===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2018/engine/nd.c,v
retrieving revision 1.13
retrieving revision 1.27
diff -u -p -r1.13 -r1.27
--- OpenXM_contrib2/asir2018/engine/nd.c	2019/01/14 09:17:34	1.13
+++ OpenXM_contrib2/asir2018/engine/nd.c	2020/06/25 02:53:31	1.27
@@ -1,4 +1,4 @@
-/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.12 2018/11/12 04:25:13 noro Exp $ */
+/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.26 2020/06/23 01:49:58 noro Exp $ */
 
 #include "nd.h"
 
@@ -8,12 +8,17 @@ struct oEGT eg_search,f4_symb,f4_conv,f4_elim1,f4_elim
 int diag_period = 6;
 int weight_check = 1;
 int (*ndl_compare_function)(UINT *a1,UINT *a2);
+/* for general module order */
+int (*ndl_base_compare_function)(UINT *a1,UINT *a2);
+int (*dl_base_compare_function)(int nv,DL a,DL b);
+int nd_base_ordtype;
 int nd_dcomp;
 int nd_rref2;
 NM _nm_free_list;
 ND _nd_free_list;
 ND_pairs _ndp_free_list;
 NODE nd_hcf;
+int Nsyz;
 
 Obj nd_top_weight;
 
@@ -55,7 +60,7 @@ static int nd_worb_len;
 static int nd_found,nd_create,nd_notfirst;
 static int nmv_adv;
 static int nd_demand;
-static int nd_module,nd_ispot,nd_mpos,nd_pot_nelim;
+static int nd_module,nd_module_ordtype,nd_mpos,nd_pot_nelim;
 static int nd_module_rank,nd_poly_weight_len;
 static int *nd_poly_weight,*nd_module_weight;
 static NODE nd_tracelist;
@@ -66,6 +71,7 @@ static NODE nd_nzlist,nd_check_splist;
 static int nd_splist;
 static int *nd_sugarweight;
 static int nd_f4red,nd_rank0,nd_last_nonzero;
+static DL *nd_sba_hm;
 
 NumberField get_numberfield();
 UINT *nd_det_compute_bound(NDV **dm,int n,int j);
@@ -78,6 +84,7 @@ NDV pltondv(VL vl,VL dvl,LIST p);
 void pltozpl(LIST l,Q *cont,LIST *pp);
 void ndl_max(UINT *d1,unsigned *d2,UINT *d);
 void nmtodp(int mod,NM m,DP *r);
+void ndltodp(UINT *d,DP *r);
 NODE reverse_node(NODE n);
 P ndc_div(int mod,union oNDC a,union oNDC b);
 P ndctop(int mod,union oNDC c);
@@ -87,6 +94,11 @@ void parse_nd_option(NODE opt);
 void dltondl(int n,DL dl,UINT *r);
 DP ndvtodp(int mod,NDV p);
 DP ndtodp(int mod,ND p);
+DPM ndvtodpm(int mod,NDV p);
+NDV dpmtondv(int mod,DPM p);
+int dpm_getdeg(DPM p,int *rank);
+void dpm_ptozp(DPM p,Z *cont,DPM *r);
+int compdmm(int nv,DMM a,DMM b);
 
 void Pdp_set_weight(NODE,VECT *);
 void Pox_cmo_rpc(NODE,Obj *);
@@ -470,8 +482,11 @@ int ndl_weight(UINT *d)
             for ( j = 0; j < nd_epw; j++, u>>=nd_bpe )
                 t += (u&nd_mask0); 
         }
-    if ( nd_module && current_module_weight_vector && MPOS(d) )
-        t += current_module_weight_vector[MPOS(d)];
+    if ( nd_module && nd_module_rank && MPOS(d) )
+        t += nd_module_weight[MPOS(d)-1];
+    for ( i = nd_exporigin; i < nd_wpd; i++ )
+      if ( d[i] && !t ) 
+        printf("afo\n");
     return t;
 }
 
@@ -486,8 +501,8 @@ int ndl_weight2(UINT *d)
         u = GET_EXP(d,i);
         t += nd_sugarweight[i]*u;
     }
-    if ( nd_module && current_module_weight_vector && MPOS(d) )
-        t += current_module_weight_vector[MPOS(d)];
+    if ( nd_module && nd_module_rank && MPOS(d) )
+        t += nd_module_weight[MPOS(d)-1];
     return t;
 }
 
@@ -515,6 +530,13 @@ void ndl_weight_mask(UINT *d)
     }
 }
 
+int ndl_glex_compare(UINT *d1,UINT *d2)
+{
+  if ( TD(d1) > TD(d2) ) return 1;
+  else if ( TD(d1) < TD(d2) ) return -1;
+  else return ndl_lex_compare(d1,d2);
+}
+
 int ndl_lex_compare(UINT *d1,UINT *d2)
 {
     int i;
@@ -684,135 +706,143 @@ int ndl_ww_lex_compare(UINT *d1,UINT *d2)
     return ndl_lex_compare(d1,d2);
 }
 
-int ndl_module_weight_compare(UINT *d1,UINT *d2)
+// common function for module glex and grlex comparison
+int ndl_module_glex_compare(UINT *d1,UINT *d2)
 {
-  int s,j;
+  int c;
 
-  if ( nd_nvar != nd_poly_weight_len )
-    error("invalid module weight : the length of polynomial weight != the number of variables");
-  s = 0;
-  for ( j = 0; j < nd_nvar; j++ )
-     s += (GET_EXP(d1,j)-GET_EXP(d2,j))*nd_poly_weight[j];
-  if ( MPOS(d1) >= 1 && MPOS(d2) >= 1 ) {
-    s += nd_module_weight[MPOS(d1)-1]-nd_module_weight[MPOS(d2)-1];
-  }
-  if ( s > 0 ) return 1;
-  else if ( s < 0 ) return -1;
-  else return 0;
-}
+  switch ( nd_module_ordtype ) {
+    case 0:
+      if ( TD(d1) > TD(d2) ) return 1;
+      else if ( TD(d1) < TD(d2) ) return -1;
+      else if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c;
+      else if ( MPOS(d1) < MPOS(d2) ) return 1;
+      else if ( MPOS(d1) > MPOS(d2) ) return -1;
+      else return 0;
+      break;
 
-int ndl_module_grlex_compare(UINT *d1,UINT *d2)
-{
-    int i,c;
+    case 1:
+      if ( nd_pot_nelim && MPOS(d1)>=nd_pot_nelim+1 && MPOS(d2) >= nd_pot_nelim+1 ) {
+         if ( TD(d1) > TD(d2) ) return 1;
+         else if ( TD(d1) < TD(d2) ) return -1;
+         if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c;
+         if ( MPOS(d1) < MPOS(d2) ) return 1;
+         else if ( MPOS(d1) > MPOS(d2) ) return -1;
+      }
+      if ( MPOS(d1) < MPOS(d2) ) return 1;
+      else if ( MPOS(d1) > MPOS(d2) ) return -1;
+      else if ( TD(d1) > TD(d2) ) return 1;
+      else if ( TD(d1) < TD(d2) ) return -1;
+      else return ndl_lex_compare(d1,d2);
+      break;
 
-    if ( nd_module_rank && (c = ndl_module_weight_compare(d1,d2)) ) return c;
-    if ( nd_ispot ) {
-    if ( nd_pot_nelim && MPOS(d1)>=nd_pot_nelim+1 && MPOS(d2) >= nd_pot_nelim+1 ) {
-            if ( TD(d1) > TD(d2) ) return 1;
-            else if ( TD(d1) < TD(d2) ) return -1;
-            if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c;
-            if ( MPOS(d1) < MPOS(d2) ) return 1;
-            else if ( MPOS(d1) > MPOS(d2) ) return -1;
-            return 0;
-    }
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    if ( TD(d1) > TD(d2) ) return 1;
-    else if ( TD(d1) < TD(d2) ) return -1;
-    if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c;
-    if ( !nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    return 0;
-}
+    case 2: // weight -> POT
+      if ( TD(d1) > TD(d2) ) return 1;
+      else if ( TD(d1) < TD(d2) ) return -1;
+      else if ( MPOS(d1) < MPOS(d2) ) return 1;
+      else if ( MPOS(d1) > MPOS(d2) ) return -1;
+      else return ndl_lex_compare(d1,d2);
+      break;
 
-int ndl_module_glex_compare(UINT *d1,UINT *d2)
-{
-    int i,c;
-
-    if ( nd_module_rank && (c = ndl_module_weight_compare(d1,d2)) ) return c;
-    if ( nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    if ( TD(d1) > TD(d2) ) return 1;
-    else if ( TD(d1) < TD(d2) ) return -1;
-    if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c;
-    if ( !nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    return 0;
+    default:    
+      error("ndl_module_glex_compare : invalid module_ordtype");
+  }
 }
 
-int ndl_module_lex_compare(UINT *d1,UINT *d2)
+// common  for module comparison
+int ndl_module_compare(UINT *d1,UINT *d2)
 {
-    int i,c;
+  int c;
 
-    if ( nd_module_rank && (c = ndl_module_weight_compare(d1,d2)) ) return c;
-    if ( nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c;
-    if ( !nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    return 0;
-}
+  switch ( nd_module_ordtype ) {
+    case 0:
+      if ( (c = (*ndl_base_compare_function)(d1,d2)) != 0 ) return c;
+      else if ( MPOS(d1) > MPOS(d2) ) return -1;
+      else if ( MPOS(d1) < MPOS(d2) ) return 1;
+      else return 0;
+      break;
 
