===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/Fgfs.c,v
retrieving revision 1.1
retrieving revision 1.8
diff -u -p -r1.1 -r1.8
--- OpenXM_contrib2/asir2000/engine/Fgfs.c	2002/09/26 04:33:16	1.1
+++ OpenXM_contrib2/asir2000/engine/Fgfs.c	2002/11/01 05:43:35	1.8
@@ -1,11 +1,176 @@
-/* $OpenXM$ */
+/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.7 2002/10/30 08:07:11 noro Exp $ */
 
 #include "ca.h"
 
+void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp);
+void gcdsf_main(VL vl,P *pa,int m,P *r);
+void ugcdsf(P *pa,int m,P *r);
+void head_monomial(V v,P p,P *coef,P *term);
+void sqfrsfmain(VL vl,P f,DCP *dcp);
+void pthrootsf(P f,Q m,P *r);
+void partial_sqfrsf(VL vl,V v,P f,P *r,DCP *dcp);
+void gcdsf(VL vl,P *pa,int k,P *r);
+void mfctrsfmain(VL vl, P f, DCP *dcp);
+void next_evaluation_point(int *mev,int n);
+void estimatelc_sf(VL vl,VL rvl,P c,DCP dc,P *lcp);
+void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P lcu,P lcv,P *up);
+void substvp_sf(VL vl,VL rvl,P f,int *mev,P *r);
+void shift_sf(VL vl, VL rvl, P f, int *mev, int sgn, P *r);
+void adjust_coef_sf(VL vl,VL rvl,P lcu,P u0,P *r);
+void extended_gcd_modyk(P u0,P v0,V x,V y,int dy,P *cu,P *cv);
+void poly_to_gfsn_poly(VL vl,P f,V v,P *r);
+void gfsn_poly_to_poly(VL vl,P f,V v,P *r);
+void poly_to_gfsn_poly_main(P f,V v,P *r);
+void gfsn_poly_to_poly_main(P f,V v,P *r);
+void gfsn_univariate_to_sfbm(P f,int dy,BM *r);
+void sfbm_to_gfsn_univariate(BM f,V x,V y,P *r);
 
+void lex_lc(P f,P *c)
+{
+	if ( !f || NUM(f) )
+		*c = f;
+	else
+		lex_lc(COEF(DC(f)),c);
+}
+
+DCP append_dc(DCP dc,DCP dct)
+{
+	DCP dcs;
+
+	if ( !dc )
+		return dct;
+	else {
+		for ( dcs = dc; NEXT(dcs); dcs = NEXT(dcs) );
+		NEXT (dcs) = dct;
+		return dc;
+	}
+}
+
+void sqfrsf(VL vl, P f, DCP *dcp)
+{
+	DCP dc,dct;
+	Obj obj;
+	P t,s,c;
+	VL tvl,nvl;
+
+	simp_ff((Obj)f,&obj); f = (P)obj;
+	lex_lc(f,&c); divsp(vl,f,c,&t); f = t;
+	monomialfctr(vl,f,&t,&dc); f = t;
+	clctv(vl,f,&tvl); vl = tvl;
+	if ( !vl )
+		;
+	else if ( !NEXT(vl) ) {
+		sfusqfr(f,&dct);
+		dc = append_dc(dc,NEXT(dct));
+	} else {
+		t = f;
+		for ( tvl = vl; tvl; tvl = NEXT(tvl) ) {
+			reordvar(vl,tvl->v,&nvl);
+			cont_pp_mv_sf(vl,NEXT(nvl),t,&c,&s); t = s;
+			sqfrsf(vl,c,&dct);
+			dc = append_dc(dc,NEXT(dct));
+		}
+		sqfrsfmain(vl,t,&dct);
+		dc = append_dc(dc,dct);
+	}
+	NEWDC(dct); DEG(dct) = ONE; COEF(dct) = (P)c; NEXT(dct) = dc;
+	*dcp = dct;
+}
+
+void sqfrsfmain(VL vl,P f,DCP *dcp)
+{
+	VL tvl;
+	DCP dc,dct,dcs;
+	P t,s;
+	Q m,m1;
+	V v;
+
+	clctv(vl,f,&tvl); vl = tvl;
+	dc = 0;
+	t = f;
+	for ( tvl = vl; tvl; tvl = NEXT(tvl) ) {
+		v = tvl->v;
+		partial_sqfrsf(vl,v,t,&s,&dct); t = s;
+		dc = append_dc(dc,dct);
+	}
+	if ( !NUM(t) ) {
+		STOQ(characteristic_sf(),m);
+		pthrootsf(t,m,&s);
+		sqfrsfmain(vl,s,&dct);
+		for ( dcs = dct; dcs; dcs = NEXT(dcs) ) {
+			mulq(DEG(dcs),m,&m1); DEG(dcs) = m1;
+		}
+		dc = append_dc(dc,dct);
+	}
+	*dcp = dc;
+}
+
+void pthrootsf(P f,Q m,P *r)
+{
+	DCP dc,dc0,dct;
+	N qn,rn;
+
+	if ( NUM(f) )
