===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/builtin/dp-supp.c,v
retrieving revision 1.8
retrieving revision 1.39
diff -u -p -r1.8 -r1.39
--- OpenXM_contrib2/asir2000/builtin/dp-supp.c	2000/12/08 06:43:09	1.8
+++ OpenXM_contrib2/asir2000/builtin/dp-supp.c	2005/08/25 18:59:11	1.39
@@ -45,10 +45,11 @@
  * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
  * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
  *
- * $OpenXM: OpenXM_contrib2/asir2000/builtin/dp-supp.c,v 1.7 2000/12/08 02:39:04 noro Exp $ 
+ * $OpenXM: OpenXM_contrib2/asir2000/builtin/dp-supp.c,v 1.38 2004/12/06 09:29:34 noro Exp $ 
 */
 #include "ca.h"
 #include "base.h"
+#include "inline.h"
 #include "parse.h"
 #include "ox.h"
 
@@ -61,13 +62,16 @@ extern int NoGCD;
 extern int GenTrace;
 extern NODE TraceList;
 
+int show_orderspec;
+
+void print_composite_order_spec(struct order_spec *spec);
+
 /* 
  * content reduction
  *
  */
 
-void dp_ptozp(p,rp)
-DP p,*rp;
+void dp_ptozp(DP p,DP *rp)
 {
 	MP m,mr,mr0;
 	int i,n;
@@ -94,9 +98,7 @@ DP p,*rp;
 	}
 }
 
-void dp_ptozp2(p0,p1,hp,rp)
-DP p0,p1;
-DP *hp,*rp;
+void dp_ptozp2(DP p0,DP p1,DP *hp,DP *rp)
 {
 	DP t,s,h,r;
 	MP m,mr,mr0,m0;
@@ -120,11 +122,34 @@ DP *hp,*rp;
 	*hp = h; *rp = r;
 }
 
-void dp_idiv(p,c,rp)
-DP p;
-Q c;
-DP *rp;
+void dp_ptozp3(DP p,Q *dvr,DP *rp)
 {
+	MP m,mr,mr0;
+	int i,n;
+	Q *w;
+	P t;
+
+	if ( !p ) {
+		*rp = 0; *dvr = 0;
+	}else {
+		for ( m =BDY(p), n = 0; m; m = NEXT(m), n++ );
+		w = (Q *)ALLOCA(n*sizeof(Q));
+		for ( m =BDY(p), i = 0; i < n; m = NEXT(m), i++ )
+			if ( NUM(m->c) )
+				w[i] = (Q)m->c;
+			else
+				ptozp(m->c,1,&w[i],&t);
+		sortbynm(w,n);	
+		qltozl(w,n,dvr);
+		for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
+			NEXTMP(mr0,mr); divsp(CO,m->c,(P)(*dvr),&mr->c); mr->dl = m->dl;
+		}
+		NEXT(mr) = 0; MKDP(p->nv,mr0,*rp); (*rp)->sugar = p->sugar;
+	}
+}
+
+void dp_idiv(DP p,Q c,DP *rp)
+{
 	Q t;
 	N nm,q;
 	int sgn,s;
@@ -153,9 +178,7 @@ DP *rp;
 	}
 }
 
-void dp_mbase(hlist,mbase)
-NODE hlist;
-NODE *mbase;
+void dp_mbase(NODE hlist,NODE *mbase)
 {
 	DL *dl;
 	DL d;
@@ -169,7 +192,8 @@ NODE *mbase;
 	while ( 1 ) {
 		insert_to_node(d,mbase,nvar);
 		for ( i = nvar-1; i >= 0; ) {
-			d->d[i]++; d->td++;
+			d->d[i]++;
+			d->td += MUL_WEIGHT(1,i);
 			for ( j = 0; j < n; j++ ) {
 				if ( _dl_redble(dl[j],d,nvar) )
 					break;
@@ -178,7 +202,7 @@ NODE *mbase;
 				for ( j = nvar-1; j >= i; j-- )
 					d->d[j] = 0;
 				for ( j = 0, td = 0; j < i; j++ )
-					td += d->d[j];
+					td += MUL_WEIGHT(d->d[j],j);
 				d->td = td;
 				i--;
 			} else
@@ -189,9 +213,7 @@ NODE *mbase;
 	}
 }
 
-int _dl_redble(d1,d2,nvar)
-DL d1,d2;
-int nvar;
+int _dl_redble(DL d1,DL d2,int nvar)
 {
 	int i;
 
@@ -206,10 +228,7 @@ int nvar;
 		return 1;
 }
 
-void insert_to_node(d,n,nvar)
-DL d;
-NODE *n;
-int nvar;
+void insert_to_node(DL d,NODE *n,int nvar)
 {
 	DL d1;
 	MP m;
@@ -238,10 +257,7 @@ int nvar;
 	}
 }
 
-void dp_vtod(c,p,rp)
-Q *c;
-DP p;
-DP *rp;
+void dp_vtod(Q *c,DP p,DP *rp)
 {
 	MP mr0,m,mr;
 	int i;
@@ -260,8 +276,7 @@ DP *rp;
 extern int mpi_mag;
 extern int PCoeffs;
 
-void dp_ptozp_d(p,rp)
-DP p,*rp;
+void dp_ptozp_d(DP p,DP *rp)
 {
 	int i,j,k,l,n,nsep;
 	MP m;
@@ -270,7 +285,6 @@ DP p,*rp;
 	VECT c,cs;
 	VECT qi,ri;
 	LIST *qr;
-	int s,id;
 	Obj dmy;
 	Q d0,d1,gcd,a,u,u1;
 	Q *q,*r;
@@ -285,6 +299,8 @@ DP p,*rp;
 	double t_e,t_d,t_d1,t_c;
 	extern int DP_NFStat;
 	extern LIST Dist;
+	void Pox_rpc();
+	void Pox_pop_local();
 
 	if ( !p )
 		*rp = 0;
@@ -292,7 +308,7 @@ DP p,*rp;
 		if ( PCoeffs ) {
 			dp_ptozp(p,rp); return;
 		}	
-		if ( !dist || p_mag(BDY(p)->c) <= mpi_mag ) {
+		if ( !Dist || p_mag(BDY(p)->c) <= mpi_mag ) {
 			dist = 0; ndist = 0;
 			if ( DP_NFStat ) fprintf(asir_out,"L");
 		} else {
@@ -361,9 +377,7 @@ DP p,*rp;
 	}
 }
 
-void dp_ptozp2_d(p0,p1,hp,rp)
-DP p0,p1;
-DP *hp,*rp;
+void dp_ptozp2_d(DP p0,DP p1,DP *hp,DP *rp)
 {
 	DP t,s,h,r;
 	MP m,mr,mr0,m0;
@@ -387,9 +401,46 @@ DP *hp,*rp;
 	*hp = h; *rp = r;
 }
 
