===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/builtin/dp-supp.c,v
retrieving revision 1.29
retrieving revision 1.49
diff -u -p -r1.29 -r1.49
--- OpenXM_contrib2/asir2000/builtin/dp-supp.c	2004/02/09 08:23:29	1.29
+++ OpenXM_contrib2/asir2000/builtin/dp-supp.c	2009/01/04 05:44:51	1.49
@@ -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 1.28 2004/02/05 08:28:53 noro Exp $ 
+ * $OpenXM: OpenXM_contrib2/asir2000/builtin/dp-supp.c,v 1.48 2007/10/21 07:47:59 noro Exp $ 
 */
 #include "ca.h"
 #include "base.h"
@@ -62,11 +62,39 @@ extern int NoGCD;
 extern int GenTrace;
 extern NODE TraceList;
 
+int show_orderspec;
+
+void print_composite_order_spec(struct order_spec *spec);
+
 /* 
  * content reduction
  *
  */
 
+static NODE RatDenomList;
+
+void init_denomlist()
+{
+	RatDenomList = 0;
+}
+
+void add_denomlist(P f)
+{
+	NODE n;
+
+	if ( OID(f)==O_P ) {
+		MKNODE(n,f,RatDenomList); RatDenomList = n;
+	}
+}
+
+LIST get_denomlist()
+{
+	LIST l;
+
+	MKLIST(l,RatDenomList); RatDenomList = 0;
+	return l;
+}
+
 void dp_ptozp(DP p,DP *rp)
 {
 	MP m,mr,mr0;
@@ -118,6 +146,32 @@ 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;
@@ -418,6 +472,7 @@ void dp_prim(DP p,DP *rp)
 	P *w;
 	Q *c;
 	Q dvr;
+	NODE tn;
 
 	if ( !p )
 		*rp = 0;
@@ -472,6 +527,7 @@ void dp_prim(DP p,DP *rp)
 				NEXTMP(mr0,mr); divsp(CO,m->c,g,&mr->c); mr->dl = m->dl;
 			}
 			NEXT(mr) = 0; MKDP(p->nv,mr0,*rp); (*rp)->sugar = p->sugar;
+			add_denomlist(g);
 		}
 	}
 }
@@ -481,7 +537,9 @@ 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);
@@ -492,6 +550,8 @@ 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;
@@ -771,6 +831,7 @@ void dp_red(DP p0,DP p1,DP p2,DP *head,DP *rest,P *dnp
 	} else {
 		ezgcdpz(CO,(P)c1,(P)c2,&g);
 		divsp(CO,(P)c1,g,&a); c1 = (Q)a; divsp(CO,(P)c2,g,&a); c2 = (Q)a;
+		add_denomlist(g);
 	}
 	NEWMP(m); m->dl = d; chsgnp((P)c1,&m->c); NEXT(m) = 0; MKDP(n,m,s); s->sugar = d->td;
 	*multp = s;
@@ -779,6 +840,81 @@ void dp_red(DP p0,DP p1,DP p2,DP *head,DP *rest,P *dnp
 	*head = h; *rest = r; *dnp = (P)c2;
 }
 
+/*
+ * m-reduction by a marked poly
+ * do content reduction over Z or Q(x,...)
+ * do nothing over finite fields
+ *
+ */
+
+
+void dp_red_marked(DP p0,DP p1,DP p2,DP hp2,DP *head,DP *rest,P *dnp,DP *multp)
+{
+	int i,n;
+	DL d1,d2,d;
+	MP m;
+	DP t,s,r,h;
+	Q c,c1,c2;
+	N gn,tn;
+	P g,a;
+	P p[2];
+
+	n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(hp2)->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(hp2)->c;
+	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);
+		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;
+		}
+	} else {
+		ezgcdpz(CO,(P)c1,(P)c2,&g);
+		divsp(CO,(P)c1,g,&a); c1 = (Q)a; divsp(CO,(P)c2,g,&a); c2 = (Q)a;
+	}
+	NEWMP(m); m->dl = d; m->c = (P)c1; NEXT(m) = 0; MKDP(n,m,s); s->sugar = d->td;
+	*multp = s;
+	muld(CO,s,p2,&t); muldc(CO,p1,(P)c2,&s); subd(CO,s,t,&r);
+	muldc(CO,p0,(P)c2,&h);
+	*head = h; *rest = r; *dnp = (P)c2;
+}
+
+void dp_red_marked_mod(DP p0,DP p1,DP p2,DP hp2,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;
+
+	n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(hp2)->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 = (P)BDY(p1)->c; c2 = (P)BDY(hp2)->c;
+	gcdprsmp(CO,mod,c1,c2,&g);
+	divsmp(CO,mod,c1,g,&u); c1 = u; divsmp(CO,mod,c2,g,&u); c2 = u;
+	if ( NUM(c2) ) {
+		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,s,p2,&t);
+	if ( NUM(c2) ) {
+		addmd(CO,mod,p1,t,&r); h = p0;
+	} else {
+		mulmdc(CO,mod,p1,c2,&s); addmd(CO,mod,s,t,&r); mulmdc(CO,mod,p0,c2,&h);
+	}
+	*head = h; *rest = r; *dnp = c2;
+}
+
 /* m-reduction over a field */
 