-int ndl_module_block_compare(UINT *d1,UINT *d2)
-{
-    int i,c;
+    case 1:
+      if ( MPOS(d1) < MPOS(d2) ) return 1;
+      else if ( MPOS(d1) > MPOS(d2) ) return -1;
+      else return (*ndl_base_compare_function)(d1,d2); 
+      break;
 
-    if ( nd_module_rank && (c = ndl_module_weight_compare(d1,d2)) ) return c;
-    if ( nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    if ( (c = ndl_block_compare(d1,d2)) != 0 ) return c;
-    if ( !nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    return 0;
-}
+    case 2: // weight -> POT
+      if ( TD(d1) > TD(d2) ) return 1;
+      else if ( TD(d1) < TD(d2) ) return -1;
+      else if ( MPOS(d1) < MPOS(d2) ) return 1;
+      else if ( MPOS(d1) > MPOS(d2) ) return -1;
+      else return (*ndl_base_compare_function)(d1,d2); 
+      break;
 
-int ndl_module_matrix_compare(UINT *d1,UINT *d2)
-{
-    int i,c;
-
-    if ( nd_module_rank && (c = ndl_module_weight_compare(d1,d2)) ) return c;
-    if ( nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    if ( (c = ndl_matrix_compare(d1,d2)) != 0 ) return c;
-    if ( !nd_ispot ) {
-        if ( MPOS(d1) < MPOS(d2) ) return 1;
-        else if ( MPOS(d1) > MPOS(d2) ) return -1;
-    }
-    return 0;
+    default:    
+      error("ndl_module_compare : invalid module_ordtype");
+  }
 }
 
-int ndl_module_composite_compare(UINT *d1,UINT *d2)
+extern DMMstack dmm_stack;
+void _addtodl(int n,DL d1,DL d2);
+int _eqdl(int n,DL d1,DL d2);
+
+int ndl_module_schreyer_compare(UINT *m1,UINT *m2)
 {
-    int i,c;
+  int pos1,pos2,t,j;
+  DMM *in;
+  DMMstack s;
+  static DL d1=0;
+  static DL d2=0;
+  static int dlen=0;
 
-    if ( nd_module_rank && (c = ndl_module_weight_compare(d1,d2)) ) return c;
-    if ( nd_ispot ) {
-        if ( MPOS(d1) > MPOS(d2) ) return 1;
-        else if ( MPOS(d1) < MPOS(d2) ) return -1;
+  pos1 = MPOS(m1); pos2 = MPOS(m2);
+  if ( pos1 == pos2 ) return (*ndl_base_compare_function)(m1,m2);
+  if ( nd_nvar > dlen ) {
+    NEWDL(d1,nd_nvar);
+    NEWDL(d2,nd_nvar);
+    dlen = nd_nvar;
+  }
+  d1->td = TD(m1);
+  for ( j = 0; j < nd_nvar; j++ ) d1->d[j] = GET_EXP(m1,j);
+  d2->td = TD(m2);
+  for ( j = 0; j < nd_nvar; j++ ) d2->d[j] = GET_EXP(m2,j);
+  for ( s = dmm_stack; s; s = NEXT(s) ) {
+    in = s->in;
+    _addtodl(nd_nvar,in[pos1]->dl,d1);
+    _addtodl(nd_nvar,in[pos2]->dl,d2);
+    if ( in[pos1]->pos == in[pos2]->pos && _eqdl(nd_nvar,d1,d2)) {
+      if ( pos1 < pos2 ) return 1;
+      else if ( pos1 > pos2 ) return -1;
+      else return 0;
     }
-    if ( (c = ndl_composite_compare(d1,d2)) != 0 ) return c;
-    if ( !nd_ispot ) {
-        if ( MPOS(d1) > MPOS(d2) ) return 1;
-        else if ( MPOS(d1) < MPOS(d2) ) return -1;
-    }
-    return 0;
+    pos1 = in[pos1]->pos;
+    pos2 = in[pos2]->pos;
+    if ( pos1 == pos2 ) return (*dl_base_compare_function)(nd_nvar,d1,d2);
+  }
+  // comparison by the bottom order
+LAST:
+  switch ( nd_base_ordtype ) {
+    case 0:
+      t = (*dl_base_compare_function)(nd_nvar,d1,d2);
+      if ( t ) return t;
+      else if ( pos1 < pos2 ) return 1;
+      else if ( pos1 > pos2 ) return -1;
+      else return 0;
+      break;
+    case 1:
+      if ( pos1 < pos2 ) return 1;
+      else if ( pos1 > pos2 ) return -1;
+      else return (*dl_base_compare_function)(nd_nvar,d1,d2);
+      break;
+    case 2:
+      if ( d1->td > d2->td  ) return 1;
+      else if ( d1->td < d2->td ) return -1;
+      else if ( pos1 < pos2 ) return 1;
+      else if ( pos1 > pos2 ) return -1;
+      else return (*dl_base_compare_function)(nd_nvar,d1,d2);
+      break;
+    default:
+      error("ndl_schreyer_compare : invalid base ordtype");
+  }
 }
 
 INLINE int ndl_equal(UINT *d1,UINT *d2)
@@ -1169,6 +1199,63 @@ INLINE int ndl_find_reducer(UINT *dg)
     return -1;
 }
 
+// ret=0,...,nd_psn-1 => reducer found
+// ret=nd_psn => reducer not found
+// ret=-1 => singular top reducible
+
+int comp_sig(SIG s1,SIG s2);
+void _ndltodl(UINT *ndl,DL dl);
+
+void print_sig(SIG s)
+{
+  int i;
+
+  fprintf(asir_out,"<<");
+  for ( i = 0; i < nd_nvar; i++ ) {
+    fprintf(asir_out,"%d",s->dl->d[i]);
+    if ( i != nd_nvar-1 ) fprintf(asir_out,",");
+  }
+  fprintf(asir_out,">>*e%d",s->pos);
+}
+
+INLINE int ndl_find_reducer_s(UINT *dg,SIG sig)
+{
+  RHist r;
+  int i,singular,ret,d,k;
+  static int wpd,nvar;
+  static SIG quo;
+  static UINT *tmp;
+
+  if ( !quo || nvar != nd_nvar ) NEWSIG(quo);
+  if ( wpd != nd_wpd ) {
+    wpd = nd_wpd;
+    tmp = (UINT *)MALLOC(wpd*sizeof(UINT));
+  }
+  d = ndl_hash_value(dg);
+  for ( r = nd_red[d], k = 0; r; r = NEXT(r), k++ ) {
+    if ( ndl_equal(dg,DL(r)) ) {
+      return r->index;
+    }
+  }
+  singular = 0;
+  for ( i = 0; i < nd_psn; i++ ) {
+    r = nd_psh[i];
+    if ( ndl_reducible(dg,DL(r)) ) {
+      ndl_sub(dg,DL(r),tmp);
+      _ndltodl(tmp,DL(quo));
+      _addtodl(nd_nvar,DL(nd_psh[i]->sig),DL(quo));
+      quo->pos = nd_psh[i]->sig->pos;
+      ret = comp_sig(sig,quo);
+      if ( ret > 0 ) { singular = 0; break; }
+      if ( ret == 0 ) { singular = 1; }
+    }
+  }
+  if ( singular ) return -1;
+  else if ( i < nd_psn )
+    nd_append_red(dg,i);
+  return i;
+}
+
 ND nd_merge(ND p1,ND p2)
 {
     int n,c;
@@ -1511,6 +1598,90 @@ int nd_nf(int mod,ND d,ND g,NDV *ps,int full,ND *rp)
     return 1;
 }
 
+// ret=1 => success
+// ret=0 => overflow
+// ret=-1 => singular top reducible
+
+int nd_nf_s(int mod,ND d,ND g,NDV *ps,int full,ND *rp)
+{
+    NM m,mrd,tail;
+    NM mul;
+    int n,sugar,psugar,sugar0,stat,index;
+    int c,c1,c2,dummy;
+    RHist h;
+    NDV p,red;
+    Q cg,cred,gcd,tq,qq;
+    Z iq;
+    DP dmul;
+    NODE node;
+    LIST hist;
+    double hmag;
+    P tp,tp1;
+    Obj tr,tr1,div;
+    union oNDC hg;
+    P cont;
+    SIG sig;
+
+    if ( !g ) {
+        *rp = d;
+        return 1;
+    }
+    if ( !mod ) hmag = ((double)p_mag(HCP(g)))*nd_scale;
+
+    sugar0 = sugar = SG(g);
+    n = NV(g);
+    mul = (NM)MALLOC(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT));
+    if ( d )
+        for ( tail = BDY(d); NEXT(tail); tail = NEXT(tail) );
+    sig = g->sig;
+    for ( ; g; ) {
+        index = ndl_find_reducer_s(HDL(g),sig);
+        if ( index >= 0 && index < nd_psn ) {
+            // reducer found
+            h = nd_psh[index];
+            ndl_sub(HDL(g),DL(h),DL(mul));
+            if ( ndl_check_bound2(index,DL(mul)) ) {
+                nd_free(g); nd_free(d);
+                return 0;
+            }
+            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)));
+            if ( !mod && g && ((double)(p_mag(HCP(g))) > hmag) ) {
+                hg = HCU(g);
+                nd_removecont2(d,g);
+                hmag = ((double)p_mag(HCP(g)))*nd_scale;
+            }
+        } else if ( index == -1 ) {
+          // singular top reducible
+          return -1;
+        } else if ( !full ) {
+            *rp = g;
+            g->sig = sig;
+            return 1;
+        } else {
+            m = BDY(g); 
+            if ( NEXT(m) ) {
+                BDY(g) = NEXT(m); NEXT(m) = 0; LEN(g)--;
+            } else {
+                FREEND(g); g = 0;
+            }
+            if ( d ) {
+                NEXT(tail)=m; tail=m; LEN(d)++;
+            } else {
+                MKND(n,m,1,d); tail = BDY(d);
+            }
+        }
+    }
+    if ( d ) {
+      SG(d) = sugar;
+      d->sig = sig;
+    }
+    *rp = d;
+    return 1;
+}
+
 int nd_nf_pbucket(int mod,ND g,NDV *ps,int full,ND *rp)
 {
     int hindex,index;
@@ -1623,6 +1794,132 @@ int nd_nf_pbucket(int mod,ND g,NDV *ps,int full,ND *rp
     }
 }
 
