===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/builtin/gr.c,v
retrieving revision 1.2
retrieving revision 1.13
diff -u -p -r1.2 -r1.13
--- OpenXM_contrib2/asir2000/builtin/gr.c	2000/04/13 06:01:01	1.2
+++ OpenXM_contrib2/asir2000/builtin/gr.c	2000/12/05 08:29:43	1.13
@@ -1,4 +1,52 @@
-/* $OpenXM: OpenXM_contrib2/asir2000/builtin/gr.c,v 1.1.1.1 1999/12/03 07:39:07 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/builtin/gr.c,v 1.12 2000/12/05 06:59:15 noro Exp $ 
+*/
 #include "ca.h"
 #include "parse.h"
 #include "base.h"
@@ -33,15 +81,15 @@ int TP,NBP,NMP,NFP,NDP,ZR,NZR;
 #define NEWDP_pairs ((DP_pairs)MALLOC(sizeof(struct dp_pairs)))
 
 extern int (*cmpdl)();
+extern int do_weyl;
 
-void Pdp_gr_flags(), Pdp_gr_print();
-void Pdp_gr_main(),Pdp_gr_mod_main(),Pdp_f4_main(),Pdp_f4_mod_main();
+extern DP_Print;
 
 void print_stat(void);
 void init_stat(void);
 int dp_load_t(int,DP *);
 void dp_load(int,DP *);
-void dp_save(int,DP);
+void dp_save(int,Obj,char *);
 void dp_make_flaglist(LIST *);
 void dp_set_flag(Obj,Obj);
 int membercheck(NODE,NODE);
@@ -59,8 +107,6 @@ DP_pairs updpairs(DP_pairs,NODE,int);
 void _dp_nf_ptozp(NODE,DP,DP *,int,int,DP *);
 void _dp_nf_ptozp_mpi(NODE,DP,DP *,int,int,DP *);
 void _dp_nf(NODE,DP,DP *,int,DP *);
-void _dp_nf_mod(NODE,DP,DP *,int,int,DP *);
-void interreduce_mod(NODE,int,int);
 NODE gb_mod(NODE,int);
 NODE gbd(NODE,int,NODE,NODE);
 NODE gb(NODE,int,NODE);
@@ -95,8 +141,8 @@ void dp_f4_mod_main(LIST,LIST,int,struct order_spec *,
 double get_rtime();
 void _dpmod_to_vect(DP,DL *,int *);
 void dp_to_vect(DP,DL *,Q *);
-NODE dp_dllist(DP f),symb_merge(NODE,NODE,int);
-
+NODE dp_dllist(DP f);
+NODE symb_merge(NODE,NODE,int),_symb_merge(NODE,NODE,int);
 extern int dp_nelim;
 extern int dp_fcoeffs;
 static DP *ps,*psm;
@@ -112,135 +158,24 @@ static int NoCriB = 0;
 static int NoGC = 0;
 static int NoMC = 0;
 static int NoRA = 0;
-int Print = 0;
-static int PrintShort = 0;
+int DP_Print = 0;
+static int DP_PrintShort = 0;
 static int ShowMag = 0;
 static int Stat = 0;
 static int Multiple = 0;
 static int Denominator = 1;
 static int Top = 0;
 static int Reverse = 0;
-static int InterReduce = 0;
 static int Max_mag = 0;
 static char *Demand = 0;
 static int PtozpRA = 0;
 LIST Dist = 0;
 int NoGCD = 0;
+int GenTrace = 0;
+int OXCheck = -1;
 int doing_f4;
+NODE TraceList;
 
-void Pdp_gr_flags(arg,rp)
-NODE arg;
-LIST *rp;
-{
-	Obj name,value;
-	NODE n;
-
-	if ( arg ) {
-		asir_assert(ARG0(arg),O_LIST,"dp_gr_flags");
-		n = BDY((LIST)ARG0(arg));
-		while ( n ) {
-			name = (Obj)BDY(n); n = NEXT(n);
-			if ( !n )
-				break;
-			else {
-				value = (Obj)BDY(n); n = NEXT(n);
-			}
-			dp_set_flag(name,value);
-		}
-	}
-	dp_make_flaglist(rp);
-}
-
-void Pdp_gr_print(arg,rp)
-NODE arg;
-Q *rp;
-{
-	Q q;
-
-	if ( arg ) {
-		asir_assert(ARG0(arg),O_N,"dp_gr_print");
-		q = (Q)ARG0(arg); Print = QTOS(q);
-	} else
-		STOQ(Print,q);
-	*rp = q;
-}
-
-void Pdp_gr_main(arg,rp)
-NODE arg;
-LIST *rp;
-{
-	LIST f,v;
-	Num homo;
-	Q m;
-	int modular;
-	struct order_spec ord;
-
-	asir_assert(ARG0(arg),O_LIST,"dp_gr_main");
-	asir_assert(ARG1(arg),O_LIST,"dp_gr_main");
-	asir_assert(ARG2(arg),O_N,"dp_gr_main");
-	asir_assert(ARG3(arg),O_N,"dp_gr_main");
-	f = (LIST)ARG0(arg); v = (LIST)ARG1(arg);
-	homo = (Num)ARG2(arg);
-	m = (Q)ARG3(arg);
-	if ( !m )
-		modular = 0;
-	else if ( PL(NM(m))>1 || (PL(NM(m)) == 1 && BD(NM(m))[0] >= 0x80000000) )
-		error("dp_gr_main : too large modulus");
-	else
-		modular = QTOS(m);
-	create_order_spec(ARG4(arg),&ord);
-	dp_gr_main(f,v,homo,modular,&ord,rp);
-}
-
-void Pdp_f4_main(arg,rp)
-NODE arg;
-LIST *rp;
-{
-	LIST f,v;
-	struct order_spec ord;
-
-	asir_assert(ARG0(arg),O_LIST,"dp_f4_main");
-	asir_assert(ARG1(arg),O_LIST,"dp_f4_main");
-	f = (LIST)ARG0(arg); v = (LIST)ARG1(arg);
-	create_order_spec(ARG2(arg),&ord);
-	dp_f4_main(f,v,&ord,rp);
-}
-
-void Pdp_f4_mod_main(arg,rp)
-NODE arg;
-LIST *rp;
-{
-	LIST f,v;
-	int m;
-	struct order_spec ord;
-
-	asir_assert(ARG0(arg),O_LIST,"dp_f4_main");
-	asir_assert(ARG1(arg),O_LIST,"dp_f4_main");
-	asir_assert(ARG2(arg),O_N,"dp_f4_main");
-	f = (LIST)ARG0(arg); v = (LIST)ARG1(arg); m = QTOS((Q)ARG2(arg));
-	create_order_spec(ARG3(arg),&ord);
-	dp_f4_mod_main(f,v,m,&ord,rp);
-}
-
-void Pdp_gr_mod_main(arg,rp)
-NODE arg;
-LIST *rp;
-{
-	LIST f,v;
-	Num homo;
-	int m;
-	struct order_spec ord;
-
-	asir_assert(ARG0(arg),O_LIST,"dp_gr_mod_main");
-	asir_assert(ARG1(arg),O_LIST,"dp_gr_mod_main");
-	asir_assert(ARG2(arg),O_N,"dp_gr_mod_main");
-	asir_assert(ARG3(arg),O_N,"dp_gr_mod_main");
-	f = (LIST)ARG0(arg); v = (LIST)ARG1(arg);
-	homo = (Num)ARG2(arg); m = QTOS((Q)ARG3(arg));
-	create_order_spec(ARG4(arg),&ord);
-	dp_gr_mod_main(f,v,homo,m,&ord,rp);
-}
-
 int eqdl(nv,dl1,dl2)
 int nv;
 DL dl1,dl2;
@@ -259,6 +194,8 @@ DL dl1,dl2;
 		return 0;
 }
 