+		pthrootgfs(f,r);
+	else {
+		dc = DC(f);
+		dc0 = 0;
+		for ( dc0 = 0; dc; dc = NEXT(dc) ) {
+			NEXTDC(dc0,dct);
+			pthrootsf(COEF(dc),m,&COEF(dct));
+			if ( DEG(dc) ) {
+				divn(NM(DEG(dc)),NM(m),&qn,&rn);
+				if ( rn )
+					error("pthrootsf : cannot happen");
+				NTOQ(qn,1,DEG(dct));
+			} else
+				DEG(dct) = 0;
+		}
+		NEXT(dct) = 0;
+		MKP(VR(f),dc0,*r);
+	}
+}
+
+void partial_sqfrsf(VL vl,V v,P f,P *r,DCP *dcp)
+{
+	P ps[2];
+	DCP dc0,dc;
+	int m;
+	P t,flat,flat1,g,df,q;
+
+	diffp(vl,f,v,&df);
+	if ( !df ) {
+		*dcp = 0;
+		*r = f;
+		return;
+	}
+	ps[0] = f; ps[1] = df;
+	gcdsf(vl,ps,2,&g);	
+	divsp(vl,f,g,&flat);
+	m = 0;
+	t = f;
+	dc0 = 0;
+	while ( !NUM(flat) ) {
+		while ( divtp(vl,t,flat,&q) ) {
+			t = q; m++;
+		}
+		ps[0] = t; ps[1] = flat;
+		gcdsf(vl,ps,2,&flat1);
+		divsp(vl,flat,flat1,&g);
+		flat = flat1;
+		NEXTDC(dc0,dc);
+		COEF(dc) = g;
+		STOQ(m,DEG(dc));
+	}
+	NEXT(dc) = 0;
+	*dcp = dc0;
+	*r = t;
+}
+
 void gcdsf(VL vl,P *pa,int k,P *r)
 {
-	P *ps,*pl,*pm,*cp;
+	P *ps,*pl,*pm;
+	P **cp;
 	int *cn;
 	DCP *ml;
 	Obj obj;
@@ -17,21 +182,21 @@ void gcdsf(VL vl,P *pa,int k,P *r)
 	for ( i = 0, m = 0; i < k; i++ ) {
 		simp_ff((Obj)pa[i],&obj);
 		if ( obj )
-			ps[m++] = obj;
+			ps[m++] = (P)obj;
 	}
 	if ( !m ) {
 		*r = 0;
 		return;
 	}
 	if ( m == 1 ) {
-		*r = BDY(n0);
+		*r = ps[0];
 		return;
 	}
 	pl = (P *)ALLOCA(m*sizeof(P));
 	ml = (DCP *)ALLOCA(m*sizeof(DCP));
 	for ( i = 0; i < m; i++ )
 		monomialfctr(vl,ps[i],&pl[i],&ml[i]);
-	gcdmonomial(vl,ml,m,&mg); simp_ff(mg,&mgsf);
+	gcdmonomial(vl,ml,m,&mg); simp_ff((Obj)mg,&obj); mgsf = (P)obj;
 	for ( i = 0, nvl = vl, avl = 0; nvl && i < m; i++ ) {
 		clctv(vl,pl[i],&tvl);
 		intersectv(nvl,tvl,&svl); nvl = svl;
@@ -73,7 +238,7 @@ void gcdsf(VL vl,P *pa,int k,P *r)
 
 void ugcdsf(P *pa,int m,P *r)
 {
-	P *pa;
+	P *ps;
 	int i;
 	UM w1,w2,w3,w;
 	int d;
@@ -83,10 +248,15 @@ void ugcdsf(P *pa,int m,P *r)
 		*r = pa[0];
 		return;
 	}
+	for ( i = 0; i < m; i++ )
+		if ( NUM(pa[i]) ) {
+			itogfs(1,r);
+			return;
+		}
 	ps = (P *)ALLOCA(m*sizeof(P));
-	v = VR(pa[0]);
 	sort_by_deg(m,pa,ps);
-	d = getdeg(ps[m-1],v);
+	v = VR(ps[m-1]);
+	d = getdeg(v,ps[m-1]);
 	w1 = W_UMALLOC(d);
 	w2 = W_UMALLOC(d);
 	w3 = W_UMALLOC(d);
@@ -96,30 +266,62 @@ void ugcdsf(P *pa,int m,P *r)
 		gcdsfum(w1,w2,w3); 
 		w = w1; w1 = w3; w3 = w;
 		if ( !DEG(w1) ) {
-			MKGFS(0,*r);
+			itogfs(1,r);
 			return;
 		}
 	}
 	sfumtop(v,w1,r);
 }
 
+/* deg(HT(p),v), where p is considered as distributed poly over F[v] */
+int gethdeg(VL vl,V v,P p)
+{
+	DCP dc;
+	Q dmax;
+	P cmax;
 
+	if ( !p )
+		return -1;
+	else if ( NUM(p) )
+		return 0;
+	else if ( VR(p) != v )
+		/* HT(p) = HT(lc(p))*x^D */
+		return gethdeg(vl,v,COEF(DC(p)));
+	else {
+		/* VR(p) = v */
+		dc = DC(p); dmax = DEG(dc); cmax = COEF(dc);
+		for ( dc = NEXT(dc); dc; dc = NEXT(dc) )
+			if ( compp(vl,COEF(dc),cmax) > 0 ) {
+				dmax = DEG(dc); cmax = COEF(dc);
+			}
+		return QTOS(dmax);
+	}
+}
+
 /* all the pa[i]'s have the same variables (=vl) */
 