+int nd_nf_pbucket_s(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;
+  PGeoBucket bucket;
+  int c,c1,c2;
+  Z cg,cred,gcd,zzz;
+  RHist h;
+  double hmag,gmag;
+  int count = 0;
+  int hcount = 0;
+  SIG sig;
+
+  if ( !g ) {
+    *rp = 0;
+    return 1;
+  }
+  sugar = SG(g);
+  n = NV(g);
+  if ( !mod ) hmag = ((double)p_mag((P)HCZ(g)))*nd_scale;
+  bucket = create_pbucket();
+  add_pbucket(mod,bucket,g);
+  d = 0;
+  mul = (NM)MALLOC(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT));
+  sig = g->sig;
+  while ( 1 ) {
+    if ( mod > 0 || mod == -1 )
+      hindex = head_pbucket(mod,bucket);
+    else if ( mod == -2 )
+      hindex = head_pbucket_lf(bucket);
+    else
+      hindex = head_pbucket_q(bucket);
+    if ( hindex < 0 ) {
+      if ( DP_Print > 3 ) printf("(%d %d)",count,hcount);
+      if ( d ) {
+        SG(d) = sugar;
+        d->sig = sig;
+      }
+      *rp = d;
+      return 1;
+    }
+    g = bucket->body[hindex];
+    index = ndl_find_reducer_s(HDL(g),sig);
+    if ( index >= 0 && index < nd_psn ) {
+      count++;
+      if ( !d ) hcount++;
+      h = nd_psh[index];
+      ndl_sub(HDL(g),DL(h),DL(mul));
+      if ( ndl_check_bound2(index,DL(mul)) ) {
+        nd_free(d);
+        free_pbucket(bucket);
+        *rp = 0;
+        return 0;
+      }
+      p = ps[index];
+      if ( mod == -1 )
+        CM(mul) = _mulsf(_invsf(HCM(p)),_chsgnsf(HCM(g)));
+      else if ( mod == -2 ) { 
+        Z inv,t;
+        divlf(ONE,HCZ(p),&inv);
+        chsgnlf(HCZ(g),&t);
+        mullf(inv,t,&CZ(mul));
+      } else if ( mod ) {
+        c1 = invm(HCM(p),mod); c2 = mod-HCM(g);
+        DMAR(c1,c2,0,mod,c); CM(mul) = c;
+      } else {
+        igcd_cofactor(HCZ(g),HCZ(p),&gcd,&cg,&cred);
+        chsgnz(cg,&CZ(mul));
+        nd_mul_c_q(d,(P)cred);
+        mulq_pbucket(bucket,cred);
+        g = bucket->body[hindex];
+        gmag = (double)p_mag((P)HCZ(g));
+      }
+      red = ndv_mul_nm(mod,mul,p);
+      bucket->body[hindex] = nd_remove_head(g);
+      red = nd_remove_head(red);
+      add_pbucket(mod,bucket,red);
+      psugar = SG(p)+TD(DL(mul));
+      sugar = MAX(sugar,psugar);
+      if ( !mod && hmag && (gmag > hmag) ) {
+         g = normalize_pbucket(mod,bucket);
+         if ( !g ) {
+           if ( d ) {
+             SG(d) = sugar;
+             d->sig = sig;
+           }
+           *rp = d;
+           return 1;
+         }
+         nd_removecont2(d,g);
+         hmag = ((double)p_mag((P)HCZ(g)))*nd_scale;
+         add_pbucket(mod,bucket,g);
+      }
+    } else if ( index == -1 ) {
+      // singular top reducible
+      return -1;
+    } else if ( !full ) {
+      g = normalize_pbucket(mod,bucket);
+      if ( g ) {
+        SG(g) = sugar;
+        g->sig = sig;
+      }
+      *rp = g;
+      return 1;
+    } else {
+      m = BDY(g); 
+      if ( NEXT(m) ) {
+        BDY(g) = NEXT(m); NEXT(m) = 0; LEN(g)--;
+      } else {
+        FREEND(g); g = 0;
+      }
+      bucket->body[hindex] = g;
+      NEXT(m) = 0;
+      if ( d ) {
+        NEXT(tail)=m; tail=m; LEN(d)++;
+      } else {
+        MKND(n,m,1,d); tail = BDY(d);
+      }
+    }
+  }
+}
+
 /* input : list of NDV, cand : list of NDV */
 
 int ndv_check_membership(int m,NODE input,int obpe,int oadv,EPOS oepos,NODE cand)
@@ -1635,7 +1932,7 @@ int ndv_check_membership(int m,NODE input,int obpe,int
     Z q;
     LIST list;
 
-    ndv_setup(m,0,cand,nd_gentrace?1:0,1);
+    ndv_setup(m,0,cand,nd_gentrace?1:0,1,0);
     n = length(cand);
 
   if ( nd_gentrace ) { nd_alltracelist = 0; nd_tracelist = 0; }
@@ -2083,7 +2380,9 @@ NODE nd_gb(int m,int ishomo,int checkonly,int gensyz,i
   int diag_count = 0;
   P cont;
   LIST list;
+struct oEGT eg1,eg2,eg_update;
 
+init_eg(&eg_update);
   Nnd_add = 0;
   g = 0; d = 0;
   for ( i = 0; i < nd_psn; i++ ) {
@@ -2148,7 +2447,7 @@ again:
         }
       }
       nfv = ndtondv(m,nf); nd_free(nf);
-      nh = ndv_newps(m,nfv,0,0);
+      nh = ndv_newps(m,nfv,0);
       if ( !m && (ishomo && ++diag_count == diag_period) ) {
         diag_count = 0;
         stat = do_diagonalize(sugar,m);
@@ -2158,7 +2457,9 @@ again:
           goto again;
         }
       }
+get_eg(&eg1);
       d = update_pairs(d,g,nh,0);
+get_eg(&eg2); add_eg(&eg_update,&eg1,&eg2);
       g = update_base(g,nh);
       FREENDP(l);
    } else {
@@ -2175,9 +2476,186 @@ again:
  }
  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); }
+print_eg("update",&eg_update);
     return g;
 }
 