+/* b[] should be cleared */
+
 void _dpmod_to_vect(f,at,b)
 DP f;
 DL *at;
@@ -364,7 +301,7 @@ LIST *rp;
 		if ( homo ) {
 			initd(&ord1); CNVars = NVars+1;
 		}
-		if ( Print && modular ) {
+		if ( DP_Print && modular ) {
 			fprintf(asir_out,"mod= %d, eval = ",m); printsubst(subst);
 		}
 		x = gb(s,m,subst);
@@ -510,7 +447,7 @@ LIST *rp;
 	int i;
 	struct order_spec ord1;
 	VL fv,vv,vc;
-	DP b,c;
+	DP b,c,c1;
 	NODE fd,fd0,fi,fi0,r,r0,t,subst,x,s,xx;
 
 	dp_fcoeffs = 0;
@@ -523,8 +460,9 @@ LIST *rp;
 	for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
 		ptod(CO,vv,(P)BDY(t),&b);
 		_dp_mod(b,m,0,&c);
+		_dp_monic(c,m,&c1);
 		if ( c ) {
-			NEXTNODE(fd0,fd); BDY(fd) = (pointer)c;
+			NEXTNODE(fd0,fd); BDY(fd) = (pointer)c1;
 		}
 	}
 	if ( fd0 ) NEXT(fd) = 0;
@@ -572,7 +510,7 @@ NODE f;
 	while ( d ) {
 		get_eg(&tmp0);
 		minsugar(d,&dm,&dr); d = dr;
-		if ( Print )
+		if ( DP_Print )
 			fprintf(asir_out,"sugar=%d\n",dm->sugar);
 		blist = 0; s0 = 0;
 		/* asph : sum of all head terms of spoly */
@@ -613,13 +551,17 @@ NODE f;
 			dp_to_vect(BDY(r),at,(Q *)mat->body[i]);
 		get_eg(&tmp1); add_eg(&eg_symb,&tmp0,&tmp1);
 		init_eg(&eg_split_symb); add_eg(&eg_split_symb,&tmp0,&tmp1);
-		if ( Print ) {
+		if ( DP_Print ) {
 			print_eg("Symb",&eg_split_symb);
 			fprintf(asir_out,"mat : %d x %d",row,col);
 			fflush(asir_out);
 		}
+#if 0
+		rank = generic_gauss_elim_hensel(mat,&nm,&dn,&rind,&cind);
+#else
 		rank = generic_gauss_elim(mat,&nm,&dn,&rind,&cind);
-		if ( Print )
+#endif
+		if ( DP_Print )
 			fprintf(asir_out,"done rank = %d\n",rank,row,col);
 		for ( i = 0; i < rank; i++ ) {
 			for ( k = 0; k < nred; k++ )
@@ -644,7 +586,7 @@ NODE f;
 			}
 		}
 	}
-	if ( Print ) {
+	if ( DP_Print ) {
 		print_eg("Symb",&eg_symb);
 		print_eg("Mod",&eg_mod); print_eg("GaussElim",&eg_elim);
 		print_eg("ChRem",&eg_chrem); print_eg("IntToRat",&eg_intrat);
@@ -653,6 +595,8 @@ NODE f;
 	return g;
 }
 
+/* initial bases are monic */
+
 NODE gb_f4_mod(f,m)
 NODE f;
 int m;
@@ -664,14 +608,15 @@ int m;
 	DP h,nf,f1,f2,f21,f21r,sp,sp1,sd,sdm,tdp;
 	MP mp,mp0;
 	NODE blist,bt,nt;
-	DL *ht,*at;
-	int **mat;
-	int *colstat;
-	int rank,nred,nonzero;
-	struct oEGT tmp0,tmp1,tmp2,eg_split_symb,eg_split_elim;
-	extern struct oEGT eg_symb,eg_elim;
+	DL *ht,*at,*st;
+	int **spmat,**redmat;
+	int *colstat,*w;
+	int rank,nred,nsp,nonzero,spcol;
+	int *indred,*isred,*ri;
+	struct oEGT tmp0,tmp1,tmp2,eg_split_symb,eg_split_elim1,eg_split_elim2;
+	extern struct oEGT eg_symb,eg_elim1,eg_elim2;
 
-	init_eg(&eg_symb); init_eg(&eg_elim);
+	init_eg(&eg_symb); init_eg(&eg_elim1); init_eg(&eg_elim2);
 	for ( gall = g = 0, d = 0, r = f; r; r = NEXT(r) ) {
 		i = (int)BDY(r);
 		d = updpairs(d,g,i);
@@ -683,7 +628,7 @@ int m;
 	while ( d ) {
 		get_eg(&tmp0);
 		minsugar(d,&dm,&dr); d = dr;
-		if ( Print )
+		if ( DP_Print )
 			fprintf(asir_out,"sugar=%d\n",dm->sugar);
 		blist = 0; s0 = 0;
 		/* asph : sum of all head terms of spoly */
@@ -703,72 +648,118 @@ int m;
 				dltod(BDY(s),nv,&tdp);
 				dp_subd(tdp,ps[(int)BDY(r)],&sd);
 				_dp_mod(sd,m,0,&sdm);
-				_mulmd(CO,m,sdm,ps[(int)BDY(r)],&f2);
+				mulmd_dup(m,sdm,ps[(int)BDY(r)],&f2);
 				MKNODE(bt,f2,blist); blist = bt;
 				s = symb_merge(s,dp_dllist(f2),nv);
 				nred++;
 			}
 		}
+		
+		get_eg(&tmp1); add_eg(&eg_symb,&tmp0,&tmp1);
+		init_eg(&eg_split_symb); add_eg(&eg_split_symb,&tmp0,&tmp1);
 
