===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/lib/sp,v
retrieving revision 1.2
retrieving revision 1.8
diff -u -p -r1.2 -r1.8
--- OpenXM_contrib2/asir2000/lib/sp	2000/03/10 07:12:06	1.2
+++ OpenXM_contrib2/asir2000/lib/sp	2000/08/22 05:04:23	1.8
@@ -1,10 +1,59 @@
-/* $OpenXM: OpenXM_contrib2/asir2000/lib/sp,v 1.1.1.1 1999/12/03 07:39:11 noro Exp $ */
+/*
+ * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED 
+ * All rights reserved.
+ * 
+ * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
+ * non-exclusive and royalty-free license to use, copy, modify and
+ * redistribute, solely for non-commercial and non-profit purposes, the
+ * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
+ * conditions of this Agreement. For the avoidance of doubt, you acquire
+ * only a limited right to use the SOFTWARE hereunder, and FLL or any
+ * third party developer retains all rights, including but not limited to
+ * copyrights, in and to the SOFTWARE.
+ * 
+ * (1) FLL does not grant you a license in any way for commercial
+ * purposes. You may use the SOFTWARE only for non-commercial and
+ * non-profit purposes only, such as academic, research and internal
+ * business use.
+ * (2) The SOFTWARE is protected by the Copyright Law of Japan and
+ * international copyright treaties. If you make copies of the SOFTWARE,
+ * with or without modification, as permitted hereunder, you shall affix
+ * to all such copies of the SOFTWARE the above copyright notice.
+ * (3) An explicit reference to this SOFTWARE and its copyright owner
+ * shall be made on your publication or presentation in any form of the
+ * results obtained by use of the SOFTWARE.
+ * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
+ * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
+ * for such modification or the source code of the modified part of the
+ * SOFTWARE.
+ * 
+ * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
+ * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
+ * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
+ * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
+ * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
+ * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
+ * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
+ * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
+ * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
+ * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
+ * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
+ * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
+ * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
+ * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
+ * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
+ * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
+ * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
+ *
+ * $OpenXM: OpenXM_contrib2/asir2000/lib/sp,v 1.7 2000/08/21 08:31:43 noro Exp $ 
+*/
 /* 
 	sp : functions related to algebraic number fields
 
 	Revision History:
 
-	99/08/24    noro    modified for 1999 release version
+	2000/03/10    noro    fixed several bugs around gathering algebraic numbers
+	1999/08/24    noro    modified for 1999 release version
 */
 
 #include "defs.h"
@@ -37,6 +86,68 @@ 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)