 void dp_red_f(DP p1,DP p2,DP *rest)
@@ -927,6 +1063,231 @@ void dp_true_nf(NODE b,DP g,DP *ps,int full,DP *rp,P *
 	*rp = d; *dnp = dn;
 }
 
+void dp_removecont2(DP p1,DP p2,DP *r1p,DP *r2p,Q *contp)
+{
+	struct oVECT v;
+	int i,n1,n2,n;
+	MP m,m0,t;
+	Q *w;
+	Q h;
+
+	if ( p1 ) {
+		for ( i = 0, m = BDY(p1); m; m = NEXT(m), i++ );
+		n1 = i;
+	} else
+		n1 = 0;
+	if ( p2 ) {
+		for ( i = 0, m = BDY(p2); m; m = NEXT(m), i++ );
+		n2 = i;
+	} else
+		n2 = 0;
+	n = n1+n2;
+	if ( !n ) {
+		*r1p = 0; *r2p = 0; *contp = ONE; return;
+	}
+	w = (Q *)ALLOCA(n*sizeof(Q));
+	v.len = n;
+	v.body = (pointer *)w;
+	i = 0;
+	if ( p1 )
+		for ( m = BDY(p1); i < n1; m = NEXT(m), i++ ) w[i] = (Q)m->c;
+	if ( p2 )
+		for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) w[i] = (Q)m->c;
+	h = w[0]; removecont_array((P *)w,n,1); divq(h,w[0],contp);
+	i = 0;
+	if ( p1 ) {
+		for ( m0 = 0, t = BDY(p1); i < n1; i++, t = NEXT(t) ) {
+			NEXTMP(m0,m); m->c = (P)w[i]; m->dl = t->dl;
+		}
+		NEXT(m) = 0;
+		MKDP(p1->nv,m0,*r1p); (*r1p)->sugar = p1->sugar;
+	} else
+		*r1p = 0;
+	if ( p2 ) {
+		for ( m0 = 0, t = BDY(p2); i < n; i++, t = NEXT(t) ) {
+			NEXTMP(m0,m); m->c = (P)w[i]; m->dl = t->dl;
+		}
+		NEXT(m) = 0;
+		MKDP(p2->nv,m0,*r2p); (*r2p)->sugar = p2->sugar;
+	} else
+		*r2p = 0;
+}
+
+/* true nf by a marked GB */
+
+void dp_true_nf_marked(NODE b,DP g,DP *ps,DP *hps,DP *rp,P *nmp,P *dnp)
+{
+	DP u,p,d,s,t,dmy,hp;
+	NODE l;
+	MP m,mr;
+	int i,n,hmag;
+	int *wb;
+	int sugar,psugar,multiple;
+	P nm,tnm1,dn,tdn,tdn1;
+	Q cont;
+
+	multiple = 0;
+	hmag = multiple*HMAG(g);
+	nm = (P)ONE;
+	dn = (P)ONE;
+	if ( !g ) {
+		*rp = 0; *dnp = dn; 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,hp = hps[wb[i]]) ) {
+				p = ps[wb[i]];
+				dp_red_marked(d,g,p,hp,&t,&u,&tdn,&dmy);
+				psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
+				sugar = MAX(sugar,psugar);
+				if ( !u ) {
+					goto last;
+				} else {
+					d = t;
+					mulp(CO,dn,tdn,&tdn1); dn = tdn1;
+				}
+				break;
+			}
+		}
+		if ( u ) {
+			g = u;
+			if ( multiple && ((d && HMAG(d)>hmag) || (HMAG(g)>hmag)) ) {
+				dp_removecont2(d,g,&t,&u,&cont); d = t; g = u;
+				mulp(CO,nm,(P)cont,&tnm1); nm = tnm1;
+				if ( d )
+					hmag = multiple*HMAG(d);
+				else
+					hmag = multiple*HMAG(g);
+			}
+		} 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;
+		}
+	}
+last:
+	if ( d ) {
+		dp_removecont2(d,0,&t,&u,&cont); d = t;
+		mulp(CO,nm,(P)cont,&tnm1); nm = tnm1;
