===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/Hgfs.c,v
retrieving revision 1.3
retrieving revision 1.12
diff -u -p -r1.3 -r1.12
--- OpenXM_contrib2/asir2000/engine/Hgfs.c	2001/06/22 08:51:12	1.3
+++ OpenXM_contrib2/asir2000/engine/Hgfs.c	2001/06/27 04:07:57	1.12
@@ -1,4 +1,4 @@
-/* $OpenXM: OpenXM_contrib2/asir2000/engine/Hgfs.c,v 1.2 2001/06/21 07:47:02 noro Exp $ */
+/* $OpenXM: OpenXM_contrib2/asir2000/engine/Hgfs.c,v 1.11 2001/06/26 09:47:05 noro Exp $ */
 
 #include "ca.h"
 
@@ -13,7 +13,23 @@ void lnfsf(int,UM,UM,struct p_pair *,UM,UM);
 void minipolysf(UM,UM,UM);
 void czsfum(UM,UM *);
 void gensqfrsfum(UM,DUM);
+void sfbmtop(int,BM,V,V,P *);
+void pp_sfp(VL,P,P *);
+void sfcsump(VL,P,P *);
+void mulsfbmarray(int,BM,ML,int,int *,V,V,P *);
+void const_term(P,UM);
 
+int comp_dum(a,b)
+DUM a,b;
+{
+	if ( DEG(a->f) > DEG(b->f) )
+		return -1;
+	else if ( DEG(a->f) < DEG(b->f) )
+		return 1;
+	else
+		return 0;
+}
+
 void fctrsf(p,dcp)
 P p;
 DCP *dcp;
@@ -61,6 +77,10 @@ DCP *dcp;
 			}
 		}
 	udc = udc1;
+	for ( i = 0; udc[i].f; i++ );
+	qsort(udc,i,sizeof(struct oDUM),
+		(int (*)(const void *,const void *))comp_dum);
+
 	NEWDC(dc0); COEF(dc0) = lc; DEG(dc0) = ONE; dc = dc0;
 	for ( n = 0; udc[n].f; n++ ) {
 		NEWDC(NEXT(dc)); dc = NEXT(dc);
@@ -534,30 +554,32 @@ int sfberle(VL,P,int,GFS *,DCP *);
 void sfgcdgen(P,ML,ML *);
 void sfhenmain(LUM,ML,ML,ML *);
 void ptosflum(int,P,LUM);
+void sfhenmain2(BM,UM,UM,int,BM *);
+void ptosfbm(int,P,BM);
 
 /* f = f(x,y) */
 
-void sfhensel(count,f,x,listp)
+void sfhensel(count,f,x,evp,sfp,listp)
 int count;
 P f;
 V x;
+GFS *evp;
+P *sfp;
 ML *listp;
 {
 	int i,j;
 	int fn,n,bound;
-	int *p;
-	int **pp;
-	ML blist,clist,rlist;
-	UM *b;
-	LUM fl,tl;
-	LUM *l;
+	ML rlist;
+	BM fl;
 	VL vl,nvl;
 	V y;
-	int dx,dy;
+	int dx,dy,mev;
 	GFS ev;
-	P f1,g,g0,t,yev,c;
+	P f1,t,yev,c,sf;
 	DCP dc;
-	LUM gl;
+	UM w,w1,q,fm,hm;
+	UM *gm;
+	struct oEGT tmp0,tmp1,eg_hensel,eg_hensel_t;
 
 	clctv(CO,f,&vl);
 	if ( vl->v != x ) {
@@ -568,34 +590,74 @@ ML *listp;
 	dx = getdeg(x,f);
 	dy = getdeg(y,f);
 	if ( dx == 1 ) {
-		*listp = blist = MLALLOC(1); blist->n = 1; blist->c[0] = 0;
