===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/nd.c,v
retrieving revision 1.11
retrieving revision 1.21
diff -u -p -r1.11 -r1.21
--- OpenXM_contrib2/asir2000/engine/nd.c	2003/07/26 01:00:32	1.11
+++ OpenXM_contrib2/asir2000/engine/nd.c	2003/08/01 08:39:54	1.21
@@ -1,10 +1,8 @@
-/* $OpenXM$ */
+/* $OpenXM: OpenXM_contrib2/asir2000/engine/nd.c,v 1.20 2003/08/01 05:03:15 noro Exp $ */
 
 #include "ca.h"
 #include "inline.h"
 
-#define USE_NDV 1
-
 #if defined(__GNUC__)
 #define INLINE inline
 #elif defined(VISUAL)
@@ -35,17 +33,30 @@ typedef struct oNDV {
 
 typedef struct oNM {
 	struct oNM *next;
+	union {
+		int m;
+		Q z;
+	} c;
 	int td;
-	int c;
 	unsigned int dl[1];
 } *NM;
 
 typedef struct oNMV {
+	union {
+		int m;
+		Q z;
+	} c;
 	int td;
-	int c;
 	unsigned int dl[1];
 } *NMV;
 
+typedef struct oRHist {
+	struct oRHist *next;
+	int index;
+	int td,sugar;
+	unsigned int dl[1];
+} *RHist;
+
 typedef struct oND_pairs {
 	struct oND_pairs *next;
 	int i1,i2;
@@ -53,35 +64,55 @@ typedef struct oND_pairs {
 	unsigned int lcm[1];
 } *ND_pairs;
 
+double nd_scale=2;
 static unsigned int **nd_bound;
-int nd_mod,nd_nvar;
+int nd_nvar;
 int is_rlex;
 int nd_epw,nd_bpe,nd_wpd;
 unsigned int nd_mask[32];
 unsigned int nd_mask0,nd_mask1;
+
 NM _nm_free_list;
 ND _nd_free_list;
 ND_pairs _ndp_free_list;
-NM *nd_red;
-int nd_red_len;
 
-extern int Top,Reverse;
+static NDV *nd_ps;
+static NDV *nd_psq;
+int *nd_psl;
+RHist *nd_psh;
 int nd_psn,nd_pslen;
+
+RHist *nd_red;
+int nd_red_len;
+
 int nd_found,nd_create,nd_notfirst;
-int *nd_psl;
-NM *nd_psh;
+int nm_adv;
+int nmv_adv;
+int nmv_len;
+NDV ndv_red;
 
-void GC_gcollect();
-NODE append_one(NODE,int);
+extern int Top,Reverse;
 
 #define HTD(d) ((d)->body->td)
 #define HDL(d) ((d)->body->dl)
-#define HC(d) ((d)->body->c)
+#define HCM(d) ((d)->body->c.m)
+#define HCQ(d) ((d)->body->c.z)
+#define CM(a) ((a)->c.m)
+#define CQ(a) ((a)->c.z)
+#define DL(a) ((a)->dl)
+#define TD(a) ((a)->td)
+#define SG(a) ((a)->sugar)
+#define LEN(a) ((a)->len)
 
+#define NM_ADV(m) (m = (NM)(((char *)m)+nm_adv))
+#define NEWRHist(r) \
+((r)=(RHist)MALLOC(sizeof(struct oRHist)+(nd_wpd-1)*sizeof(unsigned int)))
 #define NEWND_pairs(m) if(!_ndp_free_list)_NDP_alloc(); (m)=_ndp_free_list; _ndp_free_list = NEXT(_ndp_free_list)   
 #define NEWNM(m) if(!_nm_free_list)_NM_alloc(); (m)=_nm_free_list; _nm_free_list = NEXT(_nm_free_list)   
 #define MKND(n,m,d) if(!_nd_free_list)_ND_alloc(); (d)=_nd_free_list; _nd_free_list = (ND)BDY(_nd_free_list); (d)->nv=(n); BDY(d)=(m)
 
+#define NEXTRHist(r,c) \
+if(!(r)){NEWRHist(r);(c)=(r);}else{NEWRHist(NEXT(c));(c)=NEXT(c);}
 #define NEXTNM(r,c) \
 if(!(r)){NEWNM(r);(c)=(r);}else{NEWNM(NEXT(c));(c)=NEXT(c);}
 #define NEXTNM2(r,c,s) \
@@ -93,10 +124,22 @@ if(!(r)){(c)=(r)=(s);}else{NEXT(c)=(s);(c)=(s);}
 #define NEXTND_pairs(r,c) \
 if(!(r)){NEWND_pairs(r);(c)=(r);}else{NEWND_pairs(NEXT(c));(c)=NEXT(c);}
 
+void nd_removecont(int mod,ND p);
+void nd_removecont2(ND p1,ND p2);
+void ndv_removecont(int mod,NDV p);
+void ndv_mul_c_q(NDV p,Q mul);
+void nd_mul_c_q(ND p,Q mul);
+
+void GC_gcollect();
+NODE append_one(NODE,int);
+
+void removecont_array(Q *c,int n);
 ND_pairs crit_B( ND_pairs d, int s );
 void nd_gr(LIST f,LIST v,int m,struct order_spec *ord,LIST *rp);
-NODE nd_setup(NODE f);
-int nd_newps(ND a);
+void nd_gr_trace(LIST f,LIST v,int m,struct order_spec *ord,LIST *rp);
+NODE nd_setup(int mod,NODE f);
+int nd_newps(int mod,ND a);
+int nd_newps_trace(int mod,ND nf,ND nfq);
 ND_pairs nd_minp( ND_pairs d, ND_pairs *prest );
 NODE update_base(NODE nd,int ndp);
 static ND_pairs equivalent_pairs( ND_pairs d1, ND_pairs *prest );
@@ -105,68 +148,61 @@ ND_pairs crit_F( ND_pairs d1 );
 ND_pairs crit_M( ND_pairs d1 );
 ND_pairs nd_newpairs( NODE g, int t );
 ND_pairs update_pairs( ND_pairs d, NODE /* of index */ g, int t);
-NODE nd_gb(NODE f);
+NODE nd_gb(int m,NODE f);
+NODE nd_gb_trace(int m,NODE f);
 void nd_free_private_storage();
 void _NM_alloc();
 void _ND_alloc();
 int ndl_td(unsigned int *d);
-ND nd_add(ND p1,ND p2);
-ND nd_mul_nm(ND p,NM m0);
-ND nd_mul_ind_nm(int index,NM m0);
-ND nd_mul_term(ND p,int td,unsigned int *d);
-int nd_sp(ND_pairs p,ND *nf);
+ND nd_add(int mod,ND p1,ND p2);
+ND nd_add_q(ND p1,ND p2);
+ND nd_mul_nm(int mod,ND p,NM m0);
+ND nd_mul_ind_nm(int mod,int index,NM m0);
+int nd_sp(int mod,ND_pairs p,ND *nf);
 int nd_find_reducer(ND g);
-int nd_nf(ND g,int full,ND *nf);
+int nd_nf(int mod,ND g,int full,ND *nf);
 ND nd_reduce(ND p1,ND p2);
 ND nd_reduce_special(ND p1,ND p2);
 void nd_free(ND p);
 void ndl_print(unsigned int *dl);
 void nd_print(ND p);
+void nd_print_q(ND p);
+void ndv_print(NDV p);
+void ndv_print_q(NDV p);
 void ndp_print(ND_pairs d);
 int nd_length(ND p);
-void nd_monic(ND p);
-void nd_mul_c(ND p,int mul);
+void nd_mul_c(int mod,ND p,int mul);
 void nd_free_redlist();
 void nd_append_red(unsigned int *d,int td,int i);
 unsigned int *nd_compute_bound(ND p);
 unsigned int *dp_compute_bound(DP p);
-ND_pairs nd_reconstruct(ND_pairs);
+ND_pairs nd_reconstruct(int mod,int trace,ND_pairs ndp);
 void nd_setup_parameters();
 void nd_realloc(ND p,int obpe);
 ND nd_copy(ND p);
 void ndl_dup(int obpe,unsigned int *d,unsigned int *r);
 
-#if USE_NDV
-static NDV *nd_ps;
-
 #define NMV_ADV(m) (m = (NMV)(((char *)m)+nmv_adv))
 #define NEWNDV(d) ((d)=(NDV)MALLOC(sizeof(struct oNDV)))
-#define MKNDV(n,m,l,d) NEWNDV(d); (d)->nv=(n); BDY(d)=(m); (d)->len = l;
-
-int nmv_adv;
-int nmv_len;
-NDV ndv_red;
-
-void ndv_mul_c(NDV p,int mul);
-ND ndv_add(ND p1,NDV p2);
-NDV ndtondv(ND p);
-void ndv_mul_nm(NDV pv,NM m,NDV r);
-ND ndv_mul_nm_create(NDV p,NM m0);
+#define MKNDV(n,m,l,d) NEWNDV(d); NV(d)=(n); BDY(d)=(m); LEN(d) = l;
+void ndv_mul_c(int mod,NDV p,int mul);
+ND ndv_add(int mod,ND p1,NDV p2);
+ND ndv_add_q(ND p1,NDV p2);
+NDV ndtondv(int mod,ND p);
+void ndv_mul_nm(int mod,NDV pv,NM m,NDV r);
+ND ndv_mul_nm_create(int mod,NDV p,NM m0);
 void ndv_realloc(NDV p,int obpe,int oadv);
-NDV dptondv(DP);
-DP ndvtodp(NDV);
-#else
-static ND *nd_ps;
-ND dptond(DP);
-DP ndtodp(ND);
-#endif
+NDV dptondv(int,DP);
+DP ndvtodp(int,NDV);
+ND dptond(int,DP);
+DP ndtodp(int,ND);
 
 void nd_free_private_storage()
 {
 	_nd_free_list = 0;
 	_nm_free_list = 0;
 	_ndp_free_list = 0;
-	bzero(nd_red,sizeof(REDTAB_LEN*sizeof(NM)));
+	bzero(nd_red,sizeof(REDTAB_LEN*sizeof(RHist)));
 	GC_gcollect();
 }
 
