===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/builtin/strobj.c,v
retrieving revision 1.74
retrieving revision 1.85
diff -u -p -r1.74 -r1.85
--- OpenXM_contrib2/asir2000/builtin/strobj.c	2005/10/14 07:49:21	1.74
+++ OpenXM_contrib2/asir2000/builtin/strobj.c	2005/10/26 11:07:50	1.85
@@ -45,7 +45,7 @@
  * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
  * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
  *
- * $OpenXM: OpenXM_contrib2/asir2000/builtin/strobj.c,v 1.73 2005/10/14 07:39:38 noro Exp $
+ * $OpenXM: OpenXM_contrib2/asir2000/builtin/strobj.c,v 1.84 2005/10/26 10:47:00 noro Exp $
 */
 #include "ca.h"
 #include "parse.h"
@@ -64,6 +64,10 @@ struct TeXSymbol {
 };
 
 #define OPNAME(f) (((ARF)FA0(f))->name[0])
+#define IS_ZERO(f) (((f)->id==I_FORMULA) && FA0(f)==0 )
+#define IS_BINARYPWR(f) (((f)->id==I_BOP) &&(OPNAME(f)=='^'))
+#define IS_NARYADD(f) (((f)->id==I_NARYOP) &&(OPNAME(f)=='+'))
+#define IS_NARYMUL(f) (((f)->id==I_NARYOP) &&(OPNAME(f)=='*'))
 
 extern char *parse_strp;
 
@@ -83,6 +87,7 @@ void Pflatten_quote();
 void Pquote_is_integer(),Pquote_is_rational(),Pquote_is_number();
 void Pquote_is_dependent(),Pquote_is_function();
 void Pquote_normalize();
+void Pquote_normalize_comp();
 
 void Pquote_to_funargs(),Pfunargs_to_quote(),Pget_function_name();
 void Pquote_unify(),Pget_quote_id(),Pquote_match_rewrite();
@@ -121,7 +126,8 @@ struct ftab str_tab[] = {
 	{"quote_is_function",Pquote_is_function,1},
 	{"quote_is_dependent",Pquote_is_dependent,2},
 
-	{"quote_normalize",Pquote_normalize,1},
+	{"quote_normalize",Pquote_normalize,-2},
+	{"quote_normalize_comp",Pquote_normalize_comp,2,0x3},
 
 	{"quote_to_nary",Pquote_to_nary,1},
 	{"quote_to_bin",Pquote_to_bin,2},
@@ -530,7 +536,6 @@ void Pwrite_to_tb(NODE arg,Q *rp)
 }
 
 FNODE partial_eval(FNODE), fnode_to_nary(FNODE), fnode_to_bin(FNODE,int);
-FNODE fnode_normalize(FNODE);
 
 void Pquote_to_nary(NODE arg,QUOTE *rp)
 {
@@ -660,20 +665,20 @@ void Pquote_match_rewrite(NODE arg,Obj *rp)
 			NEXTNODE(s0,s);
 			pair = BDY((LIST)BDY(t));
 			ind = (int)FA0((FNODE)BDY((QUOTE)BDY(pair)));
-			value = mkfnode(1,I_FORMULA,BDY(NEXT(pair)));
+			value = BDY((QUOTE)(BDY(NEXT(pair))));
 			BDY(s) = mknode(2,ind,value);
 		}
 		if ( s0 ) NEXT(s) = 0;
 		switch ( ac = argc(arg) ) {
 			case 3:
 				h = rewrite_fnode(BDY((QUOTE)ARG2(arg)),s0);
-				*rp = eval(h);
+				MKQUOTE(q,h); *rp = (Obj)q;
 				break;
 			case 4:
 				c = rewrite_fnode(BDY((QUOTE)ARG2(arg)),s0);
 				if ( eval(c) ) {
 					h = rewrite_fnode(BDY((QUOTE)ARG3(arg)),s0);
-					*rp = eval(h);
+					MKQUOTE(q,h); *rp = (Obj)q;
 				} else
 					*rp = VOIDobj;
 				break;
@@ -1921,25 +1926,42 @@ void Pfunargs_to_quote(NODE arg,QUOTE *rp)
 	MKQUOTE(*rp,f);
 }
 
-FNODE fnode_apply(FNODE f,FNODE (*func)());
-FNODE fnode_normalize(FNODE f);
+FNODE fnode_apply(FNODE f,FNODE (*func)(),int expand);
+FNODE fnode_normalize(FNODE f,int expand);
 
 void Pquote_normalize(NODE arg,QUOTE *rp)
 {
 	QUOTE q,r;
 	FNODE f;
+	int expand,ac;
 