 		/* the first nred polys in blist are reducers */
 		/* row = the number of all the polys */
 		for ( r = blist, row = 0; r; r = NEXT(r), row++ );
+
+		/* head terms of reducers */
 		ht = (DL *)MALLOC(nred*sizeof(DL));
 		for ( r = blist, i = 0; i < nred; r = NEXT(r), i++ )
 			ht[i] = BDY((DP)BDY(r))->dl;
+
+		/* col = number of all terms */
 		for ( s = s0, col = 0; s; s = NEXT(s), col++ );
+
+		/* head terms of all terms */
 		at = (DL *)MALLOC(col*sizeof(DL));
 		for ( s = s0, i = 0; i < col; s = NEXT(s), i++ )
 			at[i] = (DL)BDY(s);
-		mat = almat(row,col);
-		for ( i = 0, r = blist; i < row; r = NEXT(r), i++ )
-			_dpmod_to_vect(BDY(r),at,mat[i]);
-		colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
-		for ( i = 0, nonzero=0; i < row; i++ )
-			for ( j = 0; j < col; j++ )
-				if ( mat[i][j] )
+
+		/* store coefficients separately in spmat and redmat */
+		nsp = row-nred;
+
+		/* reducer matrix */
+		redmat = (int **)almat(nred,col);
+		for ( i = 0, r = blist; i < nred; r = NEXT(r), i++ )
+			_dpmod_to_vect(BDY(r),at,redmat[i]);
+		/* XXX */
+/*		reduce_reducers_mod(redmat,nred,col,m); */
+		/* register the position of the head term */
+		indred = (int *)MALLOC(nred*sizeof(int));
+		bzero(indred,nred*sizeof(int));
+		isred = (int *)MALLOC(col*sizeof(int));
+		bzero(isred,col*sizeof(int));
+		for ( i = 0; i < nred; i++ ) {
+			ri = redmat[i];
+			for ( j = 0; j < col && !ri[j]; j++ );
+			indred[i] = j;
+			isred[j] = 1;
+		}
+
+		spcol = col-nred;
+		/* head terms not in ht */
+		st = (DL *)MALLOC(spcol*sizeof(DL));
+		for ( j = 0, k = 0; j < col; j++ )
+			if ( !isred[j] )
+				st[k++] = at[j];
+
+		/* spoly matrix; stored in reduced form; terms in ht[] are omitted */
+		spmat = almat(nsp,spcol);
+		w = (int *)MALLOC(col*sizeof(int));
+		for ( ; i < row; r = NEXT(r), i++ ) {
+			bzero(w,col*sizeof(int));
+			_dpmod_to_vect(BDY(r),at,w);
+			reduce_sp_by_red_mod(w,redmat,indred,nred,col,m);
+			for ( j = 0, k = 0; j < col; j++ )
+				if ( !isred[j] )
+					spmat[i-nred][k++] = w[j];
+		}
+
+		get_eg(&tmp0); add_eg(&eg_elim1,&tmp1,&tmp0);
+		init_eg(&eg_split_elim1); add_eg(&eg_split_elim1,&tmp1,&tmp0);
+
+		colstat = (int *)MALLOC_ATOMIC(spcol*sizeof(int));
+		for ( i = 0, nonzero=0; i < nsp; i++ )
+			for ( j = 0; j < spcol; j++ )
+				if ( spmat[i][j] )
 					nonzero++;
-		if ( Print )
-			fprintf(asir_out,"mat : %d x %d (nonzero=%f%%)...",
-				row,col,((double)nonzero*100)/(row*col));
-		get_eg(&tmp1); add_eg(&eg_symb,&tmp0,&tmp1);
-		init_eg(&eg_split_symb); add_eg(&eg_split_symb,&tmp0,&tmp1);
-		rank = generic_gauss_elim_mod(mat,row,col,m,colstat);
-		get_eg(&tmp2); add_eg(&eg_elim,&tmp1,&tmp2);
-		init_eg(&eg_split_elim); add_eg(&eg_split_elim,&tmp1,&tmp2);
-		if ( Print ) {
+		if ( DP_Print )
+			fprintf(asir_out,"spmat : %d x %d (nonzero=%f%%)...",
+				nsp,spcol,((double)nonzero*100)/(nsp*spcol));
+		rank = generic_gauss_elim_mod(spmat,nsp,spcol,m,colstat);
+
+		get_eg(&tmp1); add_eg(&eg_elim2,&tmp0,&tmp1);
+		init_eg(&eg_split_elim2); add_eg(&eg_split_elim2,&tmp0,&tmp1);
+
+		if ( DP_Print ) {
 			fprintf(asir_out,"done rank = %d\n",rank,row,col);
 			print_eg("Symb",&eg_split_symb);
-			print_eg("Elim",&eg_split_elim);
+			print_eg("Elim1",&eg_split_elim1);
+			print_eg("Elim2",&eg_split_elim2);
 			fprintf(asir_out,"\n");
 		}
-		for ( j = 0, i = 0; j < col; j++ )
+		for ( j = 0, i = 0; j < spcol; j++ )
 			if ( colstat[j] ) {
-				for ( k = 0; k < nred; k++ )
-					if ( !cmpdl(nv,at[j],ht[k]) )
-						break;
-				if ( k == nred ) {
-					/* this is a new base */
-					mp0 = 0;
-					NEXTMP(mp0,mp); mp->dl = at[j]; mp->c = STOI(1);
-					for ( k = j+1; k < col; k++ )
-						if ( !colstat[k] && mat[i][k] ) {
-							NEXTMP(mp0,mp); mp->dl = at[k];
-							mp->c = STOI(mat[i][k]);
-						}
-					NEXT(mp) = 0;
-					MKDP(nv,mp0,nf); nf->sugar = dm->sugar;
-					nh = newps_mod(nf,m);
-					d = updpairs(d,g,nh);
-					g = updbase(g,nh);
-					gall = append_one(gall,nh);
+				mp0 = 0;
+				NEXTMP(mp0,mp); mp->dl = st[j]; mp->c = STOI(1);
+				for ( k = j+1; k < spcol; k++ )
+					if ( !colstat[k] && spmat[i][k] ) {
+						NEXTMP(mp0,mp); mp->dl = st[k];
+						mp->c = STOI(spmat[i][k]);
 				}
+				NEXT(mp) = 0;
+				MKDP(nv,mp0,nf); nf->sugar = dm->sugar;
+				nh = newps_mod(nf,m);
+				d = updpairs(d,g,nh);
+				g = updbase(g,nh);
+				gall = append_one(gall,nh);
 				i++;
 			}
 	}
-	if ( Print ) {
+	if ( DP_Print ) {
 		print_eg("Symb",&eg_symb);
-		print_eg("Elim",&eg_elim);
+		print_eg("Elim1",&eg_elim1);
+		print_eg("Elim2",&eg_elim2);
 		fflush(asir_out);
 	}
 	return g;
@@ -899,9 +890,9 @@ NODE f,*r;
 int m;
 {
 	int i;
-	NODE s,s0;
+	NODE s,s0,f0;
 
-	f = NODE_sortb(f,1);
+	f0 = f = NODE_sortb(f,1);
 	psn = length(f); pslen = 2*psn;
 	ps = (DP *)MALLOC(pslen*sizeof(DP));
 	psh = (DL *)MALLOC(pslen*sizeof(DL));
@@ -910,11 +901,24 @@ int m;
 	for ( i = 0; i < psn; i++, f = NEXT(f) ) {
 		prim_part((DP)BDY(f),m,&ps[i]);
 		if ( Demand )
-			dp_save(i,ps[i]);
+			dp_save(i,(Obj)ps[i],0);
 		psh[i] = BDY(ps[i])->dl;
 		pss[i] = ps[i]->sugar;
 		psc[i] = BDY(ps[i])->c;
 	}
+	if ( GenTrace && (OXCheck >= 0) ) {
+		Q q;
+		STRING fname;
+		LIST input;
+		NODE arg;
+		Obj dmy;
+
+		STOQ(OXCheck,q);
+		MKSTR(fname,"register_input");
+		MKLIST(input,f0);
+		arg = mknode(3,q,fname,input);
+		Pox_cmo_rpc(arg,&dmy);
+	}
 	for ( s0 = 0, i = 0; i < psn; i++ ) {
 		NEXTNODE(s0,s); BDY(s) = (pointer)i;
 	}
@@ -926,6 +930,8 @@ void prim_part(f,m,r)
 DP f,*r;
 int m;
 {
+	P d,t;
+
 	if ( m > 0 ) {
 		if ( PCoeffs )
 			dp_prim_mod(f,m,r);
@@ -938,6 +944,11 @@ int m;
 			dp_prim(f,r);
 		else
 			dp_ptozp(f,r);
+		if ( GenTrace && TraceList ) {
+			divsp(CO,BDY(f)->c,BDY(*r)->c,&d);
+			mulp(CO,(P)ARG3(BDY((LIST)BDY(TraceList))),d,&t);
+			ARG3(BDY((LIST)BDY(TraceList))) = t;
+		}
 	}
 }
 
@@ -1020,7 +1031,7 @@ NODE *h;
 	if ( NoRA ) {
 		*h = in; return;
 	}
-	if ( Print || PrintShort ) {
+	if ( DP_Print || DP_PrintShort ) {
 		fprintf(asir_out,"reduceall\n"); fflush(asir_out);
 	}
 	r = NODE_sortbi(in,0);
@@ -1035,8 +1046,17 @@ NODE *h;
 			}
 		get_eg(&tmp0);
 		dp_load(w[i],&ps[w[i]]);
-		_dp_nf(top,ps[w[i]],ps,1,&g);
 
+		if ( GenTrace ) {
+			Q q;
+			NODE node;
+			LIST hist;
+
+			STOQ(w[i],q);
+			node = mknode(4,ONE,q,ONE,ONE);
+			MKLIST(hist,node);
+			MKNODE(TraceList,hist,0);
+		}
 		if ( !PtozpRA || !Multiple )
 			_dp_nf(top,ps[w[i]],ps,1,&g);
 		else
@@ -1047,7 +1067,7 @@ NODE *h;
 #endif
 		prim_part(g,0,&g1);
 		get_eg(&tmp1); add_eg(&eg_ra,&tmp0,&tmp1);
-		if ( Print || PrintShort ) {
+		if ( DP_Print || DP_PrintShort ) {
 			fprintf(asir_out,"."); fflush(asir_out);
 		}
 		w[i] = newps(g1,0,(NODE)0);
@@ -1056,7 +1076,7 @@ NODE *h;
 		MKNODE(t,(pointer)w[j],top); top = t;
 	}
 	*h = top;
-	if ( Print || PrintShort )
+	if ( DP_Print || DP_PrintShort )
 		fprintf(asir_out,"\n");
 }
 