@@ -515,205 +551,6 @@ int ndl_disjoint(unsigned int *d1,unsigned int *d2)
 	}
 }
 
-ND nd_reduce(ND p1,ND p2)
-{
-	int c,c1,c2,t,td,td2,mul;
-	NM m2,prev,head,cur,new;
-	unsigned int *d;
-
-	if ( !p1 )
-		return 0;
-	else {
-		c2 = invm(HC(p2),nd_mod);
-		c1 = nd_mod-HC(p1);
-		DMAR(c1,c2,0,nd_mod,mul);
-		td = HTD(p1)-HTD(p2);
-		d = (unsigned int *)ALLOCA(nd_wpd*sizeof(unsigned int));
-		ndl_sub(HDL(p1),HDL(p2),d);
-		prev = 0; head = cur = BDY(p1);
-		NEWNM(new);
-		for ( m2 = BDY(p2); m2; ) {
-			td2 = new->td = m2->td+td;
-			ndl_add(m2->dl,d,new->dl);
-			if ( !cur ) {
-				c1 = C(m2);
-				DMAR(c1,mul,0,nd_mod,c2);
-				C(new) = c2;
-				if ( !prev ) {
-					prev = new;
-					NEXT(prev) = 0;
-					head = prev;
-				} else {
-					NEXT(prev) = new;
-					NEXT(new) = 0;
-					prev = new;
-				}
-				m2 = NEXT(m2);
-				NEWNM(new);
-				continue;
-			}
-			if ( cur->td > td2 )
-				c = 1;
-			else if ( cur->td < td2 )
-				c = -1;
-			else
-				c = ndl_compare(cur->dl,new->dl);
-			switch ( c ) {
-				case 0:
-					c2 = C(m2);
-					c1 = C(cur);
-					DMAR(c2,mul,c1,nd_mod,t);
-					if ( t )
-						C(cur) = t;
-					else if ( !prev ) {
-						head = NEXT(cur);
-						FREENM(cur);
-						cur = head;
-					} else {
-						NEXT(prev) = NEXT(cur);
-						FREENM(cur);
-						cur = NEXT(prev);
-					}
-					m2 = NEXT(m2);
-					break;
-				case 1:
-					prev = cur;
-					cur = NEXT(cur);
-					break;
-				case -1:
-					if ( !prev ) {
-						/* cur = head */
-						prev = new;
-						c2 = C(m2);
-						DMAR(c2,mul,0,nd_mod,c1);
-						C(prev) = c1;
-						NEXT(prev) = head;
-						head = prev;
-					} else {
-						c2 = C(m2);
-						DMAR(c2,mul,0,nd_mod,c1);
-						C(new) = c1;
-						NEXT(prev) = new;
-						NEXT(new) = cur;
-						prev = new;
-					}
-					NEWNM(new);
-					m2 = NEXT(m2);
-					break;
-			}
-		}
-		FREENM(new);
-		if ( head ) {
-			BDY(p1) = head;
-			p1->sugar = MAX(p1->sugar,p2->sugar+td);
-			return p1;
-		} else {
-			FREEND(p1);
-			return 0;
-		}
-			
-	}
-}
-
-/* HDL(p1) = HDL(p2) */
-
-ND nd_reduce_special(ND p1,ND p2)
-{
-	int c,c1,c2,t,td,td2,mul;
-	NM m2,prev,head,cur,new;
-
-	if ( !p1 )
-		return 0;
-	else {
-		c2 = invm(HC(p2),nd_mod);
-		c1 = nd_mod-HC(p1);
-		DMAR(c1,c2,0,nd_mod,mul);
-		prev = 0; head = cur = BDY(p1);
-		NEWNM(new);
-		for ( m2 = BDY(p2); m2; ) {
-			td2 = new->td = m2->td;
-			if ( !cur ) {
-				c1 = C(m2);
-				DMAR(c1,mul,0,nd_mod,c2);
-				C(new) = c2;
-				bcopy(m2->dl,new->dl,nd_wpd*sizeof(unsigned int));
-				if ( !prev ) {
-					prev = new;
-					NEXT(prev) = 0;
-					head = prev;
-				} else {
-					NEXT(prev) = new;
-					NEXT(new) = 0;
-					prev = new;
-				}
-				m2 = NEXT(m2);
-				NEWNM(new);
-				continue;
-			}
-			if ( cur->td > td2 )
-				c = 1;
-			else if ( cur->td < td2 )
-				c = -1;
-			else
-				c = ndl_compare(cur->dl,m2->dl);
-			switch ( c ) {
-				case 0:
-					c2 = C(m2);
-					c1 = C(cur);
-					DMAR(c2,mul,c1,nd_mod,t);
-					if ( t )
-						C(cur) = t;
-					else if ( !prev ) {
-						head = NEXT(cur);
-						FREENM(cur);
-						cur = head;
-					} else {
-						NEXT(prev) = NEXT(cur);
-						FREENM(cur);
-						cur = NEXT(prev);
-					}
-					m2 = NEXT(m2);
-					break;
-				case 1:
-					prev = cur;
-					cur = NEXT(cur);
-					break;
-				case -1:
-					bcopy(m2->dl,new->dl,nd_wpd*sizeof(unsigned int));
-					if ( !prev ) {
-						/* cur = head */
-						prev = new;
-						c2 = C(m2);
-						DMAR(c2,mul,0,nd_mod,c1);
-						C(prev) = c1;
-						NEXT(prev) = head;
-						head = prev;
-					} else {
-						c2 = C(m2);
-						DMAR(c2,mul,0,nd_mod,c1);
-						C(new) = c1;
-						NEXT(prev) = new;
-						NEXT(new) = cur;
-						prev = new;
-					}
-					NEWNM(new);
-					m2 = NEXT(m2);
-					break;
-			}
-		}
-		FREENM(new);
-		if ( head ) {
-			BDY(p1) = head;
-			p1->sugar = MAX(p1->sugar,p2->sugar+td);
-			return p1;
-		} else {
-			FREEND(p1);
-			return 0;
-		}
-			
-	}
-}
-
 int ndl_check_bound2(int index,unsigned int *d2)
 {
 	unsigned int u2;
@@ -796,30 +633,40 @@ INLINE int ndl_hash_value(int td,unsigned int *d)
 
 INLINE int nd_find_reducer(ND g)
 {
-	NM m;
+	RHist r;
 	int d,k,i;
 
 	d = ndl_hash_value(HTD(g),HDL(g));
-	for ( m = nd_red[d], k = 0; m; m = NEXT(m), k++ ) {
-		if ( HTD(g) == m->td && ndl_equal(HDL(g),m->dl) ) {
+	for ( r = nd_red[d], k = 0; r; r = NEXT(r), k++ ) {
+		if ( HTD(g) == TD(r) && ndl_equal(HDL(g),DL(r)) ) {
 			if ( k > 0 ) nd_notfirst++;
 			nd_found++;
-			return m->c;
+			return r->index;
 		}
 	}
 
-	for ( i = 0; i < nd_psn; i++ ) {
-		m = nd_psh[i];
-		if ( HTD(g) >= m->td && ndl_reducible(HDL(g),m->dl) ) {
-			nd_create++;
-			nd_append_red(HDL(g),HTD(g),i);
-			return i;
+	if ( Reverse )
+		for ( i = nd_psn-1; i >= 0; i-- ) {
+			r = nd_psh[i];
+			if ( HTD(g) >= TD(r) && ndl_reducible(HDL(g),DL(r)) ) {
+				nd_create++;
+				nd_append_red(HDL(g),HTD(g),i);
+				return i;
+			}
 		}
-	}
+	else
+		for ( i = 0; i < nd_psn; i++ ) {
+			r = nd_psh[i];
+			if ( HTD(g) >= TD(r) && ndl_reducible(HDL(g),DL(r)) ) {
+				nd_create++;
+				nd_append_red(HDL(g),HTD(g),i);
+				return i;
+			}
+		}
 	return -1;
 }
 
-ND nd_add(ND p1,ND p2)
+ND nd_add(int mod,ND p1,ND p2)
 {
 	int n,c;
 	int t;
@@ -832,20 +679,20 @@ ND nd_add(ND p1,ND p2)
 		return p1;
 	else {
 		for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
-			if ( m1->td > m2->td )
+			if ( TD(m1) > TD(m2) )
 				c = 1;
-			else if ( m1->td < m2->td )
+			else if ( TD(m1) < TD(m2) )
 				c = -1;
 			else
-				c = ndl_compare(m1->dl,m2->dl);
+				c = ndl_compare(DL(m1),DL(m2));
 			switch ( c ) {
 				case 0:
-					t = ((C(m1))+(C(m2))) - nd_mod;
+					t = ((CM(m1))+(CM(m2))) - mod;
 					if ( t < 0 )
-						t += nd_mod;
+						t += mod;
 					s = m1; m1 = NEXT(m1);
 					if ( t ) {
-						NEXTNM2(mr0,mr,s); C(mr) = (t);
+						NEXTNM2(mr0,mr,s); CM(mr) = (t);
 					} else {
 						FREENM(s);
 					}
@@ -873,60 +720,126 @@ ND nd_add(ND p1,ND p2)
 		else
 			NEXT(mr) = 0;
 		BDY(p1) = mr0;
-		p1->sugar = MAX(p1->sugar,p2->sugar);
+		SG(p1) = MAX(SG(p1),SG(p2));
 		FREEND(p2);
 		return p1;
 	}
 }
 
+ND nd_add_q(ND p1,ND p2)
+{
+	int n,c;
+	ND r;
+	NM m1,m2,mr0,mr,s;
+	Q t;
+
+	if ( !p1 )
+		return p2;
+	else if ( !p2 )
+		return p1;
+	else {
+		for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
+			if ( TD(m1) > TD(m2) )
+				c = 1;
+			else if ( TD(m1) < TD(m2) )
+				c = -1;
+			else
+				c = ndl_compare(DL(m1),DL(m2));
+			switch ( c ) {
+				case 0:
+					addq(CQ(m1),CQ(m2),&t);
+					s = m1; m1 = NEXT(m1);
+					if ( t ) {
+						NEXTNM2(mr0,mr,s); CQ(mr) = (t);
+					} else {
+						FREENM(s);
+					}
+					s = m2; m2 = NEXT(m2); FREENM(s);
+					break;
+				case 1:
+					s = m1; m1 = NEXT(m1); NEXTNM2(mr0,mr,s);
+					break;
+				case -1:
+					s = m2; m2 = NEXT(m2); NEXTNM2(mr0,mr,s);
+					break;
+			}
+		}
+		if ( !mr0 )
+			if ( m1 )
+				mr0 = m1;
+			else if ( m2 )
+				mr0 = m2;
+			else
+				return 0;
+		else if ( m1 )
+			NEXT(mr) = m1;
+		else if ( m2 )
+			NEXT(mr) = m2;
+		else
+			NEXT(mr) = 0;
+		BDY(p1) = mr0;
+		SG(p1) = MAX(SG(p1),SG(p2));
+		FREEND(p2);
+		return p1;
+	}
+}
+
 #if 1
 /* ret=1 : success, ret=0 : overflow */
-int nd_nf(ND g,int full,ND *rp)
+int nd_nf(int mod,ND g,int full,ND *rp)
 {
 	ND d;
 	NM m,mrd,tail;
 	NM mul;
 	int n,sugar,psugar,sugar0,stat,index;
 	int c,c1,c2;
-#if USE_NDV
+	RHist h;
 	NDV p,red;
-#else
-	ND p,red;
-#endif
+	Q cg,cred,gcd;
+	double hmag;
 