+		*listp = rlist = MLALLOC(1); rlist->n = 1; rlist->c[0] = 0;
 		return;
 	}
 	fn = sfberle(vl,f,count,&ev,&dc);
 	if ( fn <= 1 ) {
 		/* fn == 0 => short of evaluation points */
-		*listp = blist = MLALLOC(1); blist->n = fn; blist->c[0] = 0;
+		*listp = rlist = MLALLOC(1); rlist->n = fn; rlist->c[0] = 0;
 		return;
 	}
 	/* pass the the leading coeff. to the first element */
 	c = dc->c; dc = NEXT(dc);
 	mulp(vl,dc->c,c,&t); dc->c = t;
-	blist = MLALLOC(n); 
-	blist->n = fn;
+
+	/* convert mod y-a factors into UM */
+	gm = (UM *)ALLOCA(fn*sizeof(UM));
 	for ( i = 0; i < fn; i++, dc = NEXT(dc) ) {
-		blist->c[i] = W_UMALLOC(UDEG(dc->c));
-		ptosfum(dc->c,blist->c[i]);
+		gm[i] = W_UMALLOC(UDEG(dc->c));
+		ptosfum(dc->c,gm[i]);
 	}
-	/* f(x,y) -> g = f(x,y+ev) */
-	MKV(y,t); addp(vl,t,(P)ev,&yev);
-	substp(vl,f,y,yev,&g);
-	substp(vl,g,y,0,&g0);
 
-	sfgcdgen(g0,blist,&clist);
-	blist->bound = clist->bound = dy;
-	W_LUMALLOC(dx,bound,gl);
-	ptosflum(bound,g,gl);
-	sfhenmain(gl,blist,clist,listp);
+	bound = dy+1;
+	/* f(x,y) -> f(x,y+ev) */
+	fl = BMALLOC(dx,bound);
+	ptosfbm(bound,f,fl);
+	shiftsfbm(bound,fl,FTOIF(CONT(ev)));
+
+	/* sf = f(x+ev) */
+	sfbmtop(bound,fl,x,y,&sf);
+
+	/* fm = fl mod y */
+	fm = W_UMALLOC(dx);
+	cpyum(COEF(fl)[0],fm);
+	hm = W_UMALLOC(dx);
+
+	q = W_UMALLOC(dx);
+	rlist = MLALLOC(fn); rlist->n = fn; rlist->bound = bound;
+	fprintf(asir_out,"%d candidates\n",fn);
+	init_eg(&eg_hensel);
+	for ( i = 0; i < fn-1; i++ ) {
+		fprintf(asir_out,"deg(fm) = %d, deg(gm[%d]) = %d\n",
+			DEG(fm),i,DEG(gm[i]));
+		init_eg(&eg_hensel_t);
+		get_eg(&tmp0);
+		/* fl = gm[i]*hm mod y */
+		divsfum(fm,gm[i],hm);
+		/* fl is replaced by the cofactor of gk mod y^bound */
+		/* rlist->c[i] = gk */
+		sfhenmain2(fl,gm[i],hm,bound,(BM *)&rlist->c[i]);
+		cpyum(hm,fm);
+		get_eg(&tmp1); add_eg(&eg_hensel_t,&tmp0,&tmp1);
+		add_eg(&eg_hensel,&tmp0,&tmp1);
+		print_eg("Hensel",&eg_hensel_t);
+		fprintf(asir_out,"\n");
+	}
+	print_eg("Hensel total",&eg_hensel);
+	fprintf(asir_out,"\n");
+	/* finally, fl must be the lift of gm[fn-1] */
+	rlist->c[i] = fl;
+
+#if 0
+	/* y -> y-a */
+	mev = _chsgnsf(FTOIF(CONT(ev)));
+	for ( i = 0; i < fn; i++ )