 void gcdsf_main(VL vl,P *pa,int m,P *r)
 {
+	int nv,i,i0,imin,d,d0,d1,d2,dmin,index;
+	V v,v0,vmin;
+	VL tvl,nvl,rvl,nvl0,rvl0;
+	P *pc, *ps, *ph,*lps;
+	P x,t,cont,hg,g,hm,mod,s;
+	P hge,ge,ce,he,u,cof1e,mode,mod1,adj,cof1,coadj,q;
+	GFS sf;
+
 	for ( nv = 0, tvl = vl; tvl; tvl = NEXT(tvl), nv++);
 	if ( nv == 1 ) {
 		ugcdsf(pa,m,r);
 		return;
 	}
-	/* find v s.t. min(deg(pa[i],v)) is minimal */
+	/* find v s.t. min(deg(pa[i],v)+gethdeg(pa[i],v)) is minimal */
 	tvl = vl;
 	do {
 		v = tvl->v;
 		i = 0;
 		do {
-			d = getdeg(pa[i],v);
+			d = getdeg(v,pa[i])+gethdeg(vl,v,pa[i]);
 			if ( i == 0 || (d < d0) ) {
 				d0 = d; i0 = i; v0 = v;
 			}
@@ -136,9 +338,10 @@ void gcdsf_main(VL vl,P *pa,int m,P *r)
 			NEXTVL(rvl0,rvl); rvl->v = tvl->v;
 		}
 	/* rvl = remaining variables */
-	NEXT(rvl) = 0;
+	NEXT(rvl) = 0; rvl = rvl0;
 	/* nvl = ...,vmin */
-	NEXTVL(nvl0,nvl); nvl->v = vmin; NEXT(nvl) = 0;
+	NEXTVL(nvl0,nvl); nvl->v = vmin; NEXT(nvl) = 0; nvl = nvl0;
+	MKV(vmin,x);
 
 	/* for content and primitive part */
 	pc = (P *)ALLOCA(m*sizeof(P));
@@ -146,7 +349,7 @@ void gcdsf_main(VL vl,P *pa,int m,P *r)
 	ph = (P *)ALLOCA(m*sizeof(P));
 	/* separate the contents */
 	for ( i = 0; i < m; i++ ) {
-		reorderp(vl,nvl,pa[i],&t);
+		reorderp(nvl,vl,pa[i],&t);
 		cont_pp_mv_sf(nvl,rvl,t,&pc[i],&ps[i]);
 		head_monomial(vmin,ps[i],&ph[i],&t);
 	}
@@ -160,13 +363,13 @@ void gcdsf_main(VL vl,P *pa,int m,P *r)
 
 	while ( 1 ) {
 		g = 0;
-		cofmin = 0;
+		cof1 = 0;
 		hm = 0;
-		MKGFS(0,mod);
+		itogfs(1,&mod);
 		index = 0;
-		while ( getdeg(mod,vmin) <= d+1 ) {
+		for ( index = 0; getdeg(vmin,mod) <= d+1; index++ ) {
 			/* evaluation pt */
-			MKGFS(index,s);
+			indextogfs(index,&s);
 			substp(nvl,hg,vmin,s,&hge);
 			if ( !hge )
 				continue;
@@ -175,13 +378,67 @@ void gcdsf_main(VL vl,P *pa,int m,P *r)
 			/* ge = GCD(ps[0]|x=s,...,ps[m-1]|x=s) */
 			gcdsf(nvl,ph,m,&ge);
 			head_monomial(vmin,ge,&ce,&he);
-			if ( NUM(hge) ) {
+			if ( NUM(he) ) {
 				*r = cont;
 				return;
 			}
-			divgfs(hge,ce,&t); mulp(nvl,t,ge,&u); ge = u;
+			divgfs((GFS)hge,(GFS)ce,&sf); t = (P)sf;
+			mulp(nvl,t,ge,&u); ge = u;
 			divsp(nvl,ph[imin],ge,&t); mulp(nvl,hge,t,&cof1e);
-			if ( !hm || !cmpp(he,hm) ) {
+			/* hm=0 : reset; he==hm : lucky */
+			if ( !hm || !compp(nvl,he,hm) ) {
+				substp(nvl,mod,vmin,s,&mode); divsp(nvl,mod,mode,&mod1); 
+				/* adj = mod/(mod|x=s)*(ge-g|x=s) */
+				substp(nvl,g,vmin,s,&t);
+				subp(nvl,ge,t,&u); mulp(nvl,mod1,u,&adj);
+				/* coadj = mod/(mod|vmin=s)*(cof1e-cof1e|vmin=s) */
+				substp(nvl,cof1,vmin,s,&t);
+				subp(nvl,cof1e,t,&u); mulp(nvl,mod1,u,&coadj);
+				if ( !adj ) {
+					/* adj == gcd ? */
+					for ( i = 0; i < m; i++ )
+						if ( !divtp(nvl,lps[i],g,&t) )
+							break;
+					if ( i == m ) {
+						cont_pp_mv_sf(nvl,rvl,g,&t,&u);
+						mulp(nvl,cont,u,&t);
+						reorderp(vl,nvl,t,r);
+						return;
+					}
+				} else if ( !coadj ) {
+					/* ps[imin]/coadj == gcd ? */
+					if ( divtp(nvl,lps[imin],cof1,&q) ) {