 	if ( !g ) {
 		*rp = 0;
 		return 1;
 	}
-	sugar0 = sugar = g->sugar;
+	if ( !mod )
+		hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
+
+	sugar0 = sugar = SG(g);
 	n = NV(g);
 	mul = (NM)ALLOCA(sizeof(struct oNM)+(nd_wpd-1)*sizeof(unsigned int));
 	for ( d = 0; g; ) {
 		index = nd_find_reducer(g);
 		if ( index >= 0 ) {
-			p = nd_ps[index];
-			ndl_sub(HDL(g),HDL(p),mul->dl);
-			mul->td = HTD(g)-HTD(p);
+			h = nd_psh[index];
+			ndl_sub(HDL(g),DL(h),DL(mul));
+			TD(mul) = HTD(g)-TD(h);
 #if 0
-			if ( d && (p->sugar+mul->td) > sugar ) {
+			if ( d && (SG(p)+TD(mul)) > sugar ) {
 				goto afo;				
 			}
 #endif
-			if ( ndl_check_bound2(index,mul->dl) ) {
+			if ( ndl_check_bound2(index,DL(mul)) ) {
 				nd_free(g); nd_free(d);
 				return 0;
 			}
-			c1 = invm(HC(p),nd_mod); c2 = nd_mod-HC(g);
-			DMAR(c1,c2,0,nd_mod,c); C(mul) = c;
-#if USE_NDV
-			ndv_mul_nm(nd_ps[index],mul,ndv_red);
-			g = ndv_add(g,ndv_red);
-			sugar = MAX(sugar,ndv_red->sugar);
-#else
-			red = nd_mul_ind_nm(index,mul);
-			g = nd_add(g,red);
-			sugar = MAX(sugar,red->sugar);
-#endif
+			if ( mod ) {
+				p = nd_ps[index];
+				c1 = invm(HCM(p),mod); c2 = mod-HCM(g);
+				DMAR(c1,c2,0,mod,c); CM(mul) = c;
+			} else {
+				p = nd_psq[index];
+				igcd_cofactor(HCQ(g),HCQ(p),&gcd,&cg,&cred);
+				chsgnq(cg,&CQ(mul));
+				nd_mul_c_q(d,cred); nd_mul_c_q(g,cred);
+			}
+			ndv_mul_nm(mod,p,mul,ndv_red);
+			g = ndv_add(mod,g,ndv_red);
+			sugar = MAX(sugar,SG(ndv_red));
+			if ( !mod && hmag && ((double)(p_mag((P)HCQ(g))) > hmag) ) {
+				nd_removecont2(d,g);
+				hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
+			}
 		} else if ( !full ) {
 			*rp = g;
 			return 1;
@@ -948,7 +861,7 @@ afo:
 		}
 	}
 	if ( d )
-		d->sugar = sugar;
+		SG(d) = sugar;
 	*rp = d;
 	return 1;
 }
@@ -977,23 +890,23 @@ PGeoBucket create_pbucket()
 	return g;
 }
 
-void add_pbucket(PGeoBucket g,ND d)
+void add_pbucket(int mod,PGeoBucket g,ND d)
 {
 	int l,k,m;
 
 	l = nd_length(d);
 	for ( k = 0, m = 1; l > m; k++, m <<= 2 );
 	/* 4^(k-1) < l <= 4^k */
-	d = nd_add(g->body[k],d);
+	d = nd_add(mod,g->body[k],d);
 	for ( ; d && nd_length(d) > 1<<(2*k); k++ ) {
 		g->body[k] = 0;
-		d = nd_add(g->body[k+1],d);
+		d = nd_add(int mod,g->body[k+1],d);
 	}
 	g->body[k] = d;
 	g->m = MAX(g->m,k);
 }
 
-int head_pbucket(PGeoBucket g)
+int head_pbucket(int mod,PGeoBucket g)
 {
 	int j,i,c,k,nv,sum;
 	unsigned int *di,*dj;
@@ -1009,7 +922,7 @@ int head_pbucket(PGeoBucket g)
 				j = i;
 				gj = g->body[j];
 				dj = HDL(gj);
-				sum = HC(gj);
+				sum = HCM(gj);
 			} else {
 				di = HDL(gi);
 				nv = NV(gi);
@@ -1021,17 +934,17 @@ int head_pbucket(PGeoBucket g)
 					c = ndl_compare(di,dj);
 				if ( c > 0 ) {
 					if ( sum )
-						HC(gj) = sum;
+						HCM(gj) = sum;
 					else
 						g->body[j] = nd_remove_head(gj);
 					j = i;
 					gj = g->body[j];
 					dj = HDL(gj);
-					sum = HC(gj);
+					sum = HCM(gj);
 				} else if ( c == 0 ) {
-					sum = sum+HC(gi)-nd_mod;
+					sum = sum+HCM(gi)-mod;
 					if ( sum < 0 )
-						sum += nd_mod;
+						sum += mod;
 					g->body[i] = nd_remove_head(gi);
 				}
 			}
@@ -1039,7 +952,7 @@ int head_pbucket(PGeoBucket g)
 		if ( j < 0 )
 			return -1;
 		else if ( sum ) {
-			HC(gj) = sum;
+			HCM(gj) = sum;
 			return j;
 		} else
 			g->body[j] = nd_remove_head(gj);
@@ -1053,7 +966,7 @@ ND normalize_pbucket(PGeoBucket g)
 
 	r = 0;
 	for ( i = 0; i <= g->m; i++ )
-		r = nd_add(r,g->body[i]);
+		r = nd_add(mod,r,g->body[i]);
 	return r;
 }
 
@@ -1068,8 +981,8 @@ ND nd_nf(ND g,int full)
 	if ( !g ) {
 		return 0;
 	}
-	sugar = g->sugar;
-	n = g->nv;
+	sugar = SG(g);
+	n = NV(g);
 	bucket = create_pbucket();
 	add_pbucket(bucket,g);
 	d = 0;
@@ -1077,7 +990,7 @@ ND nd_nf(ND g,int full)
 		h = head_pbucket(bucket);
 		if ( h < 0 ) {
 			if ( d )
-				d->sugar = sugar;
+				SG(d) = sugar;
 			return d;
 		}
 		g = bucket->body[h];
@@ -1086,11 +999,11 @@ ND nd_nf(ND g,int full)
 			bucket->body[h] = nd_remove_head(g);
 			red = nd_remove_head(red);
 			add_pbucket(bucket,red);
-			sugar = MAX(sugar,red->sugar);
+			sugar = MAX(sugar,SG(red));
 		} else if ( !full ) {
 			g = normalize_pbucket(bucket);
 			if ( g )
-				g->sugar = sugar;
+				SG(g) = sugar;
 			return g;
 		} else {
 			m = BDY(g); 
@@ -1112,7 +1025,7 @@ ND nd_nf(ND g,int full)
 }
 #endif
 
-NODE nd_gb(NODE f)
+NODE nd_gb(int m,NODE f)
 {
 	int i,nh,sugar,stat;
 	NODE r,g,gall;
@@ -1130,24 +1043,24 @@ NODE nd_gb(NODE f)
 	while ( d ) {
 again:
 		l = nd_minp(d,&d);
-		if ( l->sugar != sugar ) {
-			sugar = l->sugar;
+		if ( SG(l) != sugar ) {
+			sugar = SG(l);
 			fprintf(asir_out,"%d",sugar);
 		}
-		stat = nd_sp(l,&h);
+		stat = nd_sp(m,l,&h);
 		if ( !stat ) {
 			NEXT(l) = d; d = l;
-			d = nd_reconstruct(d);
+			d = nd_reconstruct(m,0,d);
 			goto again;
 		}
-		stat = nd_nf(h,!Top,&nf);
+		stat = nd_nf(m,h,!Top,&nf);
 		if ( !stat ) {
 			NEXT(l) = d; d = l;
-			d = nd_reconstruct(d);
+			d = nd_reconstruct(m,0,d);
 			goto again;
 		} else if ( nf ) {
 			printf("+"); fflush(stdout);
-			nh = nd_newps(nf);
+			nh = nd_newps(m,nf);
 			d = update_pairs(d,g,nh);
 			g = update_base(g,nh);
 			gall = append_one(gall,nh);
@@ -1160,6 +1073,60 @@ again:
 	return g;
 }
 
+NODE nd_gb_trace(int m,NODE f)
+{
+	int i,nh,sugar,stat;
+	NODE r,g,gall;
+	ND_pairs d;
+	ND_pairs l;
+	ND h,nf,nfq;
+
+	for ( gall = g = 0, d = 0, r = f; r; r = NEXT(r) ) {
+		i = (int)BDY(r);
+		d = update_pairs(d,g,i);
+		g = update_base(g,i);
+		gall = append_one(gall,i);
+	}
+	sugar = 0;
+	while ( d ) {
+again:
+		l = nd_minp(d,&d);
+		if ( SG(l) != sugar ) {
+			sugar = SG(l);
+			fprintf(asir_out,"%d",sugar);
+		}
+		stat = nd_sp(m,l,&h);
+		if ( !stat ) {
+			NEXT(l) = d; d = l;
+			d = nd_reconstruct(m,1,d);
+			goto again;
+		}
+		stat = nd_nf(m,h,!Top,&nf);
+		if ( !stat ) {
+			NEXT(l) = d; d = l;
+			d = nd_reconstruct(m,1,d);
+			goto again;
+		} else if ( nf ) {
+			/* overflow does not occur */
+			nd_sp(0,l,&h);
+			nd_nf(0,h,!Top,&nfq);
+			if ( nfq ) {
+				printf("+"); fflush(stdout);
+				nh = nd_newps_trace(m,nf,nfq);
+				d = update_pairs(d,g,nh);
+				g = update_base(g,nh);
+				gall = append_one(gall,nh);
+			} else {
+				printf("*"); fflush(stdout);
+			}
+		} else {
+			printf("."); fflush(stdout);
+		}
+		FREENDP(l);
+	}
+	return g;
+}
+
 ND_pairs update_pairs( ND_pairs d, NODE /* of index */ g, int t)
 {
 	ND_pairs d1,nd,cur,head,prev,remove;
@@ -1202,17 +1169,17 @@ ND_pairs nd_newpairs( NODE g, int t )
 	int td,ts,s;
 	ND_pairs r,r0;
 
-	dl = HDL(nd_ps[t]);
-	td = HTD(nd_ps[t]);
-	ts = nd_ps[t]->sugar - td;
+	dl = DL(nd_psh[t]);
+	td = TD(nd_psh[t]);
+	ts = SG(nd_psh[t]) - td;
 	for ( r0 = 0, h = g; h; h = NEXT(h) ) {
 		NEXTND_pairs(r0,r);
 		r->i1 = (int)BDY(h);
 		r->i2 = t;
-		ndl_lcm(HDL(nd_ps[r->i1]),dl,r->lcm);
-		r->td = ndl_td(r->lcm);
-		s = nd_ps[r->i1]->sugar-HTD(nd_ps[r->i1]);
-		r->sugar = MAX(s,ts) + r->td;
+		ndl_lcm(DL(nd_psh[r->i1]),dl,r->lcm);
+		TD(r) = ndl_td(r->lcm);
+		s = SG(nd_psh[r->i1])-TD(nd_psh[r->i1]);
+		SG(r) = MAX(s,ts) + TD(r);
 	}
 	NEXT(r) = 0;
 	return r0;
@@ -1225,15 +1192,15 @@ ND_pairs crit_B( ND_pairs d, int s )
 	int td,tdl;
 
 	if ( !d ) return 0;
-	t = HDL(nd_ps[s]);
+	t = DL(nd_psh[s]);
 	prev = 0;
 	head = cur = d;
 	lcm = (unsigned int *)ALLOCA(nd_wpd*sizeof(unsigned int));
 	while ( cur ) {
 		tl = cur->lcm;
 		if ( ndl_reducible(tl,t)
-			&& (ndl_lcm(HDL(nd_ps[cur->i1]),t,lcm),!ndl_equal(lcm,tl))
-			&& (ndl_lcm(HDL(nd_ps[cur->i2]),t,lcm),!ndl_equal(lcm,tl)) ) {
+			&& (ndl_lcm(DL(nd_psh[cur->i1]),t,lcm),!ndl_equal(lcm,tl))
+			&& (ndl_lcm(DL(nd_psh[cur->i2]),t,lcm),!ndl_equal(lcm,tl)) ) {
 			remove = cur;
 			if ( !prev ) {
 				head = cur = NEXT(cur);
@@ -1261,11 +1228,11 @@ ND_pairs crit_M( ND_pairs d1 )
 			return e;
 		}
 		id = e->lcm;
-		itd = e->td;
+		itd = TD(e);
 		for ( d3 = 0; d2; d2 = p ) {
 			p = NEXT(d2),
 			jd = d2->lcm;
-			jtd = d2->td;
+			jtd = TD(d2);
 			if ( jtd == itd  )
 				if ( id == jd );
 				else if ( ndl_reducible(jd,id) ) continue;
@@ -1302,7 +1269,7 @@ ND_pairs crit_F( ND_pairs d1 )
 
