===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/Fgfs.c,v
retrieving revision 1.2
retrieving revision 1.5
diff -u -p -r1.2 -r1.5
--- OpenXM_contrib2/asir2000/engine/Fgfs.c	2002/09/26 09:07:42	1.2
+++ OpenXM_contrib2/asir2000/engine/Fgfs.c	2002/10/23 07:54:58	1.5
@@ -1,11 +1,163 @@
-/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.1 2002/09/26 04:33:16 noro Exp $ */
+/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.4 2002/09/30 06:13:07 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 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 +169,21 @@ 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 +225,7 @@ 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 +235,15 @@ 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);
@@ -96,35 +253,62 @@ 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;
-	V v0,vmin;
+	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;
+	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;
 			}
@@ -141,9 +325,9 @@ 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 */
@@ -152,7 +336,7 @@ 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);
 	}
@@ -166,13 +350,13 @@ 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;
@@ -181,42 +365,43 @@ 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);
 			/* hm=0 : reset; he==hm : lucky */
-			if ( !hm || !cmpp(he,hm) ) {
+			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,cof1,t,&u); mulp(nvl,mod1,u,&coadj);
+				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],adj,&t) )
+						if ( !divtp(nvl,lps[i],g,&t) )
 							break;
 					if ( i == m ) {
-						cont_pp_mv_sf(nvl,rvl,adj,&t,&u);
+						cont_pp_mv_sf(nvl,rvl,g,&t,&u);
 						mulp(nvl,cont,u,&t);
-						reorderp(nvl,vl,t,r);
+						reorderp(vl,nvl,t,r);
 						return;
 					}
 				} else if ( !coadj ) {
-					/* ps[vmin]/coadj == gcd ? */
-					if ( divtp(nvl,lps[vmin],coadj,&q) ) {
+					/* 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(nvl,vl,t,r);
+							reorderp(vl,nvl,t,r);
 							return;
 						}
 					}
@@ -239,7 +424,7 @@ void gcdsf_main(VL vl,P *pa,int m,P *r)
 					/* d1==d2, but hm!=he => both are unlucky */
 					g = 0;
 					cof1 = 0;
-					MKGFS(0,mod);
+					itogfs(1,&mod);
 				}
 			}
 		}
@@ -251,16 +436,18 @@ 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));
@@ -278,8 +465,114 @@ 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;
+	DCP dc,dc0,dc1,dc2,dct;
+	int imin,inext,i,n;
+	int *da;
+	V vx,vy;
+	V *va;
+	P gcd,g,df,dfmin;
+	P pa[2];
+
+	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;
+	if ( !NEXT(NEXT(nvl)) ) {
+		/* 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;
+	}
 }