+		shiftsfbm(bound,(BM)(rlist->c[i]),mev);
+#endif
+	*evp = ev;
+	*sfp = sf;
+	*listp = rlist;
 }
 
 /* main variable of f = x */
@@ -626,13 +688,13 @@ DCP *dcp;
 	q1 = field_order_sf()-1;
 	lc = DC(f)->c;
 	for ( j = 0, fn = n + 1, index = 0; 
-		index < q1 && j < count && fn > 1; ) {
+		index < q1 && j < count && fn > 1; index++ ) {
 		MKGFS(index,m);
 		substp(vl,lc,y,(P)m,&lc0);
 		if ( lc0 ) {
 			substp(vl,f,y,(P)m,&f0);
-			ptosfum(m,f,wf); cpyum(wf,wf1); 
-			diffsfum(m,wf1,wf2); gcdsfum(m,wf1,wf2,gcd);
+			ptosfum(f0,wf); cpyum(wf,wf1); 
+			diffsfum(wf1,wf2); gcdsfum(wf1,wf2,gcd);
 			if ( DEG(gcd) == 0 ) {
 				fctrsf(f0,&dc);
 				for ( dct = NEXT(dc), i = 0; dct; dct = NEXT(dct), i++ );
@@ -715,11 +777,20 @@ ML bqlist,cqlist,*listp;
 			pp[j][0] = px[j];
 	}
 	for ( i = 1; i < bound; i++ ) {
+		fprintf(stderr,".");
+		/* at this point, f = l[0]*l[1]*...*l[np-1] mod y^i */
 		mulsflum(i+1,l[0],l[1],wb0);
 		for ( j = 2; j < np; j++ ) {
 			mulsflum(i+1,l[j],wb0,wb1);
 			tlum = wb0; wb0 = wb1; wb1 = tlum;
 		}
+#if 0
+		/* check */
+		for ( j = 0, pp = COEF(f), pp1 = COEF(wb0); j <= n; j++ )
+			for ( k = 0; k < i; k++ )
+				if ( pp[j][k] != pp1[j][k] )
+					error("henmain : cannot happen");
+#endif
 		for ( j = n, px = COEF(wt); j >= 0; j-- )
 			px[j] = 0;
 		for ( j = n, pp = COEF(f), pp1 = COEF(wb0); j >= 0; j-- )
@@ -741,8 +812,134 @@ ML bqlist,cqlist,*listp;
 		for ( j = n, px = COEF(wq0); j >= 0; j-- ) 
 			px[j] = 0;
 	}
+	fprintf(stderr,"\n");
 }
 
+/* f = g0*h0 mod y -> f = gk*hk mod y^bound, f is replaced by hk */
+
+void sfhenmain2(f,g0,h0,bound,gp)
+BM f;
+UM g0,h0;
+int bound;
+BM *gp;
+{
+	int i,j,k,l;
+	int *px,*py;
+	int **pp,**pp1;
+	int n,np,dr,tmp;
+	UM wt,wa,wb,wq,wm,q,w1,w2,wh1,wg1,ws;
+	UM wc,wd,we,wz;
+	BM wb0,wb1;
+	int ng,nh;
+	BM fk,gk,hk;
+	
+	n = degsfbm(bound,f);
+	ng = g0->d;
+	nh = h0->d;
+
+	W_BMALLOC(n,bound,wb0); W_BMALLOC(n,bound,wb1);
+	wt = W_UMALLOC(n); ws = W_UMALLOC(n);
+	wq = W_UMALLOC(n); q = W_UMALLOC(2*n);
+	wg1 = W_UMALLOC(2*n); wh1 = W_UMALLOC(2*n);
+
+	/* fk = gk*hk mod y^k */
+	W_BMALLOC(n,bound,fk);
+	cpyum(COEF(f)[0],COEF(fk)[0]);
+	gk = BMALLOC(ng,bound);