@@ -1068,13 +1088,13 @@ NODE *h;
 	NODE r,t,top;
 	int n,i,j;
 	int *w;
-	DP g;
+	DP g,p;
 	struct oEGT tmp0,tmp1;
 
 	if ( NoRA ) {
 		*h = in; return;
 	}
-	if ( Print || PrintShort ) {
+	if ( DP_Print || DP_PrintShort ) {
 		fprintf(asir_out,"reduceall\n"); fflush(asir_out);
 	}
 	r = NODE_sortbi(in,0);
@@ -1090,10 +1110,12 @@ NODE *h;
 		get_eg(&tmp0);
 		if ( PCoeffs )
 			dp_nf_mod(top,ps[w[i]],ps,m,1,&g);
-		else
-			_dp_nf_mod(top,ps[w[i]],ps,m,1,&g);
+		else {
+			dpto_dp(ps[w[i]],&p);
+			_dp_nf_mod_destructive(top,p,ps,m,1,&g);
+		}
 		get_eg(&tmp1); add_eg(&eg_ra,&tmp0,&tmp1);
-		if ( Print || PrintShort ) {
+		if ( DP_Print || DP_PrintShort ) {
 			fprintf(asir_out,"."); fflush(asir_out);
 		}
 		w[i] = newps_mod(g,m);
@@ -1102,7 +1124,7 @@ NODE *h;
 		MKNODE(t,(pointer)w[j],top); top = t;
 	}
 	*h = top;
-	if ( Print || PrintShort )
+	if ( DP_Print || DP_PrintShort )
 		fprintf(asir_out,"\n");
 }
 
@@ -1127,7 +1149,7 @@ NODE subst;
 			ps[psn] = a;
 		else
 			ps[psn] = 0;
-		dp_save(psn,a);
+		dp_save(psn,(Obj)a,0);
 	} else
 		ps[psn] = a;
 	psh[psn] = BDY(a)->dl;
@@ -1135,6 +1157,31 @@ NODE subst;
 	psc[psn] = BDY(a)->c;
 	if ( m )
 		_dp_mod(a,m,subst,&psm[psn]);
+	if ( GenTrace ) {
+		NODE tn,tr,tr1;
+		LIST trace;
+	
+		/* reverse the TraceList */
+		tn = TraceList;
+		for ( tr = 0; tn; tn = NEXT(tn) ) {
+			MKNODE(tr1,BDY(tn),tr); tr = tr1;
+		}
+		MKLIST(trace,tr);
+		if ( OXCheck >= 0 ) {
+			NODE arg;
+			Q q1,q2;
+			STRING fname;
+			Obj dmy;
+
+			STOQ(OXCheck,q1);
+			MKSTR(fname,"check_trace");
+			STOQ(psn,q2);
+			arg = mknode(5,q1,fname,a,q2,trace);
+			Pox_cmo_rpc(arg,&dmy);
+		} else
+			dp_save(psn,(Obj)trace,"t");
+		TraceList = 0;
+	}
 	return psn++;
 }
 
@@ -1210,7 +1257,18 @@ NODE f,*g;
 	}
 	for ( top = 0, i = n-1; i >= 0; i-- )
 		if ( r[i] >= 0 ) {
-			dp_load(r[i],&ps[r[i]]); dp_dehomo(ps[r[i]],&u); j = newps(u,0,0);
+			dp_load(r[i],&ps[r[i]]); dp_dehomo(ps[r[i]],&u);
+			if ( GenTrace ) {
+				Q q;
+				LIST hist;
+				NODE node;
+
+				STOQ(r[i],q);
+				node = mknode(4,0,q,0,0);
+				MKLIST(hist,node);
+				MKNODE(TraceList,hist,0);
+			}
+			j = newps(u,0,0);
 			MKNODE(t,j,top); top = t;
 		}
 	*g = top;
@@ -1298,6 +1356,8 @@ NODE subst;
 	struct oEGT tnf0,tnf1,tnfm0,tnfm1,tpz0,tpz1,tsp0,tsp1,tspm0,tspm1,tnp0,tnp1,tmp0,tmp1;
 	int skip_nf_flag;
 	double t_0;
+	Q q;
+	int new_sugar;
 	static prev_sugar = -1;
 
