===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/builtin/dp-supp.c,v
retrieving revision 1.21
retrieving revision 1.40
diff -u -p -r1.21 -r1.40
--- OpenXM_contrib2/asir2000/builtin/dp-supp.c	2002/01/28 00:54:41	1.21
+++ OpenXM_contrib2/asir2000/builtin/dp-supp.c	2006/12/12 11:50:37	1.40
@@ -45,7 +45,7 @@
  * 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 1.20 2001/10/09 01:36:05 noro Exp $ 
+ * $OpenXM: OpenXM_contrib2/asir2000/builtin/dp-supp.c,v 1.39 2005/08/25 18:59:11 ohara Exp $ 
 */
 #include "ca.h"
 #include "base.h"
@@ -62,6 +62,10 @@ extern int NoGCD;
 extern int GenTrace;
 extern NODE TraceList;
 
+int show_orderspec;
+
+void print_composite_order_spec(struct order_spec *spec);
+
 /* 
  * content reduction
  *
@@ -118,6 +122,32 @@ void dp_ptozp2(DP p0,DP p1,DP *hp,DP *rp)
 	*hp = h; *rp = r;
 }
 
+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;
@@ -371,6 +401,44 @@ void dp_ptozp2_d(DP p0,DP p1,DP *hp,DP *rp)
 	*hp = h; *rp = r;
 }
 
+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;
@@ -383,7 +451,30 @@ void dp_prim(DP p,DP *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);
@@ -420,7 +511,9 @@ void heu_nezgcdnpz(VL vl,P *pl,int m,P *pr)
 	int i,r;
 	P gcd,t,s1,s2,u;
 	Q rq;
-	
+	DCP dc;
+	extern int DP_Print;
+
 	while ( 1 ) {
 		for ( i = 0, s1 = 0; i < m; i++ ) {
 			r = random(); UTOQ(r,rq);
@@ -431,6 +524,8 @@ void heu_nezgcdnpz(VL vl,P *pl,int m,P *pr)
 			mulp(vl,pl[i],(P)rq,&t); addp(vl,s2,t,&u); s2 = u;
 		}
 		ezgcdp(vl,s1,s2,&gcd);
+		if ( DP_Print > 2 ) 
+			{ fprintf(asir_out,"(%d)",nmonop(gcd)); fflush(asir_out); }
 		for ( i = 0; i < m; i++ ) {
 			if ( !divtpz(vl,pl[i],gcd,&t) )
 				break;
@@ -688,13 +783,18 @@ void dp_red(DP p0,DP p1,DP p2,DP *head,DP *rest,P *dnp
 	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);
@@ -1222,20 +1322,51 @@ void dp_nf_tab_mod(DP p,LIST *tab,int mod,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 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);
@@ -1267,6 +1398,333 @@ int create_order_spec(Obj obj,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
  *
@@ -1364,12 +1822,16 @@ void dp_rat(DP p,DP *rp)
 }
 
 
-void homogenize_order(struct order_spec *old,int n,struct order_spec *new)
+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 ) {
@@ -1418,6 +1880,46 @@ void homogenize_order(struct order_spec *old,int n,str
 			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");
 	}
@@ -1522,6 +2024,19 @@ void dp_hm(DP p,DP *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;
@@ -1608,4 +2123,227 @@ void _print_mp(int nv,MP m)
 		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;
+	}
 }