+						for ( i = 0; i < m; i++ )
+							if ( !divtp(nvl,lps[i],q,&t) )
+								break;
+						if ( i == m ) {
+							cont_pp_mv_sf(nvl,rvl,q,&t,&u);
+							mulp(nvl,cont,u,&t);
+							reorderp(vl,nvl,t,r);
+							return;
+						}
+					}
+				}
+				addp(nvl,g,adj,&t); g = t;
+				addp(nvl,cof1,coadj,&t); cof1 = t;
+				subp(nvl,x,s,&t); mulp(nvl,mod,t,&u); mod = u;
+				hm = he;
+			} else {
+				d1 = homdeg(hm); d2 = homdeg(he);
+				if ( d1 < d2 ) /* we use current hm */
+					continue;
+				else if ( d1 > d2 ) {
+					/* use he */
+					g = ge;
+					cof1 = cof1e;
+					hm = he;
+					subp(nvl,x,s,&mod);
+				} else { 
+					/* d1==d2, but hm!=he => both are unlucky */
+					g = 0;
+					cof1 = 0;
+					itogfs(1,&mod);
+				}
 			}
 		}
 	}
@@ -192,16 +449,18 @@ void head_monomial(V v,P p,P *coef,P *term)
 	P t,s,u;
 	DCP dc;
 	GFS one;
+	VL vl;
 
-	MKGFS(0,one); t = one;
+	itogfs(1,&one);
+	t = (P)one;
 	while ( 1 ) {
 		if ( NUM(p) || VR(p) == v ) {
 			*coef = p;
 			*term = t;
 			return;
 		} else {
-			NEWDC(dc); MKGFS(0,one); 
-			COEF(dc) = one; DEG(dc) = DEG(DC(p));
+			NEWDC(dc); 
+			COEF(dc) = (P)one; DEG(dc) = DEG(DC(p));
 			MKP(VR(p),dc,s);
 			mulp(vl,t,s,&u); t = u;
 			p = COEF(DC(p));
@@ -219,8 +478,605 @@ void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp)
 	ptod(vl,rvl,p,&dp);
 	for ( t = BDY(dp), m = 0; t; t = NEXT(t), m++ );
 	ps = (P *)ALLOCA(m*sizeof(P));
-	for ( t = BDY(dp), i = 0; t; t = NEXT(t), i++ );
+	for ( t = BDY(dp), i = 0; t; t = NEXT(t), i++ )
 		ps[i] = C(t);
 	ugcdsf(ps,m,c);
-	divsp(vl,p,c,pp);
+	divsp(vl,p,*c,pp);
+}
+
+void mfctrsf(VL vl, P f, DCP *dcp)
+{
+	DCP dc0,dc,dct,dcs,dcr;
+	Obj obj;
+
+	simp_ff((Obj)f,&obj); f = (P)obj;
+	sqfrsf(vl,f,&dct);
+	dc = dc0 = dct; dct = NEXT(dct); NEXT(dc) = 0;
+	for ( ; dct; dct = NEXT(dct) ) {
+		mfctrsfmain(vl,COEF(dct),&dcs);
+		for ( dcr = dcs; dcr; dcr = NEXT(dcr) )
+			DEG(dcr) = DEG(dct);
+		for ( ; NEXT(dc); dc = NEXT(dc) );
+		NEXT(dc) = dcs;
+	}
+	*dcp = dc0;
+}
+
+/* f : sqfr, non const */
+
+void mfctrsfmain(VL vl, P f, DCP *dcp)
+{
+	VL tvl,nvl,rvl;
+	DCP dc,dc0,dc1,dc2,dct,lcfdc,dcs;
+	int imin,inext,i,j,n,k,np;
+	int *da;
+	V vx,vy;
+	V *va;
+	P *l,*tl;
+	P gcd,g,df,dfmin;
+	P pa[2];
+	P g0,pp0,spp0,c,c0,x,y,u,v,lcf,lcu,lcv,u0,v0,t,s;
+	P ype,yme;
+	GFS ev,evy;
+	P *fp0;
+	int *mev,*win;
+
+	clctv(vl,f,&tvl); vl = tvl;
+	if ( !vl )
+		error("mfctrsfmain : cannot happen");
+	if ( !NEXT(vl) ) {
+		/* univariate */
+		ufctrsf(f,&dc);
+		/* remove lc */
+		*dcp = NEXT(dc);
+		return;
+	}
+	for ( n = 0, tvl = vl; tvl; tvl = NEXT(tvl), n++ );
+	va = (V *)ALLOCA(n*sizeof(int));
+	da = (int *)ALLOCA(n*sizeof(int));
+	/* find v s.t. diff(f,v) is nonzero and deg(f,v) is minimal */
+	imin = -1;
+	for ( i = 0, tvl = vl; i < n; tvl = NEXT(tvl), i++ ) {
+		va[i] = tvl->v;	
+		da[i] = getdeg(va[i],f);
+		diffp(vl,f,va[i],&df);
+		if ( !df )
+			continue;
+		if ( imin < 0 || da[i] < da[imin] ) {
+			dfmin = df;
+			imin = i;
+		}
+	}
+	/* find v1 neq v s.t. deg(f,v) is minimal */
