===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/Hgfs.c,v
retrieving revision 1.1
retrieving revision 1.4
diff -u -p -r1.1 -r1.4
--- OpenXM_contrib2/asir2000/engine/Hgfs.c	2001/06/20 09:32:13	1.1
+++ OpenXM_contrib2/asir2000/engine/Hgfs.c	2001/06/25 01:35:21	1.4
@@ -1,4 +1,4 @@
-/* $OpenXM$ */
+/* $OpenXM: OpenXM_contrib2/asir2000/engine/Hgfs.c,v 1.3 2001/06/22 08:51:12 noro Exp $ */
 
 #include "ca.h"
 
@@ -128,12 +128,12 @@ void randsfum(d,p)
 int d;
 UM p;
 {
-	unsigned int n;
 	int i;
 
-	n = ((unsigned int)random()) % d; DEG(p) = n; COEF(p)[n] = _onesf();
-	for ( i = 0; i < (int)n; i++ )
+	for ( i = 0; i < d; i++ )
 		COEF(p)[i] = _randomsf();
+	for ( i = d-1; i >= 0 && !COEF(p)[i]; i-- );
+	p->d = i;
 }
 
 void pwrmodsfum(p,e,f,pr)
@@ -166,7 +166,7 @@ UM p,f,pr;
 	}
 }
 
-void spwrum0sf(m,f,e,r)
+void spwrsfum(m,f,e,r)
 UM f,m,r;
 N e;
 {
@@ -180,7 +180,7 @@ N e;
 		cpyum(f,r);
 	else {
 		a = divin(e,2,&e1);
-		t = W_UMALLOC(2*DEG(m)); spwrum0sf(m,f,e1,t);
+		t = W_UMALLOC(2*DEG(m)); spwrsfum(m,f,e1,t);
 		s = W_UMALLOC(2*DEG(m)); q = W_UMALLOC(2*DEG(m));
 		mulsfum(t,t,s); DEG(s) = divsfum(s,m,q);
 		if ( a ) {
@@ -190,6 +190,28 @@ N e;
 	}
 }
 
+void tracemodsfum(m,f,e,r)
+UM f,m,r;
+int e;
+{
+	UM t,s,q,u;
+	int i;
+
+	q = W_UMALLOC(2*DEG(m)+DEG(f)); /* XXX */
+	t = W_UMALLOC(2*DEG(m));
+	s = W_UMALLOC(2*DEG(m));
+	u = W_UMALLOC(2*DEG(m));
+	DEG(f) = divsfum(f,m,q);
+	cpyum(f,s);
+	cpyum(f,t);
+	for ( i = 1; i < e; i++ ) {
+		mulsfum(t,t,u);
+		DEG(u) = divsfum(u,m,q); cpyum(u,t);
+		addsfum(t,s,u); cpyum(u,s);
+	}
+	cpyum(s,r);
+}
+
 void make_qmatsf(p,tab,mp)
 UM p;
 UM *tab;
@@ -469,7 +491,7 @@ int d;
 	UM t,s,u,w,g,o;
 	N n1,n2,n3,n4,n5;
 	UM *b;
-	int n,m,i,q;
+	int n,m,i,q,ed;
 
 	if ( DEG(f) == d ) {
 		r[0] = UMALLOC(d); cpyum(f,r[0]);
@@ -483,11 +505,19 @@ int d;
 		w = W_UMALLOC(DEG(f)); g = W_UMALLOC(DEG(f));
 		o = W_UMALLOC(0); DEG(o) = 0; COEF(o)[0] = _onesf();
 		q = field_order_sf();
-		STON(q,n1); pwrn(n1,d,&n2); subn(n2,ONEN,&n3);
-		STON(2,n4); divsn(n3,n4,&n5);
+		if ( q % 2 ) {
+			STON(q,n1); pwrn(n1,d,&n2); subn(n2,ONEN,&n3);
+			STON(2,n4); divsn(n3,n4,&n5);
+		} else
+			ed = d*extdeg_sf();
 		while ( 1 ) {
-			randsfum(2*d,t); spwrum0sf(f,t,n5,s);
-			subsfum(s,o,u); cpyum(f,w); gcdsfum(w,u,g);
+			randsfum(2*d,t);
+			if ( q % 2 ) {
+				spwrsfum(f,t,n5,s); subsfum(s,o,u);
+			} else
+				tracemodsfum(f,t,ed,u);
+			cpyum(f,w);
+			gcdsfum(w,u,g);
 			if ( (DEG(g) >= 1) && (DEG(g) < DEG(f)) ) {
 				canzassf(g,d,r); 
 				cpyum(f,w); divsfum(w,g,s);
@@ -498,3 +528,437 @@ int d;
 	}
 }
 