+ND_pairs update_pairs_s(ND_pairs d,NODE g,int t,NODE syz);
+ND_pairs nd_newpairs_s( NODE g, 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);
+
+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);
+
+NODE insert_sig(NODE l,SIG s)
+{
+  int pos;
+  DL sig;
+  struct oNODE root;
+  NODE p,prev,r;
+  SIG t;
+
+  pos = s->pos; sig = DL(s);
+  root.next = l; prev = &root;
+  for ( p = l; p; p = p->next ) {
+    t = (SIG)p->body;
+    if ( t->pos == pos ) {
+      if ( _dl_redble(DL(t),sig,nd_nvar) )
+        return root.next;
+      else if ( _dl_redble(sig,DL(t),nd_nvar) )
+        // remove p
+        prev->next = p->next;
+    } else
+      prev = p;
+  }
+  NEWNODE(r); r->body = (pointer)s; r->next = 0;
+  for ( p = &root; p->next; p = p->next );
+  p->next = r;
+//  r->next = root.next;
+//  return r;
+  return root.next;
+}
+
+ND_pairs remove_spair_s(ND_pairs d,SIG sig)
+{
+  struct oND_pairs root;
+  ND_pairs prev,p;
+  SIG spsig;
+
+  root.next = d;
+  prev = &root; p = d;
+  while ( p ) {
+    spsig = p->sig;
+    if ( sig->pos == spsig->pos && _dl_redble(DL(sig),DL(spsig),nd_nvar) ) {
+      // remove p
+      prev->next = p->next;
+      Nsyz++;
+    } else
+      prev = p;
+    p = p->next;
+  }
+  return (ND_pairs)root.next;
+}
+
+struct oEGT eg_create,eg_newpairs,eg_merge;
+
+NODE nd_sba_buch(int m,int ishomo,int **indp)
+{
+  int i,nh,sugar,stat;
+  NODE r,g,t;
+  ND_pairs d;
+  ND_pairs l;
+  ND h,nf,s,head,nf1;
+  NDV nfv;
+  Z q;
+  union oNDC dn,hc;
+  P cont;
+  LIST list;
+  SIG sig;
+  NODE syzlist;
+  int Nredundant;
+  static int wpd,nvar;
+  static DL lcm,quo,mul;
+  struct oEGT eg1,eg2,eg_update,eg_remove;
+
+init_eg(&eg_remove);
+  syzlist = 0;
+  Nsyz = 0;
+  Nnd_add = 0;
+  Nredundant = 0;
+  g = 0; d = 0;
+  for ( i = 0; i < nd_psn; i++ ) {
+    d = update_pairs_s(d,g,i,0);
+    g = append_one(g,i);
+  }
+  sugar = 0;
+  NEWDL(lcm,nd_nvar); NEWDL(quo,nd_nvar); NEWDL(mul,nd_nvar);
+init_eg(&eg_create);
+init_eg(&eg_merge);
+  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;
+    sig = l->sig;
+    _ndltodl(l->lcm,lcm);
+    for ( i = 0; i < nd_psn; i++ ) {
+      if ( sig->pos == nd_psh[i]->sig->pos &&
+        _dl_redble(DL(nd_psh[i]->sig),DL(sig),nd_nvar) ) {
+        _copydl(nd_nvar,DL(sig),quo);
+        _subfromdl(nd_nvar,DL(nd_psh[i]->sig),quo);
+        _ndltodl(DL(nd_psh[i]),mul);
+        _addtodl(nd_nvar,quo,mul);
+        if ( (*cmpdl)(nd_nvar,lcm,mul) > 0 )
+          break;
+      }
+    }
+    if ( i < nd_psn ) {
+      if ( DP_Print ) fprintf(asir_out,"M");
+      Nredundant++;
+      continue;
+    }
+    if ( SG(l) != sugar ) {
+      sugar = SG(l);
+      if ( DP_Print ) fprintf(asir_out,"%d",sugar);
+    }
+    stat = nd_sp(m,0,l,&h);
+    if ( !stat ) {
+      NEXT(l) = d; d = l;
+      d = nd_reconstruct(0,d);
+      goto again;
+    }
+#if USE_GEOBUCKET
+    stat = m?nd_nf_pbucket_s(m,h,nd_ps,!Top,&nf):nd_nf_s(m,0,h,nd_ps,!Top,&nf);
+#else
+    stat = nd_nf_s(m,0,h,nd_ps,!Top,&nf);
+#endif
+    if ( !stat ) {
+      NEXT(l) = d; d = l;
+      d = nd_reconstruct(0,d);
+      goto again;
+    } else if ( stat == -1 ) {
+      if ( DP_Print ) { printf("S"); fflush(stdout); }
+      FREENDP(l);
+    } else if ( nf ) {
+      if ( DP_Print ) { printf("+"); fflush(stdout); }
+      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,g,nh,syzlist);
+      g = append_one(g,nh);
+      FREENDP(l);
+   } else {
+     // syzygy
+get_eg(&eg1);
+     d = remove_spair_s(d,sig);
+get_eg(&eg2); add_eg(&eg_remove,&eg1,&eg2);
+     syzlist = insert_sig(syzlist,sig);
+     if ( DP_Print ) { printf("."); fflush(stdout); }
+     FREENDP(l);
+   }
+ }
+ conv_ilist(nd_demand,0,g,indp);
+ if ( DP_Print ) { 
+   printf("\nnd_sba done. nd_add=%d,Nsyz=%d,Nredundant=%d\n",Nnd_add,Nsyz,Nredundant);
+   fflush(stdout); 
+   print_eg("create",&eg_create);
+   print_eg("merge",&eg_merge);
+   print_eg("remove",&eg_remove);
+   printf("\n");
+ }
+ return g;
+}
+
 /* splist = [[i1,i2],...] */
 
 int check_splist(int m,NODE splist)
@@ -2431,7 +2909,7 @@ again:
             nd_tracelist = t;
           }
         }
-        nh = ndv_newps(0,nfv,nfqv,0);
+        nh = ndv_newps(0,nfv,nfqv);
         if ( ishomo && ++diag_count == diag_period ) {
           diag_count = 0;
           if ( DP_Print > 2 ) fprintf(asir_out,"|");
@@ -2501,7 +2979,7 @@ NODE ndv_reduceall(int m,NODE f)
 
   if ( nd_nora ) return f;
   n = length(f);
-  ndv_setup(m,0,f,0,1);
+  ndv_setup(m,0,f,0,1,0);
   perm = (int *)MALLOC(n*sizeof(int));
   if ( nd_gentrace ) {
     for ( t = nd_tracelist, i = 0; i < n; i++, t = NEXT(t) )
@@ -2595,7 +3073,22 @@ ND_pairs update_pairs( ND_pairs d, NODE /* of index */
   }
 }
 
+ND_pairs merge_pairs_s(ND_pairs d,ND_pairs d1);
 
+ND_pairs update_pairs_s( ND_pairs d, NODE /* of index */ g, int t,NODE syz)
+{
+  ND_pairs d1;
+  struct oEGT eg1,eg2,eg3;
+
+  if ( !g ) return d;
+get_eg(&eg1);
+  d1 = nd_newpairs_s(g,t,syz);
+get_eg(&eg2); add_eg(&eg_create,&eg1,&eg2);
+  d = merge_pairs_s(d,d1);
+get_eg(&eg3); add_eg(&eg_merge,&eg2,&eg3);
+  return d;
+}
+
 ND_pairs nd_newpairs( NODE g, int t )
 {
   NODE h;
@@ -2605,7 +3098,7 @@ ND_pairs nd_newpairs( NODE g, int t )
 
   dl = DL(nd_psh[t]);
   ts = SG(nd_psh[t]) - TD(dl);
-  if ( nd_module && nd_intersect && (MPOS(dl) > 1) ) return 0;
+  if ( nd_module && nd_intersect && (MPOS(dl) > nd_intersect) ) return 0;
   for ( r0 = 0, h = g; h; h = NEXT(h) ) {
     if ( nd_module && (MPOS(DL(nd_psh[(long)BDY(h)])) != MPOS(dl)) )
       continue;
@@ -2633,6 +3126,201 @@ ND_pairs nd_newpairs( NODE g, int t )
   return r0;
 }
 
+
+int comp_sig(SIG s1,SIG s2)
+{
+#if 0
+  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
+  static DL m1,m2;
+  static int nvar;
+  int ret;
+
+  if ( nvar != nd_nvar ) {
+    nvar = nd_nvar; NEWDL(m1,nvar); NEWDL(m2,nvar);
+  }
+//  _ndltodl(DL(nd_psh[s1->pos]),m1);
+//  _ndltodl(DL(nd_psh[s2->pos]),m2);
+  _copydl(nd_nvar,nd_sba_hm[s1->pos],m1);
+  _copydl(nd_nvar,nd_sba_hm[s2->pos],m2);
+  _addtodl(nd_nvar,s1->dl,m1);
+  _addtodl(nd_nvar,s2->dl,m2);
+  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;
+  else return 0;
+#endif
+}
+
+int _create_spair_s(int i1,int i2,ND_pairs sp,SIG sig1,SIG sig2)
+{
+  int ret,s1,s2;
+  RHist p1,p2;
+  static int wpd;
+  static UINT *lcm;
+
+  sp->i1 = i1;
+  sp->i2 = i2;
+  p1 = nd_psh[i1];
+  p2 = nd_psh[i2];
+  ndl_lcm(DL(p1),DL(p2),sp->lcm);
+  s1 = SG(p1)-TD(DL(p1));
+  s2 = SG(p2)-TD(DL(p2));
+  SG(sp) = MAX(s1,s2) + TD(sp->lcm);
+
+  if ( wpd != nd_wpd ) {
+    wpd = nd_wpd;
+    lcm = (UINT *)MALLOC(wpd*sizeof(UINT));
+  }
+  // DL(sig1) <- sp->lcm
+  // DL(sig1) -= DL(p1)
+  // DL(sig1) += DL(p1->sig)
+  ndl_sub(sp->lcm,DL(p1),lcm);
+  _ndltodl(lcm,DL(sig1));
+  _addtodl(nd_nvar,DL(p1->sig),DL(sig1));
+  sig1->pos = p1->sig->pos;
+
+  // DL(sig2) <- sp->lcm
+  // DL(sig2) -= DL(p2)
+  // DL(sig2) += DL(p2->sig)
+  ndl_sub(sp->lcm,DL(p2),lcm);
+  _ndltodl(lcm,DL(sig2));
+  _addtodl(nd_nvar,DL(p2->sig),DL(sig2));
+  sig2->pos = p2->sig->pos;
+
+  ret = comp_sig(sig1,sig2);
+  if ( ret == 0 ) return 0;
+  else if ( ret > 0 ) sp->sig = sig1;
+  else sp->sig = sig2;
+  return 1;
+}
+
+SIG dup_sig(SIG sig)
+{
+  SIG r;
+
+  if ( !sig ) return 0;
+  else {
+    NEWSIG(r);
+    _copydl(nd_nvar,DL(sig),DL(r));
+    r->pos = sig->pos;
+    return r;
+  }
+}
+
+void dup_ND_pairs(ND_pairs to,ND_pairs from)
+{
+  to->i1 = from->i1; 
+  to->i2 = from->i2; 
+  to->sugar = from->sugar;
+  to->sugar2 = from->sugar2;
+  ndl_copy(from->lcm,to->lcm);
+  to->sig = dup_sig(from->sig);
+}
+
+ND_pairs merge_pairs_s(ND_pairs p1,ND_pairs p2)
+{
+  struct oND_pairs root;
+  ND_pairs q1,q2,r0,r;
+  int ret;
+
+  r = &root;
+  for ( q1 = p1, q2 = p2; q1 != 0 && q2 != 0; ) {
+    ret = comp_sig(q1->sig,q2->sig);
+    if ( ret < 0 ) {
+      r->next = q1; r = q1; q1 = q1->next;
+    } else if ( ret > 0 ) {
+      r->next = q2; r = q2; q2 = q2->next;
+    } else {
+      ret = DL_COMPARE(q1->lcm,q2->lcm);
+      if ( ret < 0 ) {
+        r->next = q1; r = q1; q1 = q1->next;
+        q2 = q2->next;
+      } else {
+        r->next = q2; r = q2; q2 = q2->next;
+        q1 = q1->next;
+      }
+    }
+  }
+  if ( q1 ) {
+    r->next = q1;
+  } else {
+    r->next = q2;
+  }
+  return root.next;
+}
+
+ND_pairs insert_pair_s(ND_pairs l,ND_pairs s)
+{
+  ND_pairs p,prev;
+  int ret;
+
+  for ( p = l, prev = 0; p != 0; prev = p, p = p->next ) {
+    if ( (ret = comp_sig(s->sig,p->sig)) <= 0 )
+      break;
+  }
+  if ( ret == 0 ) {
+    ret = DL_COMPARE(s->lcm,p->lcm);
+    if ( ret < 0 ) {
+      // replace p with s
+      s->next = p->next;
+      if ( prev == 0 ) {
+        return s;
+      } else {
+        prev->next = s;
+        return l;
+      }
+    } else
+      return l;
+  } else {
+    // insert s between prev and p
+    s->next = p;
+    if ( prev == 0 ) {
+      return s;
+    } else {
+      prev->next = s;
+      return l;
+    }
+  }
+}
+
+ND_pairs nd_newpairs_s( NODE g, int t, NODE syz)
+{
+  NODE h,s;
+  UINT *dl;
+  int ts,ret,i;
+  ND_pairs r,r0,_sp,sp;
+  SIG _sig1,_sig2,spsig,tsig;
+  struct oEGT eg1,eg2,eg3,eg4;
+
+  NEWND_pairs(_sp);
+  NEWSIG(_sig1); NEWSIG(_sig2);
+  r0 = 0;
+  for ( i = 0; i < t; i++ ) {
+    ret = _create_spair_s(i,t,_sp,_sig1,_sig2);
+//  for ( h = g; h; h = NEXT(h) ) {
+//    ret = _create_spair_s((long)BDY(h),t,_sp,_sig1,_sig2);
+    if ( ret ) {
+      spsig = _sp->sig;
+      for ( s = syz; s; s = s->next ) {
+        tsig = (SIG)s->body;
+        if ( tsig->pos == spsig->pos && _dl_redble(DL(tsig),DL(spsig),nd_nvar) )
+          break;
+      }
+      if ( s == 0 ) {
+        NEWND_pairs(sp);
+        dup_ND_pairs(sp,_sp);
+        r0 = insert_pair_s(r0,sp);
+      } else
+        Nsyz++;
+    }
+  }
+  return r0;
+}
+
 /* ipair = [i1,i2],[i1,i2],... */
 ND_pairs nd_ipairtospair(NODE ipair)
 {
@@ -2922,7 +3610,7 @@ int nd_tdeg(NDV c)
   return wmax;
 }
 