-void dp_prim(p,rp)
-DP p,*rp;
+int have_sf_coef(P p)
 {
+	DCP dc;
+
+	if ( !p )
+		return 0;
+	else if ( NUM(p) )
+		return NID((Num)p) == N_GFS ? 1 : 0;
+	else {
+		for ( dc = DC(p); dc; dc = NEXT(dc) )
+			if ( have_sf_coef(COEF(dc)) )
+				return 1;
+		return 0;
+	}
+}
+
+void head_coef(P p,Num *c)
+{
+	if ( !p )
+		*c = 0;
+	else if ( NUM(p) )
+		*c = (Num)p;
+	else
+		head_coef(COEF(DC(p)),c);
+}
+
+void dp_monic_sf(DP p,DP *rp)
+{
+	Num c;
+
+	if ( !p )
+		*rp = 0;
+	else {
+		head_coef(BDY(p)->c,&c);
+		divsdc(CO,p,(P)c,rp);
+	}
+}
+
+void dp_prim(DP p,DP *rp)
+{
 	P t,g;
 	DP p1;
 	MP m,mr,mr0;
@@ -400,7 +451,30 @@ DP p,*rp;
 
 	if ( !p )
 		*rp = 0;
-	else if ( dp_fcoeffs )
+	else if ( dp_fcoeffs == N_GFS ) {
+		for ( m = BDY(p); m; m = NEXT(m) )
+			if ( OID(m->c) == O_N ) {
+				/* GCD of coeffs = 1 */
+				dp_monic_sf(p,rp);
+				return;
+			} else break;
+		/* compute GCD over the finite fieid */
+		for ( m = BDY(p), n = 0; m; m = NEXT(m), n++ );
+		w = (P *)ALLOCA(n*sizeof(P));
+		for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ )
+			w[i] = m->c;
+		gcdsf(CO,w,n,&g);
+		if ( NUM(g) )
+			dp_monic_sf(p,rp);
+		else {
+			for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
+				NEXTMP(mr0,mr); divsp(CO,m->c,g,&mr->c); mr->dl = m->dl;
+			}
+			NEXT(mr) = 0; MKDP(p->nv,mr0,p1); p1->sugar = p->sugar;
+			dp_monic_sf(p1,rp);
+		}
+		return;
+	} else if ( dp_fcoeffs )
 		*rp = p;
 	else if ( NoGCD )
 		dp_ptozp(p,rp);
@@ -432,10 +506,7 @@ DP p,*rp;
 	}
 }
 
-void heu_nezgcdnpz(vl,pl,m,pr)
-VL vl;
-P *pl,*pr;
-int m;
+void heu_nezgcdnpz(VL vl,P *pl,int m,P *pr)
 {
 	int i,r;
 	P gcd,t,s1,s2,u;
@@ -461,9 +532,7 @@ int m;
 	*pr = gcd;
 }
 
-void dp_prim_mod(p,mod,rp)
-int mod;
-DP p,*rp;
+void dp_prim_mod(DP p,int mod,DP *rp)
 {
 	P t,g;
 	MP m,mr,mr0;
@@ -483,18 +552,14 @@ DP p,*rp;
 	}
 }
 
-void dp_cont(p,rp)
-DP p;
-Q *rp;
+void dp_cont(DP p,Q *rp)
 {
 	VECT v;
 
 	dp_dtov(p,&v); igcdv(v,rp);
 }
 
-void dp_dtov(dp,rp)
-DP dp;
-VECT *rp;
+void dp_dtov(DP dp,VECT *rp)
 {
 	MP m,t;
 	int i,n;
@@ -514,9 +579,7 @@ VECT *rp;
  *
  */
 
-void dp_sp(p1,p2,rp)
-DP p1,p2;
-DP *rp;
+void dp_sp(DP p1,DP p2,DP *rp)
 {
 	int i,n,td;
 	int *w;
@@ -529,7 +592,7 @@ DP *rp;
 	n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
 	w = (int *)ALLOCA(n*sizeof(int));
 	for ( i = 0, td = 0; i < n; i++ ) {
-		w[i] = MAX(d1->d[i],d2->d[i]); td += w[i];
+		w[i] = MAX(d1->d[i],d2->d[i]); td += MUL_WEIGHT(w[i],i);
 	}
 
 	NEWDL(d,n); d->td = td - d1->td;
@@ -569,28 +632,78 @@ DP *rp;
 	}
 }
 
-void dp_sp_mod(p1,p2,mod,rp)
-DP p1,p2;
-int mod;
-DP *rp;
+void _dp_sp_dup(DP p1,DP p2,DP *rp)
 {
 	int i,n,td;
 	int *w;
 	DL d1,d2,d;
 	MP m;
+	DP t,s1,s2,u;
+	Q c,c1,c2;
+	N gn,tn;
+
+	n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
+	w = (int *)ALLOCA(n*sizeof(int));
+	for ( i = 0, td = 0; i < n; i++ ) {
+		w[i] = MAX(d1->d[i],d2->d[i]); td += MUL_WEIGHT(w[i],i);
+	}
+
+	_NEWDL(d,n); d->td = td - d1->td;
+	for ( i = 0; i < n; i++ )
+		d->d[i] = w[i] - d1->d[i];
+	c1 = (Q)BDY(p1)->c; c2 = (Q)BDY(p2)->c;
+	if ( INT(c1) && INT(c2) ) {
+		gcdn(NM(c1),NM(c2),&gn);
+		if ( !UNIN(gn) ) {
+			divsn(NM(c1),gn,&tn); NTOQ(tn,SGN(c1),c); c1 = c;
+			divsn(NM(c2),gn,&tn); NTOQ(tn,SGN(c2),c); c2 = c;
+		}
+	}
+
+	_NEWMP(m); m->dl = d; m->c = (P)c2; NEXT(m) = 0;
+	_MKDP(n,m,s1); s1->sugar = d->td; _muld_dup(CO,s1,p1,&t); _free_dp(s1);
+
+	_NEWDL(d,n); d->td = td - d2->td;
+	for ( i = 0; i < n; i++ )
+		d->d[i] = w[i] - d2->d[i];
+	_NEWMP(m); m->dl = d; chsgnp((P)c1,&m->c); NEXT(m) = 0;
+	_MKDP(n,m,s2); s2->sugar = d->td; _muld_dup(CO,s2,p2,&u); _free_dp(s2);
+
+	_addd_destructive(CO,t,u,rp);
+	if ( GenTrace ) {
+		LIST hist;
+		NODE node;
+
+		node = mknode(4,ONE,0,s1,ONE);
+		MKLIST(hist,node);
+		MKNODE(TraceList,hist,0);
+
+		node = mknode(4,ONE,0,0,ONE);
+		chsgnd(s2,(DP *)&ARG2(node));
+		MKLIST(hist,node);
+		MKNODE(node,hist,TraceList); TraceList = node;
+	}
+}
+
+void dp_sp_mod(DP p1,DP p2,int mod,DP *rp)
+{
+	int i,n,td;
+	int *w;
+	DL d1,d2,d;
+	MP m;
 	DP t,s,u;
 
 	n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
 	w = (int *)ALLOCA(n*sizeof(int));
 	for ( i = 0, td = 0; i < n; i++ ) {
-		w[i] = MAX(d1->d[i],d2->d[i]); td += w[i];
+		w[i] = MAX(d1->d[i],d2->d[i]); td += MUL_WEIGHT(w[i],i);
 	}
-	NEWDL(d,n); d->td = td - d1->td;
+	NEWDL_NOINIT(d,n); d->td = td - d1->td;
 	for ( i = 0; i < n; i++ )
 		d->d[i] = w[i] - d1->d[i];
 	NEWMP(m); m->dl = d; m->c = (P)BDY(p2)->c; NEXT(m) = 0;
 	MKDP(n,m,s); s->sugar = d->td; mulmd(CO,mod,p1,s,&t);
-	NEWDL(d,n); d->td = td - d2->td;
+	NEWDL_NOINIT(d,n); d->td = td - d2->td;
 	for ( i = 0; i < n; i++ )
 		d->d[i] = w[i] - d2->d[i];
 	NEWMP(m); m->dl = d; m->c = (P)BDY(p1)->c; NEXT(m) = 0;
@@ -598,10 +711,7 @@ DP *rp;
 	submd(CO,mod,t,u,rp);
 }
 