+	cpyum(g0,COEF(gk)[0]);
+	W_BMALLOC(nh,bound,hk);
+	cpyum(h0,COEF(hk)[0]);
+
+	wc = W_UMALLOC(2*n); wd = W_UMALLOC(2*n);
+	we = W_UMALLOC(2*n); wz = W_UMALLOC(2*n);
+
+	/* compute wa,wb s.t. wa*g0+wb*h0 = 1 mod y */
+	w1 = W_UMALLOC(ng); cpyum(g0,w1);
+	w2 = W_UMALLOC(nh); cpyum(h0,w2);
+	wa = W_UMALLOC(2*n); wb = W_UMALLOC(2*n);  /* XXX */
+	eucsfum(w1,w2,wa,wb);
+
+#if 0
+	mulsfum(wa,g0,wc); mulsfum(wb,h0,wd); addsfum(wc,wd,we);
+	if ( DEG(we) != 0 || COEF(we)[0] != _onesf() )
+			error("henmain2 : cannot happen(euc)");
+#endif
+
+	fprintf(stderr,"bound=%d\n",bound);
+	for ( k = 1; k < bound; k++ ) {
+		fprintf(stderr,".");
+
+		/* at this point, f = gk*hk mod y^k */
+#if 0
+		for ( j = 0; j < k; j++ )
+			if ( !isequalum(COEF(f)[j],COEF(fk)[j]) )
+					error("henmain2 : cannot happen(history)");
+#endif
+
+		/* clear wt */
+		bzero(COEF(wt),(n+1)*sizeof(int));
+
+		/* wt = (f-gk*hk)/y^k */
+		subsfum(COEF(f)[k],COEF(fk)[k],wt);
+		
+		/* clear wq */
+		bzero(COEF(wq),(n+1)*sizeof(int));
+
+		/* compute wf1,wg1 s.t. wh1*g0+wg1*h0 = wt */
+		mulsfum(wa,wt,wh1); DEG(wh1) = divsfum(wh1,h0,q);
+		mulsfum(wh1,g0,wc); subsfum(wt,wc,wd); DEG(wd) = divsfum(wd,h0,wg1);
+
+		/* check */
+#if 0
+		if ( DEG(wd) >= 0 || DEG(wg1) > ng )
+			error("henmain2 : cannot happen(adj)");
+
+		mulsfum(wg1,h0,wc); mulsfum(wh1,g0,wd); addsfum(wc,wd,we);
+		subsfum(we,wt,wz);
+		if ( DEG(wz) >= 0 )
+			error("henmain2 : cannot happen");
+#endif
+
+		/* fk += ((wg1*hk+wh1*gk)*y^k+wg1*wh1*y^(2*k) mod y^bound */
+		/* wb0 = wh1*y^k */
+		clearsfbm(bound,n,wb0);
+		DEG(wb0) = bound;
+		cpyum(wh1,COEF(wb0)[k]);
+
+		/* wb1 = gk*wb0 mod y^bound */
+		clearsfbm(bound,n,wb1);
+		mulsfbm(bound,gk,wb0,wb1);
+		/* fk += wb1 */
+		addtosfbm(bound,wb1,fk);
+
+		/* wb0 = wg1*y^k */
+		clearsfbm(bound,n,wb0);
+		DEG(wb0) = bound;
+		cpyum(wg1,COEF(wb0)[k]);
+
+		/* wb1 = hk*wb0 mod y^bound */
+		clearsfbm(bound,n,wb1);
+		mulsfbm(bound,hk,wb0,wb1);
+		/* fk += wb1 */
+		addtosfbm(bound,wb1,fk);
+
+		/* fk += wg1*wh1*y^(2*k) mod y^bound */
+		if ( 2*k < bound ) {
+			mulsfum(wg1,wh1,wt); addsfum(COEF(fk)[2*k],wt,ws);
+			cpyum(ws,COEF(fk)[2*k]);
+		}
+