 	Max_mag = 0;
@@ -1323,10 +1383,12 @@ NODE subst;
 		get_eg(&tmp1); add_eg(&eg_mp,&tmp0,&tmp1);
 		if ( m ) {
 			get_eg(&tspm0);
-			_dp_sp_mod(psm[l->dp1],psm[l->dp2],m,&h);
+			_dp_sp_mod_dup(psm[l->dp1],psm[l->dp2],m,&h);
+			if ( h )
+				new_sugar = h->sugar;
 			get_eg(&tspm1); add_eg(&eg_spm,&tspm0,&tspm1);
 			get_eg(&tnfm0);
-			_dp_nf_mod(gall,h,psm,m,0,&nfm);
+			_dp_nf_mod_destructive(gall,h,psm,m,0,&nfm);
 			get_eg(&tnfm1); add_eg(&eg_nfm,&tnfm0,&tnfm1);
 		} else
 			nfm = (DP)1;
@@ -1345,6 +1407,12 @@ NODE subst;
 				}
 			} else
 				dp_sp(ps[l->dp1],ps[l->dp2],&h);
+			if ( GenTrace ) {
+				STOQ(l->dp1,q); ARG1(BDY((LIST)BDY(NEXT(TraceList)))) = q;
+				STOQ(l->dp2,q); ARG1(BDY((LIST)BDY(TraceList))) = q;
+			}
+			if ( h )
+				new_sugar = h->sugar;
 			get_eg(&tsp1); add_eg(&eg_sp,&tsp0,&tsp1);
 			get_eg(&tnf0);
 			t_0 = get_rtime();
@@ -1356,7 +1424,7 @@ NODE subst;
 #else
 				_dp_nf_ptozp(gall,h,ps,!Top,Multiple,&nf);
 #endif
-			if ( Print )
+			if ( DP_Print )
 				fprintf(asir_out,"(%.3g)",get_rtime()-t_0);
 			get_eg(&tnf1); add_eg(&eg_nf,&tnf0,&tnf1);
 		} else
@@ -1383,7 +1451,7 @@ skip_nf:
 					mag += p_mag((P)mp->c);
 				Max_mag = MAX(Max_mag,mag);
 			}
-			if ( Print ) {
+			if ( DP_Print ) {
 				if ( !prev )
 					fprintf(asir_out,"\n");
 				print_split_e(&tnf0,&tnf1); print_split_e(&tpz0,&tpz1);
@@ -1394,7 +1462,7 @@ skip_nf:
 				if ( ShowMag )
 					fprintf(asir_out,",mag=%d",mag);
 				fprintf(asir_out,"\n"); fflush(asir_out);
-			} else if ( PrintShort ) {
+			} else if ( DP_PrintShort ) {
 				fprintf(asir_out,"+"); fflush(asir_out);
 			}
 			prev = 1;
@@ -1402,16 +1470,16 @@ skip_nf:
 			if ( m )
 				add_eg(&eg_znfm,&tnfm0,&tnfm1);
 			ZR++;
-			if ( Print || PrintShort ) {
-				if ( h && (h->sugar != prev_sugar) ) {
-					fprintf(asir_out,"[%d]",h->sugar);	
-					prev_sugar = h->sugar;
+			if ( DP_Print || DP_PrintShort ) {
+				if ( new_sugar != prev_sugar ) {
+					fprintf(asir_out,"[%d]",new_sugar);	
+					prev_sugar = new_sugar;
 				}
 				fprintf(asir_out,"."); fflush(asir_out); prev = 0;
 			}
 		}
 	}
-	if ( Print || PrintShort )
+	if ( DP_Print || DP_PrintShort )
 		fprintf(asir_out,"gb done\n");
 	return g;
 }
@@ -1451,10 +1519,10 @@ NODE dlist;
 		l->dp2 = QTOS((Q)BDY(pair));
 		if ( m ) {
 			get_eg(&tspm0);
-			_dp_sp_mod(psm[l->dp1],psm[l->dp2],m,&h);
+			_dp_sp_mod_dup(ps[l->dp1],ps[l->dp2],m,&h);
 			get_eg(&tspm1); add_eg(&eg_spm,&tspm0,&tspm1);
 			get_eg(&tnfm0);
-			_dp_nf_mod(gall,h,psm,m,0,&nfm);
+			_dp_nf_mod_destructive(gall,h,ps,m,!Top,&nf);
 			get_eg(&tnfm1); add_eg(&eg_nfm,&tnfm0,&tnfm1);
 		} else
 			nfm = (DP)1;
@@ -1487,7 +1555,7 @@ NODE dlist;
 				return 0;
 			g = updbase(g,nh);
 			gall = append_one(gall,nh);
-			if ( Print ) {
+			if ( DP_Print ) {
 				if ( !prev )
 					fprintf(asir_out,"\n");
 				print_split_eg(&tnf0,&tnf1); fflush(asir_out);
@@ -1499,12 +1567,12 @@ NODE dlist;
 			if ( m )
 				add_eg(&eg_znfm,&tnfm0,&tnfm1);
 			ZR++;
-			if ( Print ) {
+			if ( DP_Print ) {
 				fprintf(asir_out,"."); fflush(asir_out); prev = 0;
 			}
 		}
 	}
-	if ( Print )
+	if ( DP_Print )
 		fprintf(asir_out,"gb done\n");
 	return g;
 }
@@ -1536,9 +1604,9 @@ int m;
 			get_eg(&tspm1); add_eg(&eg_spm,&tspm0,&tspm1); get_eg(&tnfm0);
 			dp_nf_mod(gall,h,ps,m,!Top,&nf);
 		} else {
-			_dp_sp_mod(ps[l->dp1],ps[l->dp2],m,&h);
+			_dp_sp_mod_dup(ps[l->dp1],ps[l->dp2],m,&h);
 			get_eg(&tspm1); add_eg(&eg_spm,&tspm0,&tspm1); get_eg(&tnfm0);
-			_dp_nf_mod(gall,h,ps,m,!Top,&nf);
+			_dp_nf_mod_destructive(gall,h,ps,m,!Top,&nf);
 		}
 		get_eg(&tnfm1); add_eg(&eg_nfm,&tnfm0,&tnfm1);
 		if ( nf ) {
@@ -1551,104 +1619,30 @@ int m;
 				return 0;
 			d = updpairs(d,g,nh);
 			g = updbase(g,nh);
-			if ( InterReduce )
-				interreduce_mod(g,nh,m);
 			gall = append_one(gall,nh);
-			if ( Print ) {
+			if ( DP_Print ) {
 				if ( !prev )
 					fprintf(asir_out,"\n");
 				print_split_eg(&tnfm0,&tnfm1); fflush(asir_out);
 				fprintf(asir_out,"(%d,%d),nb=%d,nab=%d,rp=%d,sugar=%d",l->dp1,l->dp2,length(g),length(gall),DPPlength(d),pss[nh]);
 				printdl(psh[nh]); fprintf(asir_out,"\n"); fflush(asir_out);
+			} else if ( DP_PrintShort ) {
+				fprintf(asir_out,"+"); fflush(asir_out);
 			}
 			prev = 1;
 		} else {
 			add_eg(&eg_znfm,&tnfm0,&tnfm1);
 			ZR++;
-			if ( Print ) {
+			if ( DP_Print || DP_PrintShort ) {
 				fprintf(asir_out,"."); fflush(asir_out); prev = 0;
 			}
 		}
 	}
-	if ( Print )
+	if ( DP_Print || DP_PrintShort )
 		fprintf(asir_out,"gb_mod done\n");
 	return g;
 }
 
-void interreduce_mod(g,n,m)
-NODE g;
-int n,m;
-{
-	DP nf;
-	NODE gn,t;
-	int i;
-
-	MKNODE(gn,(pointer)n,0);
-	if ( PCoeffs )
-		for ( t = g; t; t = NEXT(t) ) {
-			i = (int)BDY(t);
-			if ( i != n ) {
-				dp_nf_mod(gn,ps[i],ps,m,1,&nf); ps[i] = nf;
-			}
-		}
-	else
-		for ( t = g; t; t = NEXT(t) ) {
-			i = (int)BDY(t);
-			if ( i != n ) {
-				_dp_nf_mod(gn,ps[i],ps,m,1,&nf); ps[i] = nf;
-			}
-		}
-}
-
-void _dp_nf_mod(b,g,ps,mod,full,rp)
-NODE b;
-DP g;
-DP *ps;
-int mod,full;
-DP *rp;
-{
-	DP u,p,d,s,t;
-	NODE l;
-	MP m,mr;
-	int sugar,psugar;
-
-	if ( !g ) {
-		*rp = 0; return;
-	}
-	sugar = g->sugar;
-	for ( d = 0; g; ) {
-		for ( u = 0, l = b; l; l = NEXT(l) ) {
-			if ( dp_redble(g,p = ps[(int)BDY(l)]) ) {
-				_dp_red_mod(g,p,mod,&u);		
-				psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
-				sugar = MAX(sugar,psugar);
-				if ( !u ) {
-					if ( d )
-						d->sugar = sugar;
-					*rp = d; return;
-				}
-				break;
-			}
-		}
-		if ( u )
-			g = u;
-		else if ( !full ) {
-			if ( g ) {
-				MKDP(g->nv,BDY(g),t); t->sugar = sugar; g = t;
-			}
-			*rp = g; return;
-		} else {
-			m = BDY(g); NEWMP(mr); mr->dl = m->dl; mr->c = m->c;
-			NEXT(mr) = 0; MKDP(g->nv,mr,t); t->sugar = mr->dl->td;
-			_addmd(CO,mod,d,t,&s); d = s;
-			dp_rest(g,&t); g = t;
-		}
-	}
-	if ( d )
-		d->sugar = sugar;
-	*rp = d;
-}
-
 void _dp_nf(b,g,ps,full,rp)
 NODE b;
 DP g;
@@ -1656,8 +1650,8 @@ DP *ps;
 int full;
 DP *rp;
 {
-	DP u,p,d,s,t;
-	P dmy;
+	DP u,p,d,s,t,mult;
+	P coef;
 	NODE l;
 	MP m,mr;
 	int sugar,psugar;
@@ -1670,9 +1664,20 @@ DP *rp;
 		for ( u = 0, l = b; l; l = NEXT(l) ) {
 			if ( dl_redble(BDY(g)->dl,psh[(int)BDY(l)]) ) {
 				dp_load((int)BDY(l),&p);
-				dp_red(d,g,p,&t,&u,&dmy);
+				/* t+u = coef*(d+g) - mult*p (t = coef*d) */
+				dp_red(d,g,p,&t,&u,&coef,&mult);
 				psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
 				sugar = MAX(sugar,psugar);
+				if ( GenTrace ) {
+					LIST hist;
+					Q cq;
+					NODE node,node0;
+
+					STOQ((int)BDY(l),cq);
+					node0 = mknode(4,coef,cq,mult,ONE);
+					MKLIST(hist,node0);
+					MKNODE(node,hist,TraceList); TraceList = node;
+				}
 				if ( !u ) {
 					if ( d )
 						d->sugar = sugar;
@@ -1705,6 +1710,9 @@ DP *rp;
 
 double pz_t_e, pz_t_d, pz_t_d1, pz_t_c, im_t_s, im_t_r;
 