-void _dp_sp_mod_dup(p1,p2,mod,rp)
-DP p1,p2;
-int mod;
-DP *rp;
+void _dp_sp_mod_dup(DP p1,DP p2,int mod,DP *rp)
 {
 	int i,n,td;
 	int *w;
@@ -612,7 +722,7 @@ DP *rp;
 	n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
 	w = (int *)ALLOCA(n*sizeof(int));
 	for ( i = 0, td = 0; i < n; i++ ) {
-		w[i] = MAX(d1->d[i],d2->d[i]); td += w[i];
+		w[i] = MAX(d1->d[i],d2->d[i]); td += MUL_WEIGHT(w[i],i);
 	}
 	_NEWDL(d,n); d->td = td - d1->td;
 	for ( i = 0; i < n; i++ )
@@ -627,10 +737,7 @@ DP *rp;
 	_addmd_destructive(mod,t,u,rp);
 }
 
-void _dp_sp_mod(p1,p2,mod,rp)
-DP p1,p2;
-int mod;
-DP *rp;
+void _dp_sp_mod(DP p1,DP p2,int mod,DP *rp)
 {
 	int i,n,td;
 	int *w;
@@ -641,7 +748,7 @@ DP *rp;
 	n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
 	w = (int *)ALLOCA(n*sizeof(int));
 	for ( i = 0, td = 0; i < n; i++ ) {
-		w[i] = MAX(d1->d[i],d2->d[i]); td += w[i];
+		w[i] = MAX(d1->d[i],d2->d[i]); td += MUL_WEIGHT(w[i],i);
 	}
 	NEWDL(d,n); d->td = td - d1->td;
 	for ( i = 0; i < n; i++ )
@@ -658,14 +765,12 @@ DP *rp;
 
 /*
  * m-reduction
+ * do content reduction over Z or Q(x,...)
+ * do nothing over finite fields
  *
  */
 
-void dp_red(p0,p1,p2,head,rest,dnp,multp)
-DP p0,p1,p2;
-DP *head,*rest;
-P *dnp;
-DP *multp;
+void dp_red(DP p0,DP p1,DP p2,DP *head,DP *rest,P *dnp,DP *multp)
 {
 	int i,n;
 	DL d1,d2,d;
@@ -674,13 +779,18 @@ DP *multp;
 	Q c,c1,c2;
 	N gn,tn;
 	P g,a;
+	P p[2];
 
 	n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
 	NEWDL(d,n); d->td = d1->td - d2->td;
 	for ( i = 0; i < n; i++ )
 		d->d[i] = d1->d[i]-d2->d[i];
 	c1 = (Q)BDY(p1)->c; c2 = (Q)BDY(p2)->c;
-	if ( dp_fcoeffs ) {
+	if ( dp_fcoeffs == N_GFS ) {
+		p[0] = (P)c1; p[1] = (P)c2;
+		gcdsf(CO,p,2,&g);
+		divsp(CO,(P)c1,g,&a); c1 = (Q)a; divsp(CO,(P)c2,g,&a); c2 = (Q)a;
+	} else if ( dp_fcoeffs ) {
 		/* do nothing */
 	} else if ( INT(c1) && INT(c2) ) {
 		gcdn(NM(c1),NM(c2),&gn);
@@ -699,15 +809,36 @@ DP *multp;
 	*head = h; *rest = r; *dnp = (P)c2;
 }
 
-void dp_red_mod(p0,p1,p2,mod,head,rest,dnp)
-DP p0,p1,p2;
-int mod;
-DP *head,*rest;
-P *dnp;
+/* m-reduction over a field */
+
+void dp_red_f(DP p1,DP p2,DP *rest)
 {
 	int i,n;
 	DL d1,d2,d;
 	MP m;
+	DP t,s;
+	Obj a,b;
+
+	n = p1->nv;
+	d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
+
+	NEWDL(d,n); d->td = d1->td - d2->td;
+	for ( i = 0; i < n; i++ )
+		d->d[i] = d1->d[i]-d2->d[i];
+
+	NEWMP(m); m->dl = d;
+	divr(CO,(Obj)BDY(p1)->c,(Obj)BDY(p2)->c,&a); chsgnr(a,&b);
+	C(m) = (P)b;
+	NEXT(m) = 0; MKDP(n,m,s); s->sugar = d->td;
+
+	muld(CO,s,p2,&t); addd(CO,p1,t,rest);
+}
+
+void dp_red_mod(DP p0,DP p1,DP p2,int mod,DP *head,DP *rest,P *dnp)
+{
+	int i,n;
+	DL d1,d2,d;
+	MP m;
 	DP t,s,r,h;
 	P c1,c2,g,u;
 
@@ -722,7 +853,7 @@ P *dnp;
 		divsmp(CO,mod,c1,c2,&u); c1 = u; c2 = (P)ONEM;
 	}
 	NEWMP(m); m->dl = d; chsgnmp(mod,(P)c1,&m->c); NEXT(m) = 0;
-	MKDP(n,m,s); s->sugar = d->td; mulmd(CO,mod,p2,s,&t);
+	MKDP(n,m,s); s->sugar = d->td; mulmd(CO,mod,s,p2,&t);
 	if ( NUM(c2) ) {
 		addmd(CO,mod,p1,t,&r); h = p0;
 	} else {
@@ -731,26 +862,39 @@ P *dnp;
 	*head = h; *rest = r; *dnp = c2;
 }
 
-void _dp_red_mod_destructive(p1,p2,mod,rp)
-DP p1,p2;
-int mod;
-DP *rp;
+struct oEGT eg_red_mod;
+
+void _dp_red_mod_destructive(DP p1,DP p2,int mod,DP *rp)
 {
 	int i,n;
 	DL d1,d2,d;
 	MP m;
 	DP t,s;
-	int c,c1;
+	int c,c1,c2;
+	extern int do_weyl;
 
 	n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
 	_NEWDL(d,n); d->td = d1->td - d2->td;
 	for ( i = 0; i < n; i++ )
 		d->d[i] = d1->d[i]-d2->d[i];
-	c = invm(ITOS(BDY(p2)->c),mod); c1 = dmar(c,ITOS(BDY(p1)->c),0,mod);
+	c = invm(ITOS(BDY(p2)->c),mod); 
+	c2 = ITOS(BDY(p1)->c);
+	DMAR(c,c2,0,mod,c1);
 	_NEWMP(m); m->dl = d; m->c = STOI(mod-c1); NEXT(m) = 0;
+#if 0
 	_MKDP(n,m,s); s->sugar = d->td;
 	_mulmd_dup(mod,s,p2,&t); _free_dp(s);
+#else
+	if ( do_weyl ) {
+		_MKDP(n,m,s); s->sugar = d->td;
+		_mulmd_dup(mod,s,p2,&t); _free_dp(s);
+	} else {
+		_mulmdm_dup(mod,p2,m,&t); _FREEMP(m);
+	}
+#endif
+/* get_eg(&t0); */
 	_addmd_destructive(mod,p1,t,rp);
+/* get_eg(&t1); add_eg(&eg_red_mod,&t0,&t1); */
 }
 
 /*
@@ -758,13 +902,7 @@ DP *rp;
  *
  */
 
-void dp_true_nf(b,g,ps,full,rp,dnp)
-NODE b;
-DP g;
-DP *ps;
-int full;
-DP *rp;
-P *dnp;
+void dp_true_nf(NODE b,DP g,DP *ps,int full,DP *rp,P *dnp)
 {
 	DP u,p,d,s,t,dmy;
 	NODE l;
@@ -819,12 +957,9 @@ P *dnp;
 	*rp = d; *dnp = dn;
 }
 