+	inext = -1;
+	for ( i = 0; i < n; i++ ) {
+		if ( i == imin )
+			continue;
+		if ( inext < 0 || da[i] < da[inext] )
+			inext = i;
+	}
+	pa[0] = f;
+	pa[1] = dfmin;
+	gcdsf_main(vl,pa,2,&gcd);
+	if ( !NUM(gcd) ) {
+		/* f = gcd * f/gcd */	
+		mfctrsfmain(vl,gcd,&dc1);
+		divsp(vl,f,gcd,&g);
+		mfctrsfmain(vl,g,&dc2);
+		for ( dct = dc1; NEXT(dct); dct = NEXT(dct) );
+		NEXT(dct) = dc2;
+		*dcp = dc1;
+		return;
+	}
+	/* create vl s.t. vl[0] = va[imin], vl[1] = va[inext] */
+	nvl = 0;
+	NEXTVL(nvl,tvl); tvl->v = va[imin];
+	NEXTVL(nvl,tvl); tvl->v = va[inext];
+	for ( i = 0; i < n; i++ ) {
+		if ( i == imin || i == inext )
+			continue;
+		NEXTVL(nvl,tvl); tvl->v = va[i];
+	}
+	NEXT(tvl) = 0;
+
+	reorderp(nvl,vl,f,&g);
+	vx = nvl->v;
+	vy = NEXT(nvl)->v;
+	MKV(vx,x);
+	MKV(vy,y);
+	/* remaining variables */
+	rvl = NEXT(NEXT(nvl));
+	if ( !rvl ) {
+		/* bivariate */
+		sfbfctr(g,vx,vy,getdeg(vx,g),&dc1);
+		for ( dc0 = 0; dc1; dc1 = NEXT(dc1) ) {
+			NEXTDC(dc0,dc);
+			DEG(dc) = ONE;
+			reorderp(vl,nvl,COEF(dc1),&COEF(dc));
+		}
+		NEXT(dc) = 0;
+		*dcp = dc0;
+		return;
+	}
+	/* n >= 3;  nvl = (vx,vy,X) */
+	/* find good evaluation pt for X */
+	mev = (int *)CALLOC(n-2,sizeof(int));
+	while ( 1 ) {
+		substvp_sf(nvl,rvl,g,mev,&g0);
+		pa[0] = g0;
+		diffp(nvl,g0,vx,&pa[1]);
+		if ( pa[1] ) {
+			gcdsf(nvl,pa,2,&gcd);
+			/* XXX maybe we have to accept the case where gcd is a poly of y */
+			if ( NUM(gcd) )
+				break;
+		}
+		/* XXX if generated indices exceed q of GF(q) => error in indextogfs */
+		next_evaluation_point(mev,n-2);
+	}
+	/* g0 = g(x,y,mev) */
+	/* separate content; g0 may have the content wrt x */
+	cont_pp_sfp(nvl,g0,&c0,&pp0);
+
+	/* factorize pp0; pp0 = pp0(x,y+evy) = prod dc */
+	sfbfctr_shift(pp0,vx,vy,getdeg(vx,pp0),&evy,&spp0,&dc); pp0 = spp0;
+
+	if ( !NEXT(dc) ) {
+		/* f is irreducible */
+		NEWDC(dc); DEG(dc) = ONE; COEF(dc) = f; NEXT(dc) = 0;
+		*dcp = dc;
+		return;
+	}
+	/* ype = y+evy, yme = y-evy */
+	addp(nvl,y,(P)evy,&ype); subp(nvl,y,(P)evy,&yme);
+
+	/* shift c0; c0 <- c0(y+evy) */
+	substp(nvl,c0,vy,ype,&s); c0 = s;
+
+	/* shift f; f <- f(y+evy) */
+	substp(nvl,f,vy,ype,&s); f = s;
+
+	/* now f(x,0,mev) = c0 * prod dc */
+
+	/* factorize lc_x(f) */
+	lcf = COEF(DC(f));
+	mfctrsf(nvl,lcf,&dct); 
+	/* skip the first element (= a number) */
+	dct = NEXT(dct);
+
+	/* shift lcfdc; c <- c(X+mev) */
+	for ( lcfdc = 0; dct; dct = NEXT(dct) ) {
+		NEXTDC(lcfdc,dcs);
+		DEG(dcs) = DEG(dct);
+		shift_sf(nvl,rvl,COEF(dct),mev,1,&COEF(dcs));
+	}
+	NEXT(dcs) = 0;
+
+	/* np = number of bivariate factors */
+	for ( np = 0, dct = dc; dct; dct = NEXT(dct), np++ );
+	fp0 = (P *)ALLOCA((np+1)*sizeof(P));
+	for ( i = 0, dct = dc; i < np; dct = NEXT(dct), i++ )
+		fp0[i] = COEF(dct);
+	fp0[np] = 0;
+	l = tl = (P *)ALLOCA((np+1)*sizeof(P));
+	win = W_ALLOC(np+1);
+
+	/* f <- f(X+mev) */
+	shift_sf(nvl,rvl,f,mev,1,&s); f = s;
+
+	for ( k = 1, win[0] = 1, --np; ; ) {
+		itogfs(1,&u0);
+		/* u0 = product of selected factors */
