===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/builtin/strobj.c,v
retrieving revision 1.67
retrieving revision 1.72
diff -u -p -r1.67 -r1.72
--- OpenXM_contrib2/asir2000/builtin/strobj.c	2005/10/03 00:06:40	1.67
+++ OpenXM_contrib2/asir2000/builtin/strobj.c	2005/10/14 06:00:03	1.72
@@ -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 1.66 2005/09/30 02:20:06 noro Exp $
+ * $OpenXM: OpenXM_contrib2/asir2000/builtin/strobj.c,v 1.71 2005/10/12 14:43:36 noro Exp $
 */
 #include "ca.h"
 #include "parse.h"
@@ -63,6 +63,8 @@ struct TeXSymbol {
 	char *symbol;
 };
 
+#define OPNAME(f) (((ARF)FA0(f))->name[0])
+
 extern char *parse_strp;
 
 void Psprintf();
@@ -77,8 +79,13 @@ void Pquotetotex_tb();
 void Pquotetotex();
 void Pquotetotex_env();
 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_to_funargs(),Pfunargs_to_quote(),Pget_function_name();
-void Pquote_unify(),Pget_quote_id();
+void Pquote_unify(),Pget_quote_id(),Pquote_match_rewrite();
 void Pquote_to_nary(),Pquote_to_bin();
 void do_assign(NODE arg);
 void fnodetotex_tb(FNODE f,TB tb);
@@ -107,6 +114,15 @@ struct ftab str_tab[] = {
 	{"tb_to_string",Ptb_to_string,1},
 	{"string_to_tb",Pstring_to_tb,1},
 	{"get_quote_id",Pget_quote_id,1},
+
+	{"quote_is_number",Pquote_is_number,1},
+	{"quote_is_rational",Pquote_is_rational,1},
+	{"quote_is_integer",Pquote_is_integer,1},
+	{"quote_is_function",Pquote_is_function,1},
+	{"quote_is_dependent",Pquote_is_dependent,2},
+
+	{"quote_normalize",Pquote_normalize,1},
+
 	{"quote_to_nary",Pquote_to_nary,1},
 	{"quote_to_bin",Pquote_to_bin,2},
 	{"quotetotex_tb",Pquotetotex_tb,2},
@@ -115,6 +131,7 @@ struct ftab str_tab[] = {
 	{"flatten_quote",Pflatten_quote,-2},
 	{"quote_to_funargs",Pquote_to_funargs,1},
 	{"quote_unify",Pquote_unify,2},
+	{"quote_match_rewrite",Pquote_match_rewrite,-4},
 	{"funargs_to_quote",Pfunargs_to_quote,1},
 	{"get_function_name",Pget_function_name,1},
 	{0,0,0},
@@ -512,13 +529,14 @@ void Pwrite_to_tb(NODE arg,Q *rp)
 	*rp = 0;	
 }
 
-FNODE partial_eval(FNODE), quote_to_nary(FNODE), quote_to_bin(FNODE,int);
+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)
 {
 	FNODE f;
 
-	f = quote_to_nary(BDY((QUOTE)ARG0(arg)));
+	f = fnode_to_nary(BDY((QUOTE)ARG0(arg)));
 	MKQUOTE(*rp,f);	
 }
 
@@ -528,11 +546,78 @@ void Pquote_to_bin(NODE arg,QUOTE *rp)
 	int direction;
 
 	direction = QTOS((Q)ARG1(arg));
-	f = quote_to_bin(BDY((QUOTE)ARG0(arg)),direction);
+	f = fnode_to_bin(BDY((QUOTE)ARG0(arg)),direction);
 