+		/* gk += wg1*y^k, hk += wh1*y^k */
+		cpyum(wg1,COEF(gk)[k]);
+		cpyum(wh1,COEF(hk)[k]);
+	}
+	fprintf(stderr,"\n");
+	*gp = gk;
+	DEG(f) = bound;
+	for ( i = 0; i < bound; i++ )
+		cpyum(COEF(hk)[i],COEF(f)[i]);
+}
+
 void ptosflum(bound,f,fl)
 int bound;
 P f;
@@ -759,4 +956,454 @@ LUM fl;
 		ptosfum(COEF(dc),t);
 		bcopy(t->c,pp[d],(t->d+1)*sizeof(int));
 	}
+}
+
+/* fl->c[i] = coef_y(f,i) */
+
+void ptosfbm(bound,f,fl)
+int bound;
+P f;
+BM fl;
+{
+	DCP dc;
+	int d,i,n;
+	UM t;
+
+	n = QTOS(DEG(DC(f)));
+	clearsfbm(bound,n,fl);
+	DEG(fl) = bound;
+	t = UMALLOC(bound);
+	for ( dc = DC(f); dc; dc = NEXT(dc) ) {
+		d = QTOS(DEG(dc));
+		ptosfum(COEF(dc),t);
+		for ( i = 0; i <= DEG(t); i++ )
+			COEF(COEF(fl)[i])[d] = COEF(t)[i];
+	}
+	for ( i = 0; i < bound; i++ )
+		degum(COEF(fl)[i],n);
+}
+
+/* x : main variable */
+
+void sflumtop(bound,fl,x,y,fp)
+int bound;
+LUM fl;
+V x,y;
+P *fp;
+{
+	int i,j,n;
+	int **c;
+	UM w;
+	int *coef;
+	DCP dc,dct;
+
+	n = fl->d;
+	c = fl->c;
+	w = W_UMALLOC(bound);
+	for ( i = 0, dc = 0; i <= n; i++ ) {
+		coef = c[i];
+		for ( j = bound-1; j >= 0 && coef[j] == 0; j-- );
+		if ( j < 0 )
+			continue;
+		DEG(w) = j; bcopy(coef,COEF(w),(j+1)*sizeof(int));
+		NEWDC(dct); STOQ(i,DEG(dct));
+		sfumtop(y,w,&COEF(dct)); NEXT(dct) = dc; dc = dct;
+	}
+	MKP(x,dc,*fp);
+}
+
+/* x : main variable */
+
+void sfbmtop(bound,f,x,y,fp)
+int bound;
+BM f;
+V x,y;
+P *fp;
+{
+	UM *c;
+	int i,j,d,a;
+	GFS b;
+	DCP dc0,dc,dct;
+
+	c = COEF(f);
+	d = DEG(c[0]);
+	for ( i = 1; i < bound; i++ )
+		d = MAX(DEG(c[i]),d);
+
+	dc0 = 0;
+	for ( i = 0; i <= d; i++ ) {
+		dc = 0;
+		for ( j = 0; j < bound; j++ ) {
+			if ( DEG(c[j]) >= i && (a = COEF(c[j])[i]) ) {
+				NEWDC(dct);
+				STOQ(j,DEG(dct));
+				MKGFS(IFTOF(a),b);
+				COEF(dct) = (P)b;
+				NEXT(dct) = dc;
+				dc = dct;
+			}
+		}
+		if ( dc ) {
+			NEWDC(dct);
+			STOQ(i,DEG(dct));
+			MKP(y,dc,COEF(dct));
+			NEXT(dct) = dc0;
+			dc0 = dct;
+		}
+	}
+	if ( dc0 )
+		MKP(x,dc0,*fp);
+	else
+		*fp = 0;
+}
+
+void sfdtest(P,ML,V,V,DCP *);
+
+void sfbfctr(f,x,y,dcp)
+P f;
+V x,y;
+DCP *dcp;
+{
+	ML list;
+	P sf;
+	GFS ev;
+	DCP dc,dct;
+	BM fl;
+	int n,bound;
+