+		for ( i = 0; i < k; i++ ) {
+			mulp(nvl,u0,fp0[win[i]],&t); u0 = t;
+		}
+		/* we have to consider the content */
+		/* g0 = c0*u0*v0 */
+		mulp(nvl,LC(u0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,&lcu);
+		divsp(nvl,pp0,u0,&v0);
+		mulp(nvl,LC(v0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,&lcv);
+		mfctrsf_hensel(nvl,rvl,f,pp0,u0,v0,lcu,lcv,&u);
+		if ( u ) {
+			/* save the factor */
+			reorderp(vl,nvl,u,&t);
+			/* x -> x-mev, y -> y-evy */
+			shift_sf(vl,rvl,t,mev,-1,&s); substp(vl,s,vy,yme,tl++);
+
+			/* update f,pp0 */
+			divsp(nvl,f,u,&t); f = t;
+			divsp(nvl,pp0,u0,&t); pp0 = t;
+			/* update win, fp0 */
+			for ( i = 0; i < k-1; i++ )
+			for ( j = win[i]+1; j < win[i+1]; j++ )
+				fp0[j-i-1] = fp0[j];
+			for ( j = win[k-1]+1; j <= np; j++ )
+					fp0[j-k] = fp0[j];
+			if ( ( np -= k ) < k ) break;
+			if ( np-win[0]+1 < k )
+				if ( ++k <= np ) {
+					for ( i = 0; i < k; i++ ) 
+						win[i] = i + 1;
+					continue;
+				} else
+					break;
+			else 
+				for ( i = 1; i < k; i++ ) 
+					win[i] = win[0] + i;
+		} else {
+			if ( ncombi(1,np,k,win) == 0 )
+				if ( k == np ) break;
+				else 
+					for ( i = 0, ++k; i < k; i++ ) 
+						win[i] = i + 1;
+		}
+		reorderp(vl,nvl,f,&t);
+		/* x -> x-mev, y -> y-evy */
+		shift_sf(vl,rvl,t,mev,-1,&s); substp(vl,s,vy,yme,tl++);
+		*tl = 0;
+
+		for ( dc0 = 0, i = 0; l[i]; i++ ) {
+			NEXTDC(dc0,dc); DEG(dc) = ONE; COEF(dc) = l[i];
+		}
+		NEXT(dc) = 0; *dcp = dc0;
+	}
+}
+
+void next_evaluation_point(int *e,int n)
+{
+	int i,t,j;
+
+	for ( i = n-1; i >= 0; i-- )
+		if ( e[i] ) break;
+	if ( i < 0 ) e[n-1] = 1;
+	else if ( i == 0 ) {
+		t = e[0]; e[0] = 0; e[n-1] = t+1;
+	} else {
+		e[i-1]++; t = e[i];
+		for ( j = i; j < n-1; j++ )
+			e[j] = 0;
+		e[n-1] = t-1;
+	}
+}
+
+/* 
+ * dc : f1^E1*...*fk^Ek
+ * find e1,...,ek s.t. fi(0)^ei | c 
+ * and return f1^e1*...*fk^ek
+ * vl = (vx,vy,rvl)
+ */
+
+void estimatelc_sf(VL vl,VL rvl,P c,DCP dc,P *lcp)
+{
+	DCP dct;
+	P r,c1,c2,t,s,f;
+	int i,d;
+	Q q;
+
+	for ( dct = dc, r = (P)ONE; dct; dct = NEXT(dct) ) {
+		if ( NUM(COEF(dct)) )
+			continue;
+		/* constant part */
+		substvp_sf(vl,rvl,COEF(dct),0,&f);
+		d = QTOS(DEG(dct));
+		for ( i = 0, c1 = c; i < d; i++ )
+			if ( !divtp(vl,c1,f,&c2) )
+				break;
+			else
+				c1 = c2;
+		if ( i ) {
+			STOQ(i,q);
+			pwrp(vl,COEF(dct),q,&s); mulp(vl,r,s,&t); r = t;
+		}
+	}
+	*lcp = r;
+}
+
+void substvp_sf(VL vl,VL rvl,P f,int *mev,P *r)
+{
+	int i;
+	VL tvl;
+	P g,t;
+	GFS ev;
+
+	for ( g = f, i = 0, tvl = rvl; tvl; tvl = NEXT(tvl), i++ ) {
+		if ( !mev )
+			ev = 0;
+		else
+			indextogfs(mev[i],&ev);
+		substp(vl,g,tvl->v,(P)ev,&t); g = t;
+	}
+	*r = g;
+}
+
+/*
+ * f <- f(X+sgn*mev)
+ */
+
+void shift_sf(VL vl, VL rvl, P f, int *mev, int sgn, P *r)
+{
+	VL tvl;
+	int i;
+	P x,g,t,s;
+	GFS ev;
+
+	for ( g = f, tvl = rvl, i = 0; tvl; tvl = NEXT(tvl), i++ ) {
+		if ( !mev[i] )
+			continue;
+		indextogfs(mev[i],&ev);
+		MKV(tvl->v,x);
+		if ( sgn > 0 )
+			addp(vl,x,(P)ev,&t);
+		else