-void dp_nf_ptozp(b,g,ps,full,multiple,rp)
-NODE b;
-DP g;
-DP *ps;
-int full,multiple;
-DP *rp;
+/* nf computation over Z */
+
+void dp_nf_z(NODE b,DP g,DP *ps,int full,int multiple,DP *rp)
 {
 	DP u,p,d,s,t,dmy1;
 	P dmy;
@@ -842,8 +977,10 @@ DP *rp;
 	wb = (int *)ALLOCA(n*sizeof(int));
 	for ( i = 0, l = b; i < n; l = NEXT(l), i++ )
 		wb[i] = QTOS((Q)BDY(l));
+
 	hmag = multiple*HMAG(g);
 	sugar = g->sugar;
+
 	for ( d = 0; g; ) {
 		for ( u = 0, i = 0; i < n; i++ ) {
 			if ( dp_redble(g,p = ps[wb[i]]) ) {
@@ -891,14 +1028,64 @@ DP *rp;
 	*rp = d;
 }
 
-void dp_nf_mod(b,g,ps,mod,full,rp)
-NODE b;
-DP g;
-DP *ps;
-int mod,full;
-DP *rp;
+/* nf computation over a field */
+
+void dp_nf_f(NODE b,DP g,DP *ps,int full,DP *rp)
 {
 	DP u,p,d,s,t;
+	NODE l;
+	MP m,mr;
+	int i,n;
+	int *wb;
+	int sugar,psugar;
+
+	if ( !g ) {
+		*rp = 0; return;
+	}
+	for ( n = 0, l = b; l; l = NEXT(l), n++ );
+	wb = (int *)ALLOCA(n*sizeof(int));
+	for ( i = 0, l = b; i < n; l = NEXT(l), i++ )
+		wb[i] = QTOS((Q)BDY(l));
+
+	sugar = g->sugar;
+	for ( d = 0; g; ) {
+		for ( u = 0, i = 0; i < n; i++ ) {
+			if ( dp_redble(g,p = ps[wb[i]]) ) {
+				dp_red_f(g,p,&u);
+				psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
+				sugar = MAX(sugar,psugar);
+				if ( !u ) {
+					if ( d )
+						d->sugar = sugar;
+					*rp = d; return;
+				}
+				break;
+			}
+		}
+		if ( u )
+			g = u;
+		else if ( !full ) {
+			if ( g ) {
+				MKDP(g->nv,BDY(g),t); t->sugar = sugar; g = t;
+			}
+			*rp = g; return;
+		} else {
+			m = BDY(g); NEWMP(mr); mr->dl = m->dl; mr->c = m->c;
+			NEXT(mr) = 0; MKDP(g->nv,mr,t); t->sugar = mr->dl->td;
+			addd(CO,d,t,&s); d = s;
+			dp_rest(g,&t); g = t;
+		}
+	}
+	if ( d )
+		d->sugar = sugar;
+	*rp = d;
+}
+
+/* nf computation over GF(mod) (only for internal use) */
+
+void dp_nf_mod(NODE b,DP g,DP *ps,int mod,int full,DP *rp)
+{
+	DP u,p,d,s,t;
 	P dmy;
 	NODE l;
 	MP m,mr;
@@ -942,13 +1129,7 @@ DP *rp;
 	*rp = d;
 }
 
-void dp_true_nf_mod(b,g,ps,mod,full,rp,dnp)
-NODE b;
-DP g;
-DP *ps;
-int mod,full;
-DP *rp;
-P *dnp;
+void dp_true_nf_mod(NODE b,DP g,DP *ps,int mod,int full,DP *rp,P *dnp)
 {
 	DP u,p,d,s,t;
 	NODE l;
@@ -1003,17 +1184,12 @@ P *dnp;
 	*rp = d; *dnp = dn;
 }
 
-void _dp_nf_mod_destructive(b,g,ps,mod,full,rp)
-NODE b;
-DP g;
-DP *ps;
-int mod,full;
-DP *rp;
+void _dp_nf_mod_destructive(NODE b,DP g,DP *ps,int mod,int full,DP *rp)
 {
-	DP u,p,d,s,t;
+	DP u,p,d;
 	NODE l;
-	MP m,mr,mrd;
-	int sugar,psugar,n,h_reducible,i;
+	MP m,mrd;
+	int sugar,psugar,n,h_reducible;
 
 	if ( !g ) {
 		*rp = 0; return;
@@ -1062,13 +1238,40 @@ DP *rp;
 	_dptodp(d,rp); _free_dp(d);
 }
 
-void dp_lnf_mod(p1,p2,g,mod,r1p,r2p)
-DP p1,p2;
-NODE g;
-int mod;
-DP *r1p,*r2p;
+/* reduction by linear base over a field */
+
+void dp_lnf_f(DP p1,DP p2,NODE g,DP *r1p,DP *r2p)
 {
 	DP r1,r2,b1,b2,t,s;
+	Obj c,c1,c2;
+	NODE l,b;
+	int n;
+
+	if ( !p1 ) {
+		*r1p = p1; *r2p = p2; return;
+	}
+	n = p1->nv;
+	for ( l = g, r1 = p1, r2 = p2; l; l = NEXT(l) ) {
+			if ( !r1 ) {
+				*r1p = r1; *r2p = r2; return;
+			}
+			b = BDY((LIST)BDY(l)); b1 = (DP)BDY(b);
+			if ( dl_equal(n,BDY(r1)->dl,BDY(b1)->dl) ) {
+				b2 = (DP)BDY(NEXT(b));
+				divr(CO,(Obj)ONE,(Obj)BDY(b1)->c,&c1);
+				mulr(CO,c1,(Obj)BDY(r1)->c,&c2); chsgnr(c2,&c);
+				muldc(CO,b1,(P)c,&t); addd(CO,r1,t,&s); r1 = s;
+				muldc(CO,b2,(P)c,&t); addd(CO,r2,t,&s); r2 = s;
+			}
+	}
+	*r1p = r1; *r2p = r2;
+}
+
+/* reduction by linear base over GF(mod) */
+
+void dp_lnf_mod(DP p1,DP p2,NODE g,int mod,DP *r1p,DP *r2p)
+{
+	DP r1,r2,b1,b2,t,s;
 	P c;
 	MQ c1,c2;
 	NODE l,b;
@@ -1094,11 +1297,7 @@ DP *r1p,*r2p;
 	*r1p = r1; *r2p = r2;
 }
 
-void dp_nf_tab_mod(p,tab,mod,rp)
-DP p;
-LIST *tab;
-int mod;
-DP *rp;
+void dp_nf_tab_mod(DP p,LIST *tab,int mod,DP *rp)
 {
 	DP s,t,u;
 	MP m;
@@ -1119,22 +1318,51 @@ DP *rp;
 	*rp = s;
 }
 
+void dp_nf_tab_f(DP p,LIST *tab,DP *rp)
+{
+	DP s,t,u;
+	MP m;
+	DL h;
+	int i,n;
+
+	if ( !p ) {
+		*rp = p; return;
+	}
+	n = p->nv;
+	for ( s = 0, i = 0, m = BDY(p); m; m = NEXT(m) ) {
+		h = m->dl;
+		while ( !dl_equal(n,h,BDY((DP)BDY(BDY(tab[i])))->dl ) )
+			i++;
+		muldc(CO,(DP)BDY(NEXT(BDY(tab[i]))),m->c,&t);
+		addd(CO,s,t,&u); s = u;
+	}
+	*rp = s;
+}
+
 /*
  * setting flags
+ * call create_order_spec with vl=0 to set old type order.
  *
  */
 