+	/* sf(x) = f(x+ev) = list->c[0]*list->c[1]*... */
+	sfhensel(5,f,x,&ev,&sf,&list);
+	sfdtest(sf,list,x,y,&dc);
+	n = getdeg(x,sf);
+	bound = list->bound;
+	W_BMALLOC(n,bound,fl);
+	for ( dct = dc; dct; dct = NEXT(dct) ) {
+		ptosfbm(bound,COEF(dct),fl);
+		shiftsfbm(bound,fl,_chsgnsf(FTOIF(CONT(ev))));
+		sfbmtop(bound,fl,x,y,&COEF(dct));
+	}
+	*dcp = dc;
+}
+
+/* f = f(x,y) = list->c[0]*list->c[1]*... mod y^list->bound */
+
+void sfdtest(f,list,x,y,dcp)
+P f;
+ML list;
+V x,y;
+DCP *dcp;
+{
+	int n,np,bound;
+	int i,j,k;
+	int *win;
+	P g,lcg,factor,cofactor,lcyx;
+	P t,csum;
+	DCP dcf,dcf0,dc;
+	BM *c;
+	BM lcy;
+	UM lcg0;
+	ML wlist;
+	struct oVL vl1,vl0;
+	VL vl;
+	int z;
+
+	/* vl = [x,y] */
+	vl0.v = x; vl0.next = &vl1; vl1.v = y; vl1.next = 0; vl = &vl0;
+
+	/* setup various structures and arrays */
+	n = UDEG(f); np = list->n; bound = list->bound; win = W_ALLOC(np+1);
+	wlist = W_MLALLOC(np); wlist->n = list->n;
+	wlist->bound = list->bound;
+	c = (BM *)COEF(wlist);
+	bcopy((char *)COEF(list),(char *)c,(int)(sizeof(BM)*np));
+
+	lcg0 = W_UMALLOC(2*bound);
+
+	/* initialize g by f */
+	g = f;
+
+	/* initialize lcg */
+	mulp(vl,g,COEF(DC(g)),&lcg);
+
+	/* initialize lcg0 */
+	const_term(lcg,lcg0);
+
+	/* initialize csum = lcg(1) */
+	sfcsump(vl,lcg,&csum);
+
+	/* initialize lcy by LC(f) */
+	W_BMALLOC(0,bound,lcy);
+	NEWDC(dc); COEF(dc) = COEF(DC(g)); DEG(dc) = 0; 
+	NEWP(lcyx); VR(lcyx) = x; DC(lcyx) = dc;
+	ptosfbm(bound,lcyx,lcy);
+
+	fprintf(stderr,"np = %d\n",np);
+	for ( g = f, k = 1, dcf = dcf0 = 0, win[0] = 1, --np, z = 0; ; z++ ) {
+		if ( !(z % 1000) ) fprintf(stderr,".");
+		if ( sfdtestmain(vl,lcg,lcg0,lcy,csum,wlist,k,win,&factor,&cofactor) ) {
+			NEXTDC(dcf0,dcf); DEG(dcf) = ONE; COEF(dcf) = factor;
+			g = cofactor;
+
+			/* update lcg */
+			mulp(vl,g,COEF(DC(g)),&lcg);
+
+			/* update lcg0 */
+			const_term(lcg,lcg0);
+
+			/* update csum */
+			sfcsump(vl,lcg,&csum);
+
+			/* update lcy */
+			clearsfbm(bound,0,lcy);
+			COEF(dc) = COEF(DC(g)); ptosfbm(bound,lcyx,lcy);
+
+			for ( i = 0; i < k - 1; i++ ) 
+				for ( j = win[i] + 1; j < win[i + 1]; j++ ) 
+					c[j-i-1] = c[j];
+			for ( j = win[k-1] + 1; j <= np; j++ ) 	