 	for ( head = last = 0, p = d1; NEXT(p); ) {
 		r = w = equivalent_pairs(p,&rest);
-		s = r->sugar;
+		s = SG(r);
 		w = NEXT(w);
 		while ( w ) {
 			if ( crit_2(w->i1,w->i2) ) {
@@ -1314,10 +1281,10 @@ ND_pairs crit_F( ND_pairs d1 )
 					FREENDP(remove);
 				}
 				break;
-			} else if ( w->sugar < s ) {
+			} else if ( SG(w) < s ) {
 				FREENDP(r);
 				r = w;
-				s = r->sugar;
+				s = SG(r);
 				w = NEXT(w);
 			} else {
 				remove = w;
@@ -1338,7 +1305,7 @@ ND_pairs crit_F( ND_pairs d1 )
 
 int crit_2( int dp1, int dp2 )
 {
-	return ndl_disjoint(HDL(nd_ps[dp1]),HDL(nd_ps[dp2]));
+	return ndl_disjoint(DL(nd_psh[dp1]),DL(nd_psh[dp2]));
 }
 
 static ND_pairs equivalent_pairs( ND_pairs d1, ND_pairs *prest )
@@ -1349,12 +1316,12 @@ static ND_pairs equivalent_pairs( ND_pairs d1, ND_pair
 
 	w = d1;
 	d = w->lcm;
-	td = w->td;
+	td = TD(w);
 	s = NEXT(w);
 	NEXT(w) = 0;
 	for ( r = 0; s; s = p ) {
 		p = NEXT(s);
-		if ( td == s->td && ndl_equal(d,s->lcm) ) {
+		if ( td == TD(s) && ndl_equal(d,s->lcm) ) {
 			NEXT(s) = w;
 			w = s;
 		} else {
@@ -1372,11 +1339,11 @@ NODE update_base(NODE nd,int ndp)
 	NODE last, p, head;
 	int td,tdn;
 
-	dl = HDL(nd_ps[ndp]);
-	td = HTD(nd_ps[ndp]);
+	dl = DL(nd_psh[ndp]);
+	td = TD(nd_psh[ndp]);
 	for ( head = last = 0, p = nd; p; ) {
-		dln = HDL(nd_ps[(int)BDY(p)]);
-		tdn = HTD(nd_ps[(int)BDY(p)]);
+		dln = DL(nd_psh[(int)BDY(p)]);
+		tdn = TD(nd_psh[(int)BDY(p)]);
 		if ( tdn >= td && ndl_reducible( dln, dl ) ) {
 			p = NEXT(p);
 			if ( last ) NEXT(last) = p;
@@ -1401,16 +1368,16 @@ ND_pairs nd_minp( ND_pairs d, ND_pairs *prest )
 		return m;
 	}
 	lcm = m->lcm;
-	s = m->sugar;
-	td = m->td;
+	s = SG(m);
+	td = TD(m);
 	len = nd_psl[m->i1]+nd_psl[m->i2];
 	for ( ml = 0, l = m; p; p = NEXT(l = p) ) {
-		if (p->sugar < s)
+		if (SG(p) < s)
 			goto find;
-		else if ( p->sugar == s ) {
-			if ( p->td < td )
+		else if ( SG(p) == s ) {
+			if ( TD(p) < td )
 				goto find;
-			else if ( p->td == td ) {
+			else if ( TD(p) == td ) {
 				c = ndl_compare(p->lcm,lcm);
 				if ( c < 0 )
 					goto find;
@@ -1428,8 +1395,8 @@ find:
 		ml = l;
 		m = p;
 		lcm = m->lcm;
-		s = m->sugar;
-		td = m->td;
+		s = SG(m);
+		td = TD(m);
 		len = tlen;
 	}
 	if ( !ml ) *prest = NEXT(m);
@@ -1441,57 +1408,91 @@ find:
 	return m;
 }
 
-int nd_newps(ND a)
+int nd_newps(int mod,ND a)
 {
 	int len;
-	NM m;
+	RHist r;
+	NDV b;
 
 	if ( nd_psn == nd_pslen ) {
 		nd_pslen *= 2;
 		nd_psl = (int *)REALLOC((char *)nd_psl,nd_pslen*sizeof(int));
-#if USE_NDV
 		nd_ps = (NDV *)REALLOC((char *)nd_ps,nd_pslen*sizeof(NDV));
-#else
-		nd_ps = (ND *)REALLOC((char *)nd_ps,nd_pslen*sizeof(ND));
-#endif
-		nd_psh = (NM *)REALLOC((char *)nd_psh,nd_pslen*sizeof(NM));
+		nd_psq = (NDV *)REALLOC((char *)nd_psq,nd_pslen*sizeof(NDV));
+		nd_psh = (RHist *)REALLOC((char *)nd_psh,nd_pslen*sizeof(RHist));
 		nd_bound = (unsigned int **)
 			REALLOC((char *)nd_bound,nd_pslen*sizeof(unsigned int *));
 	}
-	nd_monic(a);
+	nd_removecont(mod,a);
 	nd_bound[nd_psn] = nd_compute_bound(a);
-	NEWNM(m); m->td = HTD(a); ndl_copy(HDL(a),m->dl); nd_psh[nd_psn] = m;
-#if USE_NDV
-	nd_ps[nd_psn]= ndtondv(a);
-	nd_psl[nd_psn] = len = nd_ps[nd_psn]->len;
+	NEWRHist(r); SG(r) = SG(a); TD(r) = HTD(a); ndl_copy(HDL(a),DL(r)); 
+	nd_psh[nd_psn] = r;
+	b = ndtondv(mod,a);
+	len = LEN(b);
+	if ( mod )
+		nd_ps[nd_psn] = b;
+	else
+		nd_psq[nd_psn] = b;
+	nd_psl[nd_psn] = len;
+	nd_free(a);
 	if ( len > nmv_len ) {
 		nmv_len = 2*len;
 		BDY(ndv_red) = (NMV)REALLOC(BDY(ndv_red),nmv_len*nmv_adv);
 	}
-#else
-	nd_ps[nd_psn] = a;
-	nd_psl[nd_psn] = nd_length(a);
-#endif
 	return nd_psn++;
 }
 
-NODE nd_setup(NODE f)
+int nd_newps_trace(int mod,ND nf,ND nfq)
 {
+	int len;
+	RHist r;
+	NDV b;
+
+	if ( nd_psn == nd_pslen ) {
+		nd_pslen *= 2;
+		nd_psl = (int *)REALLOC((char *)nd_psl,nd_pslen*sizeof(int));
+		nd_ps = (NDV *)REALLOC((char *)nd_ps,nd_pslen*sizeof(NDV));
+		nd_psq = (NDV *)REALLOC((char *)nd_psq,nd_pslen*sizeof(NDV));
+		nd_psh = (RHist *)REALLOC((char *)nd_psh,nd_pslen*sizeof(RHist));
+		nd_bound = (unsigned int **)
+			REALLOC((char *)nd_bound,nd_pslen*sizeof(unsigned int *));
+	}
+	nd_removecont(mod,nf);
+	nd_ps[nd_psn] = ndtondv(mod,nf);
+
+	nd_removecont(0,nfq);
+	nd_psq[nd_psn] = ndtondv(0,nfq);
+
+	nd_bound[nd_psn] = nd_compute_bound(nfq);
+	NEWRHist(r); SG(r) = SG(nf); TD(r) = HTD(nf); ndl_copy(HDL(nf),DL(r)); 
+	nd_psh[nd_psn] = r;
+
+	len = LEN(nd_psq[nd_psn]);
+	nd_psl[nd_psn] = len;
+
+	nd_free(nf); nd_free(nfq);
+	if ( len > nmv_len ) {
+		nmv_len = 2*len;
+		BDY(ndv_red) = (NMV)REALLOC(BDY(ndv_red),nmv_len*nmv_adv);
+	}
+	return nd_psn++;
+}
+
+NODE nd_setup(int mod,NODE f)
+{
 	int i,j,td,len,max;
 	NODE s,s0,f0;
 	unsigned int *d;
-	NM m;
+	RHist r;
+	NDV a;
 
 	nd_found = 0; nd_notfirst = 0; nd_create = 0;
 
 	nd_psn = length(f); nd_pslen = 2*nd_psn;
 	nd_psl = (int *)MALLOC(nd_pslen*sizeof(int));
-#if USE_NDV
 	nd_ps = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
-#else
-	nd_ps = (ND *)MALLOC(nd_pslen*sizeof(ND));
-#endif
-	nd_psh = (NM *)MALLOC(nd_pslen*sizeof(NM));
+	nd_psq = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
+	nd_psh = (RHist *)MALLOC(nd_pslen*sizeof(RHist));
 	nd_bound = (unsigned int **)MALLOC(nd_pslen*sizeof(unsigned int *));
 	for ( max = 0, i = 0, s = f; i < nd_psn; i++, s = NEXT(s) ) {
 		nd_bound[i] = d = dp_compute_bound((DP)BDY(s));
@@ -1499,8 +1500,8 @@ NODE nd_setup(NODE f)
 			max = MAX(d[j],max);
 	}
 	if ( !nd_red )
-		nd_red = (NM *)MALLOC(REDTAB_LEN*sizeof(NM));
-	bzero(nd_red,REDTAB_LEN*sizeof(NM));
+		nd_red = (RHist *)MALLOC(REDTAB_LEN*sizeof(RHist));
+	bzero(nd_red,REDTAB_LEN*sizeof(RHist));
 
 	if ( max < 2 )
 		nd_bpe = 2;
@@ -1514,28 +1515,28 @@ NODE nd_setup(NODE f)
 		nd_bpe = 16;
 	else
 		nd_bpe = 32;
-	
+
 	nd_setup_parameters();
 	nd_free_private_storage();
 	len = 0;
 	for ( i = 0; i < nd_psn; i++, f = NEXT(f) ) {
-#if USE_NDV
-		nd_ps[i] = dptondv((DP)BDY(f));
-		ndv_mul_c(nd_ps[i],invm(HC(nd_ps[i]),nd_mod));
-		len = MAX(len,nd_ps[i]->len);
-#else
-		nd_ps[i] = dptond((DP)BDY(f));
-		nd_mul_c(nd_ps[i],1);
-		nd_psl[i] = nd_length(nd_ps[i]);
-#endif
-		NEWNM(m); m->td = HTD(nd_ps[i]); ndl_copy(HDL(nd_ps[i]),m->dl);
-		nd_psh[i] = m;
+		NEWRHist(r);
+		a = dptondv(mod,(DP)BDY(f));
+		ndv_removecont(mod,a);
+		len = MAX(len,LEN(a));
+		SG(r) = HTD(a); TD(r) = HTD(a); ndl_copy(HDL(a),DL(r));
+		if ( mod )
+			nd_ps[i] = a;
+		else
+			nd_psq[i] = a;
+		nd_psh[i] = r;
 	}
-#if USE_NDV
 	nmv_len = 16*len;
 	NEWNDV(ndv_red);
-	BDY(ndv_red) = (NMV)MALLOC_ATOMIC(nmv_len*nmv_adv);
-#endif
+	if ( mod )
+		BDY(ndv_red) = (NMV)MALLOC_ATOMIC(nmv_len*nmv_adv);
+	else
+		BDY(ndv_red) = (NMV)MALLOC(nmv_len*nmv_adv);
 	for ( s0 = 0, i = 0; i < nd_psn; i++ ) {
 		NEXTNODE(s0,s); BDY(s) = (pointer)i;
 	}
@@ -1543,6 +1544,65 @@ NODE nd_setup(NODE f)
 	return s0;
 }
 
