===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/Fgfs.c,v
retrieving revision 1.3
retrieving revision 1.6
diff -u -p -r1.3 -r1.6
--- OpenXM_contrib2/asir2000/engine/Fgfs.c	2002/09/27 08:40:48	1.3
+++ OpenXM_contrib2/asir2000/engine/Fgfs.c	2002/10/25 02:43:40	1.6
@@ -1,4 +1,4 @@
-/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.2 2002/09/26 09:07:42 noro Exp $ */
+/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.5 2002/10/23 07:54:58 noro Exp $ */
 
 #include "ca.h"
 
@@ -6,7 +6,157 @@ 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);
+int next_evaluation_point(int *mev,int n);
+void estimatelc_sf(VL vl,P c,DCP dc,int *mev,P *lcp);
+void mfctrsf_hensel(VL vl,int *mev,P f,P pp0,P u0,P v0,P lcu,P lcv,P *up);
 
+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;
@@ -113,7 +263,31 @@ void ugcdsf(P *pa,int m,P *r)
 	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)
@@ -131,13 +305,13 @@ void gcdsf_main(VL vl,P *pa,int m,P *r)
 		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(v,pa[i]);
+			d = getdeg(v,pa[i])+gethdeg(vl,v,pa[i]);
 			if ( i == 0 || (d < d0) ) {
 				d0 = d; i0 = i; v0 = v;
 			}
@@ -298,4 +472,192 @@ void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp)
 		ps[i] = C(t);
 	ugcdsf(ps,m,c);
 	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;
+	int imin,inext,i,n,k,np;
+	int *da;
+	V vx,vy;
+	V *va;
+	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;
+	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 ) {
+		for ( g0 = g, tvl = rvl, i = 0; tvl; tvl = NEXT(tvl), i++ ) {
+			indextogfs(mev[i],&ev);
+			substp(nvl,g0,tvl->v,(P)ev,&t); g0 = t;
+		}
+		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;
+		}
+		if ( next_evaluation_point(mev,n-2) )
+			error("mfctrsfhmain : short of evaluation points");
+	}
+	/* g0 = g(x,y,mev) */
+	/* separate content; g0 may have the content wrt x */
+	cont_pp_sfp(nvl,g0,&c0,&pp0);
+
+	/* factorize pp0; spp0 = pp0(x,y+evy) = prod dc */
+	sfbfctr_shift(pp0,vx,vy,getdeg(vx,pp0),&evy,&spp0,&dc);
+
+	if ( !NEXT(dc) ) {
+		/* f is irreducible */
+		NEWDC(dc); DEG(dc) = ONE; COEF(dc) = f; NEXT(dc) = 0;
+		*dcp = dc;
+		return;
+	}
+	/* shift c0; c0 <- c0(y+evy) */
+	addp(nvl,y,(P)evy,&t);
+	substp(nvl,c0,vy,t,&s);
+	c0 = s;
+
+	/* now f(x,y+ev,mev) = c0 * prod dc */
+	/* factorize lc_x(f) */
+	lcf = COEF(DC(f));
+	mfctrsf(nvl,lcf,&lcfdc); lcfdc = NEXT(lcfdc);
+
+	/* 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;
+	win = W_ALLOC(np+1);
+	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(y+yev) = c0*u0*v0 */
+		mulp(nvl,LC(u0),c0,&c); estimatelc_sf(nvl,c,dc,mev,&lcu);
+		divsp(nvl,pp0,u0,&v0);
+		mulp(nvl,LC(v0),c0,&c); estimatelc_sf(nvl,c,dc,mev,&lcv);
+		mfctrsf_hensel(nvl,mev,f,pp0,u0,v0,lcu,lcv,&u);
+	}
+}
+
+int next_evaluation_point(int *mev,int n)
+{
+}
+
+void estimatelc_sf(VL vl,P c,DCP dc,int *mev,P *lcp)
+{
+}
+
+void mfctrsf_hensel(VL vl,int *mev,P f,P pp0,P u0,P v0,P lcu,P lcv,P *up)
+{
 }