+	ac = argc(arg);
+	if ( !ac ) error("quote_normalize : invalid argument");
 	q = (QUOTE)ARG0(arg);
+	expand = ac==2 && ARG1(arg);
 	if ( !q || OID(q) != O_QUOTE ) {
 		*rp = q;
 		return;
 	} else {
-		f = fnode_normalize(BDY(q));
+		f = fnode_normalize(BDY(q),expand);
 		MKQUOTE(r,f);
 		*rp = r;
 	}
 }
 
+void Pquote_normalize_comp(NODE arg,Q *rp)
+{
+	FNODE f1,f2;
+	int r;
+
+	f1 = BDY((QUOTE)ARG0(arg));
+	f2 = BDY((QUOTE)ARG1(arg));
+	f1 = fnode_normalize(f1,0);
+	f2 = fnode_normalize(f2,0);
+	r = fnode_normalize_comp(f1,f2);
+	STOQ(r,*rp);
+}
+
 int fnode_is_number(FNODE f)
 {
 	Obj obj;
@@ -2025,15 +2047,6 @@ int fnode_is_integer(FNODE f)
 	}
 }
 
-int fnode_is_zero(FNODE f)
-{
-	Q n;
-
-	n = eval(f);
-	if ( !n ) return 1;
-	else return 0;
-}
-
 int fnode_is_nonnegative_integer(FNODE f)
 {
 	Q n;
@@ -2093,49 +2106,52 @@ int fnode_is_dependent(FNODE f,V v)
 	}
 }
 
-FNODE fnode_normalize_add(FNODE a1,FNODE a2);
-FNODE fnode_normalize_mul(FNODE a1,FNODE a2);
-FNODE fnode_normalize_pwr(FNODE a1,FNODE a2);
+FNODE fnode_normalize_add(FNODE a1,FNODE a2,int expand);
+FNODE fnode_normalize_mul(FNODE a1,FNODE a2,int expand);
+FNODE fnode_normalize_pwr(FNODE a1,FNODE a2,int expand);
+FNODE fnode_normalize_mul_coef(Num c,FNODE f,int expand);
+FNODE fnode_expand_pwr(FNODE f,int n);
 FNODE to_narymul(FNODE f);
 FNODE to_naryadd(FNODE f);
-FNODE fnode_normalize_mul_coef(Num c,FNODE f);
+FNODE fnode_node_to_naryadd(NODE n);
+FNODE fnode_node_to_narymul(NODE n);
 void fnode_base_exp(FNODE f,FNODE *bp,FNODE *ep);
 void fnode_coef_body(FNODE f,Num *cp,FNODE *bp);
 
 
-FNODE fnode_normalize(FNODE f)
+FNODE fnode_normalize(FNODE f,int expand)
 {
 	FNODE a1,a2,mone,r,b2;
 	NODE n;
-	Num invc2,c2;
 	Q q;
 
 	STOQ(-1,q);
 	mone = mkfnode(1,I_FORMULA,q);
 	switch ( f->id ) {
 		case I_PAREN:
-			return fnode_normalize(FA0(f));
+			return fnode_normalize(FA0(f),expand);
 		
 		case I_MINUS:
-			return fnode_normalize_mul_coef((Num)q,fnode_normalize(FA0(f)));
+			return fnode_normalize_mul_coef((Num)q,
+				fnode_normalize(FA0(f),expand),expand);
 
