printf("Nredundant=%d\n",Nredundant);
+   fflush(stdout); 
    print_eg("create",&eg_create);
    print_eg("merge",&eg_merge);
    print_eg("remove",&eg_remove);
@@ -2787,6 +2955,20 @@ get_eg(&eg2); add_eg(&eg_remove,&eg1,&eg2);
    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;
 }
 
@@ -3073,7 +3255,7 @@ again:
     }
   }
   conv_ilist(nd_demand,1,g,indp);
-  if ( DP_Print ) { printf("nd_gb_trace done.\n"); fflush(stdout); }
+  if ( DP_Print ) { printf("\nnd_gb_trace done.\n"); fflush(stdout); }
   return g;
 }
 
@@ -3161,9 +3343,17 @@ 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 +3370,10 @@ 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 +3383,7 @@ 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);
       }
@@ -3246,7 +3438,7 @@ 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);
@@ -3268,7 +3460,7 @@ int comp_sig(SIG s1,SIG s2)
     else return (*cmpdl)(nd_nvar,s1->dl,s2->dl);
   } else {
     static DL m1,m2;
-    static int nvar;
+    static int nvar = 0;
     int ret;
   
     if ( nvar != nd_nvar ) {
@@ -3276,7 +3468,10 @@ 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 = (*cmpdl)(nd_nvar,m1,m2);
+    if ( nd_sba_fixord )
+      ret = cmpdl_revgradlex(nd_nvar,m1,m2);
+    else
+      ret = (*cmpdl)(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;
@@ -3439,7 +3634,7 @@ ND_pairs nd_newpairs_s(int t, NODE *syz)
   int ts,ret,i;
   ND_pairs r,r0,_sp,sp;
   SIG spsig,tsig;
-  static int nvar;
+  static int nvar = 0;
   static SIG _sig1,_sig2;
   struct oEGT eg1,eg2,eg3,eg4;
 
@@ -3518,7 +3713,7 @@ 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);
         }
@@ -3838,6 +4033,24 @@ int ndv_newps(int m,NDV a,NDV aq)
     return nd_psn++;
 }
 
+// find LM wrt grevlex
+void ndv_lm_fixord(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 = cmpdl_revgradlex(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)) */
 
@@ -3956,7 +4169,10 @@ 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_fixord )
+        ndv_lm_fixord(nd_ps[i],nd_sba_hm[i]);
+      else
+        _ndltodl(DL(nd_psh[i]),nd_sba_hm[i]);
     }
     nd_sba_pos = (NODE *)MALLOC(nd_psn*sizeof(NODE));
     for ( i = 0; i < nd_psn; i++ ) {
@@ -4098,6 +4314,7 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     int obpe,oadv,ompos,cbpe;
     VECT hvect;
 
+    NcriB = NcriMF = Ncri2 = 0;
     nd_module = 0;
     if ( !m && Demand ) nd_demand = 1;
     else nd_demand = 0;
@@ -4154,8 +4371,13 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
                   }
                 }
             } else {
-                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,nd_nzlist?0:max);
@@ -4176,9 +4398,17 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
           b = (pointer)pltondv(CO,vv,zpl);
         }
       } else {
-        if ( !m && !nd_gentrace ) 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 && !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);
@@ -4308,7 +4538,7 @@ 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;
+  NODE fd,fd0,r,r0,t,x,s,xx,nd,syz;
   int e,max,nvar,i;
   NDV b;
   int ishomo,nalg,wmax,len;
@@ -4346,17 +4576,30 @@ 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);
@@ -4372,13 +4615,15 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int
       }
       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);
+  x = f4 ? nd_sba_f4(m,&perm) : nd_sba_buch(m,ishomo || homo,&perm,&syz);
   if ( !x ) {
     *rp = 0; return;
   }
@@ -4386,6 +4631,8 @@ 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;
@@ -4399,7 +4646,16 @@ 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;
+    NODE nd;
+
+    MKLIST(gb,r0);
+    MKLIST(hsyz,syz);
+    nd = mknode(2,gb,hsyz);
+    MKLIST(*rp,nd);
+  } else
+    MKLIST(*rp,r0);
   get_eg(&eg1); init_eg(&egconv); add_eg(&egconv,&eg0,&eg1);
   print_eg("conv",&egconv); fprintf(asir_out,"\n");
 }
@@ -4665,6 +4921,7 @@ 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);
@@ -4732,8 +4989,13 @@ 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 +5016,17 @@ 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);
@@ -5492,8 +5762,10 @@ 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;
+    extern int CNVars;
 
     nd_nvar = nvar;
+    CNVars = nvar;
     if ( max ) {
         /* XXX */
         if ( do_weyl ) nd_bpe = 32;
@@ -6623,6 +6895,32 @@ int nmv_comp(NMV a,NMV b)
   return -t;
 }
 
+NDV dptondv(int mod,DP p)
+{
+  NDV d;
+  NMV m,m0;
+  MP t;
+  MP *a;
+  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 +6997,21 @@ 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;
@@ -6784,6 +7097,7 @@ 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) ) {
@@ -8118,6 +8432,7 @@ NODE nd_f4(int m,int checkonly,int **indp)
     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;
@@ -9776,12 +10091,13 @@ void parse_nd_option(NODE opt)
   char *key;
   Obj value;
 
-  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_fixord = 0; nd_sba_grevlexgb = 0;
 
   for ( t = opt; t; t = NEXT(t) ) {
     p = BDY((LIST)BDY(t));
@@ -9793,6 +10109,8 @@ 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);
@@ -9838,15 +10156,24 @@ void parse_nd_option(NODE opt)
     } else if ( !strcmp(key,"sba_f4step") ) {
       nd_sba_f4step = value?ZTOS((Q)value):0;
     } else if ( !strcmp(key,"sba_pot") ) {
-      nd_sba_pot = value?1:0;
+      nd_sba_pot = 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_fixord") ) {
+      nd_sba_fixord = value?1:0;
+    } else if ( !strcmp(key,"sba_grevlexgb") ) {
+      nd_sba_grevlexgb = value?1:0;
+    } 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);
@@ -11105,7 +11432,7 @@ 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;
   NODE r,g,rp0,nflist;
-  ND_pairs d,l,t;
+  ND_pairs d,l,t,l1;
   ND h,nf;
   NDV nfv;
   union oNDC hc;
@@ -11133,12 +11460,22 @@ 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);