-int ndv_newps(int m,NDV a,NDV aq,int f4)
+int ndv_newps(int m,NDV a,NDV aq)
 {
     int len;
     RHist r;
@@ -2958,6 +3646,7 @@ int ndv_newps(int m,NDV a,NDV aq,int f4)
         SG(r) = nd_tdeg(aq);
 #endif
         ndl_copy(HDL(aq),DL(r));
+        r->sig = dup_sig(aq->sig);
     } else {
         if ( !m ) register_hcf(a);
         nd_bound[nd_psn] = ndv_compute_bound(a);
@@ -2967,6 +3656,7 @@ int ndv_newps(int m,NDV a,NDV aq,int f4)
         SG(r) = nd_tdeg(a);
 #endif
         ndl_copy(HDL(a),DL(r));
+        r->sig = dup_sig(a->sig);
     }
     if ( nd_demand ) {
         if ( aq ) {
@@ -2992,7 +3682,7 @@ int ndv_newps(int m,NDV a,NDV aq,int f4)
 /* 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 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;
@@ -3016,7 +3706,7 @@ int ndv_setup(int mod,int trace,NODE f,int dont_sort,i
     if ( BDY(s) ) { w[i].p = BDY(s); w[i].i = j; i++; }
   if ( !dont_sort ) {
     /* XXX heuristic */
-    if ( !nd_ord->id && (nd_ord->ord.simple<2) )
+    if ( !sba && !nd_ord->id && (nd_ord->ord.simple<2) )
       qsort(w,nd_psn,sizeof(struct oNDVI),
         (int (*)(const void *,const void *))ndvi_compare_rev);
     else
@@ -3092,6 +3782,24 @@ int ndv_setup(int mod,int trace,NODE f,int dont_sort,i
       }
     }
   }
+  if ( sba ) {
+    nd_sba_hm = (DL *)MALLOC(nd_psn*sizeof(DL));
+   // setup signatures
+    for ( i = 0; i < nd_psn; i++ ) {
+      SIG sig;
+
+      NEWSIG(sig); sig->pos = i;
+      nd_ps[i]->sig = sig;
+      if ( nd_demand ) nd_ps_sym[i]->sig = sig;
+        nd_psh[i]->sig = sig;
+      if ( trace ) { 
+        nd_ps_trace[i]->sig = sig;
+        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_gentrace && nd_tracelist ) NEXT(tn) = 0;
   return 1;
 }
@@ -3224,6 +3932,7 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     int *perm;
     EPOS oepos;
     int obpe,oadv,ompos,cbpe;
+    VECT hvect;
 
     nd_module = 0;
     if ( !m && Demand ) nd_demand = 1;
@@ -3267,12 +3976,18 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     for ( t = BDY(f), max = 1; t; t = NEXT(t) )
         for ( tv = vv; tv; tv = NEXT(tv) ) {
             if ( nd_module ) {
-                s = BDY((LIST)BDY(t));
-                trank = length(s);
-                mrank = MAX(mrank,trank);
-                for ( ; s; s = NEXT(s) ) {
-                    e = getdeg(tv->v,(P)BDY(s));
-                    max = MAX(e,max);
+                if ( OID(BDY(t)) == O_DPM ) {
+                  e = dpm_getdeg((DPM)BDY(t),&trank);
+                  max = MAX(e,max);
+                  mrank = MAX(mrank,trank);
+                } else {
+                  s = BDY((LIST)BDY(t));
+                  trank = length(s);
+                  mrank = MAX(mrank,trank);
+                  for ( ; s; s = NEXT(s) ) {
+                      e = getdeg(tv->v,(P)BDY(s));
+                      max = MAX(e,max);
+                  }
                 }
             } else {
                 e = getdeg(tv->v,(P)BDY(t));
@@ -3284,9 +3999,18 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     ishomo = 1;
     for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
       if ( nd_module ) {
-        if ( !m && !nd_gentrace ) pltozpl((LIST)BDY(t),&dmy,&zpl);
-        else zpl = (LIST)BDY(t);
+        if ( OID(BDY(t)) == O_DPM ) {
+          Z cont;
+          DPM zdpm;
+
+          if ( !m && !nd_gentrace ) dpm_ptozp((DPM)BDY(t),&cont,&zdpm);
+          else zdpm = (DPM)BDY(t);
+          b = (pointer)dpmtondv(m,zdpm);
+        } else {
+          if ( !m && !nd_gentrace ) pltozpl((LIST)BDY(t),&dmy,&zpl);
+          else zpl = (LIST)BDY(t);
           b = (pointer)pltondv(CO,vv,zpl);
+        }
       } else {
         if ( !m && !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp);
         else zp = (P)BDY(t);
@@ -3312,7 +4036,7 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
             ndv_homogenize((NDV)BDY(t),obpe,oadv,oepos,ompos);
     }
 