 	MKQUOTE(*rp,f);	
 }
 
+void Pquote_is_number(NODE arg,Q *rp)
+{
+	QUOTE q;
+	int ret;
+
+	q = (QUOTE)ARG0(arg);
+	asir_assert(q,O_QUOTE,"quote_is_number");
+	ret = fnode_is_number(BDY(q));
+	STOQ(ret,*rp);
+}
+
+void Pquote_is_rational(NODE arg,Q *rp)
+{
+	QUOTE q;
+	int ret;
+
+	q = (QUOTE)ARG0(arg);
+	asir_assert(q,O_QUOTE,"quote_is_rational");
+	ret = fnode_is_rational(BDY(q));
+	STOQ(ret,*rp);
+}
+
+void Pquote_is_integer(NODE arg,Q *rp)
+{
+	QUOTE q;
+	int ret;
+
+	q = (QUOTE)ARG0(arg);
+	asir_assert(q,O_QUOTE,"quote_is_integer");
+	ret = fnode_is_integer(BDY(q));
+	STOQ(ret,*rp);
+}
+
+void Pquote_is_function(NODE arg,Q *rp)
+{
+	QUOTE q;
+	int ret;
+
+	q = (QUOTE)ARG0(arg);
+	asir_assert(q,O_QUOTE,"quote_is_function");
+	if ( q->id == I_FUNC || q->id == I_IFUNC )
+		ret = 1;
+	else
+		ret = 0;
+	STOQ(ret,*rp);
+}
+
+void Pquote_is_dependent(NODE arg,Q *rp)
+{
+	P x;
+	QUOTE q,v;
+	int ret;
+	V var;
+
+	q = (QUOTE)ARG0(arg);
+	v = (QUOTE)ARG1(arg);
+	asir_assert(q,O_QUOTE,"quote_is_dependent");
+	asir_assert(v,O_QUOTE,"quote_is_dependent");
+	x = (P)eval(BDY(v));
+	if ( !x || OID(x) != O_P )
+		*rp = 0;
+	var = VR(x);
+	ret = fnode_is_dependent(BDY(q),var);
+	STOQ(ret,*rp);
+}
+
+
 void Pquote_unify(NODE arg,Q *rp)
 {
 	FNODE f,g;
@@ -556,6 +641,49 @@ void Pquote_unify(NODE arg,Q *rp)
 		*rp = 0;
 }
 
+FNODE rewrite_fnode(FNODE,NODE);
+
+extern Obj VOIDobj;
+
+void Pquote_match_rewrite(NODE arg,Obj *rp)
+{
+	FNODE f,g,h,c,value;
+	Obj obj;
+	QUOTE q;
+	NODE r,t,s,s0,pair;
+	int ret,ind,ac;
+
+	obj = (Obj)ARG0(arg);
+	ret = quote_unify(obj,(Obj)ARG1(arg),&r);
+	if ( ret ) {
+		for ( t = r, s0 = 0; t; t = NEXT(t) ) {
+			NEXTNODE(s0,s);
+			pair = BDY((LIST)BDY(t));
+			ind = (int)FA0((FNODE)BDY((QUOTE)BDY(pair)));
+			value = mkfnode(1,I_FORMULA,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);
+				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);
+				} else
+					*rp = VOIDobj;
+				break;
+			default:
+				error("quote_match_rewrite : invalid argument");
+		}
+	} else
+		*rp = VOIDobj;
+}
+
 void do_assign(NODE arg)
 {
 	NODE t,pair;
@@ -750,11 +878,11 @@ int quote_unify(Obj f, Obj pat, NODE *rp)
 				else {
 					/* XXX converting to I_BOP */
 					if ( pid == I_NARYOP ) {
-						g = quote_to_bin(BDY((QUOTE)pat),1);
+						g = fnode_to_bin(BDY((QUOTE)pat),1);
 						MKQUOTE(q,g); pat = (Obj)q;
 					}
 					if ( id == I_NARYOP ) {
-						g = quote_to_bin(BDY((QUOTE)f),1);
+						g = fnode_to_bin(BDY((QUOTE)f),1);
 						MKQUOTE(q,g); f = (Obj)q;
 					}
 				}
@@ -1172,47 +1300,56 @@ void fnodetotex_tb(FNODE f,TB tb)
 		/* otherwise   => FA1(f), FA2(f) */
 		case I_BOP:
 			opname = ((ARF)FA0(f))->name;