+					c[j-k] = c[j];
+			if ( ( np -= k ) < k ) 
+				break;
+			if ( np - win[0] + 1 < k ) 
+				if ( ++k > np )
+					break;
+				else
+					for ( i = 0; i < k; i++ ) 
+						win[i] = i + 1;
+			else 
+				for ( i = 1; i < k; i++ ) 
+					win[i] = win[0] + i;
+		} else if ( !ncombi(1,np,k,win) ) 
+			if ( k == np ) 
+				break;
+			else
+				for ( i = 0, ++k; i < k; i++ ) 
+					win[i] = i + 1;
+	}
+	fprintf(stderr,"\n");
+	NEXTDC(dcf0,dcf); COEF(dcf) = g;
+	DEG(dcf) = ONE; NEXT(dcf) = 0; *dcp = dcf0;
+}
+
+/* lcy = LC(g), lcg = lcy*g, lcg0 = const part of lcg */
+int sfdtestmain(vl,lcg,lcg0,lcy,csum,list,k,in,fp,cofp)
+VL vl;
+P lcg;
+UM lcg0;
+BM lcy;
+P csum;
+ML list;
+int k;
+int *in;
+P *fp,*cofp;
+{
+	P fmul,csumg,q;
+	V x,y;
+
+	x = vl->v;
+	y = vl->next->v;
+	if (!sfctest(lcg0,lcy,list,k,in))
+		return 0;
+	mulsfbmarray(UDEG(lcg),lcy,list,k,in,x,y,&fmul);
+	if ( csum ) {
+		sfcsump(vl,fmul,&csumg);
+		if ( csumg ) {
+			if ( !divtp(vl,csum,csumg,&q) )
+				return 0;
+		} 
+	}
+	if ( divtp_by_sfbm(vl,lcg,fmul,&q) ) {
+		pp_sfp(vl,fmul,fp);
+		pp_sfp(vl,q,cofp);
+		return 1;
+	} else
+		return 0;
+}
+
+void const_term(f,c)
+P f;
+UM c;
+{
+	DCP dc;
+
+	for ( dc = DC(f); dc && DEG(dc); dc = NEXT(dc) );
+	if ( dc ) 
+		ptosfum(COEF(dc),c);
+	else 
+		DEG(c) = -1;
+}
+
+void const_term_sfbm(f,bound,c)
+BM f;
+int bound;
+UM c;
+{
+	int i;
+
+	for ( i = 0; i < bound; i++ )
+		if ( DEG(COEF(f)[i]) >= 0 )
+			COEF(c)[i] = COEF(COEF(f)[i])[0];
+		else
+			COEF(c)[i] = 0;
+	degum(c,bound-1);
+}
+
+/* lcy*(product of const part) | lcg0 ? */
+
+int sfctest(lcg0,lcy,list,k,in)
+UM lcg0;
+BM lcy;
+ML list;
+int k;
+int *in;
+{
+	DCP dc;
+	int bound,i,dr;
+	UM t,s,u,w;
+	BM *l;
+
+	bound = list->bound;
+	t = W_UMALLOC(2*bound);
+	s = W_UMALLOC(2*bound);
+	u = W_UMALLOC(2*bound);
+	const_term_sfbm(lcy,bound,t);
+	if ( DEG(t) < 0 )
+		return 1;
+
+	l = (BM *)list->c;
+	for ( i = 0; i < k; i++ ) {
+		const_term_sfbm(l[in[i]],bound,s);
+		mulsfum(t,s,u);
+		if ( DEG(u) >= bound )
+			degum(u,bound-1);
+		w = t; t = u; u = w;
+	}
+	cpyum(lcg0,s);
+	dr = divsfum(s,t,u);
+	if ( dr >= 0 )
+		return 0;
+	else
+		return 1;
