===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/nd.c,v
retrieving revision 1.32
retrieving revision 1.201
diff -u -p -r1.32 -r1.201
--- OpenXM_contrib2/asir2000/engine/nd.c	2003/08/19 04:38:09	1.32
+++ OpenXM_contrib2/asir2000/engine/nd.c	2013/01/30 07:44:48	1.201
@@ -1,3153 +1,7184 @@
-/* $OpenXM: OpenXM_contrib2/asir2000/engine/nd.c,v 1.31 2003/08/13 03:13:22 noro Exp $ */
+/* $OpenXM: OpenXM_contrib2/asir2000/engine/nd.c,v 1.200 2012/12/17 07:20:44 noro Exp $ */
 
-#include "ca.h"
-#include "inline.h"
+#include "nd.h"
 
-#if defined(__GNUC__)
-#define INLINE inline
-#elif defined(VISUAL)
-#define INLINE __inline
+struct oEGT eg_search;
+
+int diag_period = 6;
+int (*ndl_compare_function)(UINT *a1,UINT *a2);
+int nd_dcomp;
+NM _nm_free_list;
+ND _nd_free_list;
+ND_pairs _ndp_free_list;
+NODE nd_hcf;
+
+static NODE nd_subst;
+static VL nd_vc;
+static int nd_ntrans;
+static int nd_nalg;
+#if 0
+static int ndv_alloc;
+#endif
+#if 1
+static int nd_f4_nsp=0x7fffffff;
 #else
-#define INLINE
+static int nd_f4_nsp=50;
 #endif
+static double nd_scale=2;
+static UINT **nd_bound;
+static struct order_spec *nd_ord;
+static EPOS nd_epos;
+static BlockMask nd_blockmask;
+static int nd_nvar;
+static int nd_isrlex;
+static int nd_epw,nd_bpe,nd_wpd,nd_exporigin;
+static UINT nd_mask[32];
+static UINT nd_mask0,nd_mask1;
 
-#define USE_GEOBUCKET 1
+static NDV *nd_ps;
+static NDV *nd_ps_trace;
+static RHist *nd_psh;
+static int nd_psn,nd_pslen;
+static RHist *nd_red;
+static int *nd_work_vector;
+static int **nd_matrix;
+static int nd_matrix_len;
+static struct weight_or_block *nd_worb;
+static int nd_worb_len;
+static int nd_found,nd_create,nd_notfirst;
+static int nmv_adv;
+static int nd_demand;
+static int nd_module,nd_ispot,nd_mpos,nd_pot_nelim;
+static NODE nd_tracelist;
+static NODE nd_alltracelist;
+static int nd_gentrace,nd_gensyz,nd_nora,nd_newelim,nd_intersect;
+static int *nd_gbblock;
 
-#define REDTAB_LEN 32003
+NumberField get_numberfield();
+UINT *nd_det_compute_bound(NDV **dm,int n,int j);
+void nd_det_reconstruct(NDV **dm,int n,int j,NDV d);
+void nd_heu_nezgcdnpz(VL vl,P *pl,int m,int full,P *pr);
+int nd_monic(int m,ND *p);
+NDV plain_vect_to_ndv_q(Q *mat,int col,UINT *s0vect);
+LIST ndvtopl(int mod,VL vl,VL dvl,NDV p,int rank);
+NDV pltondv(VL vl,VL dvl,LIST p);
+void pltozpl(LIST l,Q *cont,LIST *pp);
+void ndl_max(UINT *d1,unsigned *d2,UINT *d);
+void nmtodp(int mod,NM m,DP *r);
+NODE reverse_node(NODE n);
+P ndc_div(int mod,union oNDC a,union oNDC b);
+P ndctop(int mod,union oNDC c);
+void finalize_tracelist(int i,P cont);
+void conv_ilist(int demand,int trace,NODE g,int **indp);
+void parse_nd_option(NODE opt);
+void dltondl(int n,DL dl,UINT *r);
+DP ndvtodp(int mod,NDV p);
 
-typedef struct oPGeoBucket {
-	int m;
-	struct oND *body[32];
-} *PGeoBucket;
+extern int Denominator,DP_Multiple;
 
-typedef struct oND {
-	struct oNM *body;
-	int nv;
-	int len;
-	int sugar;
-} *ND;
+void nd_free_private_storage()
+{
+    _nm_free_list = 0;
+    _ndp_free_list = 0;
+#if 0
+    GC_gcollect();
+#endif
+}
 
-typedef struct oNDV {
-	struct oNMV *body;
-	int nv;
-	int len;
-	int sugar;
-} *NDV;
+void _NM_alloc()
+{
+    NM p;
+    int i;
 
-typedef struct oNM {
-	struct oNM *next;
-	union {
-		int m;
-		Q z;
-	} c;
-	int td;
-	unsigned int dl[1];
-} *NM;
+    for ( i = 0; i < 1024; i++ ) {
+        p = (NM)MALLOC(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT));
+        p->next = _nm_free_list; _nm_free_list = p;
+    }
+}
 
-typedef struct oNMV {
-	union {
-		int m;
-		Q z;
-	} c;
-	int td;
-	unsigned int dl[1];
-} *NMV;
+void _ND_alloc()
+{
+    ND p;
+    int i;
 
-typedef struct oRHist {
-	struct oRHist *next;
-	int index;
-	int td,sugar;
-	unsigned int dl[1];
-} *RHist;
+    for ( i = 0; i < 1024; i++ ) {
+        p = (ND)MALLOC(sizeof(struct oND));
+        p->body = (NM)_nd_free_list; _nd_free_list = p;
+    }
+}
 
-typedef struct oND_pairs {
-	struct oND_pairs *next;
-	int i1,i2;
-	int td,sugar;
-	unsigned int lcm[1];
-} *ND_pairs;
+void _NDP_alloc()
+{
+    ND_pairs p;
+    int i;
 
-int (*nm_compare_generic)(NM a,NM b);
-int (*nmv_compare_generic)(NMV a,NMV b);
+    for ( i = 0; i < 1024; i++ ) {
+        p = (ND_pairs)MALLOC(sizeof(struct oND_pairs)
+            +(nd_wpd-1)*sizeof(UINT));
+        p->next = _ndp_free_list; _ndp_free_list = p;
+    }
+}
 
-double nd_scale=2;
-static unsigned int **nd_bound;
-int nd_nvar;
-int nd_isrlex;
-int nd_epw,nd_bpe,nd_wpd;
-unsigned int nd_mask[32];
-unsigned int nd_mask0,nd_mask1;
+INLINE int nd_length(ND p)
+{
+    NM m;
+    int i;
 
-NM _nm_free_list;
-ND _nd_free_list;
-ND_pairs _ndp_free_list;
+    if ( !p )
+        return 0;
+    else {
+        for ( i = 0, m = BDY(p); m; m = NEXT(m), i++ );
+        return i;
+    }
+}
 
-static NDV *nd_ps;
-static NDV *nd_psq;
-int *nd_psl;
-RHist *nd_psh;
-int nd_psn,nd_pslen;
+INLINE int ndl_reducible(UINT *d1,UINT *d2)
+{
+    UINT u1,u2;
+    int i,j;
 
-RHist *nd_red;
-int nd_red_len;
+    if ( nd_module && (MPOS(d1) != MPOS(d2)) ) return 0;
 
-int nd_found,nd_create,nd_notfirst;
-int nm_adv;
-int nmv_adv;
-int nd_degcompat;
+    if ( TD(d1) < TD(d2) ) return 0;
+#if USE_UNROLL
+    switch ( nd_bpe ) {
+        case 3:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i];
+                if ( (u1&0x38000000) < (u2&0x38000000) ) return 0;
+                if ( (u1& 0x7000000) < (u2& 0x7000000) ) return 0;
+                if ( (u1&  0xe00000) < (u2&  0xe00000) ) return 0;
+                if ( (u1&  0x1c0000) < (u2&  0x1c0000) ) return 0;
+                if ( (u1&   0x38000) < (u2&   0x38000) ) return 0;
+                if ( (u1&    0x7000) < (u2&    0x7000) ) return 0;
+                if ( (u1&     0xe00) < (u2&     0xe00) ) return 0;
+                if ( (u1&     0x1c0) < (u2&     0x1c0) ) return 0;
+                if ( (u1&      0x38) < (u2&      0x38) ) return 0;
+                if ( (u1&       0x7) < (u2&       0x7) ) return 0;
+            }
+            return 1;
+            break;
+        case 4:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i];
+                if ( (u1&0xf0000000) < (u2&0xf0000000) ) return 0;
+                if ( (u1& 0xf000000) < (u2& 0xf000000) ) return 0;
+                if ( (u1&  0xf00000) < (u2&  0xf00000) ) return 0;
+                if ( (u1&   0xf0000) < (u2&   0xf0000) ) return 0;
+                if ( (u1&    0xf000) < (u2&    0xf000) ) return 0;
+                if ( (u1&     0xf00) < (u2&     0xf00) ) return 0;
+                if ( (u1&      0xf0) < (u2&      0xf0) ) return 0;
+                if ( (u1&       0xf) < (u2&       0xf) ) return 0;
+            }
+            return 1;
+            break;
+        case 6:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i];
+                if ( (u1&0x3f000000) < (u2&0x3f000000) ) return 0;
+                if ( (u1&  0xfc0000) < (u2&  0xfc0000) ) return 0;
+                if ( (u1&   0x3f000) < (u2&   0x3f000) ) return 0;
+                if ( (u1&     0xfc0) < (u2&     0xfc0) ) return 0;
+                if ( (u1&      0x3f) < (u2&      0x3f) ) return 0;
+            }
+            return 1;
+            break;
+        case 8:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i];
+                if ( (u1&0xff000000) < (u2&0xff000000) ) return 0;
+                if ( (u1&  0xff0000) < (u2&  0xff0000) ) return 0;
+                if ( (u1&    0xff00) < (u2&    0xff00) ) return 0;
+                if ( (u1&      0xff) < (u2&      0xff) ) return 0;
+            }
+            return 1;
+            break;
+        case 16:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i];
+                if ( (u1&0xffff0000) < (u2&0xffff0000) ) return 0;
+                if ( (u1&    0xffff) < (u2&    0xffff) ) return 0;
+            }
+            return 1;
+            break;
+        case 32:
+            for ( i = nd_exporigin; i < nd_wpd; i++ )
+                if ( d1[i] < d2[i] ) return 0;
+            return 1;
+            break;
+        default:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i];
+                for ( j = 0; j < nd_epw; j++ )
+                    if ( (u1&nd_mask[j]) < (u2&nd_mask[j]) ) return 0;
+            }
+            return 1;
+    }
+#else
+    for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+        u1 = d1[i]; u2 = d2[i];
+        for ( j = 0; j < nd_epw; j++ )
+            if ( (u1&nd_mask[j]) < (u2&nd_mask[j]) ) return 0;
+    }
+    return 1;
+#endif
+}
 