-			if ( !strcmp(opname,"+") ) {
-				fnodetotex_tb((FNODE)FA1(f),tb);
-				if ( !top_is_minus((FNODE)FA2(f)) ) write_tb(opname,tb);
-				fnodetotex_tb((FNODE)FA2(f),tb);
-			} else if ( !strcmp(opname,"-") ) {
-				if ( FA1(f) ) fnodetotex_tb((FNODE)FA1(f),tb);
-				write_tb(opname,tb);
-				fnodetotex_tb((FNODE)FA2(f),tb);
-			} else if ( !strcmp(opname,"*") ) {
-				fnodetotex_tb((FNODE)FA1(f),tb);
-				write_tb(" ",tb);
-				/* XXX special care for DP */
-				f2 = (FNODE)FA2(f);
-				if ( f2->id == I_EV ) {
-					n = (NODE)FA0(f2);
-					for ( i = 0; n; n = NEXT(n), i++ ) {
-						fi = (FNODE)BDY(n);
-						if ( fi->id != I_FORMULA || FA0(fi) )
-							break;
-					}
-					if ( n )
+			switch ( opname[0] ) {
+				case '+':
+					fnodetotex_tb((FNODE)FA1(f),tb);
+					if ( !top_is_minus((FNODE)FA2(f)) ) write_tb(opname,tb);
+					fnodetotex_tb((FNODE)FA2(f),tb);
+					break;
+				case '-':
+					if ( FA1(f) ) fnodetotex_tb((FNODE)FA1(f),tb);
+					write_tb(opname,tb);
+					fnodetotex_tb((FNODE)FA2(f),tb);
+					break;
+				case '*':
+					fnodetotex_tb((FNODE)FA1(f),tb);
+					write_tb(" ",tb);
+					/* XXX special care for DP */
+					f2 = (FNODE)FA2(f);
+					if ( f2->id == I_EV ) {
+						n = (NODE)FA0(f2);
+						for ( i = 0; n; n = NEXT(n), i++ ) {
+							fi = (FNODE)BDY(n);
+							if ( fi->id != I_FORMULA || FA0(fi) )
+								break;
+						}
+						if ( n )
+							fnodetotex_tb((FNODE)FA2(f),tb);
+					} else
 						fnodetotex_tb((FNODE)FA2(f),tb);
-				} else
+					break;
+				case '/':
+					write_tb("\\frac{",tb);
+					fnodetotex_tb((FNODE)FA1(f),tb);
+					write_tb("} {",tb);
 					fnodetotex_tb((FNODE)FA2(f),tb);
-			} else if ( !strcmp(opname,"/") ) {
-				write_tb("\\frac{",tb);
-				fnodetotex_tb((FNODE)FA1(f),tb);
-				write_tb("} {",tb);
-				fnodetotex_tb((FNODE)FA2(f),tb);
-				write_tb("}",tb);
-			} else if ( !strcmp(opname,"^") ) {
-				fnodetotex_tb((FNODE)FA1(f),tb);
-				write_tb("^{",tb);
-				fnodetotex_tb(strip_paren((FNODE)FA2(f)),tb);
-				write_tb("} ",tb);
-			} else if ( !strcmp(opname,"%") ) {
-				fnodetotex_tb((FNODE)FA1(f),tb);
-				write_tb(" {\\rm mod}\\, ",tb);
-				fnodetotex_tb((FNODE)FA2(f),tb);
-			} else
-				error("invalid binary operator");
+					write_tb("}",tb);
+					break;
+				case '^':
+					fnodetotex_tb((FNODE)FA1(f),tb);
+					write_tb("^{",tb);
+					fnodetotex_tb(strip_paren((FNODE)FA2(f)),tb);
+					write_tb("} ",tb);
+					break;
+				case '%':
+					fnodetotex_tb((FNODE)FA1(f),tb);
+					write_tb(" {\\rm mod}\\, ",tb);
+					fnodetotex_tb((FNODE)FA2(f),tb);
+					break;
+				default:
+					error("invalid binary operator");
+					break;
+			}
 			break;
 