-int create_order_spec(obj,spec)
-Obj obj;
-struct order_spec *spec;
+int create_order_spec(VL vl,Obj obj,struct order_spec **specp)
 {
-	int i,j,n,s,row,col;
+	int i,j,n,s,row,col,ret;
+	struct order_spec *spec;
 	struct order_pair *l;
 	NODE node,t,tn;
 	MAT m;
 	pointer **b;
 	int **w;
 
+	if ( vl && obj && OID(obj) == O_LIST ) {
+		ret = create_composite_order_spec(vl,(LIST)obj,specp);
+		if ( show_orderspec )
+			print_composite_order_spec(*specp);
+		return ret;
+	}
+
+	*specp = spec = (struct order_spec *)MALLOC(sizeof(struct order_spec));
 	if ( !obj || NUM(obj) ) {
 		spec->id = 0; spec->obj = obj;
 		spec->ord.simple = QTOS((Q)obj);
@@ -1166,14 +1394,339 @@ struct order_spec *spec;
 		return 0;
 }
 
+void print_composite_order_spec(struct order_spec *spec)
+{
+	int nv,n,len,i,j,k,start;
+	struct weight_or_block *worb;
+
+	nv = spec->nv;
+	n = spec->ord.composite.length;
+	worb = spec->ord.composite.w_or_b;
+	for ( i = 0; i < n; i++, worb++ ) {
+		len = worb->length;
+		printf("[ ");
+		switch ( worb->type ) {
+			case IS_DENSE_WEIGHT:
+				for ( j = 0; j < len; j++ )
+					printf("%d ",worb->body.dense_weight[j]);
+				for ( ; j < nv; j++ )
+					printf("0 ");
+				break;
+			case IS_SPARSE_WEIGHT:
+				for ( j = 0, k = 0; j < nv; j++ )
+					if ( j == worb->body.sparse_weight[k].pos )
+						printf("%d ",worb->body.sparse_weight[k++].value);
+					else
+						printf("0 ");
+				break;
+			case IS_BLOCK:
+				start = worb->body.block.start;
+				for ( j = 0; j < start; j++ ) printf("0 ");
+				switch ( worb->body.block.order ) {
+					case 0:
+						for ( k = 0; k < len; k++, j++ ) printf("R ");
+						break;
+					case 1:
+						for ( k = 0; k < len; k++, j++ ) printf("G ");
+						break;
+					case 2:
+						for ( k = 0; k < len; k++, j++ ) printf("L ");
+						break;
+				}
+				for ( ; j < nv; j++ ) printf("0 ");
+				break;
+		}
+		printf("]\n");
+	}
+}
+
+struct order_spec *append_block(struct order_spec *spec,
+	int nv,int nalg,int ord)
+{
+	MAT m,mat;
+	int i,j,row,col,n;
+	Q **b,**wp;
+	int **w;
+	NODE t,s,s0;
+	struct order_pair *l,*l0;
+	int n0,nv0;
+	LIST list0,list1,list;
+	Q oq,nq;
+	struct order_spec *r;
+
+	r = (struct order_spec *)MALLOC(sizeof(struct order_spec));
+	switch ( spec->id ) {
+		case 0:
+			STOQ(spec->ord.simple,oq); STOQ(nv,nq);
+			t = mknode(2,oq,nq); MKLIST(list0,t);
+			STOQ(ord,oq); STOQ(nalg,nq);
+			t = mknode(2,oq,nq); MKLIST(list1,t);
+			t = mknode(2,list0,list1); MKLIST(list,t);
+			l = (struct order_pair *)MALLOC_ATOMIC(2*sizeof(struct order_pair));
+			l[0].order = spec->ord.simple; l[0].length = nv;
+			l[1].order = ord; l[1].length = nalg;
+			r->id = 1;  r->obj = (Obj)list;
+			r->ord.block.order_pair = l;
+			r->ord.block.length = 2;
+			r->nv = nv+nalg;
+			break;
+		case 1:
+			if ( spec->nv != nv )
+				error("append_block : number of variables mismatch");
+			l0 = spec->ord.block.order_pair;
+			n0 = spec->ord.block.length;
+			nv0 = spec->nv;
+			list0 = (LIST)spec->obj;
+			n = n0+1;
+			l = (struct order_pair *)MALLOC_ATOMIC(n*sizeof(struct order_pair));
+			for ( i = 0; i < n0; i++ )
+				l[i] = l0[i];
+			l[i].order = ord; l[i].length = nalg;
+			 for ( t = BDY(list0), s0 = 0; t; t = NEXT(t) ) {
+				NEXTNODE(s0,s); BDY(s) = BDY(t);
+			}
+			STOQ(ord,oq); STOQ(nalg,nq);
+			t = mknode(2,oq,nq); MKLIST(list,t);
+			NEXTNODE(s0,s); BDY(s) = (pointer)list; NEXT(s) = 0;
+			MKLIST(list,s0);
+			r->id = 1;  r->obj = (Obj)list;
+			r->ord.block.order_pair = l;
+			r->ord.block.length = n;
+			r->nv = nv+nalg;
+			break;
+		case 2:
+			if ( spec->nv != nv )
+				error("append_block : number of variables mismatch");
+			m = (MAT)spec->obj;
+			row = m->row; col = m->col; b = (Q **)BDY(m);
+			w = almat(row+nalg,col+nalg);
+			MKMAT(mat,row+nalg,col+nalg); wp = (Q **)BDY(mat);
+			for ( i = 0; i < row; i++ )
+				for ( j = 0; j < col; j++ ) {
+					w[i][j] = QTOS(b[i][j]);
+					wp[i][j] = b[i][j];
+				}
+			for ( i = 0; i < nalg; i++ ) {
+				w[i+row][i+col] = 1;
+				wp[i+row][i+col] = ONE;
+			}
+			r->id = 2; r->obj = (Obj)mat;
+			r->nv = col+nalg; r->ord.matrix.row = row+nalg;
+			r->ord.matrix.matrix = w;
+			break;
+		case 3:
+		default:
+			/* XXX */
+			error("append_block : not implemented yet");
+	}
+	return r;
+}
+
+int comp_sw(struct sparse_weight *a, struct sparse_weight *b)
+{
+	if ( a->pos > b->pos ) return 1;
+	else if ( a->pos < b->pos ) return -1;
+	else return 0;
+}
+
+/* order = [w_or_b, w_or_b, ... ] */
+/* w_or_b = w or b                */
+/* w = [1,2,...] or [x,1,y,2,...] */
+/* b = [@lex,x,y,...,z] etc       */
+
+int create_composite_order_spec(VL vl,LIST order,struct order_spec **specp)
+{
+	NODE wb,t,p;
+	struct order_spec *spec;
+	VL tvl;
+	int n,i,j,k,l,start,end,len,w;
+	int *dw;
+	struct sparse_weight *sw;
+	struct weight_or_block *w_or_b;
+	Obj a0;
+	NODE a;
+	V v,sv,ev;
+	SYMBOL sym;
+	int *top;
+
+	/* l = number of vars in vl */
+	for ( l = 0, tvl = vl; tvl; tvl = NEXT(tvl), l++ );
+	/* n = number of primitives in order */
+	wb = BDY(order);
+	n = length(wb);
+	*specp = spec = (struct order_spec *)MALLOC(sizeof(struct order_spec));
+	spec->id = 3;
+	spec->obj = (Obj)order;
+	spec->nv = l;
+	spec->ord.composite.length = n;
+	w_or_b = spec->ord.composite.w_or_b = (struct weight_or_block *)
+		MALLOC(sizeof(struct weight_or_block)*(n+1));
+
+	/* top : register the top variable in each w_or_b specification */