+/* Hensel related functions */
+
+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(LUM,UM,UM,int,LUM *);
+
+/* f = f(x,y) */
+
+void sfhensel(count,f,x,listp)
+int count;
+P f;
+V x;
+ML *listp;
+{
+	int i,j;
+	int fn,n,bound;
+	ML rlist;
+	LUM fl;
+	VL vl,nvl;
+	V y;
+	int dx,dy,mev;
+	GFS ev;
+	P f1,t,yev,c;
+	DCP dc;
+	LUM gl;
+	UM w,w1,q,fm,hm;
+	UM *gm;
+
+	clctv(CO,f,&vl);
+	if ( vl->v != x ) {
+		reordvar(vl,x,&nvl); reorderp(nvl,vl,f,&f1);
+		vl = nvl; f = f1;
+	}
+	y = vl->next->v;
+	dx = getdeg(x,f);
+	dy = getdeg(y,f);
+	if ( dx == 1 ) {
+		*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 = 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;
+
+	/* convert mod y-a factors into UM */
+	gm = (UM *)ALLOCA(fn*sizeof(UM));
+	for ( i = 0; i < fn; i++, dc = NEXT(dc) ) {
+		gm[i] = W_UMALLOC(UDEG(dc->c));
+		ptosfum(dc->c,gm[i]);
+	}
+
+	bound = dy+1;
+	/* f(x,y) -> f(x,y+ev) */
+	fl = LUMALLOC(dx,bound);
+	ptosflum(bound,f,fl);
+	shiftsflum(bound,fl,FTOIF(CONT(ev)));
+
+	/* fm = fl mod y */
+	fm = W_UMALLOC(dx);
+	DEG(fm) = dx;
+	for ( i = 0; i <= dx; i++ )
+		COEF(fm)[i] = COEF(fl)[i][0];
+	hm = W_UMALLOC(dx);
+
+	q = W_UMALLOC(dx);
+	rlist = MLALLOC(fn); rlist->n = fn; rlist->bound = bound;
+	for ( i = 0; i < fn-1; i++ ) {
+		fprintf(stderr,"%d\n",i);
+		/* 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,(LUM *)&rlist->c[i]);
+		cpyum(hm,fm);
+	}
+	/* finally, fl must be the lift of gm[fn-1] */
+	rlist->c[i] = fl;
+
+	/* y -> y-a */
+	w = W_UMALLOC(bound);
+	w1 = W_UMALLOC(bound);
+	mev = _chsgnsf(FTOIF(CONT(ev)));
+	for ( i = 0; i < fn; i++ )
+		shiftsflum(bound,(LUM)(rlist->c[i]),mev);
+	*listp = rlist;
+}
+
+/* main variable of f = x */
+
+int sfberle(vl,f,count,ev,dcp)
+VL vl;
+P f;
+int count;
+GFS *ev;
+DCP *dcp;
+{
+	UM wf,wf1,wf2,wfs,gcd;
+	ML flist;
+	int fn,fn1,n;
+	GFS m,fm;
+	DCP dc,dct,dc0;
+	VL nvl;
+	V x,y;
+	P g,lc,lc0,f0;
+	int j,q1,index,i;
+
+	clctv(vl,f,&nvl); vl = nvl;
+	x = vl->v; y = vl->next->v;
+	simp_ff(f,&g); g = f;
+	n = QTOS(DEG(DC(f)));
+	wf = W_UMALLOC(n); wf1 = W_UMALLOC(n); wf2 = W_UMALLOC(n);
+	wfs = W_UMALLOC(n); gcd = W_UMALLOC(n);
+	q1 = field_order_sf()-1;
+	lc = DC(f)->c;
+	for ( j = 0, fn = n + 1, index = 0; 
+		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(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++ );
+				if ( i < fn ) {
+					dc0 = dc; fn = i; fm = m;
+				}
+				j++;
+			}
+		}
+	}
+	if ( index == q1 )
+		return 0;
+	else if ( fn == 1 )
+		return 1;
+	else {
+		*dcp = dc0;
+		*ev = fm;
+		return fn;
+	}
+}
+