-extern int Top,Reverse;
+/*
+ * If the current order is a block order,
+ * then the last block is length 1 and contains
+ * the homo variable. Otherwise, the original
+ * order is either 0 or 2.
+ */
 
-#define HTD(d) ((d)->body->td)
-#define HDL(d) ((d)->body->dl)
-#define HCM(d) ((d)->body->c.m)
-#define HCQ(d) ((d)->body->c.z)
-#define CM(a) ((a)->c.m)
-#define CQ(a) ((a)->c.z)
-#define DL(a) ((a)->dl)
-#define TD(a) ((a)->td)
-#define SG(a) ((a)->sugar)
-#define LEN(a) ((a)->len)
+void ndl_homogenize(UINT *d,UINT *r,int obpe,EPOS oepos,int ompos,int weight)
+{
+    int w,i,e,n,omask0;
 
-#define NM_COMPARE(m1,m2)\
-nd_degcompat?(TD(m1)>TD(m2)?1\
-                           :(TD(m1)<TD(m2)?-1:ndl_compare(DL(m1),DL(m2))))\
-            :(*nm_compare_generic)(m1,m2)
-#define NM_ADV(m) (m = (NM)(((char *)m)+nm_adv))
-#define NEWRHist(r) \
-((r)=(RHist)MALLOC(sizeof(struct oRHist)+(nd_wpd-1)*sizeof(unsigned int)))
-#define NEWND_pairs(m) if(!_ndp_free_list)_NDP_alloc(); (m)=_ndp_free_list; _ndp_free_list = NEXT(_ndp_free_list)   
-#define NEWNM(m) if(!_nm_free_list)_NM_alloc(); (m)=_nm_free_list; _nm_free_list = NEXT(_nm_free_list)   
-#define MKND(n,m,len,d) if(!_nd_free_list)_ND_alloc(); (d)=_nd_free_list; _nd_free_list = (ND)BDY(_nd_free_list); NV(d)=(n); LEN(d)=(len); BDY(d)=(m)
+    omask0 = obpe==32?0xffffffff:((1<<obpe)-1);
+    n = nd_nvar-1;
+    ndl_zero(r);
+    for ( i = 0; i < n; i++ ) {
+        e = GET_EXP_OLD(d,i);
+        PUT_EXP(r,i,e);
+    }
+    w = TD(d);
+    PUT_EXP(r,nd_nvar-1,weight-w);
+    if ( nd_module ) MPOS(r) = d[ompos];
+    TD(r) = weight;
+    if ( nd_blockmask ) ndl_weight_mask(r);
+}
 
-#define NEXTRHist(r,c) \
-if(!(r)){NEWRHist(r);(c)=(r);}else{NEWRHist(NEXT(c));(c)=NEXT(c);}
-#define NEXTNM(r,c) \
-if(!(r)){NEWNM(r);(c)=(r);}else{NEWNM(NEXT(c));(c)=NEXT(c);}
-#define NEXTNM2(r,c,s) \
-if(!(r)){(c)=(r)=(s);}else{NEXT(c)=(s);(c)=(s);}
-#define FREENM(m) NEXT(m)=_nm_free_list; _nm_free_list=(m)
-#define FREENDP(m) NEXT(m)=_ndp_free_list; _ndp_free_list=(m)
-#define FREEND(m) BDY(m)=(NM)_nd_free_list; _nd_free_list=(m)
+void ndl_dehomogenize(UINT *d)
+{
+    UINT mask;
+    UINT h;
+    int i,bits;
 
-#define NEXTND_pairs(r,c) \
-if(!(r)){NEWND_pairs(r);(c)=(r);}else{NEWND_pairs(NEXT(c));(c)=NEXT(c);}
+    if ( nd_blockmask ) {
+        h = GET_EXP(d,nd_nvar-1);
+        XOR_EXP(d,nd_nvar-1,h);
+        TD(d) -= h;
+        ndl_weight_mask(d);
+    } else {
+        if ( nd_isrlex ) {
+            if ( nd_bpe == 32 ) {
+                h = d[nd_exporigin];
+                for ( i = nd_exporigin+1; i < nd_wpd; i++ )
+                    d[i-1] = d[i];
+                d[i-1] = 0;
+                TD(d) -= h;
+            } else {
+                bits = nd_epw*nd_bpe;
+                mask = bits==32?0xffffffff:((1<<(nd_epw*nd_bpe))-1);
+                h = (d[nd_exporigin]>>((nd_epw-1)*nd_bpe))&nd_mask0;
+                for ( i = nd_exporigin; i < nd_wpd; i++ )
+                    d[i] = ((d[i]<<nd_bpe)&mask)
+                        |(i+1<nd_wpd?((d[i+1]>>((nd_epw-1)*nd_bpe))&nd_mask0):0);
+                TD(d) -= h;
+            }
+        } else {
+            h = GET_EXP(d,nd_nvar-1);
+            XOR_EXP(d,nd_nvar-1,h);
+            TD(d) -= h;
+        }
+    }
+}
 
-void nd_init_ord(struct order_spec *spec);
-int nd_check_candidate(NODE input,NODE cand);
-void nd_removecont(int mod,ND p);
-void nd_removecont2(ND p1,ND p2);
-void ndv_removecont(int mod,NDV p);
-void ndv_dehomogenize(NDV p);
-void ndv_mul_c_q(NDV p,Q mul);
-void nd_mul_c_q(ND p,Q mul);
-ND normalize_pbucket(int mod,PGeoBucket g);
-int head_pbucket(int mod,PGeoBucket g);
-int head_pbucket_q(PGeoBucket g);
-void add_pbucket(int mod,PGeoBucket g,ND d);
-void free_pbucket(PGeoBucket b);
-void mulq_pbucket(PGeoBucket g,Q c);
-PGeoBucket create_pbucket();
-ND nd_remove_head(ND p);
+void ndl_lcm(UINT *d1,unsigned *d2,UINT *d)
+{
+    UINT t1,t2,u,u1,u2;
+    int i,j,l;
 
-void GC_gcollect();
-NODE append_one(NODE,int);
-NODE nd_reducebase(NODE x);
+    if ( nd_module && (MPOS(d1) != MPOS(d2)) )
+        error("ndl_lcm : inconsistent monomials");
+#if USE_UNROLL
+    switch ( nd_bpe ) {
+        case 3:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i];
+                t1 = (u1&0x38000000); t2 = (u2&0x38000000); u = t1>t2?t1:t2;
+                t1 = (u1& 0x7000000); t2 = (u2& 0x7000000); u |= t1>t2?t1:t2;
+                t1 = (u1&  0xe00000); t2 = (u2&  0xe00000); u |= t1>t2?t1:t2;
+                t1 = (u1&  0x1c0000); t2 = (u2&  0x1c0000); u |= t1>t2?t1:t2;
+                t1 = (u1&   0x38000); t2 = (u2&   0x38000); u |= t1>t2?t1:t2;
+                t1 = (u1&    0x7000); t2 = (u2&    0x7000); u |= t1>t2?t1:t2;
+                t1 = (u1&     0xe00); t2 = (u2&     0xe00); u |= t1>t2?t1:t2;
+                t1 = (u1&     0x1c0); t2 = (u2&     0x1c0); u |= t1>t2?t1:t2;
+                t1 = (u1&      0x38); t2 = (u2&      0x38); u |= t1>t2?t1:t2;
+                t1 = (u1&       0x7); t2 = (u2&       0x7); u |= t1>t2?t1:t2;
+                d[i] = u;
+            }
+            break;
+        case 4:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i];
+                t1 = (u1&0xf0000000); t2 = (u2&0xf0000000); u = t1>t2?t1:t2;
+                t1 = (u1& 0xf000000); t2 = (u2& 0xf000000); u |= t1>t2?t1:t2;
+                t1 = (u1&  0xf00000); t2 = (u2&  0xf00000); u |= t1>t2?t1:t2;
+                t1 = (u1&   0xf0000); t2 = (u2&   0xf0000); u |= t1>t2?t1:t2;
+                t1 = (u1&    0xf000); t2 = (u2&    0xf000); u |= t1>t2?t1:t2;
+                t1 = (u1&     0xf00); t2 = (u2&     0xf00); u |= t1>t2?t1:t2;
+                t1 = (u1&      0xf0); t2 = (u2&      0xf0); u |= t1>t2?t1:t2;
+                t1 = (u1&       0xf); t2 = (u2&       0xf); u |= t1>t2?t1:t2;
+                d[i] = u;
+            }
+            break;
+        case 6:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i];
+                t1 = (u1&0x3f000000); t2 = (u2&0x3f000000); u = t1>t2?t1:t2;
+                t1 = (u1&  0xfc0000); t2 = (u2&  0xfc0000); u |= t1>t2?t1:t2;
+                t1 = (u1&   0x3f000); t2 = (u2&   0x3f000); u |= t1>t2?t1:t2;
+                t1 = (u1&     0xfc0); t2 = (u2&     0xfc0); u |= t1>t2?t1:t2;
+                t1 = (u1&      0x3f); t2 = (u2&      0x3f); u |= t1>t2?t1:t2;
+                d[i] = u;
+            }
+            break;
+        case 8:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i];
+                t1 = (u1&0xff000000); t2 = (u2&0xff000000); u = t1>t2?t1:t2;
+                t1 = (u1&  0xff0000); t2 = (u2&  0xff0000); u |= t1>t2?t1:t2;
+                t1 = (u1&    0xff00); t2 = (u2&    0xff00); u |= t1>t2?t1:t2;
+                t1 = (u1&      0xff); t2 = (u2&      0xff); u |= t1>t2?t1:t2;
+                d[i] = u;
+            }
+            break;
+        case 16:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i];
+                t1 = (u1&0xffff0000); t2 = (u2&0xffff0000); u = t1>t2?t1:t2;
+                t1 = (u1&    0xffff); t2 = (u2&    0xffff); u |= t1>t2?t1:t2;
+                d[i] = u;
+            }
+            break;
+        case 32:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i]; 
+                d[i] = u1>u2?u1:u2;
+            }
+            break;
+        default:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i]; 
+                for ( j = 0, u = 0; j < nd_epw; j++ ) {
+                    t1 = (u1&nd_mask[j]); t2 = (u2&nd_mask[j]); u |= t1>t2?t1:t2;
+                }
+                d[i] = u;
+            }
+            break;
+    }
+#else
+    for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+        u1 = d1[i]; u2 = d2[i]; 
+        for ( j = 0, u = 0; j < nd_epw; j++ ) {
+            t1 = (u1&nd_mask[j]); t2 = (u2&nd_mask[j]); u |= t1>t2?t1:t2;
+        }
+        d[i] = u;
+    }
+#endif
+    if ( nd_module ) MPOS(d) = MPOS(d1);
+    TD(d) = ndl_weight(d);
+    if ( nd_blockmask ) ndl_weight_mask(d);
+}
 