+	top = (int *)ALLOCA(l*sizeof(int));
+	for ( i = 0; i < l; i++ ) top[i] = 0;
+
+	for ( t = wb, i = 0; t; t = NEXT(t), i++ ) {
+		if ( !BDY(t) || OID((Obj)BDY(t)) != O_LIST )
+			error("a list of lists must be specified for the key \"order\"");
+		a = BDY((LIST)BDY(t));
+		len = length(a);
+		a0 = (Obj)BDY(a);
+		if ( !a0 || OID(a0) == O_N ) {
+			/* a is a dense weight vector */
+			dw = (int *)MALLOC(sizeof(int)*len);
+			for ( j = 0, p = a; j < len; p = NEXT(p), j++ ) {
+				if ( !INT((Q)BDY(p)) )	
+					error("a dense weight vector must be specified as a list of integers");
+				dw[j] = QTOS((Q)BDY(p));
+			}
+			w_or_b[i].type = IS_DENSE_WEIGHT;
+			w_or_b[i].length = len;
+			w_or_b[i].body.dense_weight = dw;
+
+			/* find the top */
+			for ( k = 0; k < len && !dw[k]; k++ );
+			if ( k < len ) top[k] = 1;
+
+		} else if ( OID(a0) == O_P ) {
+			/* a is a sparse weight vector */
+			len >>= 1;
+			sw = (struct sparse_weight *)
+				MALLOC(sizeof(struct sparse_weight)*len);
+			for ( j = 0, p = a; j < len; j++ ) {
+				if ( !BDY(p) || OID((P)BDY(p)) != O_P )
+					error("a sparse weight vector must be specified as [var1,weight1,...]");
+				v = VR((P)BDY(p)); p = NEXT(p);
+				for ( tvl = vl, k = 0; tvl && tvl->v != v;
+					k++, tvl = NEXT(tvl) );
+				if ( !tvl )
+					error("invalid variable name in a sparse weight vector");
+				sw[j].pos = k;
+				if ( !INT((Q)BDY(p)) )
+					error("a sparse weight vector must be specified as [var1,weight1,...]");
+				sw[j].value = QTOS((Q)BDY(p)); p = NEXT(p);
+			}
+			qsort(sw,len,sizeof(struct sparse_weight),
+				(int (*)(const void *,const void *))comp_sw);
+			w_or_b[i].type = IS_SPARSE_WEIGHT;
+			w_or_b[i].length = len;
+			w_or_b[i].body.sparse_weight = sw;
+
+			/* find the top */
+			for ( k = 0; k < len && !sw[k].value; k++ );
+			if ( k < len ) top[sw[k].pos] = 1;
+		} else if ( OID(a0) == O_RANGE ) {
+			/* [range(v1,v2),w] */
+			sv = VR((P)(((RANGE)a0)->start));
+			ev = VR((P)(((RANGE)a0)->end));
+			for ( tvl = vl, start = 0; tvl && tvl->v != sv; start++, tvl = NEXT(tvl) );
+			if ( !tvl )
+				error("invalid range");
+			for ( end = start; tvl && tvl->v != ev; end++, tvl = NEXT(tvl) );
+			if ( !tvl )
+				error("invalid range");
+			len = end-start+1;
+			sw = (struct sparse_weight *)
+				MALLOC(sizeof(struct sparse_weight)*len);
+			w = QTOS((Q)BDY(NEXT(a)));
+			for ( tvl = vl, k = 0; k < start; k++, tvl = NEXT(tvl) );
+			for ( j = 0 ; k <= end; k++, tvl = NEXT(tvl), j++ ) {
+				sw[j].pos = k;
+				sw[j].value = w;
+			}
+			w_or_b[i].type = IS_SPARSE_WEIGHT;
+			w_or_b[i].length = len;
+			w_or_b[i].body.sparse_weight = sw;
+
+			/* register the top */
+			if ( w ) top[start] = 1;
+		} else if ( OID(a0) == O_SYMBOL ) {
+			/* a is a block */
+			sym = (SYMBOL)a0; a = NEXT(a); len--;
+			if ( OID((Obj)BDY(a)) == O_RANGE ) {
+				sv = VR((P)(((RANGE)BDY(a))->start));
+				ev = VR((P)(((RANGE)BDY(a))->end));
+				for ( tvl = vl, start = 0; tvl && tvl->v != sv; start++, tvl = NEXT(tvl) );
+				if ( !tvl )
+					error("invalid range");
+				for ( end = start; tvl && tvl->v != ev; end++, tvl = NEXT(tvl) );
+				if ( !tvl )
+					error("invalid range");
+				len = end-start+1;
+			} else {
+				for ( start = 0, tvl = vl; tvl->v != VR((P)BDY(a));
+				tvl = NEXT(tvl), start++ );
+				for ( p = NEXT(a), tvl = NEXT(tvl); p;
+					p = NEXT(p), tvl = NEXT(tvl) ) {
+					if ( !BDY(p) || OID((P)BDY(p)) != O_P )
+						error("a block must be specified as [ordsymbol,var1,var2,...]");
+					if ( tvl->v != VR((P)BDY(p)) ) break;
+				}
+				if ( p )
+					error("a block must be contiguous in the variable list");
+			}
+			w_or_b[i].type = IS_BLOCK;
+			w_or_b[i].length = len;
+			w_or_b[i].body.block.start = start;
+			if ( !strcmp(sym->name,"@grlex") )
+				w_or_b[i].body.block.order = 0;
+			else if ( !strcmp(sym->name,"@glex") )
+				w_or_b[i].body.block.order = 1;
+			else if ( !strcmp(sym->name,"@lex") )
+				w_or_b[i].body.block.order = 2;
+			else
+				error("invalid ordername");
+			/* register the tops */
+			for ( j = 0, k = start; j < len; j++, k++ )
+				top[k] = 1;
+		}
+	}
+	for ( k = 0; k < l && top[k]; k++ );
+	if ( k < l ) {
+		/* incomplete order specification; add @grlex */
+		w_or_b[n].type = IS_BLOCK;
+		w_or_b[n].length = l;
+		w_or_b[n].body.block.start = 0;
+		w_or_b[n].body.block.order = 0;
+		spec->ord.composite.length = n+1;
+	}
+}
+
+/* module order spec */
+
+void create_modorder_spec(int id,LIST shift,struct modorder_spec **s)
+{
+	struct modorder_spec *spec;
+	NODE n,t;
+	LIST list;
+	int *ds;
+	int i,l;
+	Q q;
+
+	*s = spec = (struct modorder_spec *)MALLOC(sizeof(struct modorder_spec));
+	spec->id = id;
+	if ( shift ) {
+		n = BDY(shift);
+		spec->len = l = length(n);
+		spec->degree_shift = ds = (int *)MALLOC_ATOMIC(l*sizeof(int));
+		for ( t = n, i = 0; t; t = NEXT(t), i++ )
+			ds[i] = QTOS((Q)BDY(t));
+	} else {
+		spec->len = 0;
+		spec->degree_shift = 0;
+	}
+	STOQ(id,q);
+	n = mknode(2,q,shift);
+	MKLIST(list,n);
+	spec->obj = (Obj)list;
+}
+
 /*
  * converters
  *
  */
 
-void dp_homo(p,rp)
-DP p;
-DP *rp;
+void dp_homo(DP p,DP *rp)
 {
 	MP m,mr,mr0;
 	int i,n,nv,td;
@@ -1197,9 +1750,7 @@ DP *rp;
 	}
 }
 
-void dp_dehomo(p,rp)
-DP p;
-DP *rp;
+void dp_dehomo(DP p,DP *rp)
 {
 	MP m,mr,mr0;
 	int i,n,nv;
@@ -1222,11 +1773,7 @@ DP *rp;
 	}
 }
 