+void sfgcdgen(f,blist,clistp)
+P f;
+ML blist,*clistp;
+{
+	int i;
+	int n,d,np;
+	UM wf,wm,wx,wy,wu,wv,wa,wb,wg,q,tum;
+	UM *in,*out;
+	ML clist;
+
+	n = UDEG(f); np = blist->n;
+	d = 2*n;
+	q = W_UMALLOC(d); wf = W_UMALLOC(d);
+	wm = W_UMALLOC(d); wx = W_UMALLOC(d);
+	wy = W_UMALLOC(d); wu = W_UMALLOC(d);
+	wv = W_UMALLOC(d); wg = W_UMALLOC(d);
+	wa = W_UMALLOC(d); wb = W_UMALLOC(d);
+	ptosfum(f,wf); DEG(wg) = 0; COEF(wg)[0] = _onesf();
+	*clistp = clist = MLALLOC(np); clist->n = np;
+	for ( i = 0, in = (UM *)blist->c, out = (UM *)clist->c; i < np; i++ ) {
+		divsfum(wf,in[i],q); tum = wf; wf = q; q = tum;
+		cpyum(wf,wx); cpyum(in[i],wy);
+		eucsfum(wx,wy,wa,wb); mulsfum(wa,wg,wm);
+		DEG(wm) = divsfum(wm,in[i],q); out[i] = UMALLOC(DEG(wm));
+		cpyum(wm,out[i]); mulsfum(q,wf,wu);
+		mulsfum(wg,wb,wv); addsfum(wu,wv,wg);
+	}
+}
+
+/*
+	sfhenmain(fl,bqlist,cqlist,listp)
+*/
+
+void sfhenmain(f,bqlist,cqlist,listp)
+LUM f;
+ML bqlist,cqlist,*listp;
+{
+	int i,j,k;
+	int *px,*py;
+	int **pp,**pp1;
+	int n,np,bound,dr,tmp;
+	UM wt,wq0,wq,wr,wm,wm0,wa,q;
+	LUM wb0,wb1,tlum;
+	UM *b,*c;
+	LUM *l;
+	ML list;
+
+	n = DEG(f); np = bqlist->n; bound = bqlist->bound;
+	*listp = list = MLALLOC(n);
+	list->n = np; list->bound = bound;
+	W_LUMALLOC(n,bound,wb0); W_LUMALLOC(n,bound,wb1);
+	wt = W_UMALLOC(n); wq0 = W_UMALLOC(n); wq = W_UMALLOC(n);
+	wr = W_UMALLOC(n); wm = W_UMALLOC(2*n); wm0 = W_UMALLOC(2*n);
+	wa = W_UMALLOC(2*n); q = W_UMALLOC(2*n);
+	b = (UM *)bqlist->c; c = (UM *)cqlist->c; l = (LUM *)list->c; 
+	for ( i = 0; i < np; i++ ) {
+		l[i] = LUMALLOC(DEG(b[i]),bound);
+		for ( j = DEG(b[i]), pp = COEF(l[i]), px = COEF(b[i]); j >= 0; j-- ) 
+			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 1
+		/* 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-- )
+			COEF(wt)[j] = _subsf(pp[j][i],pp1[j][i]);
+		degum(wt,n);
+		for ( j = n, px = COEF(wq0); j >= 0; j-- )
+			px[j] = 0;
+		for ( j = 1; j < np; j++ ) {
+			mulsfum(wt,c[j],wm); dr = divsfum(wm,b[j],q);
+			for ( k = DEG(q), px = COEF(wq0), py = COEF(q); k >= 0; k-- ) 
+				px[k] = _addsf(px[k],py[k]);
+			for ( k = dr, pp = COEF(l[j]), px = COEF(wm); k >= 0; k-- ) 
+				pp[k][i] = px[k];
+		}
+		degum(wq0,n); mulsfum(wq0,b[0],wm);
+		mulsfum(wt,c[0],wm0); addsfum(wm,wm0,wa);
+		for ( j = DEG(wa), pp = COEF(l[0]), px = COEF(wa); j >= 0; j-- ) 
+			pp[j][i] = px[j];
+		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)
+LUM f;
+UM g0,h0;
+int bound;
+LUM *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;
+	UM wc,wd,we,wz;
+	LUM wb0,wb1;
+	int ng,nh;