-    ndv_setup(m,0,fd0,(nd_gbblock||nd_splist||nd_check_splist)?1:0,0);
+    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);
     }
@@ -3334,6 +4058,11 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
   if ( !x ) {
     *rp = 0; return;
   }
+  if ( nd_gentrace ) {
+    MKVECT(hvect,nd_psn);
+    for ( i = 0; i < nd_psn; i++ )
+       ndltodp(nd_psh[i]->dl,(DP *)&BDY(hvect)[i]);
+  }
   if ( !ishomo && homo ) {
        /* dehomogenization */
     for ( t = x; t; t = NEXT(t) ) ndv_dehomogenize((NDV)BDY(t),ord);
@@ -3343,7 +4072,7 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     nd_demand = 0;
   if ( nd_module && nd_intersect ) {
     for ( j = nd_psn-1, x = 0; j >= 0; j-- )
-      if ( MPOS(DL(nd_psh[j])) > 1 ) { 
+      if ( MPOS(DL(nd_psh[j])) > nd_intersect ) { 
         MKNODE(xx,(pointer)((unsigned long)j),x); x = xx; 
       }
     conv_ilist(nd_demand,0,x,0);
@@ -3367,10 +4096,12 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     nd_setup_parameters(nd_nvar,0);
 FINAL:
     for ( r0 = 0, t = x; t; t = NEXT(t) ) {
-        NEXTNODE(r0,r); 
-        if ( nd_module ) BDY(r) = ndvtopl(m,CO,vv,BDY(t),mrank);
-        else if ( retdp ) BDY(r) = ndvtodp(m,BDY(t));
-    else BDY(r) = ndvtop(m,CO,vv,BDY(t));
+      NEXTNODE(r0,r); 
+      if ( nd_module ) {
+        if ( retdp ) BDY(r) = ndvtodpm(m,BDY(t));
+        else BDY(r) = ndvtopl(m,CO,vv,BDY(t),mrank);
+      } else if ( retdp ) BDY(r) = ndvtodp(m,BDY(t));
+      else BDY(r) = ndvtop(m,CO,vv,BDY(t));
     }
     if ( r0 ) NEXT(r) = 0;
     if ( !m && nd_nalg )
@@ -3380,8 +4111,7 @@ FINAL:
   if ( f4 ) {
             STOZ(16,bpe);
             STOZ(nd_last_nonzero,last_nonzero);
-            tr = mknode(5,*rp,(!ishomo&&homo)?ONE:0,BDY(nzlist),bpe,last_nonzero); MKLIST(*rp,tr);
-            
+            tr = mknode(6,*rp,(!ishomo&&homo)?ONE:0,BDY(nzlist),bpe,last_nonzero,hvect); MKLIST(*rp,tr);
         } else {
             tl1 = reverse_node(tl1); tl2 = reverse_node(tl2);
             tl3 = reverse_node(tl3);
@@ -3401,7 +4131,7 @@ FINAL:
             MKLIST(l1,tl1); MKLIST(l2,tl2); MKLIST(l3,t); MKLIST(l4,tl3);
             MKLIST(l5,tl4);
             STOZ(nd_bpe,bpe);
-            tr = mknode(8,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe); MKLIST(*rp,tr);
+            tr = mknode(9,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe,hvect); MKLIST(*rp,tr);
         }
     }
 #if 0
@@ -3409,6 +4139,101 @@ FINAL:
 #endif
 }
 
+void nd_sba(LIST f,LIST v,int m,int homo,int retdp,struct order_spec *ord,LIST *rp)
+{
+  VL tv,fv,vv,vc,av;
+  NODE fd,fd0,r,r0,t,x,s,xx;
+  int e,max,nvar,i;
+  NDV b;
+  int ishomo,nalg,wmax,len;
+  NMV a;
+  P p,zp;
+  Q dmy;
+  struct order_spec *ord1;
+  int j;
+  int *perm;
+  EPOS oepos;
+  int obpe,oadv,ompos,cbpe;
+
+  nd_module = 0;
+  nd_demand = 0;
+  parse_nd_option(current_option);
+
+  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);
+  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++ );
+  switch ( ord->id ) {
+    case 1:
+      if ( ord->nv != nvar )
+        error("nd_sba : invalid order specification");
+        break;
+      default:
+        break;
+  }
+  nd_nalg = 0;
+  nd_init_ord(ord);
+  // for SIG comparison
+  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);
+    }
+  }
+  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 ( 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);
+      }
+      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,fd0,0,0,1);
+  x = nd_sba_buch(m,ishomo || homo,&perm);
+  if ( !x ) {
+    *rp = 0; return;
+  }
+  if ( !ishomo && homo ) {
+       /* dehomogenization */
+    for ( t = x; t; t = NEXT(t) ) ndv_dehomogenize((NDV)BDY(t),ord);
+    nd_init_ord(ord);
+    nd_setup_parameters(nvar,0);
+  }
+  nd_demand = 0;
+  x = ndv_reducebase(x,perm);
+  x = ndv_reduceall(m,x);
+  nd_setup_parameters(nd_nvar,0);
+  for ( r0 = 0, t = x; t; t = NEXT(t) ) {
+    NEXTNODE(r0,r); 
+    if ( retdp ) BDY(r) = ndvtodp(m,BDY(t));
+    BDY(r) = ndvtop(m,CO,vv,BDY(t));
+  }
+  if ( r0 ) NEXT(r) = 0;
+  MKLIST(*rp,r0);
+}
+
 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;
@@ -3468,7 +4293,7 @@ void nd_gr_postproc(LIST f,LIST v,int m,struct order_s
         if ( b ) { NEXTNODE(fd0,fd); BDY(fd) = (pointer)b; }
     }
     if ( fd0 ) NEXT(fd) = 0;
-    ndv_setup(m,0,fd0,0,1);
+    ndv_setup(m,0,fd0,0,1,0);
     for ( x = 0, i = 0; i < nd_psn; i++ )
         x = update_base(x,i);
     if ( do_check ) {
@@ -3645,7 +4470,7 @@ void nd_gr_recompute_trace(LIST f,LIST v,int m,struct 
     if ( DP_Print ) fprintf(asir_out,"\n");
 }
 
-void nd_gr_trace(LIST f,LIST v,int trace,int homo,int f4,struct order_spec *ord,LIST *rp)
+void nd_gr_trace(LIST f,LIST v,int trace,int homo,int retdp,int f4,struct order_spec *ord,LIST *rp)
 {
     VL tv,fv,vv,vc,av;
     NODE fd,fd0,in0,in,r,r0,t,s,cand,alist;
@@ -3668,6 +4493,7 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     int *perm;
     int j,ret;
     Z jq,bpe;
+    VECT hvect;
 
     nd_module = 0;
     nd_lf = 0;
@@ -3722,6 +4548,11 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     for ( t = BDY(f), max = 1; t; t = NEXT(t) )
         for ( tv = vv; tv; tv = NEXT(tv) ) {
             if ( nd_module ) {
+              if ( OID(BDY(t)) == O_DPM ) {
+                e = dpm_getdeg((DPM)BDY(t),&trank);
+                max = MAX(e,max);
+                mrank = MAX(mrank,trank);
+              } else {
                 s = BDY((LIST)BDY(t));
                 trank = length(s);
                 mrank = MAX(mrank,trank);
@@ -3729,6 +4560,7 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
                     e = getdeg(tv->v,(P)BDY(s));
                     max = MAX(e,max);
                 }
+              }
             } else {
                 e = getdeg(tv->v,(P)BDY(t));
                 max = MAX(e,max);
@@ -3739,13 +4571,22 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     ishomo = 1;
     for ( in0 = 0, fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
         if ( nd_module ) {
-      if ( !nd_gentrace ) pltozpl((LIST)BDY(t),&dmy,&zpl);
-      else zpl = (LIST)BDY(t);
+          if ( OID(BDY(t)) == O_DPM ) {
+            Z cont;
+            DPM zdpm;
+
+            if ( !nd_gentrace ) dpm_ptozp((DPM)BDY(t),&cont,&zdpm);
+            else zdpm = (DPM)BDY(t);
+            c = (pointer)dpmtondv(m,zdpm);
+          } else {
+            if ( !nd_gentrace ) pltozpl((LIST)BDY(t),&dmy,&zpl);
+            else zpl = (LIST)BDY(t);
             c = (pointer)pltondv(CO,vv,zpl);
+          }
         } else {
-      if ( !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp);
-      else zp = (P)BDY(t);
-            c = (pointer)ptondv(CO,vv,zp);
+          if ( !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp);
+          else zp = (P)BDY(t);
+          c = (pointer)ptondv(CO,vv,zp);
         }
         if ( ishomo )
             ishomo = ishomo && ndv_ishomo(c);
@@ -3773,7 +4614,7 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     tl1 = tl2 = tl3 = tl4 = 0;
         if ( Demand )
             nd_demand = 1;
-        ret = ndv_setup(m,1,fd0,nd_gbblock?1:0,0);
+        ret = ndv_setup(m,1,fd0,nd_gbblock?1:0,0,0);
         if ( nd_gentrace ) {
             MKLIST(l1,nd_tracelist); MKNODE(nd_alltracelist,l1,0);
         }
@@ -3785,6 +4626,11 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
             else m = get_lprime(++mindex);
             continue;
         }
+        if ( nd_gentrace ) {
+          MKVECT(hvect,nd_psn);
+          for ( i = 0; i < nd_psn; i++ )
+             ndltodp(nd_psh[i]->dl,(DP *)&BDY(hvect)[i]);
+        }
         if ( !ishomo && homo ) {
             /* dehomogenization */
             for ( t = cand; t; t = NEXT(t) ) ndv_dehomogenize((NDV)BDY(t),ord);
@@ -3837,8 +4683,11 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     nd_bpe = cbpe;
     nd_setup_parameters(nd_nvar,0);
     for ( r = cand; r; r = NEXT(r) ) {
-    if ( nd_module ) BDY(r) = ndvtopl(0,CO,vv,BDY(r),mrank);
-        else BDY(r) = (pointer)ndvtop(0,CO,vv,BDY(r));
+      if ( nd_module ) {
+        if ( retdp ) BDY(r) = ndvtodpm(0,BDY(r));
+        else BDY(r) = ndvtopl(0,CO,vv,BDY(r),mrank);
+      } else if ( retdp ) BDY(r) = ndvtodp(0,BDY(r));
+      else BDY(r) = (pointer)ndvtop(0,CO,vv,BDY(r));
     }
     if ( nd_nalg )
         cand = postprocess_algcoef(av,alist,cand);
@@ -3862,7 +4711,7 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
         MKLIST(l1,tl1); MKLIST(l2,tl2); MKLIST(l3,t); MKLIST(l4,tl3);
     MKLIST(l5,tl4);
       STOZ(nd_bpe,bpe);
-        tr = mknode(8,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe); MKLIST(*rp,tr);
+        tr = mknode(9,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe,hvect); MKLIST(*rp,tr);
     }
 }
 