+NODE nd_setup_trace(int mod,NODE f)
+{
+	int i,j,td,len,max;
+	NODE s,s0,f0;
+	unsigned int *d;
+	RHist r;
+	NDV a;
+
+	nd_found = 0; nd_notfirst = 0; nd_create = 0;
+
+	nd_psn = length(f); nd_pslen = 2*nd_psn;
+	nd_psl = (int *)MALLOC(nd_pslen*sizeof(int));
+	nd_ps = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
+	nd_psq = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
+	nd_psh = (RHist *)MALLOC(nd_pslen*sizeof(RHist));
+	nd_bound = (unsigned int **)MALLOC(nd_pslen*sizeof(unsigned int *));
+	for ( max = 0, i = 0, s = f; i < nd_psn; i++, s = NEXT(s) ) {
+		nd_bound[i] = d = dp_compute_bound((DP)BDY(s));
+		for ( j = 0; j < nd_nvar; j++ )
+			max = MAX(d[j],max);
+	}
+	if ( !nd_red )
+		nd_red = (RHist *)MALLOC(REDTAB_LEN*sizeof(RHist));
+	bzero(nd_red,REDTAB_LEN*sizeof(RHist));
+
+	if ( max < 2 )
+		nd_bpe = 2;
+	else if ( max < 4 )
+		nd_bpe = 4;
+	else if ( max < 64 )
+		nd_bpe = 6;
+	else if ( max < 256 )
+		nd_bpe = 8;
+	else if ( max < 65536 )
+		nd_bpe = 16;
+	else
+		nd_bpe = 32;
+
+	nd_setup_parameters();
+	nd_free_private_storage();
+	len = 0;
+	for ( i = 0; i < nd_psn; i++, f = NEXT(f) ) {
+		a = dptondv(mod,(DP)BDY(f)); ndv_removecont(mod,a); nd_ps[i] = a;
+		a = dptondv(0,(DP)BDY(f)); ndv_removecont(0,a); nd_psq[i] = a;
+		NEWRHist(r);
+		len = MAX(len,LEN(a));
+		SG(r) = HTD(a); TD(r) = HTD(a); ndl_copy(HDL(a),DL(r));
+		nd_psh[i] = r;
+	}
+	nmv_len = 16*len;
+	NEWNDV(ndv_red);
+	BDY(ndv_red) = (NMV)MALLOC(nmv_len*nmv_adv);
+	for ( s0 = 0, i = 0; i < nd_psn; i++ ) {
+		NEXTNODE(s0,s); BDY(s) = (pointer)i;
+	}
+	if ( s0 ) NEXT(s) = 0;
+	return s0;
+}
+
 void nd_gr(LIST f,LIST v,int m,struct order_spec *ord,LIST *rp)
 {
 	struct order_spec ord1;
@@ -1565,28 +1625,71 @@ void nd_gr(LIST f,LIST v,int m,struct order_spec *ord,
 			error("nd_gr : unsupported order");
 	}
 	initd(ord);
-	nd_mod = m;
 	for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
 		ptod(CO,vv,(P)BDY(t),&b);
-		_dp_mod(b,m,0,&c);
+		NEXTNODE(fd0,fd); BDY(fd) = (pointer)b;
+	}
+	if ( fd0 ) NEXT(fd) = 0;
+	s = nd_setup(m,fd0);
+	x = nd_gb(m,s);
+#if 0
+	x = nd_reduceall(x,m);
+#endif
+	for ( r0 = 0; x; x = NEXT(x) ) {
+		NEXTNODE(r0,r); 
+		if ( m ) {
+			a = ndvtodp(m,nd_ps[(int)BDY(x)]);
+			_dtop_mod(CO,vv,a,(P *)&BDY(r));
+		} else {
+			a = ndvtodp(m,nd_psq[(int)BDY(x)]);
+			dtop(CO,vv,a,(P *)&BDY(r));
+		}
+	}
+	if ( r0 ) NEXT(r) = 0;
+	MKLIST(*rp,r0);
+	fprintf(asir_out,"found=%d,notfirst=%d,create=%d\n",
+		nd_found,nd_notfirst,nd_create);
+}
+
+void nd_gr_trace(LIST f,LIST v,int m,struct order_spec *ord,LIST *rp)
+{
+	struct order_spec ord1;
+	VL fv,vv,vc;
+	NODE fd,fd0,r,r0,t,x,s,xx;
+	DP a,b,c;
+
+	get_vars((Obj)f,&fv); pltovl(v,&vv);
+	nd_nvar = length(vv);
+	if ( ord->id )
+		error("nd_gr : unsupported order");
+	switch ( ord->ord.simple ) {
+		case 0:
+			is_rlex = 1;
+			break;
+		case 1:
+			is_rlex = 0;
+			break;
+		default:
+			error("nd_gr : unsupported order");
+	}
+	initd(ord);
+	for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
+		ptod(CO,vv,(P)BDY(t),&c);
 		if ( c ) {
 			NEXTNODE(fd0,fd); BDY(fd) = (pointer)c;
 		}
 	}
 	if ( fd0 ) NEXT(fd) = 0;
-	s = nd_setup(fd0);
-	x = nd_gb(s);
+	/* setup over GF(m) */
+	s = nd_setup_trace(m,fd0);
+	x = nd_gb_trace(m,s);
 #if 0
 	x = nd_reduceall(x,m);
 #endif
 	for ( r0 = 0; x; x = NEXT(x) ) {
 		NEXTNODE(r0,r); 
-#if USE_NDV
-		a = ndvtodp(nd_ps[(int)BDY(x)]);
-#else
-		a = ndtodp(nd_ps[(int)BDY(x)]);
-#endif
-		_dtop_mod(CO,vv,a,(P *)&BDY(r));
+		a = ndvtodp(0,nd_psq[(int)BDY(x)]);
+		dtop(CO,vv,a,(P *)&BDY(r));
 	}
 	if ( r0 ) NEXT(r) = 0;
 	MKLIST(*rp,r0);
@@ -1616,7 +1719,7 @@ DL ndltodl(int n,int td,unsigned int *ndl)
 	int i;
 
 	NEWDL(dl,n);
-	dl->td = td;
+	TD(dl) = td;
 	d = dl->d;
 	if ( is_rlex )
 		for ( i = 0; i < n; i++ )
@@ -1629,7 +1732,7 @@ DL ndltodl(int n,int td,unsigned int *ndl)
 	return dl;
 }
 
-ND dptond(DP p)
+ND dptond(int mod,DP p)
 {
 	ND d;
 	NM m0,m;
@@ -1642,18 +1745,21 @@ ND dptond(DP p)
 	m0 = 0;
 	for ( t = BDY(p); t; t = NEXT(t) ) {
 		NEXTNM(m0,m);
-		m->c = ITOS(t->c);
-		m->td = t->dl->td;
-		dltondl(n,t->dl,m->dl);
+		if ( mod )
+			CM(m) = ITOS(C(t));
+		else
+			CQ(m) = (Q)C(t);
+		TD(m) = TD(DL(t));
+		dltondl(n,DL(t),DL(m));
 	}
 	NEXT(m) = 0;
 	MKND(n,m0,d);
-	d->nv = n;
-	d->sugar = p->sugar;
+	NV(d) = n;
+	SG(d) = SG(p);
 	return d;
 }
 
-DP ndtodp(ND p)
+DP ndtodp(int mod,ND p)
 {
 	DP d;
 	MP m0,m;
@@ -1666,12 +1772,15 @@ DP ndtodp(ND p)
 	m0 = 0;
 	for ( t = BDY(p); t; t = NEXT(t) ) {
 		NEXTMP(m0,m);
-		m->c = STOI(t->c);
-		m->dl = ndltodl(n,t->td,t->dl);
+		if ( mod )
+			C(m) = STOI(CM(t));
+		else
+			C(m) = (P)CQ(t);
+		DL(m) = ndltodl(n,TD(t),DL(t));
 	}
 	NEXT(m) = 0;
 	MKDP(n,m0,d);
-	d->sugar = p->sugar;
+	SG(d) = SG(p);
 	return d;
 }
 
@@ -1703,13 +1812,30 @@ void nd_print(ND p)
 		printf("0\n");
 	else {
 		for ( m = BDY(p); m; m = NEXT(m) ) {
-			printf("+%d*",m->c);
-			ndl_print(m->dl);
+			printf("+%d*",CM(m));
+			ndl_print(DL(m));
 		}
 		printf("\n");
 	}
 }
 
+void nd_print_q(ND p)
+{
+	NM m;
+
+	if ( !p )
+		printf("0\n");
+	else {
+		for ( m = BDY(p); m; m = NEXT(m) ) {
+			printf("+");
+			printexpr(CO,CQ(m));
+			printf("*");
+			ndl_print(DL(m));
+		}
+		printf("\n");
+	}
+}
+
 void ndp_print(ND_pairs d)
 {
 	ND_pairs t;
@@ -1720,25 +1846,141 @@ void ndp_print(ND_pairs d)
 	printf("\n");
 }
 