 		case I_BOP:
 			/* arf fnode fnode */
-			a1 = fnode_normalize(FA1(f));
-			a2 = fnode_normalize(FA2(f));
+			a1 = fnode_normalize(FA1(f),expand);
+			a2 = fnode_normalize(FA2(f),expand);
 			switch ( OPNAME(f) ) {
 				case '+':
-					return fnode_normalize_add(a1,a2);
+					return fnode_normalize_add(a1,a2,expand);
 				case '-':
-					a2 = fnode_normalize_mul_coef((Num)q,a2);
-					return fnode_normalize_add(a1,a2);
+					a2 = fnode_normalize_mul_coef((Num)q,a2,expand);
+					return fnode_normalize_add(a1,a2,expand);
 				case '*':
-					return fnode_normalize_mul(a1,a2);
+					return fnode_normalize_mul(a1,a2,expand);
 				case '/':
-					a2 = fnode_normalize_pwr(a2,mone);
-					return fnode_normalize_mul(a1,a2);
+					a2 = fnode_normalize_pwr(a2,mone,expand);
+					return fnode_normalize_mul(a1,a2,expand);
 				case '^':
-					return fnode_normalize_pwr(a1,a2);
+					return fnode_normalize_pwr(a1,a2,expand);
 				default:
 					return mkfnode(3,I_BOP,FA0(f),a1,a2);
 			}
@@ -2145,18 +2161,18 @@ FNODE fnode_normalize(FNODE f)
 			switch ( OPNAME(f) ) {
 				case '+':
 					n = (NODE)FA1(f);
-					r = fnode_normalize(BDY(n)); n = NEXT(n);
+					r = fnode_normalize(BDY(n),expand); n = NEXT(n);
 					for ( ; n; n = NEXT(n) ) {
-						a1 = fnode_normalize(BDY(n));
-						r = fnode_normalize_add(r,a1);
+						a1 = fnode_normalize(BDY(n),expand);
+						r = fnode_normalize_add(r,a1,expand);
 					}
 					return r;
 				case '*':
 					n = (NODE)FA1(f);
-					r = fnode_normalize(BDY(n)); n = NEXT(n);
+					r = fnode_normalize(BDY(n),expand); n = NEXT(n);
 					for ( ; n; n = NEXT(n) ) {
-						a1 = fnode_normalize(BDY(n));
-						r = fnode_normalize_mul(r,a1);
+						a1 = fnode_normalize(BDY(n),expand);
+						r = fnode_normalize_mul(r,a1,expand);
 					}
 					return r;
 				default:
@@ -2164,11 +2180,11 @@ FNODE fnode_normalize(FNODE f)
 			}
 
 		default:
-			return fnode_apply(f,fnode_normalize);
+			return fnode_apply(f,fnode_normalize,expand);
 	}
 }
 
-FNODE fnode_apply(FNODE f,FNODE (*func)())
+FNODE fnode_apply(FNODE f,FNODE (*func)(),int expand)
 {
 	fid_spec_p spec;
 	FNODE r;
@@ -2181,13 +2197,13 @@ FNODE fnode_apply(FNODE f,FNODE (*func)())
 	for ( i = 0; i < n; i++ ) {
 		switch ( spec->type[i] ) {
 			case A_fnode:
-				r->arg[i] = func(f->arg[i]);
+				r->arg[i] = func(f->arg[i],expand);
 				break;
 			case A_node:
 				s = (NODE)f->arg[i];
 				for ( t0 = 0; s; s = NEXT(s) ) {
 					NEXTNODE(t0,t);
-					BDY(t) = (pointer)func((FNODE)BDY(s));
+					BDY(t) = (pointer)func((FNODE)BDY(s),expand);
 				}
 				if ( t0 ) NEXT(t) = 0;
 				r->arg[i] = t0;
@@ -2200,33 +2216,28 @@ FNODE fnode_apply(FNODE f,FNODE (*func)())
 	return r;
 }
 
-FNODE fnode_normalize_add(FNODE f1,FNODE f2)
+FNODE fnode_normalize_add(FNODE f1,FNODE f2,int expand)
 {
 	NODE n1,n2,r0,r;
 	FNODE b1,b2;
 	int s;
 	Num c1,c2,c;
 
-	if ( fnode_is_zero(f1) ) return f2;
-	else if ( fnode_is_zero(f2) ) return f1;
-	if ( f1->id != I_NARYOP || OPNAME(f1) != '+' ) f1 = to_naryadd(f1);
-	if ( f2->id != I_NARYOP || OPNAME(f2) != '+' ) f2 = to_naryadd(f2);
-	n1 = (NODE)FA1(f1);
-	n2 = (NODE)FA1(f2);
+	if ( IS_ZERO(f1) ) return f2;
+	else if ( IS_ZERO(f2) ) return f1;
+	f1 = to_naryadd(f1); f2 = to_naryadd(f2);
+	n1 = (NODE)FA1(f1); n2 = (NODE)FA1(f2);
 	r0 = 0;
 	while ( n1 && n2 ) {
-		fnode_coef_body(BDY(n1),&c1,&b1);
-		fnode_coef_body(BDY(n2),&c2,&b2);
-		s = compfnode(b1,b2);
-		if ( s > 0 ) {
+		fnode_coef_body(BDY(n1),&c1,&b1); fnode_coef_body(BDY(n2),&c2,&b2);
+		if ( (s = fnode_normalize_comp(b1,b2)) > 0 ) {
 			NEXTNODE(r0,r); BDY(r) = BDY(n1); n1 = NEXT(n1);
 		} else if ( s < 0 ) {
 			NEXTNODE(r0,r); BDY(r) = BDY(n2); n2 = NEXT(n2);
 		} else {
 			addnum(0,c1,c2,&c);
 			if ( c ) {
-				NEXTNODE(r0,r);
-				BDY(r) = UNIQ(c) ? b1 : fnode_normalize_mul_coef(c,b1);
+				NEXTNODE(r0,r); BDY(r) = fnode_normalize_mul_coef(c,b1,expand);
 			}
 			n1 = NEXT(n1); n2 = NEXT(n2);
 		}
@@ -2240,91 +2251,96 @@ FNODE fnode_normalize_add(FNODE f1,FNODE f2)
 	else if ( r0 )
 		NEXT(r) = 0;
 