-void removecont_array(Q *c,int n);
-ND_pairs crit_B( ND_pairs d, int s );
-void nd_gr(LIST f,LIST v,int m,struct order_spec *ord,LIST *rp);
-void nd_gr_trace(LIST f,LIST v,int m,int homo,struct order_spec *ord,LIST *rp);
-void nd_setup(int mod,NODE f);
-void nd_setup_trace(int mod,NODE f);
-int nd_newps(int mod,ND a);
-int nd_newps_trace(int mod,ND nf,ND nfq);
-ND_pairs nd_minp( ND_pairs d, ND_pairs *prest );
-NODE update_base(NODE nd,int ndp);
-static ND_pairs equivalent_pairs( ND_pairs d1, ND_pairs *prest );
-int crit_2( int dp1, int dp2 );
-ND_pairs crit_F( ND_pairs d1 );
-ND_pairs crit_M( ND_pairs d1 );
-ND_pairs nd_newpairs( NODE g, int t );
-ND_pairs update_pairs( ND_pairs d, NODE /* of index */ g, int t);
-NODE nd_gb(int m,int checkonly);
-NODE nd_gb_trace(int m);
-void nd_free_private_storage();
-void _NM_alloc();
-void _ND_alloc();
-int ndl_td(unsigned int *d);
-int ndl_dehomogenize(unsigned int *p);
-ND nd_add(int mod,ND p1,ND p2);
-ND nd_add_q(ND p1,ND p2);
-ND nd_mul_nm(int mod,ND p,NM m0);
-ND nd_mul_ind_nm(int mod,int index,NM m0);
-int nd_sp(int mod,ND_pairs p,ND *nf);
-int nd_find_reducer(ND g);
-int nd_find_reducer_direct(ND g,NDV *ps,int len);
-int nd_nf(int mod,ND g,int full,ND *nf);
-int nd_nf_pbucket(int mod,ND g,int full,ND *nf);
-int nd_nf_direct(int mod,ND g,NDV *ps,int len,int full,ND *rp);
-int nd_nf_direct_pbucket(int mod,ND g,NDV *ps,int len,int full,ND *rp);
-ND nd_reduce(ND p1,ND p2);
-ND nd_reduce_special(ND p1,ND p2);
-NODE nd_reduceall(int m,NODE f);
-int nd_gbcheck(int m,NODE f);
-int nd_membercheck(int m,NODE f);
-void nd_free(ND p);
-void ndv_free(NDV p);
-void ndl_print(unsigned int *dl);
-void nd_print(ND p);
-void nd_print_q(ND p);
-void ndv_print(NDV p);
-void ndv_print_q(NDV p);
-void ndp_print(ND_pairs d);
-int nd_length(ND p);
-void nd_mul_c(int mod,ND p,int mul);
-void nd_free_redlist();
-void nd_append_red(unsigned int *d,int td,int i);
-unsigned int *nd_compute_bound(ND p);
-unsigned int *dp_compute_bound(DP p);
-ND_pairs nd_reconstruct(int mod,int trace,ND_pairs ndp);
-void nd_reconstruct_direct(int mod,NDV *ps,int len);
-void nd_setup_parameters();
-void nd_realloc(ND p,int obpe);
-ND nd_copy(ND p);
-void ndl_dup(int obpe,unsigned int *d,unsigned int *r);
+void ndl_max(UINT *d1,unsigned *d2,UINT *d)
+{
+    UINT t1,t2,u,u1,u2;
+    int i,j,l;
 
-#define NMV_ADV(m) (m = (NMV)(((char *)m)+nmv_adv))
-#define NEWNDV(d) ((d)=(NDV)MALLOC(sizeof(struct oNDV)))
-#define MKNDV(n,m,l,d) NEWNDV(d); NV(d)=(n); BDY(d)=(m); LEN(d) = l;
-void ndv_mul_c(int mod,NDV p,int mul);
-NDV ndtondv(int mod,ND p);
-ND ndvtond(int mod,NDV p);
-ND ndv_mul_nm(int mod,NDV p,NM m0);
-void ndv_realloc(NDV p,int obpe,int oadv);
-NDV dptondv(int,DP);
-DP ndvtodp(int,NDV);
-ND dptond(int,DP);
-DP ndtodp(int,ND);
+    for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+        u1 = d1[i]; u2 = d2[i]; 
+        for ( j = 0, u = 0; j < nd_epw; j++ ) {
+            t1 = (u1&nd_mask[j]); t2 = (u2&nd_mask[j]); u |= t1>t2?t1:t2;
+        }
+        d[i] = u;
+    }
+}
 
-void nd_free_private_storage()
+int ndl_weight(UINT *d)
 {
-	_nd_free_list = 0;
-	_nm_free_list = 0;
-	_ndp_free_list = 0;
-	bzero(nd_red,sizeof(REDTAB_LEN*sizeof(RHist)));
-	GC_gcollect();
+    UINT t,u;
+    int i,j;
+
+    if ( current_dl_weight_vector )
+        for ( i = 0, t = 0; i < nd_nvar; i++ ) {
+            u = GET_EXP(d,i);
+            t += MUL_WEIGHT(u,i);
+        }
+    else
+        for ( t = 0, i = nd_exporigin; i < nd_wpd; i++ ) {
+            u = d[i];
+            for ( j = 0; j < nd_epw; j++, u>>=nd_bpe )
+                t += (u&nd_mask0); 
+        }
+    if ( nd_module && current_module_weight_vector && MPOS(d) )
+        t += current_module_weight_vector[MPOS(d)];
+    return t;
 }
 
-void _NM_alloc()
+void ndl_weight_mask(UINT *d)
 {
-	NM p;
-	int i;
+    UINT t,u;
+    UINT *mask;
+    int i,j,k,l;
 
-	for ( i = 0; i < 1024; i++ ) {
-		p = (NM)GC_malloc(sizeof(struct oNM)+(nd_wpd-1)*sizeof(unsigned int));
-		p->next = _nm_free_list; _nm_free_list = p;
-	}
+    l = nd_blockmask->n;
+    for ( k = 0; k < l; k++ ) {
+        mask = nd_blockmask->mask[k];
+        if ( current_dl_weight_vector )
+            for ( i = 0, t = 0; i < nd_nvar; i++ ) {
+                u = GET_EXP_MASK(d,i,mask);
+                t += MUL_WEIGHT(u,i);
+            }
+        else
+            for ( t = 0, i = nd_exporigin; i < nd_wpd; i++ ) {
+                u = d[i]&mask[i];
+                for ( j = 0; j < nd_epw; j++, u>>=nd_bpe )
+                    t += (u&nd_mask0); 
+            }
+        d[k+1] = t;
+    }
 }
 
-void _ND_alloc()
+int ndl_lex_compare(UINT *d1,UINT *d2)
 {
-	ND p;
-	int i;
+    int i;
 
-	for ( i = 0; i < 1024; i++ ) {
-		p = (ND)GC_malloc(sizeof(struct oND));
-		p->body = (NM)_nd_free_list; _nd_free_list = p;
-	}
+    d1 += nd_exporigin;
+    d2 += nd_exporigin;
+    for ( i = nd_exporigin; i < nd_wpd; i++, d1++, d2++ )
+        if ( *d1 > *d2 )
+            return nd_isrlex ? -1 : 1;
+        else if ( *d1 < *d2 )
+            return nd_isrlex ? 1 : -1;
+    return 0;
 }
 
-void _NDP_alloc()
+int ndl_block_compare(UINT *d1,UINT *d2)
 {
-	ND_pairs p;
-	int i;
+    int i,l,j,ord_o,ord_l;
+    struct order_pair *op;
+    UINT t1,t2,m;
+    UINT *mask;
 
-	for ( i = 0; i < 1024; i++ ) {
-		p = (ND_pairs)GC_malloc(sizeof(struct oND_pairs)
-			+(nd_wpd-1)*sizeof(unsigned int));
-		p->next = _ndp_free_list; _ndp_free_list = p;
-	}
+    l = nd_blockmask->n;
+    op = nd_blockmask->order_pair; 
+    for ( j = 0; j < l; j++ ) {
+        mask = nd_blockmask->mask[j];
+        ord_o = op[j].order;
+        if ( ord_o < 2 )
+            if ( (t1=d1[j+1]) > (t2=d2[j+1]) ) return 1;
+            else if ( t1 < t2 ) return -1;
+        for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+            m = mask[i];
+            t1 = d1[i]&m;
+            t2 = d2[i]&m;
+            if ( t1 > t2 )
+                return !ord_o ? -1 : 1;
+            else if ( t1 < t2 )
+                return !ord_o ? 1 : -1;
+        }
+    }
+    return 0;
 }
 
-INLINE int nd_length(ND p)
+int ndl_matrix_compare(UINT *d1,UINT *d2)
 {
-	NM m;
-	int i;
+    int i,j,s;
+    int *v;
 
-	if ( !p )
-		return 0;
-	else {
-		for ( i = 0, m = BDY(p); m; m = NEXT(m), i++ );
-		return i;
-	}
+    for ( j = 0; j < nd_nvar; j++ )
+        nd_work_vector[j] = GET_EXP(d1,j)-GET_EXP(d2,j);
+    for ( i = 0; i < nd_matrix_len; i++ ) {
+        v = nd_matrix[i];
+        for ( j = 0, s = 0; j < nd_nvar; j++ )
+            s += v[j]*nd_work_vector[j];
+        if ( s > 0 ) return 1;
+        else if ( s < 0 ) return -1;
+    }
+    return 0;
 }
 
-INLINE int ndl_reducible(unsigned int *d1,unsigned int *d2)
+int ndl_composite_compare(UINT *d1,UINT *d2)
 {
-	unsigned int u1,u2;
-	int i,j;
+    int i,j,s,start,end,len,o;
+    int *v;
+    struct sparse_weight *sw;
 