-void nd_monic(ND p)
+void nd_removecont(int mod,ND p)
 {
+	int i,n;
+	Q *w;
+	Q dvr,t;
+	NM m;
+	struct oVECT v;
+	N q,r;
+
+	if ( mod )
+		nd_mul_c(mod,p,invm(HCM(p),mod));
+	else {
+		for ( m = BDY(p), n = 0; m; m = NEXT(m), n++ );
+		w = (Q *)ALLOCA(n*sizeof(Q));
+		v.len = n;
+		v.body = (pointer *)w;
+		for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ )
+			w[i] = CQ(m);
+		removecont_array(w,n);
+		for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) CQ(m) = w[i];	
+	}
+}
+
+void nd_removecont2(ND p1,ND p2)
+{
+	int i,n1,n2,n;
+	Q *w;
+	Q dvr,t;
+	NM m;
+	struct oVECT v;
+	N q,r;
+
+	if ( !p1 ) {
+		nd_removecont(0,p2); return;
+	} else if ( !p2 ) {
+		nd_removecont(0,p1); return;
+	}
+	n1 = nd_length(p1);
+	n2 = nd_length(p2);
+	n = n1+n2;
+	w = (Q *)ALLOCA(n*sizeof(Q));
+	v.len = n;
+	v.body = (pointer *)w;
+	for ( m = BDY(p1), i = 0; i < n1; m = NEXT(m), i++ )
+		w[i] = CQ(m);
+	for ( m = BDY(p2); i < n; m = NEXT(m), i++ )
+		w[i] = CQ(m);
+	removecont_array(w,n);
+	for ( m = BDY(p1), i = 0; i < n1; m = NEXT(m), i++ ) CQ(m) = w[i];	
+	for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) CQ(m) = w[i];	
+}
+
+void ndv_removecont(int mod,NDV p)
+{
+	int i,len;
+	Q *w;
+	Q dvr,t;
+	NMV m;
+
+	if ( mod )
+		ndv_mul_c(mod,p,invm(HCM(p),mod));
+	else {
+		len = p->len;
+		w = (Q *)ALLOCA(len*sizeof(Q));
+		for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ )
+			w[i] = CQ(m);
+		sortbynm(w,len);
+		qltozl(w,len,&dvr);
+		for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ ) {
+			divq(CQ(m),dvr,&t); CQ(m) = t;
+		}
+	}
+}
+
+void removecont_array(Q *c,int n)
+{
+	struct oVECT v;
+	Q d0,d1,a,u,u1,gcd;
+	int i;
+	N qn,rn,gn;
+	Q *q,*r;
+
+	q = (Q *)ALLOCA(n*sizeof(Q));
+	r = (Q *)ALLOCA(n*sizeof(Q));
+	v.id = O_VECT; v.len = n; v.body = (pointer *)c;
+	igcdv_estimate(&v,&d0);
+	for ( i = 0; i < n; i++ ) {
+		divn(NM(c[i]),NM(d0),&qn,&rn);
+		NTOQ(qn,SGN(c[i])*SGN(d0),q[i]);
+		NTOQ(rn,SGN(c[i]),r[i]);
+	}
+	for ( i = 0; i < n; i++ )
+		if ( r[i] )
+			break;
+	if ( i < n ) {
+		v.id = O_VECT; v.len = n; v.body = (pointer *)r;
+		igcdv(&v,&d1);
+		gcdn(NM(d0),NM(d1),&gn); NTOQ(gn,1,gcd);
+		divsn(NM(d0),gn,&qn); NTOQ(qn,1,a);
+		for ( i = 0; i < n; i++ ) {
+			mulq(a,q[i],&u);
+			if ( r[i] ) {
+				divsn(NM(r[i]),gn,&qn); NTOQ(qn,SGN(r[i]),u1);
+				addq(u,u1,&q[i]);
+			} else
+				q[i] = u;
+		}
+	}
+	for ( i = 0; i < n; i++ )
+		c[i] = q[i];
+}
+
+void nd_mul_c(int mod,ND p,int mul)
+{
+	NM m;
+	int c,c1;
+
 	if ( !p )
 		return;
-	else
-		nd_mul_c(p,invm(HC(p),nd_mod));
+	for ( m = BDY(p); m; m = NEXT(m) ) {
+		c1 = CM(m);
+		DMAR(c1,mul,0,mod,c);
+		CM(m) = c;
+	}
 }
 
-void nd_mul_c(ND p,int mul)
+void nd_mul_c_q(ND p,Q mul)
 {
 	NM m;
-	int c,c1;
+	Q c;
 
 	if ( !p )
 		return;
 	for ( m = BDY(p); m; m = NEXT(m) ) {
-		c1 = C(m);
-		DMAR(c1,mul,0,nd_mod,c);
-		C(m) = c;
+		mulq(CQ(m),mul,&c); CQ(m) = c;
 	}
 }
 
@@ -1759,14 +2001,14 @@ void nd_free(ND p)
 
 void nd_append_red(unsigned int *d,int td,int i)
 {
-	NM m,m0;
+	RHist m,m0;
 	int h;
 
-	NEWNM(m);
+	NEWRHist(m);
 	h = ndl_hash_value(td,d);
-	m->c = i;
-	m->td = td;
-	ndl_copy(d,m->dl);
+	m->index = i;
+	TD(m) = td;
+	ndl_copy(d,DL(m));
 	NEXT(m) = nd_red[h];
 	nd_red[h] = m;
 }
@@ -1782,15 +2024,14 @@ unsigned int *dp_compute_bound(DP p)
 	d1 = (unsigned int *)ALLOCA(nd_nvar*sizeof(unsigned int));
 	d2 = (unsigned int *)ALLOCA(nd_nvar*sizeof(unsigned int));
 	m = BDY(p);
-	bcopy(m->dl->d,d1,nd_nvar*sizeof(unsigned int));
+	bcopy(DL(m)->d,d1,nd_nvar*sizeof(unsigned int));
 	for ( m = NEXT(BDY(p)); m; m = NEXT(m) ) {
-		d = m->dl->d;
+		d = DL(m)->d;
 		for ( i = 0; i < nd_nvar; i++ )
 			d2[i] = d[i] > d1[i] ? d[i] : d1[i];
 		t = d1; d1 = d2; d2 = t;
 	}
-	l = ((nd_nvar+(sizeof(unsigned int)-1))
-		/sizeof(unsigned int))*sizeof(unsigned int);
+	l = (nd_nvar+31);
 	t = (unsigned int *)MALLOC_ATOMIC(l*sizeof(unsigned int));
 	bzero(t,l*sizeof(unsigned int));
 	bcopy(d1,t,nd_nvar*sizeof(unsigned int));
@@ -1809,11 +2050,10 @@ unsigned int *nd_compute_bound(ND p)
 	d2 = (unsigned int *)ALLOCA(nd_wpd*sizeof(unsigned int));
 	bcopy(HDL(p),d1,nd_wpd*sizeof(unsigned int));
 	for ( m = NEXT(BDY(p)); m; m = NEXT(m) ) {
-		ndl_lcm(m->dl,d1,d2);
+		ndl_lcm(DL(m),d1,d2);
 		t = d1; d1 = d2; d2 = t;
 	}
-	l = ((nd_nvar+(sizeof(unsigned int)-1))
-		/sizeof(unsigned int))*sizeof(unsigned int);
+	l = nd_nvar+31;
 	t = (unsigned int *)MALLOC_ATOMIC(l*sizeof(unsigned int));
 	bzero(t,l*sizeof(unsigned int));
 	for ( i = 0; i < nd_nvar; i++ )
@@ -1837,21 +2077,22 @@ void nd_setup_parameters() {
 		nd_mask[nd_epw-i-1] = (nd_mask0<<(i*nd_bpe));
 		nd_mask1 |= (1<<(nd_bpe-1))<<(i*nd_bpe);
 	}
-#if USE_NDV
+	nm_adv = sizeof(struct oNM)+(nd_wpd-1)*sizeof(unsigned int);
 	nmv_adv = sizeof(struct oNMV)+(nd_wpd-1)*sizeof(unsigned int);
-#endif
 }
 
-ND_pairs nd_reconstruct(ND_pairs d)
+/* mod < 0 => realloc nd_ps and pd_psq */
+
+ND_pairs nd_reconstruct(int mod,int trace,ND_pairs d)
 {
 	int i,obpe,oadv;
-	NM prev_nm_free_list,mr0,mr,m;
+	NM prev_nm_free_list;
+	RHist mr0,mr;
+	RHist r;
 	ND_pairs s0,s,t,prev_ndp_free_list;
-	
+
 	obpe = nd_bpe;
-#if USE_NDV
 	oadv = nmv_adv;
-#endif
 	if ( obpe < 4 )
 		nd_bpe = 4;
 	else if ( obpe < 6 )
@@ -1870,42 +2111,41 @@ ND_pairs nd_reconstruct(ND_pairs d)
 	prev_ndp_free_list = _ndp_free_list;
 	_nm_free_list = 0;
 	_ndp_free_list = 0;
-	for ( i = 0; i < nd_psn; i++ ) {
-#if USE_NDV
-		ndv_realloc(nd_ps[i],obpe,oadv);
-#else
-		nd_realloc(nd_ps[i],obpe);
-#endif
-	}
+	if ( mod != 0 )
+		for ( i = nd_psn-1; i >= 0; i-- )
+			ndv_realloc(nd_ps[i],obpe,oadv);
+	if ( !mod || trace )
+		for ( i = nd_psn-1; i >= 0; i-- )
+			ndv_realloc(nd_psq[i],obpe,oadv);
 	s0 = 0;
 	for ( t = d; t; t = NEXT(t) ) {
 		NEXTND_pairs(s0,s);
 		s->i1 = t->i1;
 		s->i2 = t->i2;
-		s->td = t->td;
-		s->sugar = t->sugar;
+		TD(s) = TD(t);
+		SG(s) = SG(t);
 		ndl_dup(obpe,t->lcm,s->lcm);
 	}
 	for ( i = 0; i < REDTAB_LEN; i++ ) {
-		for ( mr0 = 0, m = nd_red[i]; m; m = NEXT(m) ) {
-			NEXTNM(mr0,mr);
-			mr->c = m->c;
-			mr->td = m->td;
-			ndl_dup(obpe,m->dl,mr->dl);
+		for ( mr0 = 0, r = nd_red[i]; r; r = NEXT(r) ) {
+			NEXTRHist(mr0,mr);
+			mr->index = r->index;
+			SG(mr) = SG(r);
+			TD(mr) = TD(r);
+			ndl_dup(obpe,DL(r),DL(mr));
 		}
 		if ( mr0 ) NEXT(mr) = 0;
 		nd_red[i] = mr0;
 	}
 	for ( i = 0; i < nd_psn; i++ ) {
-		NEWNM(m); m->td = nd_psh[i]->td; ndl_dup(obpe,nd_psh[i]->dl,m->dl);
-		nd_psh[i] = m;
+		NEWRHist(r); SG(r) = SG(nd_psh[i]);
+		TD(r) = TD(nd_psh[i]); ndl_dup(obpe,DL(nd_psh[i]),DL(r));
+		nd_psh[i] = r;
 	}
 	if ( s0 ) NEXT(s) = 0;
 	prev_nm_free_list = 0;
 	prev_ndp_free_list = 0;
-#if USE_NDV
 	BDY(ndv_red) = (NMV)REALLOC(BDY(ndv_red),nmv_len*nmv_adv);
-#endif
 	GC_gcollect();
 	return s0;
 }
@@ -1918,6 +2158,8 @@ void ndl_dup(int obpe,unsigned int *d,unsigned int *r)
 	oepw = (sizeof(unsigned int)*8)/obpe;
 	cepw = nd_epw;
 	cbpe = nd_bpe;
+	for ( i = 0; i < nd_wpd; i++ )
+		r[i] = 0;
 	if ( is_rlex )
 		for ( i = 0; i < n; i++ ) {
 			ei = (d[(n-1-i)/oepw]>>((oepw-((n-1-i)%oepw)-1)*obpe))
@@ -1940,9 +2182,9 @@ void nd_realloc(ND p,int obpe)
 		m = BDY(p);
 		for ( mr0 = 0; m; m = NEXT(m) ) {
 			NEXTNM(mr0,mr);
-			C(mr) = C(m);
-			mr->td = m->td;
-			ndl_dup(obpe,m->dl,mr->dl);
+			CM(mr) = CM(m);
+			TD(mr) = TD(m);
+			ndl_dup(obpe,DL(m),DL(mr));
 		}
 		NEXT(mr) = 0; 
 		BDY(p) = mr0;
@@ -1961,19 +2203,18 @@ ND nd_copy(ND p)
 		s = sizeof(struct oNM)+(nd_wpd-1)*sizeof(unsigned int);
 		for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
 			NEXTNM(mr0,mr);
-			C(mr) = C(m);
-			mr->td = m->td;
-			ndl_copy(m->dl,mr->dl);
+			CM(mr) = CM(m);
+			TD(mr) = TD(m);
+			ndl_copy(DL(m),DL(mr));
 		}
 		NEXT(mr) = 0; 
 		MKND(NV(p),mr0,r);
-		r->sugar = p->sugar;
+		SG(r) = SG(p);
 		return r;
 	}
 }
 