-	if ( !r0 )
-		return mkfnode(1,I_FORMULA,0);
-	else if ( !NEXT(r0) )
-		return BDY(r0);
-	else
-		return mkfnode(2,I_NARYOP,addfs,r0);
+	return fnode_node_to_naryadd(r0);
 }
 
-FNODE fnode_normalize_mul(FNODE f1,FNODE f2)
+FNODE fnode_node_to_naryadd(NODE n)
 {
+	if ( !n ) return mkfnode(1,I_FORMULA,0);
+	else if ( !NEXT(n) ) return BDY(n);
+	else return mkfnode(2,I_NARYOP,addfs,n);
+}
+
+FNODE fnode_node_to_narymul(NODE n)
+{
+	if ( !n ) return mkfnode(1,I_FORMULA,ONE);
+	else if ( !NEXT(n) ) return BDY(n);
+	else return mkfnode(2,I_NARYOP,mulfs,n);
+}
+
+FNODE fnode_normalize_mul(FNODE f1,FNODE f2,int expand)
+{
 	NODE n1,n2,r0,r,r1;
-	FNODE b1,b2,e1,e2,cc;
+	FNODE b1,b2,e1,e2,cc,t,t1;
 	FNODE *m;
 	int s;
 	Num c1,c2,c,e;
-	int l1,l2,l,i,j;
+	int l1,l,i,j;
 
-	if ( fnode_is_zero(f1) || fnode_is_zero(f2) ) return 0;
+	if ( IS_ZERO(f1) || IS_ZERO(f2) ) return mkfnode(1,I_FORMULA,0);
+	else if ( fnode_is_number(f1) ) 
+		return fnode_normalize_mul_coef((Num)eval(f1),f2,expand);
+	else if ( fnode_is_number(f2) ) 
+		return fnode_normalize_mul_coef((Num)eval(f2),f1,expand);
 
-	if ( f1->id != I_NARYOP || OPNAME(f1) != '*' ) f1 = to_narymul(f1);
-	if ( f2->id != I_NARYOP || OPNAME(f2) != '*' ) f2 = to_narymul(f2);
-	n1 = (NODE)FA1(f1);
-	n2 = (NODE)FA1(f2);
-	if ( fnode_is_number(BDY(n1)) )
-		if ( fnode_is_number(BDY(n2)) ) {
-			mulnum(0,eval(BDY(n1)),eval(BDY(n2)),&c);
-			n1 = NEXT(n1); n2 = NEXT(n2);
-		} else {
-			c = eval(BDY(n1)); n1 = NEXT(n1);
+	if ( expand && IS_NARYADD(f1) ) {
+		t = mkfnode(1,I_FORMULA,0);
+		for ( n1 = (NODE)FA1(f1); n1; n1 = NEXT(n1) ) {
+			t1 = fnode_normalize_mul(BDY(n1),f2,expand);
+			t = fnode_normalize_add(t,t1,expand);
 		}
-	else if ( fnode_is_number(BDY(n2)) ) {
-		c = eval(BDY(n2)); n2 = NEXT(n2);
-	} else
-		c = (Num)ONE;
+		return t;
+	}
+	if ( expand && IS_NARYADD(f2) ) {
+		t = mkfnode(1,I_FORMULA,0);
+		for ( n2 = (NODE)FA1(f2); n2; n2 = NEXT(n2) ) {
+			t1 = fnode_normalize_mul(f1,BDY(n2),expand);
+			t = fnode_normalize_add(t,t1,expand);
+		}
+		return t;
+	}
+
+	fnode_coef_body(f1,&c1,&b1); fnode_coef_body(f2,&c2,&b2);
+	mulnum(0,c1,c2,&c);
 	if ( !c ) return mkfnode(1,I_FORMULA,0);
 