-	switch ( nd_bpe ) {
-		case 4:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				if ( (u1&0xf0000000) < (u2&0xf0000000) ) return 0;
-				if ( (u1&0xf000000) < (u2&0xf000000) ) return 0;
-				if ( (u1&0xf00000) < (u2&0xf00000) ) return 0;
-				if ( (u1&0xf0000) < (u2&0xf0000) ) return 0;
-				if ( (u1&0xf000) < (u2&0xf000) ) return 0;
-				if ( (u1&0xf00) < (u2&0xf00) ) return 0;
-				if ( (u1&0xf0) < (u2&0xf0) ) return 0;
-				if ( (u1&0xf) < (u2&0xf) ) return 0;
-			}
-			return 1;
-			break;
-		case 6:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				if ( (u1&0x3f000000) < (u2&0x3f000000) ) return 0;
-				if ( (u1&0xfc0000) < (u2&0xfc0000) ) return 0;
-				if ( (u1&0x3f000) < (u2&0x3f000) ) return 0;
-				if ( (u1&0xfc0) < (u2&0xfc0) ) return 0;
-				if ( (u1&0x3f) < (u2&0x3f) ) return 0;
-			}
-			return 1;
-			break;
-		case 8:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				if ( (u1&0xff000000) < (u2&0xff000000) ) return 0;
-				if ( (u1&0xff0000) < (u2&0xff0000) ) return 0;
-				if ( (u1&0xff00) < (u2&0xff00) ) return 0;
-				if ( (u1&0xff) < (u2&0xff) ) return 0;
-			}
-			return 1;
-			break;
-		case 16:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				if ( (u1&0xffff0000) < (u2&0xffff0000) ) return 0;
-				if ( (u1&0xffff) < (u2&0xffff) ) return 0;
-			}
-			return 1;
-			break;
-		case 32:
-			for ( i = 0; i < nd_wpd; i++ )
-				if ( d1[i] < d2[i] ) return 0;
-			return 1;
-			break;
-		default:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				for ( j = 0; j < nd_epw; j++ )
-					if ( (u1&nd_mask[j]) < (u2&nd_mask[j]) ) return 0;
-			}
-			return 1;
-	}
+    for ( j = 0; j < nd_nvar; j++ )
+        nd_work_vector[j] = GET_EXP(d1,j)-GET_EXP(d2,j);
+    for ( i = 0; i < nd_worb_len; i++ ) {
+        len = nd_worb[i].length;
+        switch ( nd_worb[i].type ) {
+            case IS_DENSE_WEIGHT:
+                v = nd_worb[i].body.dense_weight;
+                for ( j = 0, s = 0; j < len; j++ )
+                    s += v[j]*nd_work_vector[j];
+                if ( s > 0 ) return 1;
+                else if ( s < 0 ) return -1;
+                break;
+            case IS_SPARSE_WEIGHT:
+                sw = nd_worb[i].body.sparse_weight;
+                for ( j = 0, s = 0; j < len; j++ )
+                    s += sw[j].value*nd_work_vector[sw[j].pos];
+                if ( s > 0 ) return 1;
+                else if ( s < 0 ) return -1;
+                break;
+            case IS_BLOCK:
+                o = nd_worb[i].body.block.order;
+                start = nd_worb[i].body.block.start;
+                switch ( o ) {
+                    case 0:
+                        end = start+len;
+                        for ( j = start, s = 0; j < end; j++ )
+                            s += MUL_WEIGHT(nd_work_vector[j],j);
+                        if ( s > 0 ) return 1;
+                        else if ( s < 0 ) return -1;
+                        for ( j = end-1; j >= start; j-- )
+                            if ( nd_work_vector[j] < 0 ) return 1;
+                            else if ( nd_work_vector[j] > 0 ) return -1;
+                        break;
+                    case 1:
+                        end = start+len;
+                        for ( j = start, s = 0; j < end; j++ )
+                            s += MUL_WEIGHT(nd_work_vector[j],j);
+                        if ( s > 0 ) return 1;
+                        else if ( s < 0 ) return -1;
+                        for ( j = start; j < end; j++ )
+                            if ( nd_work_vector[j] > 0 ) return 1;
+                            else if ( nd_work_vector[j] < 0 ) return -1;
+                        break;
+                    case 2:
+                        for ( j = start; j < end; j++ )
+                            if ( nd_work_vector[j] > 0 ) return 1;
+                            else if ( nd_work_vector[j] < 0 ) return -1;
+                        break;
+                }
+                break;
+        }
+    }
+    return 0;
 }
 
-/* returns the exponent of homo variable */
+/* TDH -> WW -> TD-> RL */
 
-int ndl_dehomogenize(unsigned int *d)
+int ndl_ww_lex_compare(UINT *d1,UINT *d2)
 {
-	unsigned int mask;
-	unsigned int h;
-	int i,bits;
+    int i,m,e1,e2;
 
-	if ( nd_isrlex ) {
-		if ( nd_bpe == 32 ) {
-			h = d[0];
-			for ( i = 1; i < nd_wpd; i++ )
-				d[i-1] = d[i];
-			d[i-1] = 0;
-			return h;
-		} else {
-			bits = nd_epw*nd_bpe;
-			mask = bits==32?0xffffffff:((1<<(nd_epw*nd_bpe))-1);
-			h = (d[0]>>((nd_epw-1)*nd_bpe))&nd_mask0;
-			for ( i = 0; i < nd_wpd; i++ )
-				d[i] = ((d[i]<<nd_bpe)&mask)
-					|(i+1<nd_wpd?((d[i+1]>>((nd_epw-1)*nd_bpe))&nd_mask0):0);
-			return h;
+    if ( TD(d1) > TD(d2) ) return 1;
+    else if ( TD(d1) < TD(d2) ) return -1;
+    m = nd_nvar>>1;
+    for ( i = 0, e1 = e2 = 0; i < m; i++ ) {
+        e1 += current_weyl_weight_vector[i]*(GET_EXP(d1,m+i)-GET_EXP(d1,i));
+        e2 += current_weyl_weight_vector[i]*(GET_EXP(d2,m+i)-GET_EXP(d2,i));
+    }
+    if ( e1 > e2 ) return 1;
+    else if ( e1 < e2 ) return -1;
+    return ndl_lex_compare(d1,d2);
+}
+
+int ndl_module_grlex_compare(UINT *d1,UINT *d2)
+{
+    int i,c;
+
+    if ( nd_ispot ) {
+		if ( nd_pot_nelim && MPOS(d1)>=nd_pot_nelim+1 && MPOS(d2) >= nd_pot_nelim+1 ) {
+            if ( TD(d1) > TD(d2) ) return 1;
+            else if ( TD(d1) < TD(d2) ) return -1;
+            if ( c = ndl_lex_compare(d1,d2) ) return c;
+            if ( MPOS(d1) < MPOS(d2) ) return 1;
+            else if ( MPOS(d1) > MPOS(d2) ) return -1;
+            return 0;
 		}
-	} else {
-		/* do nothing */
-		return d[nd_wpd-1];
-	}
+        if ( MPOS(d1) < MPOS(d2) ) return 1;
+        else if ( MPOS(d1) > MPOS(d2) ) return -1;
+    }
+    if ( TD(d1) > TD(d2) ) return 1;
+    else if ( TD(d1) < TD(d2) ) return -1;
+    if ( c = ndl_lex_compare(d1,d2) ) return c;
+    if ( !nd_ispot ) {
+        if ( MPOS(d1) < MPOS(d2) ) return 1;
+        else if ( MPOS(d1) > MPOS(d2) ) return -1;
+    }
+    return 0;
 }
 
-void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned int *d)
+int ndl_module_glex_compare(UINT *d1,UINT *d2)
 {
-	unsigned int t1,t2,u,u1,u2;
-	int i,j;
+    int i,c;
 
-	switch ( nd_bpe ) {
-		case 4:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				t1 = (u1&0xf0000000); t2 = (u2&0xf0000000); u = t1>t2?t1:t2;
-				t1 = (u1&0xf000000); t2 = (u2&0xf000000); u |= t1>t2?t1:t2;
-				t1 = (u1&0xf00000); t2 = (u2&0xf00000); u |= t1>t2?t1:t2;
-				t1 = (u1&0xf0000); t2 = (u2&0xf0000); u |= t1>t2?t1:t2;
-				t1 = (u1&0xf000); t2 = (u2&0xf000); u |= t1>t2?t1:t2;
-				t1 = (u1&0xf00); t2 = (u2&0xf00); u |= t1>t2?t1:t2;
-				t1 = (u1&0xf0); t2 = (u2&0xf0); u |= t1>t2?t1:t2;
-				t1 = (u1&0xf); t2 = (u2&0xf); u |= t1>t2?t1:t2;
-				d[i] = u;
-			}
-			break;
-		case 6:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				t1 = (u1&0x3f000000); t2 = (u2&0x3f000000); u = t1>t2?t1:t2;
-				t1 = (u1&0xfc0000); t2 = (u2&0xfc0000); u |= t1>t2?t1:t2;
-				t1 = (u1&0x3f000); t2 = (u2&0x3f000); u |= t1>t2?t1:t2;
-				t1 = (u1&0xfc0); t2 = (u2&0xfc0); u |= t1>t2?t1:t2;
-				t1 = (u1&0x3f); t2 = (u2&0x3f); u |= t1>t2?t1:t2;
-				d[i] = u;
-			}
-			break;
-		case 8:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				t1 = (u1&0xff000000); t2 = (u2&0xff000000); u = t1>t2?t1:t2;
-				t1 = (u1&0xff0000); t2 = (u2&0xff0000); u |= t1>t2?t1:t2;
-				t1 = (u1&0xff00); t2 = (u2&0xff00); u |= t1>t2?t1:t2;
-				t1 = (u1&0xff); t2 = (u2&0xff); u |= t1>t2?t1:t2;
-				d[i] = u;
-			}
-			break;
-		case 16:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				t1 = (u1&0xffff0000); t2 = (u2&0xffff0000); u = t1>t2?t1:t2;
-				t1 = (u1&0xffff); t2 = (u2&0xffff); u |= t1>t2?t1:t2;
-				d[i] = u;
-			}
-			break;
-		case 32:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i]; 
-				d[i] = u1>u2?u1:u2;
-			}
-			break;
-		default:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i]; 
-				for ( j = 0, u = 0; j < nd_epw; j++ ) {
-					t1 = (u1&nd_mask[j]); t2 = (u2&nd_mask[j]); u |= t1>t2?t1:t2;
-				}
-				d[i] = u;
-			}
-			break;
-	}
+    if ( nd_ispot ) {
+        if ( MPOS(d1) < MPOS(d2) ) return 1;
+        else if ( MPOS(d1) > MPOS(d2) ) return -1;
+    }
+    if ( TD(d1) > TD(d2) ) return 1;
+    else if ( TD(d1) < TD(d2) ) return -1;
+    if ( c = ndl_lex_compare(d1,d2) ) return c;
+    if ( !nd_ispot ) {
+        if ( MPOS(d1) < MPOS(d2) ) return 1;
+        else if ( MPOS(d1) > MPOS(d2) ) return -1;
+    }
+    return 0;
 }
 