+	LUM fk,gk,hk;
+	
+	n = f->d;
+	ng = g0->d;
+	nh = h0->d;
+
+	W_LUMALLOC(n,bound,wb0); W_LUMALLOC(n,bound,wb1);
+	wt = 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_LUMALLOC(n,bound,fk);
+	DEG(fk) = n;
+	for ( j = 0; j <= n; j++ )
+		COEF(fk)[j][0] = COEF(f)[j][0];
+
+	gk = LUMALLOC(ng,bound);
+	DEG(gk) = ng;
+	for ( j = 0; j <= ng; j++ )
+		COEF(gk)[j][0] = COEF(g0)[j];
+
+	W_LUMALLOC(nh,bound,hk);
+	DEG(hk) = nh;
+	for ( j = 0; j <= nh; j++ )
+		COEF(hk)[j][0] = COEF(h0)[j];
+
+	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");
+#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, pp = COEF(f), pp1 = COEF(fk); j <= n; j++ )
+			for ( l = 0; l < k; l++ )
+				if ( pp[j][l] != pp1[j][l] )
+					error("henmain2 : cannot happen");
+#endif
+
+		/* clear wt */
+		bzero(COEF(wt),(n+1)*sizeof(int));
+
+		/* wt = (f-gk*hk)/y^k */
+		pp = COEF(f); pp1 = COEF(fk);
+		for ( j = n; j >= 0; j-- )
+			COEF(wt)[j] = _subsf(pp[j][k],pp1[j][k]);
+		degum(wt,n);
+		
+		/* 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");
+
+		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 */
+		clearsflum(bound,n,wb0);
+		DEG(wb0) = DEG(wh1);
+		for ( i = 0; i <= DEG(wh1); i++ )
+			COEF(wb0)[i][k] = COEF(wh1)[i];
+		/* wb1 = gk*wb0 mod y^bound */
+		clearsflum(bound,n,wb1);
+		mulsflum(bound,gk,wb0,wb1);
+		/* fk += wb1 */
+		addtosflum(bound,wb1,fk);
+
+		/* wb0 = wg1*y^k */
+		clearsflum(bound,n,wb0);
+		DEG(wb0) = DEG(wg1);
+		for ( i = 0; i <= DEG(wg1); i++ )
+			COEF(wb0)[i][k] = COEF(wg1)[i];
+		/* wb1 = hk*wb0 mod y^bound */
+		clearsflum(bound,n,wb1);
+		mulsflum(bound,hk,wb0,wb1);
+		/* fk += wb1 */
+		addtosflum(bound,wb1,fk);
+
+		/* fk += wg1*wh1*y^(2*k) mod y^bound */
+		if ( 2*k < bound ) {
+			mulsfum(wg1,wh1,wt);
+			for ( i = 0; i <= DEG(wt); i++ )
+				COEF(fk)[i][2*k] = _addsf(COEF(fk)[i][2*k],COEF(wt)[i]);
+		}
+
+		/* gk += wg1*y^k, hk += wh1*y^k */
+		for ( i = 0; i <= DEG(wg1); i++ )
+			COEF(gk)[i][k] = COEF(wg1)[i];
+		for ( i = 0; i <= DEG(wh1); i++ )
+			COEF(hk)[i][k] = COEF(wh1)[i];
+	}
+	fprintf(stderr,"\n");
+	*gp = gk;
+	for ( i = 0; i <= DEG(hk); i++ )
+		for ( j = 0; j <= bound; j++ )
+			COEF(f)[i][j] = COEF(hk)[i][j];
+	DEG(f) = DEG(hk);
+}
+
+void ptosflum(bound,f,fl)
+int bound;
+P f;
+LUM fl;
+{
+	DCP dc;
+	int **pp;
+	int d;
+	UM t;
+
+	t = UMALLOC(bound);
+	for ( dc = DC(f), pp = COEF(fl); dc; dc = NEXT(dc) ) {
+		d = QTOS(DEG(dc));
+		ptosfum(COEF(dc),t);
+		bcopy(t->c,pp[d],(t->d+1)*sizeof(int));
+	}
+}
+
+/* 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);
+}