-	l1 = length(n1);
-	l2 = length(n2);
-	l = l1+l2;
+
+	n1 = (NODE)FA1(to_narymul(b1)); n2 = (NODE)FA1(to_narymul(b2));
+	l1 = length(n1); l = l1+length(n2);
 	m = (FNODE *)ALLOCA(l*sizeof(FNODE));
 	for ( r = n1, i = 0; i < l1; r = NEXT(r), i++ ) m[i] = BDY(r);
 	for ( r = n2; r; r = NEXT(r) ) {
 		if ( i == 0 )
 			m[i++] = BDY(r);
 		else {
-			fnode_base_exp(m[i-1],&b1,&e1);
-			fnode_base_exp(BDY(r),&b2,&e2);
-			if ( compfnode(b1,b2) ) {
-				for ( j = i-1; j >= 0; j-- ) {
-					MKNODE(r1,m[j],r); r = r1;
-				}
-				cc = mkfnode(1,I_FORMULA,c);
-				MKNODE(r1,cc,r); r = r1;
-				return mkfnode(2,I_NARYOP,mulfs,r);
-			} else {
-				addnum(0,eval(e1),eval(e2),&e);
-				if ( !e ) i--;
-				else if ( UNIQ(e) )
-					m[i-1] = b1;
-				else
-					m[i-1] = mkfnode(3,I_BOP,pwrfs,b1,mkfnode(1,I_FORMULA,e));
-			}
+			fnode_base_exp(m[i-1],&b1,&e1); fnode_base_exp(BDY(r),&b2,&e2);
+			if ( compfnode(b1,b2) ) break;
+			addnum(0,eval(e1),eval(e2),&e);
+			if ( !e ) i--;
+			else if ( UNIQ(e) )
+				m[i-1] = b1;
+			else
+				m[i-1] = mkfnode(3,I_BOP,pwrfs,b1,mkfnode(1,I_FORMULA,e));
 		}
 	}
-	if ( !i ) return mkfnode(1,I_FORMULA,c);
-	else {
-		r = 0;
-		for ( j = i-1; j >= 0; j-- ) {
-			MKNODE(r1,m[j],r); r = r1;
-		}
-		cc = mkfnode(1,I_FORMULA,c);
-		MKNODE(r1,cc,r); 
-		r = r1;
-		return mkfnode(2,I_NARYOP,mulfs,r);
+	for ( j = i-1; j >= 0; j-- ) {
+		MKNODE(r1,m[j],r); r = r1;
 	}
+	if ( !UNIQ(c) ) {
+		cc = mkfnode(1,I_FORMULA,c); MKNODE(r1,cc,r); r = r1;
+	}
+	return fnode_node_to_narymul(r);
 }
 
-FNODE fnode_normalize_pwr(FNODE f1,FNODE f2)
+FNODE fnode_normalize_pwr(FNODE f1,FNODE f2,int expand)
 {
 	FNODE b,b1,e1,e,cc,r;
 	Num c,c1;
 	NODE arg,n;
+	Q q;
 