-int ndl_td(unsigned int *d)
+int ndl_module_lex_compare(UINT *d1,UINT *d2)
 {
-	unsigned int t,u;
-	int i,j;
+    int i,c;
 
-	for ( t = 0, i = 0; i < nd_wpd; i++ ) {
-		u = d[i];
-		for ( j = 0; j < nd_epw; j++, u>>=nd_bpe )
-			t += (u&nd_mask0); 
-	}
-	return t;
+    if ( nd_ispot ) {
+        if ( MPOS(d1) < MPOS(d2) ) return 1;
+        else if ( MPOS(d1) > MPOS(d2) ) return -1;
+    }
+    if ( c = ndl_lex_compare(d1,d2) ) return c;
+    if ( !nd_ispot ) {
+        if ( MPOS(d1) < MPOS(d2) ) return 1;
+        else if ( MPOS(d1) > MPOS(d2) ) return -1;
+    }
+    return 0;
 }
 
-INLINE int ndl_compare(unsigned int *d1,unsigned int *d2)
+int ndl_module_block_compare(UINT *d1,UINT *d2)
 {
-	int i;
+    int i,c;
 
-	for ( i = 0; i < nd_wpd; i++, d1++, d2++ )
-		if ( *d1 > *d2 )
-			return nd_isrlex ? -1 : 1;
-		else if ( *d1 < *d2 )
-			return nd_isrlex ? 1 : -1;
-	return 0;
+    if ( nd_ispot ) {
+        if ( MPOS(d1) < MPOS(d2) ) return 1;
+        else if ( MPOS(d1) > MPOS(d2) ) return -1;
+    }
+    if ( c = ndl_block_compare(d1,d2) ) return c;
+    if ( !nd_ispot ) {
+        if ( MPOS(d1) < MPOS(d2) ) return 1;
+        else if ( MPOS(d1) > MPOS(d2) ) return -1;
+    }
+    return 0;
 }
 
-INLINE int ndl_equal(unsigned int *d1,unsigned int *d2)
+int ndl_module_matrix_compare(UINT *d1,UINT *d2)
 {
-	int i;
+    int i,c;
 
-	for ( i = 0; i < nd_wpd; i++ )
-		if ( d1[i] != d2[i] )
-			return 0;
-	return 1;
+    if ( nd_ispot ) {
+        if ( MPOS(d1) < MPOS(d2) ) return 1;
+        else if ( MPOS(d1) > MPOS(d2) ) return -1;
+    }
+    if ( c = ndl_matrix_compare(d1,d2) ) return c;
+    if ( !nd_ispot ) {
+        if ( MPOS(d1) < MPOS(d2) ) return 1;
+        else if ( MPOS(d1) > MPOS(d2) ) return -1;
+    }
+    return 0;
 }
 
-INLINE void ndl_copy(unsigned int *d1,unsigned int *d2)
+int ndl_module_composite_compare(UINT *d1,UINT *d2)
 {
-	int i;
+    int i,c;
 
-	switch ( nd_wpd ) {
-		case 1:
-			d2[0] = d1[0];
-			break;
-		case 2:
-			d2[0] = d1[0];
-			d2[1] = d1[1];
-			break;
-		default:
-			for ( i = 0; i < nd_wpd; i++ )
-				d2[i] = d1[i];
-			break;
-	}
+    if ( nd_ispot ) {
+        if ( MPOS(d1) > MPOS(d2) ) return 1;
+        else if ( MPOS(d1) < MPOS(d2) ) return -1;
+    }
+    if ( c = ndl_composite_compare(d1,d2) ) return c;
+    if ( !nd_ispot ) {
+        if ( MPOS(d1) > MPOS(d2) ) return 1;
+        else if ( MPOS(d1) < MPOS(d2) ) return -1;
+    }
+    return 0;
 }
 
-INLINE void ndl_add(unsigned int *d1,unsigned int *d2,unsigned int *d)
+INLINE int ndl_equal(UINT *d1,UINT *d2)
 {
-	int i;
+    int i;
 
-	switch ( nd_wpd ) {
-		case 1:
-			d[0] = d1[0]+d2[0];
-			break;
-		case 2:
-			d[0] = d1[0]+d2[0];
-			d[1] = d1[1]+d2[1];
-			break;
-		default:
-			for ( i = 0; i < nd_wpd; i++ )
-				d[i] = d1[i]+d2[i];
-			break;
-	}
+    switch ( nd_wpd ) {
+        case 2:
+            if ( TD(d2) != TD(d1) ) return 0;
+            if ( d2[1] != d1[1] ) return 0;
+            return 1;
+            break;
+        case 3:
+            if ( TD(d2) != TD(d1) ) return 0;
+            if ( d2[1] != d1[1] ) return 0;
+            if ( d2[2] != d1[2] ) return 0;
+            return 1;
+            break;
+        default:
+            for ( i = 0; i < nd_wpd; i++ )
+                if ( *d1++ != *d2++ ) return 0;
+            return 1;
+            break;
+    }
 }
 
-INLINE void ndl_add2(unsigned int *d1,unsigned int *d2)
+INLINE void ndl_copy(UINT *d1,UINT *d2)
 {
-	int i;
+    int i;
 
-	switch ( nd_wpd ) {
-		case 1:
-			d2[0] += d1[0];
-			break;
-		case 2:
-			d2[0] += d1[0];
-			d2[1] += d1[1];
-			break;
-		default:
-			for ( i = 0; i < nd_wpd; i++ )
-				d2[i] += d1[i];
-			break;
-	}
+    switch ( nd_wpd ) {
+        case 2:
+            TD(d2) = TD(d1);
+            d2[1] = d1[1];
+            break;
+        case 3:
+            TD(d2) = TD(d1);
+            d2[1] = d1[1];
+            d2[2] = d1[2];
+            break;
+        default:
+            for ( i = 0; i < nd_wpd; i++ )
+                d2[i] = d1[i];
+            break;
+    }
 }
 
-void ndl_sub(unsigned int *d1,unsigned int *d2,unsigned int *d)
+INLINE void ndl_zero(UINT *d)
 {
-	int i;
+    int i;
+    for ( i = 0; i < nd_wpd; i++ ) d[i] = 0;
+}
 
-	for ( i = 0; i < nd_wpd; i++ )
-		d[i] = d1[i]-d2[i];
+INLINE void ndl_add(UINT *d1,UINT *d2,UINT *d)
+{
+    int i;
+
+    if ( nd_module ) {
+        if ( MPOS(d1) && MPOS(d2) && (MPOS(d1) != MPOS(d2)) ) 
+        error("ndl_add : invalid operation");
+    }
+#if 1
+    switch ( nd_wpd ) {
+        case 2:
+            TD(d) = TD(d1)+TD(d2);
+            d[1] = d1[1]+d2[1];
+            break;
+        case 3:
+            TD(d) = TD(d1)+TD(d2);
+            d[1] = d1[1]+d2[1];
+            d[2] = d1[2]+d2[2];
+            break;
+        default:
+            for ( i = 0; i < nd_wpd; i++ ) d[i] = d1[i]+d2[i];
+            break;
+    }
+#else
+    for ( i = 0; i < nd_wpd; i++ ) d[i] = d1[i]+d2[i];
+#endif
 }
 
-int ndl_disjoint(unsigned int *d1,unsigned int *d2)
+/* d1 += d2 */
+INLINE void ndl_addto(UINT *d1,UINT *d2)
 {
-	unsigned int t1,t2,u,u1,u2;
-	int i,j;
+    int i;
 
-	switch ( nd_bpe ) {
-		case 4:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				t1 = u1&0xf0000000; t2 = u2&0xf0000000; if ( t1&&t2 ) return 0;
-				t1 = u1&0xf000000; t2 = u2&0xf000000; if ( t1&&t2 ) return 0;
-				t1 = u1&0xf00000; t2 = u2&0xf00000; if ( t1&&t2 ) return 0;
-				t1 = u1&0xf0000; t2 = u2&0xf0000; if ( t1&&t2 ) return 0;
-				t1 = u1&0xf000; t2 = u2&0xf000; if ( t1&&t2 ) return 0;
-				t1 = u1&0xf00; t2 = u2&0xf00; if ( t1&&t2 ) return 0;
-				t1 = u1&0xf0; t2 = u2&0xf0; if ( t1&&t2 ) return 0;
-				t1 = u1&0xf; t2 = u2&0xf; if ( t1&&t2 ) return 0;
-			}
-			return 1;
-			break;
-		case 6:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				t1 = u1&0x3f000000; t2 = u2&0x3f000000; if ( t1&&t2 ) return 0;
-				t1 = u1&0xfc0000; t2 = u2&0xfc0000; if ( t1&&t2 ) return 0;
-				t1 = u1&0x3f000; t2 = u2&0x3f000; if ( t1&&t2 ) return 0;
-				t1 = u1&0xfc0; t2 = u2&0xfc0; if ( t1&&t2 ) return 0;
-				t1 = u1&0x3f; t2 = u2&0x3f; if ( t1&&t2 ) return 0;
-			}
-			return 1;
-			break;
-		case 8:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				t1 = u1&0xff000000; t2 = u2&0xff000000; if ( t1&&t2 ) return 0;
-				t1 = u1&0xff0000; t2 = u2&0xff0000; if ( t1&&t2 ) return 0;
-				t1 = u1&0xff00; t2 = u2&0xff00; if ( t1&&t2 ) return 0;
-				t1 = u1&0xff; t2 = u2&0xff; if ( t1&&t2 ) return 0;
-			}
-			return 1;
-			break;
-		case 16:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				t1 = u1&0xffff0000; t2 = u2&0xffff0000; if ( t1&&t2 ) return 0;
-				t1 = u1&0xffff; t2 = u2&0xffff; if ( t1&&t2 ) return 0;
-			}
-			return 1;
-			break;
-		case 32:
-			for ( i = 0; i < nd_wpd; i++ )
-				if ( d1[i] && d2[i] ) return 0;
-			return 1;
-			break;
-		default:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				for ( j = 0; j < nd_epw; j++ ) {
-					if ( (u1&nd_mask0) && (u2&nd_mask0) ) return 0;
-					u1 >>= nd_bpe; u2 >>= nd_bpe;
-				}
-			}
-			return 1;
-			break;
-	}
+    if ( nd_module ) {
+        if ( MPOS(d1) && MPOS(d2) && (MPOS(d1) != MPOS(d2)) ) 
+            error("ndl_addto : invalid operation");
+    }
+#if 1
+    switch ( nd_wpd ) {
+        case 2:
+            TD(d1) += TD(d2);
+            d1[1] += d2[1];
+            break;
+        case 3:
+            TD(d1) += TD(d2);
+            d1[1] += d2[1];
+            d1[2] += d2[2];
+            break;
+        default:
+            for ( i = 0; i < nd_wpd; i++ ) d1[i] += d2[i];
+            break;
+    }
+#else
+    for ( i = 0; i < nd_wpd; i++ ) d1[i] += d2[i];
+#endif
 }
 
