===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/lib/sp,v
retrieving revision 1.9
retrieving revision 1.18
diff -u -p -r1.9 -r1.18
--- OpenXM_contrib2/asir2000/lib/sp	2001/10/12 06:07:05	1.9
+++ OpenXM_contrib2/asir2000/lib/sp	2018/04/06 07:40:44	1.18
@@ -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 1.17 2016/02/04 04:17:21 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;
@@ -197,6 +211,10 @@ def flatmf(L) {
 def af(P,AL)
 {
 	RESTIME=UFTIME=GCDTIME=SQTIME=0;
+    V = var(P);
+    LC = coef(P,deg(P,V),V);
+    if ( ntype(LC) != 1 )
+      P = simpalg(1/LC*P);
 	S = reverse(asq(P));
 	for ( L = []; S != []; S = cdr(S) ) {
 		FM = car(S); F = FM[0]; M = FM[1];
@@ -213,6 +231,10 @@ def af_sp(P,AL,HINT)
 {
 	if ( !P || type(P) == NUM )
 		return [P];
+    V = var(P);
+    LC = coef(P,deg(P,V),V);
+    if ( ntype(LC) != 1 )
+      P = simpalg(1/LC*P);
 	P1 = simpcoef(simpalg(P));
 	return af_spmain(P1,AL,1,HINT,P1,[]);
 }
@@ -645,6 +667,15 @@ 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 +820,13 @@ 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 +854,7 @@ 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 +1068,7 @@ 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 +1302,9 @@ 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;
@@ -1327,18 +1363,27 @@ def resfctr(F,L,V,N)
 	N = ptozp(N);
 	V0 = var(N);
 	DN = diff(N,V0);
-	for ( I = 0, J = 2, Len = deg(N,V0)+1; I < 5; J++ ) {
-		M = prime(J);
-		G = gcd(N,DN,M);
-		if ( !deg(G,V0) ) {            
-			I++;
-			T = nfctr_mod(N,M);
-			if ( T < Len ) {
-				Len = T; M0 = M;
-			}
-		}
-	}
-	S = spm(L,V,M0);
+	LC = coef(N,deg(N,V0),V0);
+	LCD = coef(DN,deg(DN,V0),V0);
+  J = 2;
+  while ( 1 ) {
+    Len = deg(N,V0)+1;
+	  for ( I = 0; I < 5; J++ ) {
+		  M = prime(J);
+		  if ( !(LC%M) || !(LCD%M))
+			  continue;
+		  G = gcd(N,DN,M);
+		  if ( !deg(G,V0) ) {            
+			  I++;
+			  T = nfctr_mod(N,M);
+			  if ( T < Len ) {
+				  Len = T; M0 = M;
+			  }
+		  }
+	  }
+	  S = spm(L,V,M0);
+    if ( S ) break;
+  }
 	T = resfctr_mod(F,S,M0);
 	return [T,S,M0];
 }
@@ -1352,7 +1397,7 @@ 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)
@@ -1368,11 +1413,13 @@ def spm(L,V,M)
 		U = modfctr(car(L),M);
 		for ( T = cdr(U), R = []; T != []; T = cdr(T) ) {
 			S = car(T);
+      if ( S[1] > 1 ) return 0;
 			R = cons([subst(S[0],var(S[0]),a_),[var(S[0]),a_]],R);
 		}
 		return R;
 	}
 	L1 = spm(cdr(L),cdr(V),M);
+  if ( !L1 ) return 0;
 	F0 = car(L); V0 = car(V); VR = cdr(V);
 	for ( T = L1, R = []; T != []; T = cdr(T) ) {
 		S = car(T);
@@ -1380,6 +1427,7 @@ def spm(L,V,M)
 		U = fctr_mod(F1,V0,S[0],M);
 		VS = var(S[0]);
 		for ( W = U; W != []; W = cdr(W) ) {
+      if ( car(W)[1] > 1 ) return 0;
 			A = car(car(W)); 
 			if ( deg(A,V0) == 1 ) {
 				A = monic_mod(A,V0,S[0],M);