+}
+
+/* main var of f is x */
+
+void mulsfbmarray(n,lcy,list,k,in,x,y,g)
+int n;
+BM lcy;
+ML list;
+int k;
+int *in;
+V x,y;
+P *g;
+{
+	int bound,i;
+	BM wb0,wb1,t,lcbm;
+	BM *l;
+
+	bound = list->bound;
+	W_BMALLOC(n,bound,wb0); W_BMALLOC(n,bound,wb1);
+	l = (BM *)list->c;
+	clearsfbm(bound,n,wb0);
+	mulsfbm(bound,lcy,l[in[0]],wb0);
+	for ( i = 1; i < k; i++ ) {
+		clearsfbm(bound,n,wb1);
+		mulsfbm(bound,l[in[i]],wb0,wb1);
+		t = wb0; wb0 = wb1; wb1 = t;
+	}
+	sfbmtop(bound,wb0,x,y,g);
+}
+
+void sfcsump(vl,f,s)
+VL vl;
+P f;
+P *s;
+{
+	P t,u;
+	DCP dc;
+
+	for ( dc = DC(f), t = 0; dc; dc = NEXT(dc) ) {
+		addp(vl,COEF(dc),t,&u); t = u;
+	}
+	*s = t;
+}
+
+/* *fp = primitive part of f w.r.t. x */
+
+void pp_sfp(vl,f,fp)
+VL vl;
+P f;
+P *fp;
+{
+	V x,y;
+	int d;
+	UM t,s,gcd;
+	DCP dc;
+	P dvr;
+
+	x = vl->v;
+	y = vl->next->v;
+	d = getdeg(y,f);
+	if ( d == 0 )
+		*fp = f;  /* XXX */
+	else {
+		t = W_UMALLOC(2*d);
+		s = W_UMALLOC(2*d);
+		gcd = W_UMALLOC(2*d);
+		dc = DC(f);
+		ptosfum(COEF(dc),gcd);
+		for ( dc = NEXT(dc); dc; dc = NEXT(dc) ) {
+			ptosfum(COEF(dc),t);
+			gcdsfum(gcd,t,s);
+			cpyum(s,gcd);
+		}
+		sfumtop(y,gcd,&dvr);
+		divsp(vl,f,dvr,fp);
+	}
+}
+
+int divtp_by_sfbm(vl,f,g,qp)
+VL vl;
+P f,g;
+P *qp;
+{
+	V x,y;
+	int fx,fy,gx,gy;
+	BM fl,gl,ql;
+	UM *cf,*cg,*cq;
+	UM hg,q,t,s;
+	int i,j,dr;
+
+	x = vl->v; y = vl->next->v;
+	fx = getdeg(x,f); fy = getdeg(y,f);
+	gx = getdeg(x,g); gy = getdeg(y,g);
+
+	if ( fx < gx || fy < gy )
+		return 0;
+	W_BMALLOC(fx,fy+1,fl); ptosfbm(fy+1,f,fl); cf = COEF(fl);
+	W_BMALLOC(gx,gy+1,gl); ptosfbm(gy+1,g,gl); cg = COEF(gl);
+	W_BMALLOC(fx-gx,fy-gy+1,ql); cq = COEF(ql);
+
+	hg = cg[gy];
+	q = W_UMALLOC(fx); t = W_UMALLOC(fx); s = W_UMALLOC(fx);
+
+	for ( i = fy; i >= gy; i-- ) {
+		if ( DEG(cf[i]) < 0 )
+			continue;
+		dr = divsfum(cf[i],hg,q);
+		if ( dr >= 0 )
+			return 0;
+		if ( DEG(q) > fx-gx )
+			return 0;
+		cpyum(q,cq[i-gy]);
+		for ( j = 0; j <= gy; j++ ) {
+			mulsfum(cg[j],q,t);
+			subsfum(cf[j+i-gy],t,s);
+			cpyum(s,cf[j+i-gy]);
+		}
+	}
+	for ( j = gy-1; j >= 0 && DEG(cf[j]) < 0; j-- );
+	if ( j >= 0 )
+		return 0;
+	sfbmtop(DEG(ql),ql,x,y,qp);
 }