-int ndl_check_bound2(int index,unsigned int *d2)
+INLINE void ndl_sub(UINT *d1,UINT *d2,UINT *d)
 {
-	unsigned int u2;
-	unsigned int *d1;
-	int i,j,ind,k;
+    int i;
 
-	d1 = nd_bound[index];
-	ind = 0;
-	switch ( nd_bpe ) {
-		case 4:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u2 = d2[i];
-				if ( d1[ind++]+((u2>>28)&0xf) >= 0x10 ) return 1;
-				if ( d1[ind++]+((u2>>24)&0xf) >= 0x10 ) return 1;
-				if ( d1[ind++]+((u2>>20)&0xf) >= 0x10 ) return 1;
-				if ( d1[ind++]+((u2>>16)&0xf) >= 0x10 ) return 1;
-				if ( d1[ind++]+((u2>>12)&0xf) >= 0x10 ) return 1;
-				if ( d1[ind++]+((u2>>8)&0xf) >= 0x10 ) return 1;
-				if ( d1[ind++]+((u2>>4)&0xf) >= 0x10 ) return 1;
-				if ( d1[ind++]+(u2&0xf) >= 0x10 ) return 1;
-			}
-			return 0;
-			break;
-		case 6:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u2 = d2[i];
-				if ( d1[ind++]+((u2>>24)&0x3f) >= 0x40 ) return 1;
-				if ( d1[ind++]+((u2>>18)&0x3f) >= 0x40 ) return 1;
-				if ( d1[ind++]+((u2>>12)&0x3f) >= 0x40 ) return 1;
-				if ( d1[ind++]+((u2>>6)&0x3f) >= 0x40 ) return 1;
-				if ( d1[ind++]+(u2&0x3f) >= 0x40 ) return 1;
-			}
-			return 0;
-			break;
-		case 8:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u2 = d2[i];
-				if ( d1[ind++]+((u2>>24)&0xff) >= 0x100 ) return 1;
-				if ( d1[ind++]+((u2>>16)&0xff) >= 0x100 ) return 1;
-				if ( d1[ind++]+((u2>>8)&0xff) >= 0x100 ) return 1;
-				if ( d1[ind++]+(u2&0xff) >= 0x100 ) return 1;
-			}
-			return 0;
-			break;
-		case 16:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u2 = d2[i];
-				if ( d1[ind++]+((u2>>16)&0xffff) > 0x10000 ) return 1;
-				if ( d1[ind++]+(u2&0xffff) > 0x10000 ) return 1;
-			}
-			return 0;
-			break;
-		case 32:
-			for ( i = 0; i < nd_wpd; i++ )
-				if ( d1[i]+d2[i]<d1[i] ) return 1;
-			return 0;
-			break;
-		default:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u2 = d2[i];
-				k = (nd_epw-1)*nd_bpe;
-				for ( j = 0; j < nd_epw; j++, k -= nd_bpe )
-					if ( d1[ind++]+((u2>>k)&nd_mask0) > nd_mask0 ) return 1;
-			}
-			return 0;
-			break;
-	}
+    for ( i = 0; i < nd_wpd; i++ ) d[i] = d1[i]-d2[i];
 }
 
-int ndl_check_bound2_direct(unsigned int *d1,unsigned int *d2)
+int ndl_disjoint(UINT *d1,UINT *d2)
 {
-	unsigned int u1,u2;
-	int i,j,k;
+    UINT t1,t2,u,u1,u2;
+    int i,j;
 
-	switch ( nd_bpe ) {
-		case 4:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				if ( ((u1>>28)&0xf)+((u2>>28)&0xf) >= 0x10 ) return 1;
-				if ( ((u1>>24)&0xf)+((u2>>24)&0xf) >= 0x10 ) return 1;
-				if ( ((u1>>20)&0xf)+((u2>>20)&0xf) >= 0x10 ) return 1;
-				if ( ((u1>>16)&0xf)+((u2>>16)&0xf) >= 0x10 ) return 1;
-				if ( ((u1>>12)&0xf)+((u2>>12)&0xf) >= 0x10 ) return 1;
-				if ( ((u1>>8)&0xf)+((u2>>8)&0xf) >= 0x10 ) return 1;
-				if ( ((u1>>4)&0xf)+((u2>>4)&0xf) >= 0x10 ) return 1;
-				if ( (u1&0xf)+(u2&0xf) >= 0x10 ) return 1;
-			}
-			return 0;
-			break;
-		case 6:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				if ( ((u1>>24)&0x3f)+((u2>>24)&0x3f) >= 0x40 ) return 1;
-				if ( ((u1>>18)&0x3f)+((u2>>18)&0x3f) >= 0x40 ) return 1;
-				if ( ((u1>>12)&0x3f)+((u2>>12)&0x3f) >= 0x40 ) return 1;
-				if ( ((u1>>6)&0x3f)+((u2>>6)&0x3f) >= 0x40 ) return 1;
-				if ( (u1&0x3f)+(u2&0x3f) >= 0x40 ) return 1;
-			}
-			return 0;
-			break;
-		case 8:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				if ( ((u1>>24)&0xff)+((u2>>24)&0xff) >= 0x100 ) return 1;
-				if ( ((u1>>16)&0xff)+((u2>>16)&0xff) >= 0x100 ) return 1;
-				if ( ((u1>>8)&0xff)+((u2>>8)&0xff) >= 0x100 ) return 1;
-				if ( (u1&0xff)+(u2&0xff) >= 0x100 ) return 1;
-			}
-			return 0;
-			break;
-		case 16:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-					if ( ((u1>>16)&0xffff)+((u2>>16)&0xffff) > 0x10000 ) return 1;
-					if ( (u2&0xffff)+(u2&0xffff) > 0x10000 ) return 1;
-			}
-			return 0;
-			break;
-		case 32:
-			for ( i = 0; i < nd_wpd; i++ )
-				if ( d1[i]+d2[i]<d1[i] ) return 1;
-			return 0;
-			break;
-		default:
-			for ( i = 0; i < nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				k = (nd_epw-1)*nd_bpe;
-				for ( j = 0; j < nd_epw; j++, k -= nd_bpe )
-					if ( ((u1>>k)&nd_mask0)+((u2>>k)&nd_mask0) > nd_mask0 )
-						return 1;
-			}
-			return 0;
-			break;
-	}
+    if ( nd_module && (MPOS(d1) == MPOS(d2)) ) return 0;
+#if USE_UNROLL
+    switch ( nd_bpe ) {
+        case 3:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i];
+                t1 = u1&0x38000000; t2 = u2&0x38000000; if ( t1&&t2 ) return 0;
+                t1 = u1& 0x7000000; t2 = u2& 0x7000000; if ( t1&&t2 ) return 0;
+                t1 = u1&  0xe00000; t2 = u2&  0xe00000; if ( t1&&t2 ) return 0;
+                t1 = u1&  0x1c0000; t2 = u2&  0x1c0000; if ( t1&&t2 ) return 0;
+                t1 = u1&   0x38000; t2 = u2&   0x38000; if ( t1&&t2 ) return 0;
+                t1 = u1&    0x7000; t2 = u2&    0x7000; if ( t1&&t2 ) return 0;
+                t1 = u1&     0xe00; t2 = u2&     0xe00; if ( t1&&t2 ) return 0;
+                t1 = u1&     0x1c0; t2 = u2&     0x1c0; if ( t1&&t2 ) return 0;
+                t1 = u1&      0x38; t2 = u2&      0x38; if ( t1&&t2 ) return 0;
+                t1 = u1&       0x7; t2 = u2&       0x7; if ( t1&&t2 ) return 0;
+            }
+            return 1;
+            break;
+        case 4:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i];
+                t1 = u1&0xf0000000; t2 = u2&0xf0000000; if ( t1&&t2 ) return 0;
+                t1 = u1& 0xf000000; t2 = u2& 0xf000000; if ( t1&&t2 ) return 0;
+                t1 = u1&  0xf00000; t2 = u2&  0xf00000; if ( t1&&t2 ) return 0;
+                t1 = u1&   0xf0000; t2 = u2&   0xf0000; if ( t1&&t2 ) return 0;
+                t1 = u1&    0xf000; t2 = u2&    0xf000; if ( t1&&t2 ) return 0;
+                t1 = u1&     0xf00; t2 = u2&     0xf00; if ( t1&&t2 ) return 0;
+                t1 = u1&      0xf0; t2 = u2&      0xf0; if ( t1&&t2 ) return 0;
+                t1 = u1&       0xf; t2 = u2&       0xf; if ( t1&&t2 ) return 0;
+            }
+            return 1;
+            break;
+        case 6:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i];
+                t1 = u1&0x3f000000; t2 = u2&0x3f000000; if ( t1&&t2 ) return 0;
+                t1 = u1&  0xfc0000; t2 = u2&  0xfc0000; if ( t1&&t2 ) return 0;
+                t1 = u1&   0x3f000; t2 = u2&   0x3f000; if ( t1&&t2 ) return 0;
+                t1 = u1&     0xfc0; t2 = u2&     0xfc0; if ( t1&&t2 ) return 0;
+                t1 = u1&      0x3f; t2 = u2&      0x3f; if ( t1&&t2 ) return 0;
+            }
+            return 1;
+            break;
+        case 8:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i];
+                t1 = u1&0xff000000; t2 = u2&0xff000000; if ( t1&&t2 ) return 0;
+                t1 = u1&  0xff0000; t2 = u2&  0xff0000; if ( t1&&t2 ) return 0;
+                t1 = u1&    0xff00; t2 = u2&    0xff00; if ( t1&&t2 ) return 0;
+                t1 = u1&      0xff; t2 = u2&      0xff; if ( t1&&t2 ) return 0;
+            }
+            return 1;
+            break;
+        case 16:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i];
+                t1 = u1&0xffff0000; t2 = u2&0xffff0000; if ( t1&&t2 ) return 0;
+                t1 = u1&    0xffff; t2 = u2&    0xffff; if ( t1&&t2 ) return 0;
+            }
+            return 1;
+            break;
+        case 32:
+            for ( i = nd_exporigin; i < nd_wpd; i++ )
+                if ( d1[i] && d2[i] ) return 0;
+            return 1;
+            break;
+        default:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u1 = d1[i]; u2 = d2[i];
+                for ( j = 0; j < nd_epw; j++ ) {
+                    if ( (u1&nd_mask0) && (u2&nd_mask0) ) return 0;
+                    u1 >>= nd_bpe; u2 >>= nd_bpe;
+                }
+            }
+            return 1;
+            break;
+    }
+#else
+    for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+        u1 = d1[i]; u2 = d2[i];
+        for ( j = 0; j < nd_epw; j++ ) {
+            if ( (u1&nd_mask0) && (u2&nd_mask0) ) return 0;
+            u1 >>= nd_bpe; u2 >>= nd_bpe;
+        }
+    }
+    return 1;
+#endif
 }
 