+		d->sugar = sugar;
+	}
+	*rp = d; *nmp = nm; *dnp = dn;
+}
+
+void dp_true_nf_marked_mod(NODE b,DP g,DP *ps,DP *hps,int mod,DP *rp,P *dnp)
+{
+	DP hp,u,p,d,s,t;
+	NODE l;
+	MP m,mr;
+	int i,n;
+	int *wb;
+	int sugar,psugar;
+	P dn,tdn,tdn1;
+
+	dn = (P)ONEM;
+	if ( !g ) {
+		*rp = 0; *dnp = dn; 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,hp = hps[wb[i]]) ) {
+				p = ps[wb[i]];
+				dp_red_marked_mod(d,g,p,hp,mod,&t,&u,&tdn);	
+				psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
+				sugar = MAX(sugar,psugar);
+				if ( !u ) {
+					if ( d )
+						d->sugar = sugar;
+					*rp = d; *dnp = dn; return;
+				} else {
+					d = t;
+					mulmp(CO,mod,dn,tdn,&tdn1); dn = tdn1;
+				}
+				break;
+			}
+		}
+		if ( u )
+			g = u;
+		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;
+			addmd(CO,mod,d,t,&s); d = s;
+			dp_rest(g,&t); g = t;
+		}
+	}
+	if ( d )
+		d->sugar = sugar;
+	*rp = d; *dnp = dn;
+}
+
+/* true nf by a marked GB and collect quotients */
+
+DP *dp_true_nf_and_quotient_marked (NODE b,DP g,DP *ps,DP *hps,DP *rp,P *dnp)
+{
+	DP u,p,d,s,t,dmy,hp,mult;
+	DP *q;
+	NODE l;
+	MP m,mr;
+	int i,n,j;
+	int *wb;
+	int sugar,psugar,multiple;
+	P nm,tnm1,dn,tdn,tdn1;
+	Q cont;
+
+	dn = (P)ONE;
+	if ( !g ) {
+		*rp = 0; *dnp = dn; 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));
+	q = (DP *)MALLOC(n*sizeof(DP));
+	for ( i = 0; i < n; i++ ) q[i] = 0;
+	sugar = g->sugar;
+	for ( d = 0; g; ) {
+		for ( u = 0, i = 0; i < n; i++ ) {
+			if ( dp_redble(g,hp = hps[wb[i]]) ) {
+				p = ps[wb[i]];
+				dp_red_marked(d,g,p,hp,&t,&u,&tdn,&mult);
+				psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
+				sugar = MAX(sugar,psugar);
+				for ( j = 0; j < n; j++ ) {
+					muldc(CO,q[j],(P)tdn,&dmy); q[j] = dmy;
+				}
+				addd(CO,q[wb[i]],mult,&dmy); q[wb[i]] = dmy;
+				mulp(CO,dn,tdn,&tdn1); dn = tdn1;
+				d = t;
+				if ( !u ) goto last;
+				break;
+			}
+		}
+		if ( u ) {
+			g = u;
+		} 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;
+		}
+	}
+last:
+	if ( d ) d->sugar = sugar;
+	*rp = d; *dnp = dn;
+	return q;
+}
+
 /* nf computation over Z */
 
 void dp_nf_z(NODE b,DP g,DP *ps,int full,int multiple,DP *rp)
@@ -1311,21 +1672,27 @@ void dp_nf_tab_f(DP p,LIST *tab,DP *rp)
 
 /*
  * setting flags
+ * call create_order_spec with vl=0 to set old type order.
  *
  */
 
 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;
+	VECT v;
+	pointer **b,*bv;
 	int **w;
 