 		case I_COP:
@@ -1782,4 +1919,492 @@ 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_normalize_nary(FNODE f);
+
+void Pquote_normalize(NODE arg,QUOTE *rp)
+{
+	QUOTE q,r;
+	FNODE f;
+
+	q = (QUOTE)ARG0(arg);
+	if ( !q || OID(q) != O_QUOTE ) {
+		*rp = q;
+		return;
+	} else {
+		f = fnode_normalize(BDY(q));
+		MKQUOTE(r,f);
+		*rp = r;
+	}
+}
+
+int fnode_is_number(FNODE f)
+{
+	Obj obj;
+
+	switch ( f->id ) {
+		case I_MINUS: case I_PAREN:
+			return fnode_is_number(FA0(f));
+				
+		case I_FORMULA:
+			obj = FA0(f);
+			if ( !obj ) return 1;
+			else if ( OID(obj) == O_QUOTE ) 
+				return fnode_is_number(BDY((QUOTE)obj));
+			else if ( NUM(obj) ) return 1;
+			else return 0;
+		
+		case I_BOP:
+			return fnode_is_number(FA1(f)) && fnode_is_number(FA2(f));
+		
+		default:
+			return 0;
+	}
+}
+
+int fnode_is_rational(FNODE f)
+{
+	Obj obj;
+
+	switch ( f->id ) {
+		case I_MINUS: case I_PAREN:
+			return fnode_is_number(FA0(f));
+				
+		case I_FORMULA:
+			obj = FA0(f);
+			if ( !obj ) return 1;
+			else if ( OID(obj) == O_QUOTE ) 
+				return fnode_is_rational(BDY((QUOTE)obj));
+			else if ( NUM(obj) && RATN(obj) ) return 1;
+			else return 0;
+		
+		case I_BOP:
+			if ( !strcmp(((ARF)FA0(f))->name,"^")  )
+				return fnode_is_rational(FA1(f)) && fnode_is_integer(FA2(f));
+			else
+				return fnode_is_rational(FA1(f)) && fnode_is_rational(FA2(f));
+		
+		default:
+			return 0;
+	}
+}
+
+int fnode_is_integer(FNODE f)
+{
+	Obj obj;
+
+	switch ( f->id ) {
+		case I_MINUS: case I_PAREN:
+			return fnode_is_integer(FA0(f));
+				
+		case I_FORMULA:
+			obj = FA0(f);
+			if ( !obj ) return 1;
+			else if ( OID(obj) == O_QUOTE ) 
+				return fnode_is_integer(BDY((QUOTE)obj));
+			else if ( INT(obj)) return 1;
+			else return 0;
+		
+		case I_BOP:
+			switch ( ((ARF)FA0(f))->name[0] ) {
+				case '^':
+					return fnode_is_integer(FA1(f)) 
+						&& fnode_is_nonnegative_integer(FA2(f));
+				case '/':
+					return fnode_is_integer(FA1(f)) && 
+						( fnode_is_one(FA2(f)) || fnode_is_minusone(FA2(f)) );
+				default:
+					return fnode_is_integer(FA1(f)) && fnode_is_integer(FA2(f));
+			}
+			break;
+
+		default:
+			return 0;
+	}
+}
+
+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;
+
+	n = eval(f);
+	if ( !n || (INT(n) && SGN(n) > 0) ) return 1;
+	else return 0;
+}
+
+int fnode_is_one(FNODE f)
+{
+	Q n;
+
+	n = eval(f);
+	if ( UNIQ(n) ) return 1;
+	else return 0;
+}
+
+int fnode_is_minusone(FNODE f)
+{
+	Q n;
+
+	n = eval(f);
+	if ( MUNIQ(n) ) return 1;
+	else return 0;
+}
+
+int fnode_is_dependent(FNODE f,V v)
+{
+	Obj obj;
+	FNODE arg;
+	NODE t;
+
+	switch ( f->id ) {
+		case I_MINUS: case I_PAREN:
+			return fnode_is_dependent(FA0(f),v);
+				
+		case I_FORMULA:
+			obj = FA0(f);
+			if ( !obj ) return 0;
+			else if ( OID(obj) == O_QUOTE ) 
+				return fnode_is_dependent(BDY((QUOTE)obj),v);
+			else if ( obj_is_dependent(obj,v) ) return 1;
+			else return 0;
+		
+		case I_BOP:
+			return fnode_is_dependent(FA1(f),v) || fnode_is_dependent(FA2(f),v);
+	
+		case I_FUNC:
+			arg = (FNODE)FA1(f);
+			for ( t = FA0(arg); t; t = NEXT(t) )
+				if ( fnode_is_dependent(BDY(t),v) ) return 1;
+			return 0;
+
+		default:
+			return 0;
+	}
+}
+
+FNODE fnode_normalize_add(FNODE a1,FNODE a2);
+FNODE fnode_normalize_mul(FNODE a1,FNODE a2);
+FNODE to_narymul(FNODE f);
+FNODE to_naryadd(FNODE f);
+FNODE fnode_normalize_mul_coef(Num c,FNODE f);
+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 a1,a2,mone,r;
+	NODE n;
+	Q q;
+
+	STOQ(-1,q);
+	mone = mkfnode(1,I_FORMULA,q);
+	switch ( f->id ) {
+		case I_PAREN:
+			return fnode_normalize(FA0(f));
+		
+		case I_MINUS:
+			return fnode_normalize_mul_coef((Num)q,fnode_normalize(FA0(f)));
+
+		case I_BOP:
+			/* arf fnode fnode */