-#if USE_NDV
-int nd_sp(ND_pairs p,ND *rp)
+int nd_sp(int mod,ND_pairs p,ND *rp)
 {
 	NM m;
 	NDV p1,p2;
@@ -1981,117 +2222,171 @@ int nd_sp(ND_pairs p,ND *rp)
 	unsigned int *lcm;
 	int td;
 
-	p1 = nd_ps[p->i1];
-	p2 = nd_ps[p->i2];
+	if ( mod ) {
+		p1 = nd_ps[p->i1]; p2 = nd_ps[p->i2];
+	} else {
+		p1 = nd_psq[p->i1]; p2 = nd_psq[p->i2];
+	}
 	lcm = p->lcm;
-	td = p->td;
+	td = TD(p);
 	NEWNM(m);
-	C(m) = HC(p2); m->td = td-HTD(p1); ndl_sub(lcm,HDL(p1),m->dl);
-	if ( ndl_check_bound2(p->i1,m->dl) )
+	CQ(m) = HCQ(p2);
+	TD(m) = td-HTD(p1); ndl_sub(lcm,HDL(p1),DL(m));
+	if ( ndl_check_bound2(p->i1,DL(m)) )
 		return 0;
-	t1 = ndv_mul_nm_create(p1,m);
-	C(m) = nd_mod-HC(p1); m->td = td-HTD(p2); ndl_sub(lcm,HDL(p2),m->dl);
-	if ( ndl_check_bound2(p->i2,m->dl) ) {
+	t1 = ndv_mul_nm_create(mod,p1,m);
+	if ( mod )
+		CM(m) = mod-HCM(p1); 
+	else
+		chsgnq(HCQ(p1),&CQ(m));
+	TD(m) = td-HTD(p2); ndl_sub(lcm,HDL(p2),DL(m));
+	if ( ndl_check_bound2(p->i2,DL(m)) ) {
 		nd_free(t1);
 		return 0;
 	}
-	ndv_mul_nm(p2,m,ndv_red);
+	ndv_mul_nm(mod,p2,m,ndv_red);
 	FREENM(m);
-	*rp = ndv_add(t1,ndv_red);
+	*rp = ndv_add(mod,t1,ndv_red);
 	return 1;
 }
 
-void ndv_mul_c(NDV p,int mul)
+void ndv_mul_c(int mod,NDV p,int mul)
 {
 	NMV m;
 	int c,c1,len,i;
 
 	if ( !p )
 		return;
-	len = p->len;
+	len = LEN(p);
 	for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
-		c1 = C(m);
-		DMAR(c1,mul,0,nd_mod,c);
-		C(m) = c;
+		c1 = CM(m);
+		DMAR(c1,mul,0,mod,c);
+		CM(m) = c;
 	}
 }
 
-void ndv_mul_nm(NDV p,NM m0,NDV r)
+void ndv_mul_c_q(NDV p,Q mul)
 {
+	NMV m;
+	Q c;
+	int len,i;
+
+	if ( !p )
+		return;
+	len = LEN(p);
+	for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
+		mulq(CQ(m),mul,&c); CQ(m) = c;
+	}
+}
+
+void ndv_mul_nm(int mod,NDV p,NM m0,NDV r)
+{
 	NMV m,mr,mr0;
 	unsigned int *d,*dt,*dm;
 	int c,n,td,i,c1,c2,len;
+	Q q;
 
 	if ( !p )
 		/* XXX */
-		r->len = 0;
+		LEN(r) = 0;
 	else {
-		n = NV(p); m = BDY(p); len = p->len;
-		d = m0->dl; td = m0->td; c = C(m0);
+		n = NV(p); m = BDY(p); len = LEN(p);
+		d = DL(m0); td = TD(m0);
 		mr = BDY(r);
-		for ( ; len > 0; len--, NMV_ADV(m), NMV_ADV(mr) ) {
-			c1 = C(m); DMAR(c1,c,0,nd_mod,c2); C(mr) = c2;
-			mr->td = m->td+td; ndl_add(m->dl,d,mr->dl);
+		if ( mod ) {
+			c = CM(m0);
+			for ( ; len > 0; len--, NMV_ADV(m), NMV_ADV(mr) ) {
+				c1 = CM(m); DMAR(c1,c,0,mod,c2); CM(mr) = c2;
+				TD(mr) = TD(m)+td; ndl_add(DL(m),d,DL(mr));
+			}
+		} else {
+			q = CQ(m0);
+			for ( ; len > 0; len--, NMV_ADV(m), NMV_ADV(mr) ) {
+				mulq(CQ(m),q,&CQ(mr));
+				TD(mr) = TD(m)+td; ndl_add(DL(m),d,DL(mr));
+			}
 		}
 		NV(r) = NV(p);
-		r->len = p->len;
-		r->sugar = p->sugar + td;
+		LEN(r) = LEN(p);
+		SG(r) = SG(p) + td;
 	}
 }
 
-ND ndv_mul_nm_create(NDV p,NM m0)
+ND ndv_mul_nm_create(int mod,NDV p,NM m0)
 {
 	NM mr,mr0;
 	NMV m;
 	unsigned int *d,*dt,*dm;
 	int c,n,td,i,c1,c2,len;
+	Q q;
 	ND r;
 
 	if ( !p )
 		return 0;
 	else {
 		n = NV(p); m = BDY(p);
-		d = m0->dl; td = m0->td; c = C(m0);
-		len = p->len;
+		d = DL(m0); td = TD(m0); 
+		len = LEN(p);
 		mr0 = 0;
-		for ( i = 0; i < len; i++, NMV_ADV(m) ) {
-			NEXTNM(mr0,mr);
-			c1 = C(m);
-			DMAR(c1,c,0,nd_mod,c2);
-			C(mr) = c2;
-			mr->td = m->td+td;
-			ndl_add(m->dl,d,mr->dl);
+		if ( mod ) {
+			c = CM(m0);
+			for ( i = 0; i < len; i++, NMV_ADV(m) ) {
+				NEXTNM(mr0,mr);
+				c1 = CM(m);
+				DMAR(c1,c,0,mod,c2);
+				CM(mr) = c2;
+				TD(mr) = TD(m)+td;
+				ndl_add(DL(m),d,DL(mr));
+			}
+		} else {
+			q = CQ(m0);
+			for ( i = 0; i < len; i++, NMV_ADV(m) ) {
+				NEXTNM(mr0,mr);
+				mulq(CQ(m),q,&CQ(mr));
+				TD(mr) = TD(m)+td;
+				ndl_add(DL(m),d,DL(mr));
+			}
 		}
 		NEXT(mr) = 0; 
 		MKND(NV(p),mr0,r);
-		r->sugar = p->sugar + td;
+		SG(r) = SG(p) + td;
 		return r;
 	}
 }
 
-ND ndv_add(ND p1,NDV p2)
+ND ndv_add(int mod,ND p1,NDV p2)
 {
 	register NM prev,cur,new;
 	int c,c1,c2,t,td,td2,mul,len,i;
 	NM head;
 	unsigned int *d;
 	NMV m2;
+	Q q;
 
 	if ( !p1 )
 		return 0;
+	else if ( !mod )
+		return ndv_add_q(p1,p2);
 	else {
 		prev = 0; head = cur = BDY(p1);
-		NEWNM(new); len = p2->len;
+		NEWNM(new); len = LEN(p2);
 		for ( m2 = BDY(p2), i = 0; cur && i < len; ) {
-			td2 = new->td = m2->td;
-			if ( cur->td > td2 ) c = 1;
-			else if ( cur->td < td2 ) c = -1;
-			else c = ndl_compare(cur->dl,m2->dl);
+			td2 = TD(new) = TD(m2);
+			if ( TD(cur) > td2 ) {
+				prev = cur; cur = NEXT(cur);
+				continue;
+			} else if ( TD(cur) < td2 ) c = -1;
+			else if ( nd_wpd == 1 ) {
+				if ( DL(cur)[0] > DL(m2)[0] ) c = is_rlex ? -1 : 1;
+				else if ( DL(cur)[0] < DL(m2)[0] ) c = is_rlex ? 1 : -1;
+				else c = 0;
+			}
+			else c = ndl_compare(DL(cur),DL(m2));
 			switch ( c ) {
 				case 0:
-					t = C(m2)+C(cur)-nd_mod;
-					if ( t < 0 ) t += nd_mod;
-					if ( t ) C(cur) = t;
+					t = CM(m2)+CM(cur)-mod;
+					if ( t < 0 ) t += mod;
+					if ( t ) CM(cur) = t;
 					else if ( !prev ) {
 						head = NEXT(cur); FREENM(cur); cur = head;
 					} else {
@@ -2103,8 +2398,8 @@ ND ndv_add(ND p1,NDV p2)
 					prev = cur; cur = NEXT(cur);
 					break;
 				case -1:
-					ndl_copy(m2->dl,new->dl);
-					C(new) = C(m2);
+					ndl_copy(DL(m2),DL(new));
+					CQ(new) = CQ(m2);
 					if ( !prev ) {
 						/* cur = head */
 						prev = new; NEXT(prev) = head; head = prev;
@@ -2116,7 +2411,7 @@ ND ndv_add(ND p1,NDV p2)
 			}
 		}
 		for ( ; i < len; i++, NMV_ADV(m2) ) {
-			td2 = new->td = m2->td; C(new) = C(m2); ndl_copy(m2->dl,new->dl);
+			td2 = TD(new) = TD(m2); CQ(new) = CQ(m2); ndl_copy(DL(m2),DL(new));
 			if ( !prev ) {
 				prev = new; NEXT(prev) = 0; head = prev;
 			} else {
@@ -2126,7 +2421,7 @@ ND ndv_add(ND p1,NDV p2)
 		}
 		FREENM(new);
 		if ( head ) {
-			BDY(p1) = head; p1->sugar = MAX(p1->sugar,p2->sugar);
+			BDY(p1) = head; SG(p1) = MAX(SG(p1),SG(p2));
 			return p1;
 		} else {
 			FREEND(p1);
@@ -2136,27 +2431,112 @@ ND ndv_add(ND p1,NDV p2)
 	}
 }
 