-	if ( vl && obj && OID(obj) == O_LIST )
-		return create_composite_order_spec(vl,(LIST)obj,specp);
+	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) ) {
@@ -1355,6 +1722,14 @@ int create_order_spec(VL vl,Obj obj,struct order_spec 
 		spec->nv = col; spec->ord.matrix.row = row;
 		spec->ord.matrix.matrix = w;
 		return 1;
+	} else if ( OID(obj) == O_VECT ) {
+		v = (VECT)obj; bv = BDY(v);
+		if ( v->len < 2 ) error("create_order_spec : invalid argument");
+		create_order_spec(0,(Obj)bv[1],&spec);
+		spec->id += 256; spec->obj = obj;
+		spec->istop = bv[0]==0;
+		*specp = spec;
+		return 1;
 	} else
 		return 0;
 }
@@ -1405,6 +1780,95 @@ void print_composite_order_spec(struct order_spec *spe
 	}
 }
 
+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,...] */
@@ -1443,14 +1907,19 @@ int create_composite_order_spec(VL vl,LIST order,struc
 	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++ )
+			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;
@@ -1465,14 +1934,20 @@ int create_composite_order_spec(VL vl,LIST order,struc
 			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");
+					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;
@@ -1522,10 +1997,13 @@ int create_composite_order_spec(VL vl,LIST order,struc
 				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) )
+					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");
+					error("a block must be contiguous in the variable list");
 			}
 			w_or_b[i].type = IS_BLOCK;
 			w_or_b[i].length = len;
@@ -1552,9 +2030,37 @@ int create_composite_order_spec(VL vl,LIST order,struc
 		w_or_b[n].body.block.order = 0;
 		spec->ord.composite.length = n+1;
 	}
-	if ( 1 ) print_composite_order_spec(spec);
 }
 