+			a1 = fnode_normalize(FA1(f));
+			a2 = fnode_normalize(FA2(f));
+			switch ( OPNAME(f) ) {
+				case '+':
+					return fnode_normalize_add(a1,a2);
+				case '-':
+					a2 = fnode_normalize_mul_coef((Num)q,a2);
+					return fnode_normalize_add(a1,a2);
+				case '*':
+					return fnode_normalize_mul(a1,a2);
+				case '/':
+					a2 = mkfnode(3,I_BOP,pwrfs,a2,mone);
+					return fnode_normalize_mul(FA1(f),a2);
+				default:
+					return mkfnode(3,I_BOP,FA0(f),a1,a2);
+			}
+			break;
+
+		case I_NARYOP:
+			switch ( OPNAME(f) ) {
+				case '+':
+					n = BDY((NODE)FA1(f));
+					r = fnode_normalize(BDY(n)); n = NEXT(n);
+					for ( ; n; n = NEXT(n) ) {
+						a1 = fnode_normalize(BDY(n));
+						r = fnode_normalize_add(r,a1);
+					}
+					return r;
+				case '*':
+					n = BDY((NODE)FA1(f));
+					r = fnode_normalize(BDY(n)); n = NEXT(n);
+					for ( ; n; n = NEXT(n) ) {
+						a1 = fnode_normalize(BDY(n));
+						r = fnode_normalize_mul(r,a1);
+					}
+					return r;
+				default:
+					error("fnode_normallize : cannot happen");
+			}
+
+		default:
+			return fnode_apply(f,fnode_normalize);
+	}
+}
+
+FNODE fnode_apply(FNODE f,FNODE (*func)())
+{
+	fid_spec_p spec;
+	FNODE r;
+	int i,n;
+	NODE t,t0,s;
+
+	get_fid_spec(f->id,&spec);
+	for ( n = 0; spec->type[n] != A_end; n++ );
+	NEWFNODE(r,n); r->id = f->id;
+	for ( i = 0; i < n; i++ ) {
+		switch ( spec->type[i] ) {
+			case A_fnode:
+				r->arg[i] = func(f->arg[i]);
+				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));
+				}
+				if ( t0 ) NEXT(t) = 0;
+				r->arg[i] = t0;
+				break;
+			default:
+				r->arg[i] = f->arg[i];
+				break;
+		}
+	}
+	return r;
+}
+
+FNODE fnode_normalize_add(FNODE f1,FNODE f2)
+{
+	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);
+	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 ) {
+			NEXTNODE(r0,r); BDY(r) = b1; n1 = NEXT(n1);
+		} else if ( s < 0 ) {
+			NEXTNODE(r0,r); BDY(r) = b2; n2 = NEXT(n2);
+		} else {
+			addnum(0,c1,c2,&c);
+			if ( c ) {
+				NEXTNODE(r0,r); BDY(r) = fnode_normalize_mul_coef(c,b1);
+			}
+			n1 = NEXT(n1); n2 = NEXT(n2);
+		}
+	}
+	if ( n1 )
+		if ( r0 ) NEXT(r) = n1;
+		else r0 = n1;
+	else if ( n2 )
+		if ( r0 ) NEXT(r) = n2;
+		else r0 = n2;
+	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);
+}
+
+FNODE fnode_normalize_mul(FNODE f1,FNODE f2)
+{
+	NODE n1,n2,r0,r,r1;
+	FNODE b1,b2,e1,e2,cc;
+	FNODE *m;
+	int s;
+	Num c1,c2,c,e;
+	int l1,l2,l,i,j;
+
+	if ( fnode_is_zero(f1) || fnode_is_zero(f2) ) return 0;
+
+	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);
+		}
+	else if ( fnode_is_number(BDY(n2)) ) {
+		c = eval(BDY(n2)); n2 = NEXT(n2);
+	} else
+		c = (Num)ONE;
+	if ( !c ) return mkfnode(1,I_FORMULA,0);
+
+	l1 = length(n1);
+	l2 = length(n2);
+	l = l1+l2;
+	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));
+			}
+		}
+	}
+	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);
+	}
+}
+
+/* f = b^e */
+void fnode_base_exp(FNODE f,FNODE *bp,FNODE *ep)
+{
+	if ( f->id == I_BOP && OPNAME(f) == '^' ) {
+		*bp = FA1(f); *ep = FA2(f);
+	} else {
+		*bp = f; *ep = mkfnode(1,I_FORMULA,ONE);		
+	}
+}
+
+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;
+	return r;
+}
+
+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;
+	return r;
+}
+
+FNODE fnode_normalize_mul_coef(Num c,FNODE f)
+{
+	FNODE cc;
+	Num c1,c2;
+	NODE n,r0,r;
+
+	if ( !c )
+		return mkfnode(I_FORMULA,0);
+	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); 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));
+		}
+		return mkfnode(2,I_NARYOP,FA0(f),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));
+		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);
+		} else {
+			*cp = (Num)ONE; *bp = f;
+		}
+	} else {
+		*cp = (Num)ONE; *bp = f;
+	}
 }