-	if ( fnode_is_zero(f2) ) return mkfnode(1,I_FORMULA,ONE);
-	else if ( fnode_is_zero(f1) ) return mkfnode(1,I_FORMULA,0);
+	if ( IS_ZERO(f2) ) return mkfnode(1,I_FORMULA,ONE);
+	else if ( IS_ZERO(f1) ) return mkfnode(1,I_FORMULA,0);
 	else if ( fnode_is_one(f2) ) return f1;
 	else if ( fnode_is_number(f1) )
 		if ( fnode_is_integer(f2) ) {
@@ -2332,36 +2348,52 @@ FNODE fnode_normalize_pwr(FNODE f1,FNODE f2)
 			return mkfnode(1,I_FORMULA,c);
 		} else
 			return mkfnode(3,I_BOP,pwrfs,f1,f2);
-	else if ( f1->id == I_BOP && OPNAME(f1) == '^' ) {
+	else if ( IS_BINARYPWR(f1) ) {
 		b1 = FA1(f1); e1 = FA2(f1);
-		e = fnode_normalize_mul(e1,f2);
+		e = fnode_normalize_mul(e1,f2,expand);
 		if ( fnode_is_one(e) )
 			return b1;
 		else
 			return mkfnode(3,I_BOP,FA0(f1),b1,e);
-	} else if ( f1->id == I_NARYOP && OPNAME(f1) == '*' ) {
+	} else if ( IS_NARYMUL(f1) && fnode_is_integer(f2) ) {
 		fnode_coef_body(f1,&c1,&b1);
-		if ( fnode_is_integer(f2) ) {
-			pwrnum(0,(Num)c1,(Num)eval(f2),&c);
-			cc = mkfnode(1,I_FORMULA,c);
-			b = fnode_normalize_pwr(b1,f2);
-			if ( fnode_is_one(cc) )
-				return b;
-			else {
-				NEWFNODE(r,2);
-				r->id = I_NARYOP; FA0(r) = mulfs; FA1(r) = mknode(2,cc,b);
-				return r;
-			}
-		} else
-			return mkfnode(3,I_BOP,pwrfs,f1,f2);
+		pwrnum(0,(Num)c1,(Num)eval(f2),&c);
+		cc = mkfnode(1,I_FORMULA,c);
+		b = fnode_normalize_pwr(b1,f2,expand);
+		if ( fnode_is_one(cc) )
+			return b;
+		else
+			return fnode_node_to_narymul(mknode(2,cc,b));
+	} else if ( expand && fnode_is_integer(f2) 
+			&& fnode_is_nonnegative_integer(f2) ) {
+		q = (Q)eval(f2);
+		if ( PL(NM(q)) > 1 ) error("fnode_normalize_pwr : exponent too large");
+		return fnode_expand_pwr(f1,QTOS(q));
 	} else
 		return mkfnode(3,I_BOP,pwrfs,f1,f2);
 }
 
+FNODE fnode_expand_pwr(FNODE f,int n)
+{
+	int n1;
+	FNODE f1,f2;
+
+	if ( !n ) return mkfnode(1,I_FORMULA,ONE);
+	else if ( IS_ZERO(f) ) return mkfnode(1,I_FORMULA,0);
+	else if ( n == 1 ) return f;
+	else {
+		n1 = n/2;
+		f1 = fnode_expand_pwr(f,n1);
+		f2 = fnode_normalize_mul(f1,f1,1);
+		if ( n%2 ) f2 = fnode_normalize_mul(f2,f,1);
+		return f2;
+	}
+}
+
 /* f = b^e */
 void fnode_base_exp(FNODE f,FNODE *bp,FNODE *ep)
 {
-	if ( f->id == I_BOP && OPNAME(f) == '^' ) {
+	if ( IS_BINARYPWR(f) ) {
 		*bp = FA1(f); *ep = FA2(f);
 	} else {
 		*bp = f; *ep = mkfnode(1,I_FORMULA,ONE);		
@@ -2373,11 +2405,10 @@ FNODE to_naryadd(FNODE f)
 	FNODE r;
 	NODE n;
 
-	NEWFNODE(r,2);
-	r->id = I_NARYOP;
-	FA0(r) = addfs;
-	MKNODE(n,f,0);
-	FA1(r) = n;
+	if ( IS_NARYADD(f) ) return f;
+
+	NEWFNODE(r,2); r->id = I_NARYOP;
+	FA0(r) = addfs; MKNODE(n,f,0); FA1(r) = n;
 	return r;
 }
 
@@ -2386,80 +2417,194 @@ FNODE to_narymul(FNODE f)
 	FNODE r;
 	NODE n;
 
-	NEWFNODE(r,2);
-	r->id = I_NARYOP;
-	FA0(r) = mulfs;
-	MKNODE(n,f,0);
-	FA1(r) = n;
+	if ( IS_NARYMUL(f) ) return f;
+
+	NEWFNODE(r,2); r->id = I_NARYOP;
+	FA0(r) = mulfs; MKNODE(n,f,0); FA1(r) = n;
 	return r;
 }
 
-FNODE fnode_normalize_mul_coef(Num c,FNODE f)
+FNODE fnode_normalize_mul_coef(Num c,FNODE f,int expand)
 {
-	FNODE cc;
+	FNODE b1,cc;
 	Num c1,c2;
-	NODE n,r0,r;
+	NODE n,r,r0;
 