-void dp_mod(p,mod,subst,rp)
-DP p;
-int mod;
-NODE subst;
-DP *rp;
+void dp_mod(DP p,int mod,NODE subst,DP *rp)
 {
 	MP m,mr,mr0;
 	P t,s,s1;
@@ -1253,9 +1800,7 @@ DP *rp;
 	}
 }
 
-void dp_rat(p,rp)
-DP p;
-DP *rp;
+void dp_rat(DP p,DP *rp)
 {
 	MP m,mr,mr0;
 
@@ -1273,14 +1818,16 @@ DP *rp;
 }
 
 
-void homogenize_order(old,n,new)
-struct order_spec *old,*new;
-int n;
+void homogenize_order(struct order_spec *old,int n,struct order_spec **newp)
 {
 	struct order_pair *l;
 	int length,nv,row,i,j;
 	int **newm,**oldm;
+	struct order_spec *new;
+	int onv,nnv,nlen,olen,owlen;
+	struct weight_or_block *owb,*nwb;
 
+	*newp = new = (struct order_spec *)MALLOC(sizeof(struct order_spec));
 	switch ( old->id ) {
 		case 0:
 			switch ( old->ord.simple ) {
@@ -1329,14 +1876,52 @@ int n;
 			new->id = 2; new->nv = nv+1;
 			new->ord.matrix.row = row+1; new->ord.matrix.matrix = newm;
 			break;
+		case 3:
+			onv = old->nv;
+			nnv = onv+1;
+			olen = old->ord.composite.length;
+			nlen = olen+1;
+			owb = old->ord.composite.w_or_b;
+			nwb = (struct weight_or_block *)
+				MALLOC(nlen*sizeof(struct weight_or_block));
+			for ( i = 0; i < olen; i++ ) {
+				nwb[i].type = owb[i].type;
+				switch ( owb[i].type ) {
+					case IS_DENSE_WEIGHT:
+						owlen = owb[i].length;
+						nwb[i].length = owlen+1;
+						nwb[i].body.dense_weight = (int *)MALLOC((owlen+1)*sizeof(int));
+						for ( j = 0; j < owlen; j++ )
+							nwb[i].body.dense_weight[j] = owb[i].body.dense_weight[j];
+						nwb[i].body.dense_weight[owlen] = 0;
+						break;
+					case IS_SPARSE_WEIGHT:
+						nwb[i].length = owb[i].length;
+						nwb[i].body.sparse_weight = owb[i].body.sparse_weight;
+						break;
+					case IS_BLOCK:
+						nwb[i].length = owb[i].length;
+						nwb[i].body.block = owb[i].body.block;
+						break;
+				}
+			}
+			nwb[i].type = IS_SPARSE_WEIGHT;
+			nwb[i].body.sparse_weight = 
+				(struct sparse_weight *)MALLOC(sizeof(struct sparse_weight));
+			nwb[i].body.sparse_weight[0].pos = onv;
+			nwb[i].body.sparse_weight[0].value = 1;
+			new->id = 3;
+			new->nv = nnv;
+			new->ord.composite.length = nlen;
+			new->ord.composite.w_or_b = nwb;
+			print_composite_order_spec(new);
+			break;
 		default:
 			error("homogenize_order : invalid input");
 	}
 }
 
-void qltozl(w,n,dvr)
-Q *w,*dvr;
-int n;
+void qltozl(Q *w,int n,Q *dvr)
 {
 	N nm,dn;
 	N g,l1,l2,l3;
@@ -1364,15 +1949,12 @@ int n;
 	*dvr = d;
 }
 
-int comp_nm(a,b)
-Q *a,*b;
+int comp_nm(Q *a,Q *b)
 {
 	return cmpn((*a)?NM(*a):0,(*b)?NM(*b):0);
 }
 
-void sortbynm(w,n)
-Q *w;
-int n;
+void sortbynm(Q *w,int n)
 {
 	qsort(w,n,sizeof(Q),(int (*)(const void *,const void *))comp_nm);
 }
@@ -1383,8 +1965,7 @@ int n;
  *
  */
 
-int dp_redble(p1,p2)
-DP p1,p2;
+int dp_redble(DP p1,DP p2)
 {
 	int i,n;
 	DL d1,d2;
@@ -1400,9 +1981,7 @@ DP p1,p2;
 	}
 }
 
-void dp_subd(p1,p2,rp)
-DP p1,p2;
-DP *rp;
+void dp_subd(DP p1,DP p2,DP *rp)
 {
 	int i,n;
 	DL d1,d2,d;
@@ -1418,10 +1997,7 @@ DP *rp;
 	*rp = s;
 }
 
-void dltod(d,n,rp)
-DL d;
-int n;
-DP *rp;
+void dltod(DL d,int n,DP *rp)
 {
 	MP m;
 	DP s;
@@ -1431,9 +2007,7 @@ DP *rp;
 	*rp = s;
 }
 
-void dp_hm(p,rp)
-DP p;
-DP *rp;
+void dp_hm(DP p,DP *rp)
 {
 	MP m,mr;
 
@@ -1446,9 +2020,21 @@ DP *rp;
 	}
 }
 
-void dp_rest(p,rp)
-DP p,*rp;
+void dp_ht(DP p,DP *rp)
 {
+	MP m,mr;
+
+	if ( !p )
+		*rp = 0;
+	else {
+		m = BDY(p);
+		NEWMP(mr); mr->dl = m->dl; mr->c = (P)ONE; NEXT(mr) = 0;
+		MKDP(p->nv,mr,*rp); (*rp)->sugar = mr->dl->td; 	/* XXX */
+	}
+}
+
+void dp_rest(DP p,DP *rp)
+{
 	MP m;
 
 	m = BDY(p);
@@ -1461,24 +2047,21 @@ DP p,*rp;
 	}
 }
 
-DL lcm_of_DL(nv,dl1,dl2,dl)
-int nv;
-DL dl1,dl2;
-register DL dl;
+DL lcm_of_DL(int nv,DL dl1,DL dl2,DL dl)
 {
-	register int n, *d1, *d2, *d, td;
+	register int i, *d1, *d2, *d, td;
 
 	if ( !dl ) NEWDL(dl,nv);
 	d = dl->d,  d1 = dl1->d,  d2 = dl2->d;
-	for ( td = 0, n = nv; --n >= 0; d1++, d2++, d++ )
-		td += (*d = *d1 > *d2 ? *d1 : *d2 );
+	for ( td = 0, i = 0; i < nv; d1++, d2++, d++, i++ ) {
+		*d = *d1 > *d2 ? *d1 : *d2;
+		td += MUL_WEIGHT(*d,i);
+	}
 	dl->td = td;
 	return dl;
 }
 
-int dl_equal(nv,dl1,dl2)
-int nv;
-DL dl1, dl2;
+int dl_equal(int nv,DL dl1,DL dl2)
 {
     register int *d1, *d2, n;
 
@@ -1488,8 +2071,7 @@ DL dl1, dl2;
     return 1;
 }
 
-int dp_nt(p)
-DP p;
+int dp_nt(DP p)
 {
 	int i;
 	MP m;
@@ -1502,3 +2084,262 @@ DP p;
 	}
 }
 
