===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/lib/sp,v
retrieving revision 1.9
retrieving revision 1.16
diff -u -p -r1.9 -r1.16
--- OpenXM_contrib2/asir2000/lib/sp	2001/10/12 06:07:05	1.9
+++ OpenXM_contrib2/asir2000/lib/sp	2010/07/14 04:48:14	1.16
@@ -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/lib/sp,v 1.8 2000/08/22 05:04:23 noro Exp $ 
+ * $OpenXM: OpenXM_contrib2/asir2000/lib/sp,v 1.15 2006/06/23 08:57:47 noro Exp $ 
 */
 /* 
 	sp : functions related to algebraic number fields
@@ -60,9 +60,23 @@
 #include "defs.h"
 
 extern ASCENT,GCDTIME,UFTIME,RESTIME,SQTIME,PRINT$
-extern Ord$
+extern SpOrd$
 extern USE_PARI_FACTOR$
 
+/* gen_sp can handle non-monic poly */
+
+def gen_sp(P)
+{
+	P = ptozp(P);
+	V = var(P);
+	D = deg(P,V);
+	LC = coef(P,D,V);
+	F = LC^(D-1)*subst(P,V,V/LC);
+	/* F must be monic */
+	L = sp(F);
+	return cons(map(subst,car(L),V,LC*V),cdr(L));
+}
+
 def sp(P)
 {
 	RESTIME=UFTIME=GCDTIME=SQTIME=0;
@@ -645,6 +659,15 @@ def ufctrhint2(P,HINT,PP,AL)
 		return [[P,1]];
 	if ( AL == [] )
 		return ufctrhint(P,HINT);
+	
+	/* if P != norm(PP) then call the generic ufctrhint() */
+	for ( T = AL, E = 1; T != []; T = cdr(T) ) {
+		D = defpoly(car(T)); E *= deg(D,var(D));
+	}
+	if ( E*deg(PP,var(PP)) != deg(P,var(P)) )
+		return ufctrhint(P,HINT);
+
+	/* P = norm(PP) */
 	L = resfctr(algptorat(PP),map(defpoly,AL),map(algtorat,AL),P);
 	for ( T = reverse(L[1]), DL = []; T != []; T = cdr(T) )
 		DL = cons(deg(car(car(T)),a_),DL);
@@ -789,8 +812,13 @@ def norm_ch_lag(V,VM,P,P0) {
 
 def cr_gcda(P1,P2)
 {
-	if ( !(V = var(P1)) || !var(P2) )
+	if ( !P1 )
+		return P2;
+	if ( !P2 )
+		return P1;
+	if ( !var(P1) || !var(P2) )
 		return 1;
+	V = var(P1);
 	EXT = union_sort(getalgtreep(P1),getalgtreep(P2));
 	if ( EXT == [] )
 		return gcd(P1,P2);
@@ -818,7 +846,7 @@ def cr_gcda(P1,P2)
 				break;
 		if ( J != length(DL) )
 			continue;
-		Ord = 2; NOSUGAR = 1;
+		SpOrd = 2; NOSUGAR = 1;
 		T = ag_mod(G1 % MOD,G2 % MOD,ML,VL,MOD);
 		if ( dp_gr_print() )
 			print(".");
@@ -1032,7 +1060,7 @@ def ag_mod(F1,F2,D,VL,MOD)
 	VL = cons(V,VL); B = append([F1,F2],D); N = length(VL);
     while ( 1 ) {
 		FLAGS = dp_gr_flags(); dp_gr_flags(["Reverse",1,"NoSugar",1]);
-		G = dp_gr_mod_main(B,VL,0,MOD,Ord);
+		G = dp_gr_mod_main(B,VL,0,MOD,SpOrd);
 		dp_gr_flags(FLAGS);
 		if ( length(G) == 1 )
 			return 1;
@@ -1266,9 +1294,9 @@ def ag_mod_single6(F1,F2,D,MOD)
 
 def inverse_by_gr_mod(C,D,MOD)
 {
-	Ord = 2;
+	SpOrd = 2;
 	dp_gr_flags(["NoSugar",1]);
-	G = dp_gr_mod_main(cons(x*C-1,D),cons(x,vars(D)),0,MOD,Ord);
+	G = dp_gr_mod_main(cons(x*C-1,D),cons(x,vars(D)),0,MOD,SpOrd);
 	dp_gr_flags(["NoSugar",0]);
 	if ( length(G) == 1 )
 		return 1;
@@ -1327,8 +1355,12 @@ def resfctr(F,L,V,N)
 	N = ptozp(N);
 	V0 = var(N);
 	DN = diff(N,V0);
+	LC = coef(N,deg(N,V0),V0);
+	LCD = coef(DN,deg(DN,V0),V0);
 	for ( I = 0, J = 2, Len = deg(N,V0)+1; I < 5; J++ ) {
 		M = prime(J);
+		if ( !(LC%M) || !(LCD%M))
+			continue;
 		G = gcd(N,DN,M);
 		if ( !deg(G,V0) ) {            
 			I++;
@@ -1352,7 +1384,7 @@ def resfctr_mod(F,L,M)
 		C = res(var(MP),B,MP) % M;
 		R = cons(flatten(cdr(modfctr(C,M))),R);
 	}
-	return R;
+	return reverse(R);
 }
 
 def flatten(L)