+extern int GenTrace;
+extern NODE TraceList;
+
 void _dp_nf_ptozp(b,g,ps,full,multiple,r)
 NODE b;
 DP g;
@@ -1726,6 +1734,9 @@ DP *r;
 	extern int kara_mag;
 	double get_rtime();	
 	double t_0,t_00,tt,ttt,t_p,t_m,t_m1,t_m2,t_s,t_g,t_a;
+	LIST hist;
+	NODE node;
+	Q rcred,mrcred;
 
 	if ( !g ) {
 		*r = 0; return;
@@ -1745,6 +1756,7 @@ DP *r;
 	dc = 0; dp = 0; rc = ONE; rp = g;
 	MKSTR(imul,"dp_imul_index");
 
+	/* g = dc*dp+rc*rp */
 	for ( ; rp; ) {
 		for ( u = 0, l = b; l; l = NEXT(l) ) {
 			if ( dl_redble(BDY(rp)->dl,psh[(int)BDY(l)]) ) {
@@ -1758,14 +1770,13 @@ DP *r;
 
 				t_0 = get_rtime();
 				dp_subd(rp,red,&shift);
-#if INET
 				if ( Dist && ndist && HMAG(red) > kara_bit ) {
 					NODE n0,n1,n2,n3;
 					int i,s,id;
 					Obj dmy;
 					Q ind;
 
-					if ( Print )
+					if ( DP_Print )
 						fprintf(asir_out,"d");
 					i = (int)BDY(l); STOQ(i,ind);
 					chsgnp((P)cred,(P *)&mcred);
@@ -1776,11 +1787,9 @@ DP *r;
 					muldc(CO,rp,(P)cr,&t);
 					NEXT(n0)=0;
 					Pox_pop_local(n0,&t1);
-				} else
-#endif
-				{
+				} else {
 /*					
-					if ( Print )
+					if ( DP_Print )
 						fprintf(asir_out,"l");
 */
 					t_00 = get_rtime();
@@ -1799,10 +1808,23 @@ DP *r;
 
 				psugar = (BDY(rp)->dl->td - BDY(red)->dl->td) + red->sugar;
 				sugar = MAX(sugar,psugar);
+				if ( GenTrace ) {
+					/* u = cr*rp + (-cred)*shift*red */ 
+					STOQ((int)BDY(l),cq);
+					node = mknode(4,cr,cq,0,0);
+					mulq(cred,rc,&rcred);
+					chsgnnum((Num)rcred,(Num *)&mrcred);
+					muldc(CO,shift,(P)mrcred,(DP *)&ARG2(node));
+					MKLIST(hist,node);
+				}
 				if ( !u ) {
 					if ( dp )
 						dp->sugar = sugar;
 					*r = dp;
+					if ( GenTrace ) {
+						ARG3(BDY(hist)) = ONE;
+						MKNODE(node,hist,TraceList); TraceList = node;
+					}
 					goto final;
 				}
 				break;
@@ -1811,23 +1833,19 @@ DP *r;
 		if ( u ) {
 			if ( HMAG(u) > hmag ) {
 				t_0 = get_rtime();
-#if INET
 				if ( Dist && HMAG(u) > kara_bit ) {
-					if ( Print )
+					if ( DP_Print )
 						fprintf(asir_out,"D");
 					dp_ptozp_d(dist,ndist,u,&t);
 				} else {
-					if ( Print )
+					if ( DP_Print )
 						fprintf(asir_out,"L");
 					dp_ptozp_d(0,0,u,&t);
 				}
-#else
-				dp_ptozp(u,&t); /* XXX */
-#endif
 				tt = get_rtime()-t_0; t_g += tt;
 				t_0 = get_rtime();
 				divsn(NM((Q)BDY(u)->c),NM((Q)BDY(t)->c),&cn); NTOQ(cn,1,cont);
-				if ( !dp_fcoeffs && Print ) {
+				if ( !dp_fcoeffs && DP_Print ) {
 					fprintf(asir_out,"(%d)",p_mag((P)cont)*100/p_mag((P)BDY(u)->c));
 					fflush(asir_out);
 				}
@@ -1839,11 +1857,20 @@ DP *r;
 				tt = get_rtime()-t_0; t_a += tt;
 				rp = t;
 				hmag = multiple*HMAG(rp)/denom;
+				if ( GenTrace ) {
+					NTOQ(gn,1,gcd);
+					ARG3(BDY(hist)) = (pointer)gcd;
+					MKNODE(node,hist,TraceList); TraceList = node;
+				}
 			} else {
 				t_0 = get_rtime();
 				mulq(cr,dc,&dcq); dc = dcq;
 				tt = get_rtime()-t_0; t_a += tt;
 				rp = u;
+				if ( GenTrace ) {
+					ARG3(BDY(hist)) = (pointer)ONE;
+					MKNODE(node,hist,TraceList); TraceList = node;
+				}
 			}
 		} else if ( !full ) {
 			if ( rp ) {
@@ -1867,11 +1894,15 @@ DP *r;
 			tt = get_rtime()-t_0; t_a += tt;
 		}
 	}
+	if ( GenTrace ) {
+		mulq(ARG3(BDY((LIST)BDY(TraceList))),dc,&cq);
+		ARG3(BDY((LIST)BDY(TraceList))) = (pointer)cq;
+	}
 	if ( dp )
 		dp->sugar = sugar;
 	*r = dp;
 final:
-	if ( Print )
+	if ( DP_Print )
 		fprintf(asir_out,"(%.3g %.3g %.3g %.3g %.3g %.3g %.3g %.3g %.3g %.3g %.3g)",
 			t_p,t_m,t_m1,t_m2,t_s,
 			t_g,t_a,
@@ -1942,10 +1973,10 @@ DP *r;
 				t_00 = get_rtime();
 				if ( Dist && ndist 
 					&& HMAG(rp) > mpi_mag && p_mag((P)cr) > mpi_mag ) {
-					if ( Print ) fprintf(asir_out,"~");
+					if ( DP_Print ) fprintf(asir_out,"~");
 					dp_imul_d(rp,cr,&t);
 				} else {
-					if ( Print ) fprintf(asir_out,"_");
+					if ( DP_Print ) fprintf(asir_out,"_");
 					muldc(CO,rp,(P)cr,&t);
 				}
 				ttt = get_rtime()-t_00; t_m1 += ttt/dp_nt(rp);
@@ -1954,10 +1985,10 @@ DP *r;
 				chsgnp((P)cred,(P *)&mcred);
 				if ( Dist && ndist 
 					&& HMAG(red) > mpi_mag && p_mag((P)mcred) > mpi_mag ) {
-					if ( Print ) fprintf(asir_out,"=");
+					if ( DP_Print ) fprintf(asir_out,"=");
 					dp_imul_d(red,mcred,&t1);
 				} else {
-					if ( Print ) fprintf(asir_out,"_");
+					if ( DP_Print ) fprintf(asir_out,"_");
 					muldc(CO,red,(P)mcred,&t1);
 				}
 				ttt = get_rtime()-t_00; t_m2 += ttt/dp_nt(red);
@@ -1983,18 +2014,18 @@ DP *r;
 			if ( HMAG(u) > hmag ) {
 				t_0 = get_rtime();
 				if ( Dist && HMAG(u) > mpi_mag ) {
-					if ( Print )
+					if ( DP_Print )
 						fprintf(asir_out,"D");
 					dp_ptozp_d(dist,ndist,u,&t);
 				} else {
-					if ( Print )
+					if ( DP_Print )
 						fprintf(asir_out,"L");
 					dp_ptozp_d(0,0,u,&t);
 				}
 				tt = get_rtime()-t_0; t_g += tt;
 				t_0 = get_rtime();
 				divsn(NM((Q)BDY(u)->c),NM((Q)BDY(t)->c),&cn); NTOQ(cn,1,cont);
-				if ( Print ) {
+				if ( DP_Print ) {
 					fprintf(asir_out,"(%d)",p_mag((P)cont)*100/p_mag((P)BDY(u)->c));
 					fflush(asir_out);
 				}
@@ -2038,7 +2069,7 @@ DP *r;
 		dp->sugar = sugar;
 	*r = dp;
 final:
-	if ( Print )
+	if ( DP_Print )
 		fprintf(asir_out,"(%.3g %.3g %.3g %.3g %.3g %.3g %.3g %.3g %.3g %.3g %.3g)",
 			t_p,t_m,t_m1,t_m2,t_s,
 			t_g,t_a,
@@ -2144,13 +2175,16 @@ int t;
 		dl1 = DPPlength(d1); NFP += (dl-dl1); dl = dl1;
 	} else
 		dl = 1;
-	for ( dd = 0; d1; d1 = nd ) {
-		nd = NEXT(d1);
-		if ( !criterion_2( d1->dp1, d1->dp2 ) ) {
-			NEXT(d1) = dd;
-			dd = d1;
+	if ( !do_weyl )
+		for ( dd = 0; d1; d1 = nd ) {
+			nd = NEXT(d1);
+			if ( !criterion_2( d1->dp1, d1->dp2 ) ) {
+				NEXT(d1) = dd;
+				dd = d1;
+			}
 		}
-	}
+	else
+		dd = d1;
 	dl1 = DPPlength(dd); NDP += (dl-dl1);
 	get_eg(&tup1);
 	add_eg(&eg_up,&tup0,&tup1);
@@ -2178,7 +2212,12 @@ register int t;
 		last = p;
 		dp = p->dp1 = (int)BDY(r);  p->dp2 = t;
 		p->lcm = lcm_of_DL(CNVars, dl = psh[dp], tdl, (DL)0 );
-		p->sugar = (ts > (s = pss[dp] - dl->td) ? ts : s) + p->lcm->td;
+#if 0
+		if ( do_weyl )
+			p->sugar = dl_weight(p->lcm);
+		else
+#endif
+			p->sugar = (ts > (s = pss[dp] - dl->td) ? ts : s) + p->lcm->td;
 	}
 	return last;
 }
@@ -2353,6 +2392,17 @@ DL dl1, dl2;
 	return 1;
 }
 