@@ -3914,6 +4763,27 @@ DL ndltodl(int n,UINT *ndl)
     return dl;
 }
 
+void _ndltodl(UINT *ndl,DL dl)
+{
+    int *d;
+    int i,j,l,s,ord_l,n;
+    struct order_pair *op;
+
+    n = nd_nvar;
+    dl->td = TD(ndl);
+    d = dl->d;
+    if ( nd_blockmask ) {
+        l = nd_blockmask->n;
+        op = nd_blockmask->order_pair;
+        for ( j = 0, s = 0; j < l; j++ ) {
+            ord_l = op[j].length;
+            for ( i = 0; i < ord_l; i++, s++ ) d[s] = GET_EXP(ndl,s);
+        }
+    } else {
+        for ( i = 0; i < n; i++ ) d[i] = GET_EXP(ndl,i);
+    }
+}
+
 void nmtodp(int mod,NM m,DP *r)
 {
     DP dp;
@@ -3926,6 +4796,18 @@ void nmtodp(int mod,NM m,DP *r)
     *r = dp;
 }
 
+void ndltodp(UINT *d,DP *r)
+{
+    DP dp;
+    MP mr;
+
+    NEWMP(mr); 
+    mr->dl = ndltodl(nd_nvar,d);
+    mr->c = (Obj)ONE;
+    NEXT(mr) = 0; MKDP(nd_nvar,mr,dp); dp->sugar = mr->dl->td;
+    *r = dp;
+}
+
 void ndl_print(UINT *dl)
 {
     int n;
@@ -4090,7 +4972,7 @@ void ndv_homogenize(NDV p,int obpe,int oadv,EPOS oepos
     NMV m,mr0,mr,t;
 
     len = p->len;
-    for ( m = BDY(p), i = 0, max = 1; i < len; NMV_OADV(m), i++ )
+    for ( m = BDY(p), i = 0, max = 0; i < len; NMV_OADV(m), i++ )
         max = MAX(max,TD(DL(m)));
     mr0 = nmv_adv>oadv?(NMV)REALLOC(BDY(p),len*nmv_adv):BDY(p);
     m = (NMV)((char *)mr0+(len-1)*oadv);
@@ -4418,7 +5300,7 @@ UINT *nd_compute_bound(ND p)
 int nd_get_exporigin(struct order_spec *ord)
 {
     switch ( ord->id ) {
-        case 0: case 2: case 256: case 258:
+        case 0: case 2: case 256: case 258: case 300:
             return 1+nd_module;
         case 1: case 257:
             /* block order */
@@ -4554,6 +5436,7 @@ ND_pairs nd_reconstruct(int trace,ND_pairs d)
         NEXTND_pairs(s0,s);
         s->i1 = t->i1;
         s->i2 = t->i2;
+        s->sig = t->sig;
         SG(s) = SG(t);
         ndl_reconstruct(LCM(t),LCM(s),obpe,oepos);
     }
@@ -4572,12 +5455,14 @@ ND_pairs nd_reconstruct(int trace,ND_pairs d)
             h = ndl_hash_value(DL(mr));
             NEXT(mr) = nd_red[h];
             nd_red[h] = mr;
+            mr->sig = r->sig;
         }
     for ( i = 0; i < REDTAB_LEN; i++ ) old_red[i] = 0;
     old_red = 0;
     for ( i = 0; i < nd_psn; i++ ) {
         NEWRHist(r); SG(r) = SG(nd_psh[i]);
         ndl_reconstruct(DL(nd_psh[i]),DL(r),obpe,oepos);
+        r->sig = nd_psh[i]->sig;
         nd_psh[i] = r;
     }
     if ( s0 ) NEXT(s) = 0;
@@ -4697,6 +5582,8 @@ int nd_sp(int mod,int trace,ND_pairs p,ND *rp)
         MKLIST(hist,node); MKNODE(node,hist,nd_tracelist);
         nd_tracelist = node;
     }
+    if ( *rp )
+      (*rp)->sig = p->sig;
     FREENM(m1); FREENM(m2);
     return 1;
 }
@@ -5075,6 +5962,7 @@ NDV ndv_dup_realloc(NDV p,int obpe,int oadv,EPOS oepos
     }
     MKNDV(NV(p),mr0,len,r);
     SG(r) = SG(p);
+    r->sig = p->sig;
     return r;
 }
 
@@ -5196,31 +6084,32 @@ NDV ptondv(VL vl,VL dvl,P p)
 
 void pltozpl(LIST l,Q *cont,LIST *pp)
 {
-    NODE nd,nd1;
-    int n;
-    P *pl;
-    Q *cl;
-    int i;
-    P dmy;
-    Z dvr;
-    LIST r;
+  NODE nd,nd1;
+  int n;
+  P *pl;
+  Q *cl;
+  int i;
+  P dmy;
+  Z dvr,inv;
+  LIST r;
 
-    nd = BDY(l); n = length(nd);
-    pl = (P *)MALLOC(n*sizeof(P));
-    cl = (Q *)MALLOC(n*sizeof(P));
-    for ( i = 0; i < n; i++, nd = NEXT(nd) )
-        ptozp((P)BDY(nd),1,&cl[i],&dmy);
-    qltozl(cl,n,&dvr);
-    nd = BDY(l);
-    for ( i = 0; i < n; i++, nd = NEXT(nd) ) {
-        divsp(CO,(P)BDY(nd),(P)dvr,&pl[i]);
-    }
-    nd = 0;
-    for ( i = n-1; i >= 0; i-- ) {
-        MKNODE(nd1,pl[i],nd); nd = nd1;
-    }
-    MKLIST(r,nd);
-    *pp = r;
+  nd = BDY(l); n = length(nd);
+  pl = (P *)MALLOC(n*sizeof(P));
+  cl = (Q *)MALLOC(n*sizeof(Q));
+  for ( i = 0; i < n; i++, nd = NEXT(nd) ) {
+    ptozp((P)BDY(nd),1,&cl[i],&dmy);
+  }
+  qltozl(cl,n,&dvr);
+  divz(ONE,dvr,&inv);
+  nd = BDY(l);
+  for ( i = 0; i < n; i++, nd = NEXT(nd) )
+    divsp(CO,(P)BDY(nd),(P)dvr,&pl[i]);
+  nd = 0;
+  for ( i = n-1; i >= 0; i-- ) {
+    MKNODE(nd1,pl[i],nd); nd = nd1;
+  }
+  MKLIST(r,nd);
+  *pp = r;
 }
 
 /* (a1,a2,...,an) -> a1*e(1)+...+an*e(n) */
@@ -5406,9 +6295,112 @@ NDV ndtondv(int mod,ND p)
     }
     MKNDV(NV(p),m0,len,d);
     SG(d) = SG(p);
+    d->sig = p->sig;
     return d;
 }
 
+static int dmm_comp_nv;
+
+int dmm_comp(DMM *a,DMM *b)
+{
+   return -compdmm(dmm_comp_nv,*a,*b);
+}
+
+void dmm_sort_by_ord(DMM *a,int len,int nv)
+{
+  dmm_comp_nv = nv;
+  qsort(a,len,sizeof(DMM),(int (*)(const void *,const void *))dmm_comp);
+}
+
+void dpm_sort(DPM p,DPM *rp)
+{
+  DMM t,t1;
+  int len,i,n;
+  DMM *a;
+  DPM d;
+ 
+  if ( !p ) *rp = 0;
+  for ( t = BDY(p), len = 0; t; t = NEXT(t), len++ );
+  a = (DMM *)MALLOC(len*sizeof(DMM));
+  for ( i = 0, t = BDY(p); i < len; i++, t = NEXT(t) ) a[i] = t;
+  n = p->nv;
+  dmm_sort_by_ord(a,len,n);  
+  t = 0;
+  for ( i = len-1; i >= 0; i-- ) {
+    NEWDMM(t1); 
+    t1->c = a[i]->c;
+    t1->dl = a[i]->dl;
+    t1->pos = a[i]->pos;
+    t1->next = t;
+    t = t1;
+  }
+  MKDPM(n,t,d);
+  SG(d) = SG(p);
+  *rp = d;
+}
+
+int dpm_comp(DPM *a,DPM *b)
+{
+  return -compdpm(CO,*a,*b);
+}
+
+NODE dpm_sort_list(NODE l)
+{
+  int i,len;
+  NODE t,t1;
+  DPM *a;
+  
+  len = length(l);
+  a = (DPM *)MALLOC(len*sizeof(DPM));
+  for ( t = l, i = 0; i < len; i++, t = NEXT(t) ) a[i] = (DPM)BDY(t);
+  qsort(a,len,sizeof(DPM),(int (*)(const void *,const void *))dpm_comp);
+  t = 0;
+  for ( i = len-1; i >= 0; i-- ) {
+    MKNODE(t1,(pointer)a[i],t); t = t1;
+  }
+  return t;
+}
+
+int nmv_comp(NMV a,NMV b)
+{
+  int t;
+  t = DL_COMPARE(a->dl,b->dl);
+  return -t;
+}
+
+NDV dpmtondv(int mod,DPM p)
+{
+  NDV d;
+  NMV m,m0;
+  DMM t;
+  DMM *a;
+  int i,len,n;
+
+  if ( !p ) return 0;
+  for ( t = BDY(p), len = 0; t; t = NEXT(t), len++ );
+  a = (DMM *)MALLOC(len*sizeof(DMM));
+  for ( i = 0, t = BDY(p); i < len; i++, t = NEXT(t) ) a[i] = t;
+  n = p->nv;
+  dmm_sort_by_ord(a,len,n);  
+  if ( mod > 0 || mod == -1 )
+    m0 = m = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(len*nmv_adv);
+  else
+    m0 = m = MALLOC(len*nmv_adv);
+#if 0
+  ndv_alloc += nmv_adv*len;
+#endif
+  for ( i = 0; i < len; i++, NMV_ADV(m) ) {
+    dltondl(n,a[i]->dl,DL(m));
+    MPOS(DL(m)) = a[i]->pos;
+    TD(DL(m)) = ndl_weight(DL(m));
+    CZ(m) = (Z)a[i]->c;
+  }
+  qsort(m0,len,nmv_adv,(int (*)(const void *,const void *))nmv_comp);
+  MKNDV(NV(p),m0,len,d);
+  SG(d) = SG(p);
+  return d;
+}
+
 ND ndvtond(int mod,NDV p)
 {
     ND d;
@@ -5451,6 +6443,29 @@ DP ndvtodp(int mod,NDV p)
     return d;
 }
 