+ND ndv_add_q(ND p1,NDV p2)
+{
+	register NM prev,cur,new;
+	int c,c1,c2,t,td,td2,mul,len,i;
+	NM head;
+	unsigned int *d;
+	NMV m2;
+	Q q;
+
+	if ( !p1 )
+		return 0;
+	else {
+		prev = 0; head = cur = BDY(p1);
+		NEWNM(new); len = LEN(p2);
+		for ( m2 = BDY(p2), i = 0; cur && i < len; ) {
+			td2 = TD(new) = TD(m2);
+			if ( TD(cur) > td2 ) {
+				prev = cur; cur = NEXT(cur);
+				continue;
+			} else if ( TD(cur) < td2 ) c = -1;
+			else if ( nd_wpd == 1 ) {
+				if ( DL(cur)[0] > DL(m2)[0] ) c = is_rlex ? -1 : 1;
+				else if ( DL(cur)[0] < DL(m2)[0] ) c = is_rlex ? 1 : -1;
+				else c = 0;
+			}
+			else c = ndl_compare(DL(cur),DL(m2));
+			switch ( c ) {
+				case 0:
+					addq(CQ(cur),CQ(m2),&q);
+					if ( q )
+						CQ(cur) = q;
+					else if ( !prev ) {
+						head = NEXT(cur); FREENM(cur); cur = head;
+					} else {
+						NEXT(prev) = NEXT(cur); FREENM(cur); cur = NEXT(prev);
+					}
+					NMV_ADV(m2); i++;
+					break;
+				case 1:
+					prev = cur; cur = NEXT(cur);
+					break;
+				case -1:
+					ndl_copy(DL(m2),DL(new));
+					CQ(new) = CQ(m2);
+					if ( !prev ) {
+						/* cur = head */
+						prev = new; NEXT(prev) = head; head = prev;
+					} else {
+						NEXT(prev) = new; NEXT(new) = cur; prev = new;
+					}
+					NEWNM(new); NMV_ADV(m2); i++;
+					break;
+			}
+		}
+		for ( ; i < len; i++, NMV_ADV(m2) ) {
+			td2 = TD(new) = TD(m2); CQ(new) = CQ(m2); ndl_copy(DL(m2),DL(new));
+			if ( !prev ) {
+				prev = new; NEXT(prev) = 0; head = prev;
+			} else {
+				NEXT(prev) = new; NEXT(new) = 0; prev = new;
+			}
+			NEWNM(new);
+		}
+		FREENM(new);
+		if ( head ) {
+			BDY(p1) = head; SG(p1) = MAX(SG(p1),SG(p2));
+			return p1;
+		} else {
+			FREEND(p1);
+			return 0;
+		}
+			
+	}
+}
+
 void ndv_realloc(NDV p,int obpe,int oadv)
 {
-	NMV m,mr,mr0;
-	int len,i;
+	NMV m,mr,mr0,t;
+	int len,i,k;
 
-#define NMV_OADV(m) (m = (NMV)(((char *)m)+oadv))
+#define NMV_OPREV(m) (m = (NMV)(((char *)m)-oadv))
+#define NMV_PREV(m) (m = (NMV)(((char *)m)-nmv_adv))
 
 	if ( p ) {
-		m = BDY(p); len = p->len;
-		mr0 = mr = (NMV)MALLOC_ATOMIC(len*nmv_adv);
-		bzero(mr0,len*nmv_adv);
-		for ( i = 0; i < len; i++, NMV_OADV(m), NMV_ADV(mr) ) {
-			C(mr) = C(m);
-			mr->td = m->td;
-			ndl_dup(obpe,m->dl,mr->dl);
+		m = BDY(p); len = LEN(p);
+		if ( nmv_adv > oadv )
+			mr0 = (NMV)REALLOC(BDY(p),len*nmv_adv);
+		else
+			mr0 = BDY(p);
+		m = (NMV)((char *)mr0+(len-1)*oadv);
+		mr = (NMV)((char *)mr0+(len-1)*nmv_adv);
+		t = (NMV)ALLOCA(nmv_adv);
+		for ( i = 0; i < len; i++, NMV_OPREV(m), NMV_PREV(mr) ) {
+			CQ(t) = CQ(m);
+			TD(t) = TD(m);
+			for ( k = 0; k < nd_wpd; k++ ) DL(t)[k] = 0;
+			ndl_dup(obpe,DL(m),DL(t));
+			CQ(mr) = CQ(t);
+			TD(mr) = TD(t);
+			ndl_copy(DL(t),DL(mr));
 		}
 		BDY(p) = mr0;
 	}
 }
 
-NDV ndtondv(ND p)
+NDV ndtondv(int mod,ND p)
 {
 	NDV d;
 	NMV m,m0;
@@ -2166,40 +2546,51 @@ NDV ndtondv(ND p)
 	if ( !p )
 		return 0;
 	len = nd_length(p);	
-	m0 = m = (NMV)MALLOC_ATOMIC(len*nmv_adv);
+	if ( mod )
+		m0 = m = (NMV)MALLOC_ATOMIC(len*nmv_adv);
+	else
+		m0 = m = (NMV)MALLOC(len*nmv_adv);
 	for ( t = BDY(p), i = 0; t; t = NEXT(t), i++, NMV_ADV(m) ) {
-		m->td = t->td;
-		ndl_copy(t->dl,m->dl);
-		m->c = t->c;
+		TD(m) = TD(t);
+		ndl_copy(DL(t),DL(m));
+		CQ(m) = CQ(t);
 	}
 	MKNDV(NV(p),m0,len,d);
-	d->sugar = p->sugar;
+	SG(d) = SG(p);
 	return d;
 }
 
-NDV dptondv(DP p)
+NDV dptondv(int mod,DP p)
 {
 	NDV d;
 	NMV m0,m;
 	MP t;
+	DP q;
 	int l,i,n;
 
 	if ( !p )
 		return 0;
 	for ( t = BDY(p), l = 0; t; t = NEXT(t), l++ );
-	m0 = m = (NMV)MALLOC_ATOMIC(l*nmv_adv);
+	if ( mod ) {
+		_dp_mod(p,mod,0,&q); p = q;
+		m0 = m = (NMV)MALLOC_ATOMIC(l*nmv_adv);
+	} else
+		m0 = m = (NMV)MALLOC(l*nmv_adv);
 	n = NV(p);
 	for ( t = BDY(p), i = 0; i < l; i++, t = NEXT(t), NMV_ADV(m) ) {
-		m->c = ITOS(t->c);
-		m->td = t->dl->td;
-		dltondl(n,t->dl,m->dl);
+		if ( mod )
+			CM(m) = ITOS(C(t));
+		else
+			CQ(m) = (Q)C(t);
+		TD(m) = TD(DL(t));
+		dltondl(n,DL(t),DL(m));
 	}
 	MKNDV(n,m0,l,d);
-	d->sugar = p->sugar;
+	SG(d) = SG(p);
 	return d;
 }
 
-DP ndvtodp(NDV p)
+DP ndvtodp(int mod,NDV p)
 {
 	DP d;
 	MP m0,m;
@@ -2209,16 +2600,19 @@ DP ndvtodp(NDV p)
 	if ( !p )
 		return 0;
 	m0 = 0;
-	len = p->len;
+	len = LEN(p);
 	n = NV(p);
 	for ( t = BDY(p), i = 0; i < len; i++, NMV_ADV(t) ) {
 		NEXTMP(m0,m);
-		m->c = STOI(t->c);
-		m->dl = ndltodl(n,t->td,t->dl);
+		if ( mod ) 
+			C(m) = STOI(CM(t));
+		else
+			C(m) = (P)CQ(t);
+		DL(m) = ndltodl(n,TD(t),DL(t));
 	}
 	NEXT(m) = 0;
 	MKDP(NV(p),m0,d);
-	d->sugar = p->sugar;
+	SG(d) = SG(p);
 	return d;
 }
 
@@ -2230,126 +2624,30 @@ void ndv_print(NDV p)
 	if ( !p )
 		printf("0\n");
 	else {
-		len = p->len;
+		len = LEN(p);
 		for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
-			printf("+%d*",m->c);
-			ndl_print(m->dl);
+			printf("+%d*",CM(m));
+			ndl_print(DL(m));
 		}
 		printf("\n");
 	}
 }
-#else
-int nd_sp(ND_pairs p,ND *rp)
-{
-	NM m;
-	ND p1,p2;
-	ND t1,t2;
-	unsigned int *lcm;
-	int td;
 
-	p1 = nd_ps[p->i1];
-	p2 = nd_ps[p->i2];
-	lcm = p->lcm;
-	td = p->td;
-	NEWNM(m);
-	C(m) = HC(p2); m->td = td-HTD(p1); ndl_sub(lcm,HDL(p1),m->dl);
-	if ( ndl_check_bound2(p->i1,m->dl) )
-		return 0;
-	t1 = nd_mul_ind_nm(p->i1,m);
-	C(m) = nd_mod-HC(p1); m->td = td-HTD(p2); ndl_sub(lcm,HDL(p2),m->dl);
-	if ( ndl_check_bound2(p->i2,m->dl) ) {
-		nd_free(t1);
-		return 0;
-	}
-	t2 = nd_mul_ind_nm(p->i2,m);
-	FREENM(m);
-	*rp = nd_add(t1,t2);
-	return 1;
-}
-
-ND nd_mul_nm(ND p,NM m0)
+void ndv_print_q(NDV p)
 {
-	NM m,mr,mr0;
-	unsigned int *d,*dt,*dm;
-	int c,n,td,i,c1,c2;
-	int *pt,*p1,*p2;
-	ND r;
-
+	NMV m;
+	int i,len;
+    
 	if ( !p )
-		return 0;
+		printf("0\n");
 	else {
-		n = NV(p); m = BDY(p);
-		d = m0->dl; td = m0->td; c = C(m0);
-		mr0 = 0;
-		for ( ; m; m = NEXT(m) ) {
-			NEXTNM(mr0,mr);
-			c1 = C(m);
-			DMAR(c1,c,0,nd_mod,c2);
-			C(mr) = c2;
-			mr->td = m->td+td;
-			ndl_add(m->dl,d,mr->dl);
+		len = LEN(p);
+		for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
+			printf("+");
+			printexpr(CO,CQ(m));
+			printf("*");
+			ndl_print(DL(m));
 		}
-		NEXT(mr) = 0; 
-		MKND(NV(p),mr0,r);
-		r->sugar = p->sugar + td;
-		return r;
+		printf("\n");
 	}
 }
-
-ND nd_mul_ind_nm(int index,NM m0)
-{
-	register int c1,c2,c;
-	register NM m,new,prev;
-	NM mr0;
-	unsigned int *d;
-	int n,td,i,len,d0,d1;
-	ND p,r;
-
-	p = nd_ps[index];
-	len = nd_psl[index];
-	n = NV(p); m = BDY(p);
-	d = m0->dl; td = m0->td; c = C(m0);
-
-	NEWNM(mr0);
-	c1 = C(m); DMAR(c1,c,0,nd_mod,c2); C(mr0) = c2;
-	mr0->td = m->td+td; ndl_add(m->dl,d,mr0->dl);
-	prev = mr0; m = NEXT(m);
-	len--;
-
-	switch ( nd_wpd ) {
-		case 1:
-			d0 = d[0];
-			while ( len-- ) {
-				c1 = C(m); DMAR(c1,c,0,nd_mod,c2); 
-				NEWNM(new); C(new) = c2;
-				new->td = m->td+td; new->dl[0] = m->dl[0]+d0;
-				m = NEXT(m); NEXT(prev) = new; prev = new;
-			}
-			break;
-		case 2:
-			d0 = d[0]; d1 = d[1];
-			while ( len-- ) {
-				c1 = C(m); DMAR(c1,c,0,nd_mod,c2); 
-				NEWNM(new); C(new) = c2;
-				new->td = m->td+td; 
-				new->dl[0] = m->dl[0]+d0;
-				new->dl[1] = m->dl[1]+d1;
-				m = NEXT(m); NEXT(prev) = new; prev = new;
-			}
-			break;
-		default:
-			while ( len-- ) {
-				c1 = C(m); DMAR(c1,c,0,nd_mod,c2);
-				NEWNM(new); C(new) = c2;
-				new->td = m->td+td; ndl_add(m->dl,d,new->dl);
-				m = NEXT(m); NEXT(prev) = new; prev = new;
-			}
-			break;
-	}
-
-	NEXT(prev) = 0; 
-	MKND(NV(p),mr0,r);
-	r->sugar = p->sugar + td;
-	return r;
-}
-#endif