+int dl_weight(dl)
+DL dl;
+{
+	int n,w,i;
+
+	n = CNVars/2;
+	for ( i = 0, w = 0; i < n; i++ )
+		w += (-dl->d[i]+dl->d[n+i]);
+	return w;
+}
+
 int gbcheck(f)
 NODE f;
 {
@@ -2370,7 +2420,7 @@ NODE f;
 		g = updbase(g,i);
 		gall = append_one(gall,i);
 	}
-	if ( Print || PrintShort ) {
+	if ( DP_Print || DP_PrintShort ) {
 		fprintf(asir_out,"gbcheck total %d pairs\n",DPPlength(d)); fflush(asir_out);
 	}
 	while ( d ) {
@@ -2379,13 +2429,13 @@ NODE f;
 		dp_load(l->dp1,&dp1); dp_load(l->dp2,&dp2); dp_sp(dp1,dp2,&h);
 		_dp_nf(gall,h,ps,1,&nf);
 		get_eg(&tmp1); add_eg(&eg_gc,&tmp0,&tmp1);
-		if ( Print || PrintShort ) {
+		if ( DP_Print || DP_PrintShort ) {
 			fprintf(asir_out,"."); fflush(asir_out);
 		}
 		if ( nf )
 			return 0;
 	}
-	if ( Print || PrintShort )
+	if ( DP_Print || DP_PrintShort )
 		fprintf(asir_out,"\n");
 	return 1;
 }
@@ -2398,22 +2448,22 @@ NODE f,x;
 
 	if ( NoMC )
 		return 1;
-	if ( Print || PrintShort ) {
+	if ( DP_Print || DP_PrintShort ) {
 		fprintf(asir_out,"membercheck\n"); fflush(asir_out);
 	}
 	for ( ; f; f = NEXT(f) ) {
 		get_eg(&tmp0);
 		_dp_nf(x,(DP)BDY(f),ps,1,&g);
 		get_eg(&tmp1); add_eg(&eg_mc,&tmp0,&tmp1);
-		if ( Print ) {
+		if ( DP_Print ) {
 			print_split_eg(&tmp0,&tmp1); fflush(asir_out);
-		} else if ( PrintShort ) {
+		} else if ( DP_PrintShort ) {
 			fprintf(asir_out,"."); fflush(asir_out);
 		}
 		if ( g )
 			return 0;
 	}
-	if ( Print || PrintShort )
+	if ( DP_Print || DP_PrintShort )
 		fprintf(asir_out,"\n");
 	return 1;
 }
@@ -2452,22 +2502,24 @@ Obj name,value;
 		Top = v;
 	else if ( !strcmp(n,"ShowMag") )
 		ShowMag = v;
-	else if ( !strcmp(n,"PrintShort") )
-		PrintShort = v;
-	else if ( !strcmp(n,"Print") )
-		Print = v;
+	else if ( !strcmp(n,"DP_PrintShort") )
+		DP_PrintShort = v;
+	else if ( !strcmp(n,"DP_Print") )
+		DP_Print = v;
 	else if ( !strcmp(n,"Stat") )
 		Stat = v;
 	else if ( !strcmp(n,"Reverse") )
 		Reverse = v;
-	else if ( !strcmp(n,"InterReduce") )
-		InterReduce = v;
 	else if ( !strcmp(n,"Multiple") )
 		Multiple = v;
 	else if ( !strcmp(n,"Denominator") )
 		Denominator = v;
 	else if ( !strcmp(n,"PtozpRA") )
 		PtozpRA = v;
+	else if ( !strcmp(n,"GenTrace") )
+		GenTrace = v;
+	else if ( !strcmp(n,"OXCheck") )
+		OXCheck = v;
 }
 
 void dp_make_flaglist(list)
@@ -2480,10 +2532,11 @@ LIST *list;
 	STOQ(Multiple,v); MKNODE(n,v,0); MKSTR(name,"Multiple"); MKNODE(n1,name,n); n = n1;
 	STOQ(Denominator,v); MKNODE(n1,v,n); n = n1; MKSTR(name,"Denominator"); MKNODE(n1,name,n); n = n1;
 	MKNODE(n1,Dist,n); n = n1; MKSTR(name,"Dist"); MKNODE(n1,name,n); n = n1;
-	STOQ(InterReduce,v); MKNODE(n1,v,n); n = n1; MKSTR(name,"InterReduce"); MKNODE(n1,name,n); n = n1;
 	STOQ(Reverse,v); MKNODE(n1,v,n); n = n1; MKSTR(name,"Reverse"); MKNODE(n1,name,n); n = n1;
 	STOQ(Stat,v); MKNODE(n1,v,n); n = n1; MKSTR(name,"Stat"); MKNODE(n1,name,n); n = n1;
-	STOQ(Print,v); MKNODE(n1,v,n); n = n1; MKSTR(name,"Print"); MKNODE(n1,name,n); n = n1;
+	STOQ(DP_Print,v); MKNODE(n1,v,n); n = n1; MKSTR(name,"DP_Print"); MKNODE(n1,name,n); n = n1;
+	STOQ(OXCheck,v); MKNODE(n1,v,n); n = n1; MKSTR(name,"OXCheck"); MKNODE(n1,name,n); n = n1;
+	STOQ(GenTrace,v); MKNODE(n1,v,n); n = n1; MKSTR(name,"GenTrace"); MKNODE(n1,name,n); n = n1;
 	STOQ(PtozpRA,v); MKNODE(n1,v,n); n = n1; MKSTR(name,"PtozpRA"); MKNODE(n1,name,n); n = n1;
 	STOQ(ShowMag,v); MKNODE(n1,v,n); n = n1; MKSTR(name,"ShowMag"); MKNODE(n1,name,n); n = n1;
 	STOQ(Top,v); MKNODE(n1,v,n); n = n1; MKSTR(name,"Top"); MKNODE(n1,name,n); n = n1;
@@ -2503,26 +2556,21 @@ LIST *list;
 