+DPM ndvtodpm(int mod,NDV p)
+{
+  DMM m,m0;
+  DPM d;
+  NMV t;
+  int i,len;
+
+  if ( !p ) return 0;
+  m0 = 0;
+  len = p->len;
+  for ( t = BDY(p), i = 0; i < len; NMV_ADV(t), i++ ) {
+    NEXTDMM(m0,m);
+    m->dl = ndltodl(nd_nvar,DL(t));
+    m->c = (Obj)ndctop(mod,t->c);
+    m->pos = MPOS(DL(t));
+  }
+  NEXT(m) = 0;
+  MKDPM(nd_nvar,m0,d);
+  SG(d) = SG(p);
+  return d;
+}
+
+
 DP ndtodp(int mod,ND p)
 {
     MP m,m0;
@@ -5538,12 +6553,15 @@ NODE ndv_reducebase(NODE x,int *perm)
 
 /* XXX incomplete */
 
+extern DMMstack dmm_stack;
+int ndl_module_schreyer_compare(UINT *a,UINT *b);
+
 void nd_init_ord(struct order_spec *ord)
 {
   nd_module = (ord->id >= 256);
   if ( nd_module ) {
     nd_dcomp = -1;
-    nd_ispot = ord->ispot;
+    nd_module_ordtype = ord->module_ordtype;
     nd_pot_nelim = ord->pot_nelim;
     nd_poly_weight_len = ord->nv;
     nd_poly_weight = ord->top_weight;
@@ -5607,40 +6625,73 @@ void nd_init_ord(struct order_spec *ord)
         case 256:
             switch ( ord->ord.simple ) {
                 case 0:
+                    nd_dcomp = 0;
                     nd_isrlex = 1;
-                    ndl_compare_function = ndl_module_grlex_compare;
+                    ndl_compare_function = ndl_module_glex_compare;
                     break;
                 case 1:
+                    nd_dcomp = 0;
                     nd_isrlex = 0;
                     ndl_compare_function = ndl_module_glex_compare;
                     break;
                 case 2:
+                    nd_dcomp = 0;
                     nd_isrlex = 0;
-                    ndl_compare_function = ndl_module_lex_compare;
+                    ndl_compare_function = ndl_module_compare;
+                    ndl_base_compare_function = ndl_lex_compare;
                     break;
                 default:
-                    error("nd_gr : unsupported order");
+                    error("nd_init_ord : unsupported order");
             }
             break;
         case 257:
             /* block order */
             nd_isrlex = 0;
-            ndl_compare_function = ndl_module_block_compare;
+            ndl_compare_function = ndl_module_compare;
+            ndl_base_compare_function = ndl_block_compare;
             break;
         case 258:
             /* matrix order */
             nd_isrlex = 0;
             nd_matrix_len = ord->ord.matrix.row;
             nd_matrix = ord->ord.matrix.matrix;
-            ndl_compare_function = ndl_module_matrix_compare;
+            ndl_compare_function = ndl_module_compare;
+            ndl_base_compare_function = ndl_matrix_compare;
             break;
         case 259:
             /* composite order */
             nd_isrlex = 0;
             nd_worb_len = ord->ord.composite.length;
             nd_worb = ord->ord.composite.w_or_b;
-            ndl_compare_function = ndl_module_composite_compare;
+            ndl_compare_function = ndl_module_compare;
+            ndl_base_compare_function = ndl_composite_compare;
             break;
+        case 300:
+            /* schreyer order */
+            if ( ord->base->id != 256 )
+               error("nd_init_ord : unsupported base order");
+            ndl_compare_function = ndl_module_schreyer_compare;
+            dmm_stack = ord->dmmstack;
+            switch ( ord->base->ord.simple ) {
+                case 0:
+                    nd_isrlex = 1;
+                    ndl_base_compare_function = ndl_glex_compare;
+                    dl_base_compare_function = cmpdl_revgradlex;
+                    break;
+                case 1:
+                    nd_isrlex = 0;
+                    ndl_base_compare_function = ndl_glex_compare;
+                    dl_base_compare_function = cmpdl_gradlex;
+                    break;
+                case 2:
+                    nd_isrlex = 0;
+                    ndl_base_compare_function = ndl_lex_compare;
+                    dl_base_compare_function = cmpdl_lex;
+                    break;
+                default:
+                    error("nd_init_ord : unsupported order");
+            }
+            break;
     }
     nd_ord = ord;
 }
@@ -5676,7 +6727,7 @@ EPOS nd_create_epos(struct order_spec *ord)
 
     epos = (EPOS)MALLOC_ATOMIC(nd_nvar*sizeof(struct oEPOS));
     switch ( ord->id ) {
-        case 0: case 256:
+        case 0: case 256: case 300:
             if ( nd_isrlex ) {
                 for ( i = 0; i < nd_nvar; i++ ) {
                     epos[i].i = nd_exporigin + (nd_nvar-1-i)/nd_epw;
@@ -5779,7 +6830,7 @@ void nd_nf_p(Obj f,LIST g,LIST v,int m,struct order_sp
     ndf = (pointer)ndvtond(m,ndvf);
 
     /* dont sort, dont removecont */
-    ndv_setup(m,0,in0,1,1);
+    ndv_setup(m,0,in0,1,1,0);
     nd_scale=2;
     stat = nd_nf(m,0,ndf,nd_ps,1,&nf);
     if ( !stat )
@@ -6753,7 +7804,7 @@ NODE nd_f4(int m,int checkonly,int **indp)
                 nd_removecont(m,nf1);
                 nf = ndtondv(m,nf1);
             }
-            nh = ndv_newps(m,nf,0,1);
+            nh = ndv_newps(m,nf,0);
             d = update_pairs(d,g,nh,0);
             g = update_base(g,nh);
         }
@@ -6881,7 +7932,7 @@ NODE nd_f4_trace(int m,int **indp)
             nfv = ndv_dup(0,nfqv);
             ndv_mod(m,nfv);
             ndv_removecont(m,nfv);
-            nh = ndv_newps(0,nfv,nfqv,1);
+            nh = ndv_newps(0,nfv,nfqv);
             d = update_pairs(d,g,nh,0);
             g = update_base(g,nh);
         }
@@ -7679,7 +8730,9 @@ int ndv_ishomo(NDV p)
     h = TD(DL(m));
     NMV_ADV(m);
     for ( len--; len; len--, NMV_ADV(m) )
-        if ( TD(DL(m)) != h ) return 0;
+        if ( TD(DL(m)) != h ) {
+          return 0;
+        }
     return 1;
 }
 
@@ -8329,6 +9382,8 @@ void parse_nd_option(NODE opt)
             nd_newelim = value?1:0;
     else if ( !strcmp(key,"intersect") )
             nd_intersect = value?1:0;
+    else if ( !strcmp(key,"syzgen") )
+            nd_intersect = ZTOS((Q)value);
     else if ( !strcmp(key,"lf") )
             nd_lf = value?1:0;
     else if ( !strcmp(key,"trace") ) {
@@ -8884,7 +9939,7 @@ void nd_f4_lf_trace(LIST f,LIST v,int trace,int homo,s
             ndv_homogenize((NDV)BDY(t),obpe,oadv,oepos,ompos);
     }
     if ( MaxDeg > 0 ) nocheck = 1;
-    ret = ndv_setup(-2,m,fd0,nd_gbblock?1:0,0);
+    ret = ndv_setup(-2,m,fd0,nd_gbblock?1:0,0,0);
     if ( ret )
       cand = nd_f4_lf_trace_main(m,&perm);
     if ( !ret || !cand ) {
@@ -9000,7 +10055,7 @@ NODE nd_f4_lf_trace_main(int m,int **indp)
             if ( DL_COMPARE(HDL(nfv),HDL(nfqv)) ) return 0;
             ndv_removecont(m,nfv);
             ndv_removecont(-2,nfqv);
-            nh = ndv_newps(-2,nfv,nfqv,1);
+            nh = ndv_newps(-2,nfv,nfqv);
             d = update_pairs(d,g,nh,0);
             g = update_base(g,nh);
         }