+			subp(vl,x,(P)ev,&t);
+		substp(vl,g,tvl->v,t,&s); g = s;
+	}
+	*r = g;
+}
+
+/*
+ * pp(f(0)) = u0*v0
+ */
+
+void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P lcu,P lcv,P *up)
+{
+	VL tvl,onevl;
+	P t,s,w,u,v,ff,si,wu,wv,fj,cont;
+	UM ydy;
+	V vx,vy;
+	int dy,n,i,dbd,nv,j;
+	int *md;
+	P *uh,*vh;
+	P x,du0,dv0,m,q,r;
+	P *cu,*cv;
+	GFSN inv;
+
+	/* adjust coeffs */
+	/* u0 = am x^m+ ... -> lcu*x^m + a(m-1)*(lcu(0)/am)*x^(m-1)+... */
+	/* v0 = bm x^l+ ... -> lcv*x^l + b(l-1)*(lcv(0)/bl)*x^(l-1)+... */
+	adjust_coef_sf(vl,rvl,lcu,u0,&u);
+	adjust_coef_sf(vl,rvl,lcv,v0,&v);
+	vx = vl->v; vy = NEXT(vl)->v;
+	n = getdeg(vx,f);
+	dy = getdeg(vy,f)+1;
+	MKV(vx,x);
+	cu = (P *)ALLOCA((n+1)*sizeof(P));
+	cv = (P *)ALLOCA((n+1)*sizeof(P));
+
+	/* ydy = y^dy */
+	ydy = C_UMALLOC(dy); COEF(ydy)[dy] = 1;
+	setmod_gfsn(ydy);
+
+	/* (R[y]/(y^dy))[x,X] */
+	poly_to_gfsn_poly(vl,f,vy,&t); ff = t;
+	poly_to_gfsn_poly(vl,u,vy,&t); u = t;
+	poly_to_gfsn_poly(vl,v,vy,&t); v = t;
+	substvp_sf(vl,rvl,u,0,&u0);
+	substvp_sf(vl,rvl,v,0,&v0);
+
+	/* compute a(x,y), b(x,y) s.t. a*u0+b*v0 = 1 mod y^dy */
+	extended_gcd_modyk(u0,v0,vx,vy,dy,&cu[0],&cv[0]);
+
+	/* du0 = LC(u0)^(-1)*u0 mod y^dy */
+	/* dv0 = LC(v0)^(-1)*v0 mod y^dy */
+	invgfsn((GFSN)LC(u0),&inv); mulp(vl,u0,(P)inv,&du0);
+	invgfsn((GFSN)LC(v0),&inv); mulp(vl,v0,(P)inv,&dv0);
+
+	/* cu[i]*u0+cv[i]*v0 = x^i mod y^dy */
+	for ( i = 1; i <= n; i++ ) {
+		mulp(vl,x,cu[i-1],&m); divsrp(vl,m,dv0,&q,&cu[i]);
+		mulp(vl,x,cv[i-1],&m); divsrp(vl,m,du0,&q,&cv[i]);
+	}
+	dbd = dbound(vx,f)+1;	
+
+	/* extract homogeneous parts */
+	W_CALLOC(dbd,P,uh); W_CALLOC(dbd,P,vh);
+	for ( i = 0; i <= dbd; i++ ) {
+		exthpc(vl,vx,u,i,&uh[i]); exthpc(vl,vx,v,i,&vh[i]);
+	}
+
+	/* register degrees in each variables */
+	for ( nv = 0, tvl = rvl; tvl; tvl = NEXT(tvl), nv++ );
+	md = (int *)ALLOCA(nv*sizeof(int));
+	for ( i = 0, tvl = rvl; i < nv; tvl = NEXT(tvl), i++ )
+		md[i] = getdeg(tvl->v,ff);
+
+	/* XXX for removing content of factor wrt vx */
+	NEWVL(onevl); onevl->v = vx; NEXT(onevl) = 0;
+
+	for ( j = 1; j <= dbd; j++ ) {
+		for ( i = 0, tvl = rvl; i < nv; tvl = NEXT(tvl), i++ )
+			if ( getdeg(tvl->v,u)+getdeg(tvl->v,v) > md[i] ) {
+				*up = 0;
+				return;
+			}
+		for ( i = 0, t = 0; i <= j; i++ ) {
+			mulp(vl,uh[i],vh[j-i],&s); addp(vl,s,t,&w); t = w;
+		}
+		/* s = degree j part of (f-uv) */
+		exthpc(vl,vx,ff,j,&fj); subp(vl,fj,t,&s);
+		for ( i = 0, wu = 0, wv = 0; i <= n; i++ ) {
+			if ( s )
+				si = 0;
+			else if ( VR(s) == vx )
+				coefp(s,i,&si);
+			else if ( i == 0 )
+				si = s;
+			else
+				si = 0;
+			if ( si ) {
+				mulp(vl,si,cu[i],&m); addp(vl,wu,m,&t); wu = t;
+				mulp(vl,si,cv[i],&m); addp(vl,wv,m,&t); wv = t;
+			}
+		}
+		if ( !wu ) {
+			gfsn_poly_to_poly(vl,u,vy,&t); u = t;
+			if ( divtp(vl,f,u,&q) ) {
+				cont_pp_mv_sf(vl,onevl,u,&cont,up);
+				return;
+			}
+		}
+		if ( !wv ) {
+			gfsn_poly_to_poly(vl,v,vy,&t); v = t;
+			if ( divtp(vl,f,u,&q) ) {
+				cont_pp_mv_sf(vl,onevl,q,&cont,up);
+				return;
+			}