 	if ( !c )
 		return mkfnode(I_FORMULA,0);
-	else if ( UNIQ(c) )
-		return f;
-	else if ( fnode_is_number(f) ) {
-		mulnum(0,c,eval(f),&c1); return mkfnode(1,I_FORMULA,c1);
-	} else if ( f->id == I_NARYOP && OPNAME(f) == '*' ) {
-		cc = (FNODE)BDY((NODE)FA1(f));
-		if ( fnode_is_number(cc) ) {
-			mulnum(0,c,eval(cc),&c2);
-			if ( UNIQ(c2) )
-				n = NEXT((NODE)FA1(f));
-			else {
-				cc = mkfnode(1,I_FORMULA,c2);
-				MKNODE(n,cc,NEXT((NODE)FA1(f)));
-			}
-		} else { 
-			cc = mkfnode(1,I_FORMULA,c);
-			MKNODE(n,cc,(NODE)FA1(f));
+	else {
+		fnode_coef_body(f,&c1,&b1);
+		mulnum(0,c,c1,&c2);
+		if ( UNIQ(c2) ) return b1;
+		else {
+			cc = mkfnode(1,I_FORMULA,c2);
+			if ( fnode_is_number(b1) ) {
+				if ( !fnode_is_one(b1) )
+					error("fnode_normalize_mul_coef : cannot happen");
+				else
+					return cc;
+			} else if ( IS_NARYMUL(b1) ) {
+				MKNODE(n,cc,FA1(b1));
+				return fnode_node_to_narymul(n);
+			} else if ( expand && IS_NARYADD(b1) ) {
+				for ( r0 = 0, n = (NODE)FA1(b1); n; n = NEXT(n) ) {
+					NEXTNODE(r0,r);
+					BDY(r) = fnode_normalize_mul_coef(c2,BDY(n),expand);
+				}
+				if ( r0 ) NEXT(r) = 0;
+				return fnode_node_to_naryadd(r0);
+			} else 
+				return fnode_node_to_narymul(mknode(2,cc,b1));
 		}
-		if ( NEXT(n) )
-			return mkfnode(2,I_NARYOP,FA0(f),n);
-		else
-			return (FNODE)BDY(n);
-	} else if ( f->id == I_NARYOP && OPNAME(f) == '+' ) {
-		for ( r0 = 0, n = (NODE)FA1(f); n; n = NEXT(n) ) {
-			NEXTNODE(r0,r);
-			BDY(r) = fnode_normalize_mul_coef(c,BDY(n));
-		}
-		if ( r0 ) NEXT(r) = 0;
-		return mkfnode(2,I_NARYOP,FA0(f),r0);
-	} else {
-		cc = mkfnode(1,I_FORMULA,c);
-		n = mknode(2,cc,f);
-		return mkfnode(2,I_NARYOP,mulfs,n);
 	}
 }
 
 void fnode_coef_body(FNODE f,Num *cp,FNODE *bp)
 {
 	FNODE c;
-	NODE n;
 
