===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/lib/sp,v
retrieving revision 1.5
retrieving revision 1.6
diff -u -p -r1.5 -r1.6
--- OpenXM_contrib2/asir2000/lib/sp	2000/04/20 02:20:16	1.5
+++ OpenXM_contrib2/asir2000/lib/sp	2000/04/20 02:30:35	1.6
@@ -1,10 +1,10 @@
-/* $OpenXM: OpenXM_contrib2/asir2000/lib/sp,v 1.1.1.1 1999/12/03 07:39:11 noro Exp $ */
+/* $OpenXM$ */
 /* 
 	sp : functions related to algebraic number fields
 
 	Revision History:
 
-	2000/04/20    noro    fixed bugs around gathering algebraic numbers
+	2000/03/10    noro    fixed several bugs around gathering algebraic numbers
 	1999/08/24    noro    modified for 1999 release version
 */
 
@@ -38,6 +38,68 @@ def sp(P)
 			L = aflist(append(H,append([X-A,R],cdr(T))),AL);
 		}
 	}
+}
+
+/*
+	Input:
+		F=F(x,a1,...,an)
+		DL = [[an,dn(an,...,a1)],...,[a2,d2(a2,a1)],[a1,d1(a1)]]
+		'ai' denotes a root of di(t).
+	Output:
+		irreducible factorization of F over Q(a1,...,an)
+		[[F1(x,a1,...,an),e1],...,[Fk(x,a1,...,an),ek]]
+		'ej' denotes the multiplicity of Fj.
+*/
+
+def af_noalg(F,DL)
+{
+	DL = reverse(DL);
+	N = length(DL);
+	Tab = newvect(N);
+	/* Tab = [[a1,r1],...]; ri is a root of di(t,r(i-1),...,r1). */
+	AL = [];
+	for ( I = 0; I < N; I++ ) {
+		T = DL[I];
+		for ( J = 0, DP = T[1]; J < I; J++ )
+			DP = subst(DP,Tab[J][0],Tab[J][1]);
+		B = newalg(DP);
+		Tab[I] = [T[0],B];
+		F = subst(F,T[0],B);
+		AL = cons(B,AL);
+	}
+	FL = af(F,AL);
+	for ( T = FL, R = []; T != []; T = cdr(T) )
+		R = cons([conv_noalg(T[0][0],Tab),T[0][1]],R);
+	return reverse(R);
+}
+
+/*
+	Input:
+		F=F(x) univariate polynomial over the rationals
+	Output:
+		[FL,DL]
+		DL = [[an,dn(an,...,a1)],...,[a2,d2(a2,a1)],[a1,d1(a1)]]
+		'ai' denotes a root of di(t).
+		FL = [F1,F2,...]
+		irreducible factors of F over Q(a1,...,an)
+*/
+
+def sp_noalg(F)
+{
+	L = sp(F);
+	FL = map(algptorat,L[0]);
+	for ( T = L[1], DL = []; T != []; T = cdr(T) )
+		DL = cons([algtorat(T[0][0]),T[0][1]],DL);
+	return [FL,reverse(DL)];
+}
+
+def conv_noalg(F,Tab)
+{
+	N = size(Tab)[0];
+	F = algptorat(F);
+	for ( I = N-1; I >= 0; I-- )
+		F = subst(F,algtorat(Tab[I][1]),Tab[I][0]);
+	return F;
 }
 
 def aflist(L,AL)