+/* 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
  *
@@ -1658,6 +2164,8 @@ void homogenize_order(struct order_spec *old,int n,str
 	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 ) {
@@ -1708,6 +2216,46 @@ 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");
 	}
@@ -1812,6 +2360,19 @@ 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;
@@ -1934,3 +2495,462 @@ void dp_sort(DP p,DP *rp)
 	*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;
+	}
+}
+
+/* return 1 if 0 <_w1 v && v <_w2 0 */
+
+int in_c12(int n,int *v,int row1,int **w1,int row2, int **w2)
+{
+	int t1,t2;
+
+	t1 = compare_zero(n,v,row1,w1);
+	t2 = compare_zero(n,v,row2,w2);
+	if ( t1 > 0 && t2 < 0 ) return 1;
+	else return 0;
+}
+
+/* 0 < u => 1, 0 > u => -1 */
+
+int compare_zero(int n,int *u,int row,int **w)
+{
+	int i,j,t;
+	int *wi;
+
+	for ( i = 0; i < row; i++ ) {
+		wi = w[i];
+		for ( j = 0, t = 0; j < n; j++ ) t += u[j]*wi[j];
+		if ( t > 0 ) return 1;
+		else if ( t < 0 ) return -1;
+	}
+	return 0;
+}
+
+/* functions for generic groebner walk */
+/* u=0 means u=-infty */
+
+int compare_facet_preorder(int n,int *u,int *v,
+	int row1,int **w1,int row2,int **w2)
+{
+	int i,j,s,t,tu,tv;
+	int *w2i,*uv;
+
+	if ( !u ) return 1;
+	uv = W_ALLOC(n);
+	for ( i = 0; i < row2; i++ ) {
+		w2i = w2[i];
+		for ( j = 0, tu = tv = 0; j < n; j++ )
+			if ( s = w2i[j] ) {
+				tu += s*u[j]; tv += s*v[j];
+			}
+		for ( j = 0; j < n; j++ ) uv[j] = u[j]*tv-v[j]*tu;
+		t = compare_zero(n,uv,row1,w1);
+		if ( t > 0 ) return 1;
+		else if ( t < 0 ) return 0;
+	}
+	return 1;
+}
+
+Q inner_product_with_small_vector(VECT w,int *v)
+{
+	int n,i;
+	Q q,s,t,u;
+
+	n = w->len;
+	s = 0;
+	for ( i = 0; i < n; i++ ) {
+		STOQ(v[i],q); mulq((Q)w->body[i],q,&t); addq(t,s,&u); s = u;
+	}
+	return s;
+}
+
+Q compute_last_t(NODE g,NODE gh,Q t,VECT w1,VECT w2,NODE *homo,VECT *wp)
+{
+	int n,i;
+	int *wt;
+	Q last,d1,d2,dn,nm,s,t1;
+	VECT wd,wt1,wt2,w;
+	NODE tg,tgh;
+	MP f;
+	int *h;
+	NODE r0,r;
+	MP m0,m;
+	DP d;
+
+	n = w1->len;
+	wt = W_ALLOC(n);
+	last = ONE;
+	/* t1 = 1-t */
+	for ( tg = g, tgh = gh; tg; tg = NEXT(tg), tgh = NEXT(tgh ) ) {
+		f = BDY((DP)BDY(tg));
+		h = BDY((DP)BDY(tgh))->dl->d;
+		for ( ; f; f = NEXT(f) ) {
+			for ( i = 0; i < n; i++ ) wt[i] = h[i]-f->dl->d[i];
+			for ( i = 0; i < n && !wt[i]; i++ );
+			if ( i == n ) continue;
+			d1 = inner_product_with_small_vector(w1,wt);
+			d2 = inner_product_with_small_vector(w2,wt);
+			nm = d1; subq(d1,d2,&dn);
+			/* if d1=d2 then nothing happens */
+			if ( !dn ) continue;
+			/* s satisfies ds = 0*/
+			divq(nm,dn,&s);
+
+			if ( cmpq(s,t) > 0 && cmpq(s,last) < 0 ) 
+				last = s;
+			else if ( !cmpq(s,t) ) {
+				if ( cmpq(d2,0) < 0 ) {
+					last = t;
+					break;
+				}
+			}
+		}
+	}
+	if ( !last ) {
+		dn = ONE; nm = 0;
+	} else {
+		NTOQ(NM(last),1,nm);
+		if ( INT(last) ) dn = ONE;
+		else {
+			NTOQ(DN(last),1,dn);
+		}
+	}
+	/* (1-n/d)*w1+n/d*w2 -> w=(d-n)*w1+n*w2 */
+	subq(dn,nm,&t1); mulvect(CO,(Obj)w1,(Obj)t1,(Obj *)&wt1); 
+	mulvect(CO,(Obj)w2,(Obj)nm,(Obj *)&wt2); addvect(CO,wt1,wt2,&w);
+
+	r0 = 0;
+	for ( tg = g, tgh = gh; tg; tg = NEXT(tg), tgh = NEXT(tgh ) ) {
+		f = BDY((DP)BDY(tg));
+		h = BDY((DP)BDY(tgh))->dl->d;
+		for ( m0 = 0; f; f = NEXT(f) ) {
+			for ( i = 0; i < n; i++ ) wt[i] = h[i]-f->dl->d[i];
+			for ( i = 0; i < n && !wt[i]; i++ );