 #define DELIM '/'
 
-#if defined(THINK_C)
-#undef DELIM
-#define DELIM ':'
-#endif
-
-void dp_save(index,p)
+void dp_save(index,p,prefix)
 int index;
-DP p;
+Obj p;
+char *prefix;
 {
 	FILE *fp;
 	char path[BUFSIZ];
 
-	sprintf(path,"%s%c%d",Demand,DELIM,index);
-#if defined(VISUAL) || defined(THINK_C)
+	if ( prefix )
+		sprintf(path,"%s%c%s%d",Demand,DELIM,prefix,index);
+	else
+		sprintf(path,"%s%c%d",Demand,DELIM,index);
 	if ( !(fp = fopen(path,"wb") ) )
-#else
-	if ( !(fp = fopen(path,"w") ) )
-#endif
 		error("dp_save : cannot open a file");
-	savevl(fp,VC); saveobj(fp,(Obj)p); fclose(fp);
+	savevl(fp,VC); saveobj(fp,p); fclose(fp);
 }
 
 void dp_load(index,p)
@@ -2536,11 +2584,7 @@ DP *p;
 		*p = ps[index];
 	else {
 		sprintf(path,"%s%c%d",Demand,DELIM,index);
-#if defined(VISUAL) || defined(THINK_C)
 		if ( !(fp = fopen(path,"rb") ) )
-#else
-		if ( !(fp = fopen(path,"r") ) )
-#endif
 			error("dp_load : cannot open a file");
 		skipvl(fp); loadobj(fp,(Obj *)p); fclose(fp);
 	}
@@ -2554,11 +2598,7 @@ DP *p;
 	char path[BUFSIZ];
 
 	sprintf(path,"%s%c%d",Demand,DELIM,index);
-#if defined(VISUAL) || defined(THINK_C)
 	if ( !(fp = fopen(path,"rb") ) )
-#else
-	if ( !(fp = fopen(path,"r") ) )
-#endif
 		return 0;
 	else {
 		skipvl(fp); loadobj(fp,(Obj *)p); fclose(fp); return 1;
@@ -2574,7 +2614,7 @@ void init_stat() {
 }
 
 void print_stat() {
-	if ( !Print && !Stat )
+	if ( !DP_Print && !Stat )
 		return;
 	print_eg("UP",&eg_up); print_eg("SP",&eg_sp); print_eg("SPM",&eg_spm);
 	print_eg("NF",&eg_nf); print_eg("NFM",&eg_nfm); print_eg("ZNFM",&eg_znfm);
@@ -2582,160 +2622,3 @@ void print_stat() {
 	print_eg("RA",&eg_ra); print_eg("MC",&eg_mc); print_eg("GC",&eg_gc);
 	fprintf(asir_out,"T=%d,B=%d M=%d F=%d D=%d ZR=%d NZR=%d\n",TP,NBP,NMP,NFP,NDP,ZR,NZR);
 }
-
-/*
- * Old codes 
- */
-
-#if 0
-void _dp_nf_ptozp(b,g,ps,full,multiple,rp)
-NODE b;
-DP g;
-DP *ps;
-int full,multiple;
-DP *rp;
-{
-	DP u,p,d,s,t,dmy;
-	NODE l;
-	MP m,mr;
-	int i,n;
-	int hmag,denom;
-	int sugar,psugar;
-	NODE dist;
-	int ndist;
-	int kara_bit;
-	extern int kara_mag;
-
-	if ( !g ) {
-		*rp = 0; return;
-	}
-	denom = Denominator?Denominator:1;
-	hmag = multiple*HMAG(g)/denom;
-	kara_bit = kara_mag*27; /* XXX */
-	if ( Dist ) {
-		dist = BDY(Dist);
-		ndist = length(dist);
-	}
-	sugar = g->sugar;
-	for ( d = 0; g; ) {
-		for ( u = 0, l = b; l; l = NEXT(l) ) {
-			if ( dl_redble(BDY(g)->dl,psh[(int)BDY(l)]) ) {
-				dp_load((int)BDY(l),&p);
-				dp_red(d,g,p,&t,&u,&dmy);
-				psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
-				sugar = MAX(sugar,psugar);
-				if ( !u ) {
-					if ( d )
-						d->sugar = sugar;
-					*rp = d; return;
-				}
-				d = t;
-				break;
-			}
-		}
-		if ( u ) {
-			g = u;
-			if ( d ) {
-				if ( HMAG(d) > hmag ) {
-					if ( Dist && HMAG(g) > kara_bit )
-						dp_ptozp2_d(dist,ndist,d,g,&t,&u);
-					else
-						dp_ptozp2(d,g,&t,&u);
-					d = t; g = u;
-					hmag = multiple*HMAG(d)/denom;
-				}
-			} else {
-				if ( HMAG(g) > hmag ) {
-#if INET
-					if ( Dist && HMAG(g) > kara_bit ) {
-						dp_ptozp_d(dist,ndist,g,&t);
-					} else
-#endif
-						dp_ptozp(g,&t);
-					g = t;
-					hmag = multiple*HMAG(g)/denom;
-				}
-			}
-		}
-		else if ( !full ) {
-			if ( g ) {
-				MKDP(g->nv,BDY(g),t); t->sugar = sugar; g = t;
-			}
-			*rp = g; return;
-		} else {
-			m = BDY(g); NEWMP(mr); mr->dl = m->dl; mr->c = m->c;
-			NEXT(mr) = 0; MKDP(g->nv,mr,t); t->sugar = mr->dl->td;
-			addd(CO,d,t,&s); d = s;
-			dp_rest(g,&t); g = t;
-		}
-	}
-	if ( d )
-		d->sugar = sugar;
-	*rp = d;
-}
-
-int criterion_2(dp1,dp2)
-{
-	DP g1,g2,g,s1,s2;
-
-	monomial_gcd(ps[dp1],&g1); monomial_gcd(ps[dp2],&g2);
-	dp_gcd(g1,g2,&g);
-	dp_subd(ps[dp1],g,&s1); dp_subd(ps[dp2],g,&s2);
-	return _criterion_2(s1,s2);
-}
-
-int _criterion_2( dp1, dp2 )
-DP dp1, dp2;
-{
-	register int i, *d1, *d2;
-
-	d1 = BDY(dp1)->dl->d; d2 = BDY(dp2)->dl->d;
-	for ( i = CNVars; --i >= 0; d1++, d2++ )
-		if ( (*d1 <= *d2 ? *d1 : *d2) > 0  ) return 0;
-	return 1;
-}
-
-void dp_gcd(p1,p2,rp)
-DP p1,p2;
-DP *rp;
-{
-	int i,n,td;
-	DL d1,d2,d;
-	MP m;
-	DP s;
-
-	n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
-	NEWDL(d,n);
-	for ( i = 0, td = 0; i < n; i++ ) {
-		d->d[i] = MIN(d1->d[i],d2->d[i]);
-		td += d->d[i];
-	}
-	d->td = td;
-	NEWMP(m); m->dl = d; m->c = (P)ONE; NEXT(m) = 0; MKDP(n,m,s); s->sugar = d->td;
-	*rp = s;
-}
-
-void monomial_gcd(p,rp)
-DP p;
-DP *rp;
-{
-	int n,i,td;
-	DL d,d1;
-	MP m;
-	DP s;
-
-	n = p->nv; m = BDY(p); d = m->dl;
-	NEWDL(d1,n);
-	for ( i = 0; i < n; i++ )
-		d1->d[i] = d->d[i];
-	for ( m = NEXT(m); m; m = NEXT(m) ) {
-		d = m->dl;
-		for ( i = 0; i < n; i++ )
-			d1->d[i] = MIN(d1->d[i],d->d[i]);
-	}
-	for ( i = 0, td = 0; i < n; i++ )
-		td += d1->d[i];
-	NEWMP(m); m->dl = d1; m->c = (P)ONE; NEXT(m) = 0; MKDP(n,m,s); s->sugar = d->td;
-	*rp = s;
-}
-#endif