-INLINE int ndl_hash_value(int td,unsigned int *d)
+int ndl_check_bound(UINT *d1,UINT *d2)
 {
-	int i;
-	int r;
+    UINT u2;
+    int i,j,ind,k;
 
-	r = td;
-	for ( i = 0; i < nd_wpd; i++ )	
-		r = ((r<<16)+d[i])%REDTAB_LEN;
-	return r;
+    ind = 0;
+#if USE_UNROLL
+    switch ( nd_bpe ) {
+        case 3:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u2 = d2[i];
+                if ( d1[ind++]+((u2>>27)&0x7) >= 0x8 ) return 1;
+                if ( d1[ind++]+((u2>>24)&0x7) >= 0x8 ) return 1;
+                if ( d1[ind++]+((u2>>21)&0x7) >= 0x8 ) return 1;
+                if ( d1[ind++]+((u2>>18)&0x7) >= 0x8 ) return 1;
+                if ( d1[ind++]+((u2>>15)&0x7) >= 0x8 ) return 1;
+                if ( d1[ind++]+((u2>>12)&0x7) >= 0x8 ) return 1;
+                if ( d1[ind++]+((u2>>9)&0x7) >= 0x8 ) return 1;
+                if ( d1[ind++]+((u2>>6)&0x7) >= 0x8 ) return 1;
+                if ( d1[ind++]+((u2>>3)&0x7) >= 0x8 ) return 1;
+                if ( d1[ind++]+(u2&0x7) >= 0x8 ) return 1;
+            }
+            return 0;
+            break;
+        case 4:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u2 = d2[i];
+                if ( d1[ind++]+((u2>>28)&0xf) >= 0x10 ) return 1;
+                if ( d1[ind++]+((u2>>24)&0xf) >= 0x10 ) return 1;
+                if ( d1[ind++]+((u2>>20)&0xf) >= 0x10 ) return 1;
+                if ( d1[ind++]+((u2>>16)&0xf) >= 0x10 ) return 1;
+                if ( d1[ind++]+((u2>>12)&0xf) >= 0x10 ) return 1;
+                if ( d1[ind++]+((u2>>8)&0xf) >= 0x10 ) return 1;
+                if ( d1[ind++]+((u2>>4)&0xf) >= 0x10 ) return 1;
+                if ( d1[ind++]+(u2&0xf) >= 0x10 ) return 1;
+            }
+            return 0;
+            break;
+        case 6:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u2 = d2[i];
+                if ( d1[ind++]+((u2>>24)&0x3f) >= 0x40 ) return 1;
+                if ( d1[ind++]+((u2>>18)&0x3f) >= 0x40 ) return 1;
+                if ( d1[ind++]+((u2>>12)&0x3f) >= 0x40 ) return 1;
+                if ( d1[ind++]+((u2>>6)&0x3f) >= 0x40 ) return 1;
+                if ( d1[ind++]+(u2&0x3f) >= 0x40 ) return 1;
+            }
+            return 0;
+            break;
+        case 8:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u2 = d2[i];
+                if ( d1[ind++]+((u2>>24)&0xff) >= 0x100 ) return 1;
+                if ( d1[ind++]+((u2>>16)&0xff) >= 0x100 ) return 1;
+                if ( d1[ind++]+((u2>>8)&0xff) >= 0x100 ) return 1;
+                if ( d1[ind++]+(u2&0xff) >= 0x100 ) return 1;
+            }
+            return 0;
+            break;
+        case 16:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u2 = d2[i];
+                if ( d1[ind++]+((u2>>16)&0xffff) > 0x10000 ) return 1;
+                if ( d1[ind++]+(u2&0xffff) > 0x10000 ) return 1;
+            }
+            return 0;
+            break;
+        case 32:
+            for ( i = nd_exporigin; i < nd_wpd; i++ )
+                if ( d1[i]+d2[i]<d1[i] ) return 1;
+            return 0;
+            break;
+        default:
+            for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+                u2 = d2[i];
+                k = (nd_epw-1)*nd_bpe;
+                for ( j = 0; j < nd_epw; j++, k -= nd_bpe )
+                    if ( d1[ind++]+((u2>>k)&nd_mask0) > nd_mask0 ) return 1;
+            }
+            return 0;
+            break;
+    }
+#else
+    for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+        u2 = d2[i];
+        k = (nd_epw-1)*nd_bpe;
+        for ( j = 0; j < nd_epw; j++, k -= nd_bpe )
+            if ( d1[ind++]+((u2>>k)&nd_mask0) > nd_mask0 ) return 1;
+    }
+    return 0;
+#endif
 }
 
-INLINE int nd_find_reducer(ND g)
+int ndl_check_bound2(int index,UINT *d2)
 {
-	RHist r;
-	int d,k,i;
+    return ndl_check_bound(nd_bound[index],d2);
+}
 
-	d = ndl_hash_value(HTD(g),HDL(g));
-	for ( r = nd_red[d], k = 0; r; r = NEXT(r), k++ ) {
-		if ( HTD(g) == TD(r) && ndl_equal(HDL(g),DL(r)) ) {
-			if ( k > 0 ) nd_notfirst++;
-			nd_found++;
-			return r->index;
-		}
-	}
-	if ( Reverse )
-		for ( i = nd_psn-1; i >= 0; i-- ) {
-			r = nd_psh[i];
-			if ( HTD(g) >= TD(r) && ndl_reducible(HDL(g),DL(r)) ) {
-				nd_create++;
-				nd_append_red(HDL(g),HTD(g),i);
-				return i;
-			}
-		}
-	else
-		for ( i = 0; i < nd_psn; i++ ) {
-			r = nd_psh[i];
-			if ( HTD(g) >= TD(r) && ndl_reducible(HDL(g),DL(r)) ) {
-				nd_create++;
-				nd_append_red(HDL(g),HTD(g),i);
-				return i;
-			}
-		}
-	return -1;
+INLINE int ndl_hash_value(UINT *d)
+{
+    int i;
+    int r;
+
+    r = 0;
+    for ( i = 0; i < nd_wpd; i++ )    
+        r = ((r<<16)+d[i])%REDTAB_LEN;
+    return r;
 }
 
-INLINE int nd_find_reducer_direct(ND g,NDV *ps,int len)
+INLINE int ndl_find_reducer(UINT *dg)
 {
-	NDV r;
-	RHist s;
-	int d,k,i;
+    RHist r;
+    int d,k,i;
 
-	if ( Reverse )
-		for ( i = len-1; i >= 0; i-- ) {
-			r = ps[i];
-			if ( HTD(g) >= HTD(r) && ndl_reducible(HDL(g),HDL(r)) ) {
-				nd_append_red(HDL(g),HTD(g),i);
-				return i;
-			}
-		}
-	else
-		for ( i = 0; i < len; i++ ) {
-			r = ps[i];
-			if ( HTD(g) >= HTD(r) && ndl_reducible(HDL(g),HDL(r)) ) {
-				nd_append_red(HDL(g),HTD(g),i);
-				return i;
-			}
-		}
-	return -1;
+    d = ndl_hash_value(dg);
+    for ( r = nd_red[d], k = 0; r; r = NEXT(r), k++ ) {
+        if ( ndl_equal(dg,DL(r)) ) {
+            if ( k > 0 ) nd_notfirst++;
+            nd_found++;
+            return r->index;
+        }
+    }
+    if ( Reverse )
+        for ( i = nd_psn-1; i >= 0; i-- ) {
+            r = nd_psh[i];
+            if ( ndl_reducible(dg,DL(r)) ) {
+                nd_create++;
+                nd_append_red(dg,i);
+                return i;
+            }
+        }
+    else
+        for ( i = 0; i < nd_psn; i++ ) {
+            r = nd_psh[i];
+            if ( ndl_reducible(dg,DL(r)) ) {
+                nd_create++;
+                nd_append_red(dg,i);
+                return i;
+            }
+        }
+    return -1;
 }
 
-ND nd_add(int mod,ND p1,ND p2)
+ND nd_merge(ND p1,ND p2)
 {
-	int n,c;
-	int t,can;
-	ND r;
-	NM m1,m2,mr0,mr,s;
+    int n,c;
+    int t,can,td1,td2;
+    ND r;
+    NM m1,m2,mr0,mr,s;
 
-	if ( !p1 )
-		return p2;
-	else if ( !p2 )
-		return p1;
-	else if ( !mod )
-		return nd_add_q(p1,p2);
-	else {
-		can = 0;
-		for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
-			c = NM_COMPARE(m1,m2);
-			switch ( c ) {
-				case 0:
-					t = ((CM(m1))+(CM(m2))) - mod;
-					if ( t < 0 )
-						t += mod;
-					s = m1; m1 = NEXT(m1);
-					if ( t ) {
-						can++;
-						NEXTNM2(mr0,mr,s); CM(mr) = (t);
-					} else {
-						can += 2;
-						FREENM(s);
-					}
-					s = m2; m2 = NEXT(m2); FREENM(s);
-					break;
-				case 1:
-					s = m1; m1 = NEXT(m1); NEXTNM2(mr0,mr,s);
-					break;
-				case -1:
-					s = m2; m2 = NEXT(m2); NEXTNM2(mr0,mr,s);
-					break;
-			}
-		}
-		if ( !mr0 )
-			if ( m1 )
-				mr0 = m1;
-			else if ( m2 )
-				mr0 = m2;
-			else
-				return 0;
-		else if ( m1 )
-			NEXT(mr) = m1;
-		else if ( m2 )
-			NEXT(mr) = m2;
-		else
-			NEXT(mr) = 0;
-		BDY(p1) = mr0;
-		SG(p1) = MAX(SG(p1),SG(p2));
-		LEN(p1) = LEN(p1)+LEN(p2)-can;
-		FREEND(p2);
-		return p1;
-	}
+    if ( !p1 ) return p2;
+    else if ( !p2 ) return p1;
+    else {
+        can = 0;
+        for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
+            c = DL_COMPARE(DL(m1),DL(m2));
+            switch ( c ) {
+                case 0:
+                    s = m1; m1 = NEXT(m1);
+                    can++; NEXTNM2(mr0,mr,s);
+                    s = m2; m2 = NEXT(m2); FREENM(s);
+                    break;
+                case 1:
+                    s = m1; m1 = NEXT(m1); NEXTNM2(mr0,mr,s);
+                    break;
+                case -1:
+                    s = m2; m2 = NEXT(m2); NEXTNM2(mr0,mr,s);
+                    break;
+            }
+        }
+        if ( !mr0 )
+            if ( m1 ) mr0 = m1;
+            else if ( m2 ) mr0 = m2;
+            else return 0;
+        else if ( m1 ) NEXT(mr) = m1;
+        else if ( m2 ) NEXT(mr) = m2;
+        else NEXT(mr) = 0;
+        BDY(p1) = mr0;
+        SG(p1) = MAX(SG(p1),SG(p2));
+        LEN(p1) = LEN(p1)+LEN(p2)-can;
+        FREEND(p2);
+        return p1;
+    }
 }
 