+		}
+		addp(vl,u,wu,&t); u = t;
+		addp(vl,uh[j],wu,&t); uh[j] = t;
+		addp(vl,v,wv,&t); v = t;
+		addp(vl,vh[j],wv,&t); vh[j] = t;
+	}
+}
+
+void adjust_coef_sf(VL vl,VL rvl,P lcu,P u0,P *r)
+{
+	P lcu0,cu;
+	DCP dc0,dcu,dc;
+
+	substvp_sf(vl,rvl,lcu,0,&lcu0);
+	divsp(vl,lcu0,LC(u0),&cu);
+	for ( dc0 = 0, dcu = DC(u0); dcu; dcu = NEXT(dcu) ) {
+		if ( !dc0 ) {
+			NEXTDC(dc0,dc);
+			COEF(dc) = lcu;
+		} else {
+			NEXTDC(dc0,dc);
+			mulp(vl,cu,COEF(dcu),&COEF(dc));
+		}
+		DEG(dc) = DEG(dcu);
+	}
+	NEXT(dc) = 0;
+	MKP(VR(u0),dc0,*r);
+}
+
+void extended_gcd_modyk(P u0,P v0,V x,V y,int dy,P *cu,P *cv)
+{
+	BM g,h,a,b;
+
+	gfsn_univariate_to_sfbm(u0,dy,&g);	
+	gfsn_univariate_to_sfbm(v0,dy,&h);	
+	sfexgcd_by_hensel(g,h,dy,&a,&b);
+	sfbm_to_gfsn_univariate(a,x,y,cu);
+	sfbm_to_gfsn_univariate(b,x,y,cv);
+}
+
+/* (F[y])[x] -> F[x][y] */
+
+void gfsn_univariate_to_sfbm(P f,int dy,BM *r)
+{
+	int dx,d,i;
+	BM b;
+	UM cy;
+	DCP dc;
+
+	dx = getdeg(VR(f),f);	
+	b = BMALLOC(dx,dy);
+	DEG(b) = dy;
+	for ( dc = DC(f); dc; dc = NEXT(dc) ) {
+		/* d : degree in x, cy : poly in y */
+		d = QTOS(DEG(dc));
+		cy = BDY((GFSN)COEF(dc));
+		for ( i = DEG(cy); i >= 0; i-- )
+			COEF(COEF(b)[i])[d] = COEF(cy)[i];
+	}
+	*r = b;
+}
+
+void sfbm_to_gfsn_univariate(BM f,V x,V y,P *r)
+{
+	P g;
+	VL vl;
+
+	sfbmtop(f,x,y,&g);
+	NEWVL(vl); vl->v = x;
+	NEWVL(NEXT(vl)); NEXT(vl)->v = y;
+	NEXT(NEXT(vl)) = 0;
+	poly_to_gfsn_poly(vl,g,y,r);
+}
+
+void poly_to_gfsn_poly(VL vl,P f,V v,P *r)
+{
+	VL tvl,nvl0,nvl;
+	P g;
+
+	/* (x,y,...,v,...) -> (x,y,...,v) */
+	for ( nvl0 = 0, tvl = vl; tvl; tvl = NEXT(tvl) ) {
+		if ( tvl->v != v ) {
+			NEXTVL(nvl0,nvl);
+			nvl->v = tvl->v;
+		}
+	}
+	NEXTVL(nvl0,nvl);
+	nvl->v = v;
+	NEXT(nvl) = 0;
+	reorderp(nvl0,vl,f,&g);
+	poly_to_gfsn_poly_main(g,v,r);
+}
+
+void poly_to_gfsn_poly_main(P f,V v,P *r)
+{
+	int d;
+	UM u;
+	GFSN g;
+	DCP dc,dct,dc0;
+
+	if ( !f || NUM(f) )
+		*r = f;
+	else if ( VR(f) == v ) {
+		d = getdeg(v,f);
+		u = UMALLOC(d);
+		ptosfum(f,u);		
+		MKGFSN(u,g);
+		*r = (P)g;
+	} else {
+		for ( dc0 = 0, dct = DC(f); dct; dct = NEXT(dct) ) {
+			NEXTDC(dc0,dc);
+			DEG(dc) = DEG(dct);
+			poly_to_gfsn_poly_main(COEF(dct),v,&COEF(dc));
+		}
+		NEXT(dc) = 0;
+		MKP(VR(f),dc0,*r);
+	}
+}
+
+void gfsn_poly_to_poly(VL vl,P f,V v,P *r)
+{
+	VL tvl,nvl0,nvl;
+	P g;
+
+	gfsn_poly_to_poly_main(f,v,&g);
+	/* (x,y,...,v,...) -> (x,y,...,v) */
+	for ( nvl0 = 0, tvl = vl; tvl; tvl = NEXT(tvl) ) {
+		if ( tvl->v != v ) {
+			NEXTVL(nvl0,nvl);
+			nvl->v = tvl->v;
+		}
+	}
+	NEXTVL(nvl0,nvl);
+	nvl->v = v;
+	NEXT(nvl) = 0;
+	reorderp(vl,nvl0,g,r);
+}
+
+void gfsn_poly_to_poly_main(P f,V v,P *r)
+{
+	DCP dc,dc0,dct;
+
+	if ( !f )
+		*r = f;
+	else if ( NUM(f) ) {
+		if ( NID((Num)f) == N_GFSN )
+			sfumtop(v,BDY((GFSN)f),r);
+		else
+			*r = f;
+	} else {
+		for ( dc0 = 0, dct = DC(f); dct; dct = NEXT(dct) ) {
+			NEXTDC(dc0,dc);
+			DEG(dc) = DEG(dct);
+			gfsn_poly_to_poly_main(COEF(dct),v,&COEF(dc));
+		}
+		NEXT(dc) = 0;
+		MKP(VR(f),dc0,*r);
+	}
 }