+int dp_homogeneous(DP p)
+{
+	MP m;
+	int d;
+
+	if ( !p )
+		return 1;
+	else {
+		m = BDY(p);
+		d = m->dl->td;
+		m = NEXT(m);
+		for ( ; m; m = NEXT(m) ) {
+			if ( m->dl->td != d )
+				return 0;
+		}
+		return 1;
+	}
+}
+
+void _print_mp(int nv,MP m)
+{
+	int i;
+
+	if ( !m )
+		return;
+	for ( ; m; m = NEXT(m) ) {
+		fprintf(stderr,"%d<",ITOS(C(m)));
+		for ( i = 0; i < nv; i++ ) {
+			fprintf(stderr,"%d",m->dl->d[i]);
+			if ( i != nv-1 )
+				fprintf(stderr," ");
+		}
+		fprintf(stderr,">",C(m));
+	}
+	fprintf(stderr,"\n");
+}
+
+static int cmp_mp_nvar;
+
+int comp_mp(MP *a,MP *b)
+{
+	return -(*cmpdl)(cmp_mp_nvar,(*a)->dl,(*b)->dl);
+}
+
+void dp_sort(DP p,DP *rp)
+{
+	MP t,mp,mp0;
+	int i,n;
+	DP r;
+	MP *w;
+
+	if ( !p ) {
+		*rp = 0;
+		return;
+	}
+	for ( t = BDY(p), n = 0; t; t = NEXT(t), n++ );
+	w = (MP *)ALLOCA(n*sizeof(MP));
+	for ( t = BDY(p), i = 0; i < n; t = NEXT(t), i++ )
+		w[i] = t;
+	cmp_mp_nvar = NV(p);
+	qsort(w,n,sizeof(MP),(int (*)(const void *,const void *))comp_mp);
+	mp0 = 0;
+	for ( i = n-1; i >= 0; i-- ) {
+		NEWMP(mp); mp->dl = w[i]->dl; C(mp) = C(w[i]);
+		NEXT(mp) = mp0; mp0 = mp;
+	}
+	MKDP(p->nv,mp0,r);
+	r->sugar = p->sugar;
+	*rp = r;
+}
+
+DP extract_initial_term_from_dp(DP p,int *weight,int n);
+LIST extract_initial_term(LIST f,int *weight,int n);
+
+DP extract_initial_term_from_dp(DP p,int *weight,int n)
+{
+	int w,t,i,top;
+	MP m,r0,r;
+	DP dp;
+
+	if ( !p ) return 0;
+	top = 1;
+	for ( m = BDY(p); m; m = NEXT(m) ) {
+		for ( i = 0, t = 0; i < n; i++ )	
+			t += weight[i]*m->dl->d[i];
+		if ( top || t > w ) {
+			r0 = 0;
+			w = t;
+			top = 0;
+		}
+		if ( t == w ) {
+			NEXTMP(r0,r);
+			r->dl = m->dl;
+			r->c = m->c;
+		}
+	}
+	NEXT(r) = 0;
+	MKDP(p->nv,r0,dp);
+	return dp;
+}
+
+LIST extract_initial_term(LIST f,int *weight,int n)
+{
+	NODE nd,r0,r;
+	Obj p;
+	LIST l;
+
+	nd = BDY(f);
+	for ( r0 = 0; nd; nd = NEXT(nd) ) {
+		NEXTNODE(r0,r);
+		p = (Obj)BDY(nd);
+		BDY(r) = (pointer)extract_initial_term_from_dp((DP)p,weight,n);
+	}
+	if ( r0 ) NEXT(r) = 0;
+	MKLIST(l,r0);
+	return l;
+}
+
+LIST dp_initial_term(LIST f,struct order_spec *ord)
+{
+	int n,l,i;
+	struct weight_or_block *worb;
+	int *weight;
+
+	switch ( ord->id ) {
+		case 2: /* matrix order */
+			/* extract the first row */
+			n = ord->nv;
+			weight = ord->ord.matrix.matrix[0];
+			return extract_initial_term(f,weight,n);
+		case 3: /* composite order */
+			/* the first w_or_b */
+			worb = ord->ord.composite.w_or_b;
+			switch ( worb->type ) {
+				case IS_DENSE_WEIGHT:
+					n = worb->length;
+					weight = worb->body.dense_weight;
+					return extract_initial_term(f,weight,n);
+				case IS_SPARSE_WEIGHT:
+					n = ord->nv;
+					weight = (int *)ALLOCA(n*sizeof(int));
+					for ( i = 0; i < n; i++ ) weight[i] = 0;
+					l = worb->length;
+					for ( i = 0; i < l; i++ )
+						weight[worb->body.sparse_weight[i].pos]
+							=  worb->body.sparse_weight[i].value;
+					return extract_initial_term(f,weight,n);
+				default:
+					error("dp_initial_term : unsupported order");
+			}
+		default:
+			error("dp_initial_term : unsupported order");
+	}
+}
+
+int highest_order_dp(DP p,int *weight,int n);
+LIST highest_order(LIST f,int *weight,int n);
+
+int highest_order_dp(DP p,int *weight,int n)
+{
+	int w,t,i,top;
+	MP m;
+
+	if ( !p ) return -1;
+	top = 1;
+	for ( m = BDY(p); m; m = NEXT(m) ) {
+		for ( i = 0, t = 0; i < n; i++ )	
+			t += weight[i]*m->dl->d[i];
+		if ( top || t > w ) {
+			w = t;
+			top = 0;
+		}
+	}
+	return w;
+}
+
+LIST highest_order(LIST f,int *weight,int n)
+{
+	int h;
+	NODE nd,r0,r;
+	Obj p;
+	LIST l;
+	Q q;
+
+	nd = BDY(f);
+	for ( r0 = 0; nd; nd = NEXT(nd) ) {
+		NEXTNODE(r0,r);
+		p = (Obj)BDY(nd);
+		h = highest_order_dp((DP)p,weight,n);
+		STOQ(h,q);
+		BDY(r) = (pointer)q;
+	}
+	if ( r0 ) NEXT(r) = 0;
+	MKLIST(l,r0);
+	return l;
+}
+
+LIST dp_order(LIST f,struct order_spec *ord)
+{
+	int n,l,i;
+	struct weight_or_block *worb;
+	int *weight;
+
+	switch ( ord->id ) {
+		case 2: /* matrix order */
+			/* extract the first row */
+			n = ord->nv;
+			weight = ord->ord.matrix.matrix[0];
+			return highest_order(f,weight,n);
+		case 3: /* composite order */
+			/* the first w_or_b */
+			worb = ord->ord.composite.w_or_b;
+			switch ( worb->type ) {
+				case IS_DENSE_WEIGHT:
+					n = worb->length;
+					weight = worb->body.dense_weight;
+					return highest_order(f,weight,n);
+				case IS_SPARSE_WEIGHT:
+					n = ord->nv;
+					weight = (int *)ALLOCA(n*sizeof(int));
+					for ( i = 0; i < n; i++ ) weight[i] = 0;
+					l = worb->length;
+					for ( i = 0; i < l; i++ )
+						weight[worb->body.sparse_weight[i].pos]
+							=  worb->body.sparse_weight[i].value;
+					return highest_order(f,weight,n);
+				default:
+					error("dp_initial_term : unsupported order");
+			}
+		default:
+			error("dp_initial_term : unsupported order");
+	}
+}
+
+int dpv_ht(DPV p,DP *h)
+{
+	int len,max,maxi,i,t;
+	DP *e;
+	MP m,mr;
+
+	len = p->len;
+	e = p->body;
+	max = -1;
+	maxi = -1;
+	for ( i = 0; i < len; i++ )
+		if ( e[i] && (t = BDY(e[i])->dl->td) > max ) {
+			max = t;
+			maxi = i;
+		}
+	if ( max < 0 ) {
+		*h = 0;
+		return -1;
+	} else {
+		m = BDY(e[maxi]);
+		NEWMP(mr); mr->dl = m->dl; mr->c = (P)ONE; NEXT(mr) = 0;
+		MKDP(e[maxi]->nv,mr,*h); (*h)->sugar = mr->dl->td;  /* XXX */
+		return maxi;
+	}
+}