 	if ( fnode_is_number(f) ) {
 		*cp = eval(f); *bp = mkfnode(1,I_FORMULA,ONE);
-	} else if ( f->id == I_NARYOP && OPNAME(f) == '*' ) {
-		c = (FNODE)BDY((NODE)FA1(f));
+	} else if ( IS_NARYMUL(f) ) {
+		c=(FNODE)BDY((NODE)FA1(f));
 		if ( fnode_is_number(c) ) {
 			*cp = eval(c);
-			n = NEXT((NODE)FA1(f));
-			if ( !n )
-				*bp = mkfnode(1,I_FORMULA,ONE);
-			else if ( !NEXT(n) )
-				*bp = BDY(n);
-			else
-				*bp = mkfnode(2,I_NARYOP,FA0(f),n);
+			*bp = fnode_node_to_narymul(NEXT((NODE)FA1(f)));
 		} else {
 			*cp = (Num)ONE; *bp = f;
 		}
 	} else {
 		*cp = (Num)ONE; *bp = f;
 	}
+}
+
+int fnode_normalize_comp_pwr(FNODE f1,FNODE f2);
+
+int fnode_normalize_comp(FNODE f1,FNODE f2)
+{
+	NODE n1,n2;
+	int r,i1,i2;
+	char *nm1,*nm2;
+	FNODE b1,b2,e1,e2,g;
+	Num ee,ee1,c1,c2;
+
+	if ( IS_NARYADD(f1) || IS_NARYADD(f2) ) {
+		f1 = to_naryadd(f1); f2 = to_naryadd(f2);
+		n1 = (NODE)FA1(f1); n2 = (NODE)FA1(f2);
+		while ( n1 && n2 )
+			if ( r = fnode_normalize_comp(BDY(n1),BDY(n2)) ) return r;
+			else {
+				n1 = NEXT(n1); n2 = NEXT(n2);
+			}
+		return n1?1:(n2?-1:0);
+	}
+	if ( IS_NARYMUL(f1) || IS_NARYMUL(f2) ) {
+		fnode_coef_body(f1,&c1,&b1);
+		fnode_coef_body(f2,&c2,&b2);
+		if ( !compfnode(b1,b2) ) return compnum(0,c1,c2);
+		b1 = to_narymul(b1); b2 = to_narymul(b2);
+		n1 = (NODE)FA1(b1); n2 = (NODE)FA1(b2);
+		while ( 1 ) {
+			while ( n1 && n2 && !compfnode(BDY(n1),BDY(n2)) ) {
+				n1 = NEXT(n1); n2 = NEXT(n2);
+			}
+			if ( !n1 || !n2 ) {
+				return n1?1:(n2?-1:0);
+			}
+			fnode_base_exp(BDY(n1),&b1,&e1);
+			fnode_base_exp(BDY(n2),&b2,&e2);
+
+			if ( r = fnode_normalize_comp(b1,b2) ) {
+				if ( r > 0 )
+					return fnode_normalize_comp(e1,mkfnode(1,I_FORMULA,0));
+				else if ( r < 0 )
+					return fnode_normalize_comp(mkfnode(1,I_FORMULA,0),e2);
+			} else {
+				n1 = NEXT(n1); n2 = NEXT(n2);
+				if ( fnode_is_number(e1) && fnode_is_number(e2) ) {
+					/* f1 = t b^e1 ... , f2 = t b^e2 ... */
+					subnum(0,eval(e1),eval(e2),&ee);
+					if ( ee ) {
+						g = mkfnode(3,I_BOP,pwrfs,b1,mkfnode(1,I_FORMULA,ee));
+						MKNODE(n1,g,n1);
+					}
+				} else {
+					r = fnode_normalize_comp(e1,e2);
+					if ( r > 0 ) return 1;
+					else if ( r < 0 ) return -1;
+				}
+			}
+		}
+	}
+	if ( IS_BINARYPWR(f1) || IS_BINARYPWR(f2) )
+		return fnode_normalize_comp_pwr(f1,f2);
+				
+	/* now, IDs of f1 and f2 must be I_FORMULA, I_FUNC, or I_PVAR */
+	switch ( f1->id ) {
+		case I_FORMULA:
+			switch ( f2->id ) {
+				case I_FORMULA:
+					return arf_comp(CO,FA0(f1),FA0(f2));
+				case I_FUNC: case I_PVAR:
+					return -1;
+				default:
+					error("fnode_normalize_comp : undefined");
+			}
+			break;
+		case I_FUNC:
+			switch ( f2->id ) {
+				case I_FORMULA:
+					return 1;
+				case I_FUNC:
+					nm1 = ((FUNC)FA0(f1))->name; nm2 = ((FUNC)FA0(f2))->name;
+					r = strcmp(nm1,nm2);
+					if ( r > 0 ) return 1;
+					else if ( r < 0 ) return -1;
+					else {
+						/* compare args */
+						n1 = FA0((FNODE)FA1(f1)); n2 = FA0((FNODE)FA1(f2));
+						while ( n1 && n2 )
+							if ( r = fnode_normalize_comp(BDY(n1),BDY(n2)) ) return r;
+							else {
+								n1 = NEXT(n1); n2 = NEXT(n2);
+							}
+						return n1?1:(n2?-1:0);
+					}
+					break;
+				case I_PVAR:
+					return -1;
+				default:
+					error("fnode_normalize_comp : undefined");
+			}
+		case I_PVAR:
+			switch ( f2->id ) {
+				case I_FORMULA: case I_FUNC:
+					return 1;
+				case I_PVAR:
+					i1 = (int)FA0(f1); i2 = (int)FA0(f2);
+					if ( i1 > i2 ) return 1;
+					else if ( i1 < i2 ) return -1;
+					else return 0;
+				default:
+					error("fnode_normalize_comp : undefined");
+			}
+			break;
+		default:
+			error("fnode_normalize_comp : undefined");
+	}
+}
+
+int fnode_normalize_comp_pwr(FNODE f1,FNODE f2)
+{
+	FNODE b1,b2,e1,e2;
+	int r;
+
+	fnode_base_exp(f1,&b1,&e1);
+	fnode_base_exp(f2,&b2,&e2);
+	if ( r = fnode_normalize_comp(b1,b2) ) {
+		if ( r > 0 )
+			return fnode_normalize_comp(e1,mkfnode(1,I_FORMULA,0));
+		else if ( r < 0 )
+			return fnode_normalize_comp(mkfnode(1,I_FORMULA,0),e2);
+	} else return fnode_normalize_comp(e1,e2);
 }