+			if ( !inner_product_with_small_vector(w,wt) ) {
+				NEXTMP(m0,m); m->c = f->c; m->dl = f->dl;
+			}
+		}
+		NEXT(m) = 0;
+		MKDP(((DP)BDY(tg))->nv,m0,d);  d->sugar = ((DP)BDY(tg))->sugar;
+		NEXTNODE(r0,r); BDY(r) = (pointer)d;
+	}
+	NEXT(r) = 0;
+	*homo = r0;
+	*wp = w;
+	return last;
+}
+
+/* return 0 if last_w = infty */
+
+NODE compute_last_w(NODE g,NODE gh,int n,int **w,
+	int row1,int **w1,int row2,int **w2)
+{
+	DP d;
+	MP f,m0,m;
+	int *wt,*v,*h;
+	NODE t,s,n0,tn,n1,r0,r;
+	int i;
+
+	wt = W_ALLOC(n);
+	n0 = 0;
+	for ( t = g, s = gh; t; t = NEXT(t), s = NEXT(s) ) {
+		f = BDY((DP)BDY(t));
+		h = BDY((DP)BDY(s))->dl->d;
+		for ( ; f; f = NEXT(f) ) {
+			for ( i = 0; i < n; i++ ) wt[i] = h[i]-f->dl->d[i];
+			for ( i = 0; i < n && !wt[i]; i++ );
+			if ( i == n ) continue;
+
+			if ( in_c12(n,wt,row1,w1,row2,w2) && 
+				compare_facet_preorder(n,*w,wt,row1,w1,row2,w2) ) {
+				v = (int *)MALLOC_ATOMIC(n*sizeof(int));
+				for ( i = 0; i < n; i++ ) v[i] = wt[i];
+				MKNODE(n1,v,n0); n0 = n1;
+			}
+		}
+	}
+	if ( !n0 ) return 0;
+	for ( t = n0; t; t = NEXT(t) ) {
+		v = (int *)BDY(t);
+		for ( s = n0; s; s = NEXT(s) )
+			if ( !compare_facet_preorder(n,v,(int *)BDY(s),row1,w1,row2,w2) )
+				break;
+		if ( !s ) {
+			*w = v;
+			break;
+		}
+	}
+	if ( !t )
+		error("compute_last_w : cannot happen");
+	r0 = 0;
+	for ( t = g, s = gh; t; t = NEXT(t), s = NEXT(s) ) {
+		f = BDY((DP)BDY(t));
+		h = BDY((DP)BDY(s))->dl->d;
+		for ( m0 = 0; f; f = NEXT(f) ) {
+			for ( i = 0; i < n; i++ ) wt[i] = h[i]-f->dl->d[i];
+			for ( i = 0; i < n && !wt[i]; i++ );
+			if ( i == n  ||
+				(compare_facet_preorder(n,wt,*w,row1,w1,row2,w2)
+				&& compare_facet_preorder(n,*w,wt,row1,w1,row2,w2)) ) {
+				NEXTMP(m0,m); m->c = f->c; m->dl = f->dl;
+			}
+		}
+		NEXT(m) = 0;
+		MKDP(((DP)BDY(t))->nv,m0,d);  d->sugar = ((DP)BDY(t))->sugar;
+		NEXTNODE(r0,r); BDY(r) = (pointer)d;
+	}
+	NEXT(r) = 0;
+	return r0;
+}
+
+/* compute a sufficient set of d(f)=u-v */
+
+NODE compute_essential_df(DP *g,DP *gh,int ng)
+{
+	int nv,i,j,k,t,lj;
+	NODE r,r1,ri,rt,r0;
+	MP m;
+	MP *mj;
+	DL di,hj,dl,dlt;
+	int *d,*dt;
+	LIST l;
+	Q q;
+
+	nv = g[0]->nv;
+	r = 0;
+	for ( j = 0; j < ng; j++ ) {
+		for ( m = BDY(g[j]), lj = 0; m; m = NEXT(m), lj++ );
+		mj = (MP *)ALLOCA(lj*sizeof(MP));
+		for ( m = BDY(g[j]), k = 0; m; m = NEXT(m), k++ )
+			mj[k] = m;
+		for ( i = 0; i < lj; i++ ) {
+			for ( di = mj[i]->dl, k = i+1; k < lj; k++ )
+				if ( _dl_redble(di,mj[k]->dl,nv) ) break;
+			if ( k < lj ) mj[i] = 0;
+		}
+		hj = BDY(gh[j])->dl;
+		_NEWDL(dl,nv); d = dl->d;
+		r0 = r;
+		for ( i = 0; i < lj; i++ ) {
+			if ( mj[i] && !dl_equal(nv,di=mj[i]->dl,hj) ) {
+				for ( k = 0, t = 0; k < nv; k++ ) {
+					d[k] = hj->d[k]-di->d[k];
+					t += d[k];
+				}
+				dl->td = t;	
+#if 1
+				for ( rt = r0; rt; rt = NEXT(rt) ) {
+					dlt = (DL)BDY(rt);
+					if ( dlt->td != dl->td ) continue;
+					for ( dt = dlt->d, k = 0; k < nv; k++ )
+						if ( d[k] != dt[k] ) break;
+					if ( k == nv ) break;
+				}
+#else
+				rt = 0;
+#endif
+				if ( !rt ) {
+					MKNODE(r1,dl,r); r = r1;
+					_NEWDL(dl,nv); d = dl->d;
+				}
+			}
+		}
+	}
+	for ( rt = r; rt; rt = NEXT(rt) ) {
+		dl = (DL)BDY(rt); d = dl->d;
+		ri = 0;
+		for ( k = nv-1; k >= 0; k-- ) {
+			STOQ(d[k],q);
+			MKNODE(r1,q,ri); ri = r1;
+		}
+		MKNODE(r1,0,ri); MKLIST(l,r1);
+		BDY(rt) = (pointer)l;
+	}
+	return r;
+}