-ND nd_add_q(ND p1,ND p2)
+ND nd_add(int mod,ND p1,ND p2)
 {
-	int n,c,can;
-	ND r;
-	NM m1,m2,mr0,mr,s;
-	Q t;
+    int n,c;
+    int t,can,td1,td2;
+    ND r;
+    NM m1,m2,mr0,mr,s;
 
-	if ( !p1 )
-		return p2;
-	else if ( !p2 )
-		return p1;
-	else {
-		can = 0;
-		for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
-			c = NM_COMPARE(m1,m2);
-			switch ( c ) {
-				case 0:
-					addq(CQ(m1),CQ(m2),&t);
-					s = m1; m1 = NEXT(m1);
-					if ( t ) {
-						can++;
-						NEXTNM2(mr0,mr,s); CQ(mr) = (t);
-					} else {
-						can += 2;
-						FREENM(s);
-					}
-					s = m2; m2 = NEXT(m2); FREENM(s);
-					break;
-				case 1:
-					s = m1; m1 = NEXT(m1); NEXTNM2(mr0,mr,s);
-					break;
-				case -1:
-					s = m2; m2 = NEXT(m2); NEXTNM2(mr0,mr,s);
-					break;
-			}
-		}
-		if ( !mr0 )
-			if ( m1 )
-				mr0 = m1;
-			else if ( m2 )
-				mr0 = m2;
-			else
-				return 0;
-		else if ( m1 )
-			NEXT(mr) = m1;
-		else if ( m2 )
-			NEXT(mr) = m2;
-		else
-			NEXT(mr) = 0;
-		BDY(p1) = mr0;
-		SG(p1) = MAX(SG(p1),SG(p2));
-		LEN(p1) = LEN(p1)+LEN(p2)-can;
-		FREEND(p2);
-		return p1;
-	}
+    if ( !p1 ) return p2;
+    else if ( !p2 ) return p1;
+    else if ( mod == -1 ) return nd_add_sf(p1,p2);
+    else if ( !mod ) return nd_add_q(p1,p2);
+    else {
+        can = 0;
+        for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
+            c = DL_COMPARE(DL(m1),DL(m2));
+            switch ( c ) {
+                case 0:
+                    t = ((CM(m1))+(CM(m2))) - mod;
+                    if ( t < 0 ) t += mod;
+                    s = m1; m1 = NEXT(m1);
+                    if ( t ) {
+                        can++; NEXTNM2(mr0,mr,s); CM(mr) = (t);
+                    } else {
+                        can += 2; FREENM(s);
+                    }
+                    s = m2; m2 = NEXT(m2); FREENM(s);
+                    break;
+                case 1:
+                    s = m1; m1 = NEXT(m1); NEXTNM2(mr0,mr,s);
+                    break;
+                case -1:
+                    s = m2; m2 = NEXT(m2); NEXTNM2(mr0,mr,s);
+                    break;
+            }
+        }
+        if ( !mr0 )
+            if ( m1 ) mr0 = m1;
+            else if ( m2 ) mr0 = m2;
+            else return 0;
+        else if ( m1 ) NEXT(mr) = m1;
+        else if ( m2 ) NEXT(mr) = m2;
+        else NEXT(mr) = 0;
+        BDY(p1) = mr0;
+        SG(p1) = MAX(SG(p1),SG(p2));
+        LEN(p1) = LEN(p1)+LEN(p2)-can;
+        FREEND(p2);
+        return p1;
+    }
 }
 
-/* ret=1 : success, ret=0 : overflow */
-int nd_nf(int mod,ND g,int full,ND *rp)
+/* XXX on opteron, the inlined manipulation of destructive additon of
+ * two NM seems to make gcc optimizer get confused, so the part is
+ * done in a function.
+ */
+
+int nm_destructive_add_q(NM *m1,NM *m2,NM *mr0,NM *mr)
 {
-	ND d;
-	NM m,mrd,tail;
-	NM mul;
-	int n,sugar,psugar,sugar0,stat,index;
-	int c,c1,c2,dummy;
-	RHist h;
-	NDV p,red;
-	Q cg,cred,gcd;
-	double hmag;
+    NM s;
+    P t;
+    int can;
 
-	if ( !g ) {
-		*rp = 0;
-		return 1;
-	}
-	if ( !mod )
-		hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
+    addp(nd_vc,CP(*m1),CP(*m2),&t);
+    s = *m1; *m1 = NEXT(*m1);
+    if ( t ) {
+        can = 1; NEXTNM2(*mr0,*mr,s); CP(*mr) = (t);
+    } else {
+        can = 2; FREENM(s);
+    }
+    s = *m2; *m2 = NEXT(*m2); FREENM(s);
+    return can;
+}
 
-	sugar0 = sugar = SG(g);
-	n = NV(g);
-	mul = (NM)ALLOCA(sizeof(struct oNM)+(nd_wpd-1)*sizeof(unsigned int));
-	for ( d = 0; g; ) {
-		index = nd_find_reducer(g);
-		if ( index >= 0 ) {
-			h = nd_psh[index];
-			ndl_sub(HDL(g),DL(h),DL(mul));
-			TD(mul) = HTD(g)-TD(h);
-#if 0
-			if ( d && (SG(p)+TD(mul)) > sugar ) {
-				goto afo;				
-			}
+ND nd_add_q(ND p1,ND p2)
+{
+    int n,c,can;
+    ND r;
+    NM m1,m2,mr0,mr,s;
+    P t;
+
+    if ( !p1 ) return p2;
+    else if ( !p2 ) return p1;
+    else {
+        can = 0;
+        for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
+            c = DL_COMPARE(DL(m1),DL(m2));
+            switch ( c ) {
+                case 0:
+#if defined(__x86_64__)
+                    can += nm_destructive_add_q(&m1,&m2,&mr0,&mr);
+#else
+                    addp(nd_vc,CP(m1),CP(m2),&t);
+                    s = m1; m1 = NEXT(m1);
+                    if ( t ) {
+                        can++; NEXTNM2(mr0,mr,s); CP(mr) = (t);
+                    } else {
+                        can += 2; FREENM(s);
+                    }
+                    s = m2; m2 = NEXT(m2); FREENM(s);
 #endif
-			if ( ndl_check_bound2(index,DL(mul)) ) {
-				nd_free(g); nd_free(d);
-				return 0;
-			}
-			if ( mod ) {
-				p = nd_ps[index];
-				c1 = invm(HCM(p),mod); c2 = mod-HCM(g);
-				DMAR(c1,c2,0,mod,c); CM(mul) = c;
-			} else {
-				p = nd_psq[index];
-				igcd_cofactor(HCQ(g),HCQ(p),&gcd,&cg,&cred);
-				chsgnq(cg,&CQ(mul));
-				nd_mul_c_q(d,cred); nd_mul_c_q(g,cred);
-			}
-			g = nd_add(mod,g,ndv_mul_nm(mod,p,mul));
-			sugar = MAX(sugar,SG(p)+TD(mul));
-			if ( !mod && hmag && g && ((double)(p_mag((P)HCQ(g))) > hmag) ) {
-				nd_removecont2(d,g);
-				hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
-			}
-		} else if ( !full ) {
-			*rp = g;
-			return 1;
-		} else {
-afo:
-			m = BDY(g); 
-			if ( NEXT(m) ) {
-				BDY(g) = NEXT(m); NEXT(m) = 0;
-				LEN(g)--;
-			} else {
-				FREEND(g); g = 0;
-			}
-			if ( d ) {
-				NEXT(tail)=m;
-				tail=m;
-				LEN(d)++;
-			} else {
-				MKND(n,m,1,d);
-				tail = BDY(d);
-			}
-		}
-	}
-	if ( d )
-		SG(d) = sugar;
-	*rp = d;
-	return 1;
+                    break;
+                case 1:
+                    s = m1; m1 = NEXT(m1); NEXTNM2(mr0,mr,s);
+                    break;
+                case -1:
+                    s = m2; m2 = NEXT(m2); NEXTNM2(mr0,mr,s);
+                    break;
+            }
+        }
+        if ( !mr0 )
+            if ( m1 ) mr0 = m1;
+            else if ( m2 ) mr0 = m2;
+            else return 0;
+        else if ( m1 ) NEXT(mr) = m1;
+        else if ( m2 ) NEXT(mr) = m2;
+        else NEXT(mr) = 0;
+        BDY(p1) = mr0;
+        SG(p1) = MAX(SG(p1),SG(p2));
+        LEN(p1) = LEN(p1)+LEN(p2)-can;
+        FREEND(p2);
+        return p1;
+    }
 }
 
-int nd_nf_pbucket(int mod,ND g,int full,ND *rp)
+ND nd_add_sf(ND p1,ND p2)
 {
-	int hindex,index;
-	NDV p;
-	ND u,d,red;
-	NODE l;
-	NM mul,m,mrd,tail;
-	int sugar,psugar,n,h_reducible;
-	PGeoBucket bucket;
-	int c,c1,c2;
-	Q cg,cred,gcd,zzz;
-	RHist h;
-	double hmag,gmag;
+    int n,c,can;
+    ND r;
+    NM m1,m2,mr0,mr,s;
+    int t;
 
-	if ( !g ) {
-		*rp = 0;
-		return 1;
-	}
-	sugar = SG(g);
-	n = NV(g);
-	if ( !mod )
-		hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
-	bucket = create_pbucket();
-	add_pbucket(mod,bucket,g);
-	d = 0;
-	mul = (NM)ALLOCA(sizeof(struct oNM)+(nd_wpd-1)*sizeof(unsigned int));
-	while ( 1 ) {
-		hindex = mod?head_pbucket(mod,bucket):head_pbucket_q(bucket);
-		if ( hindex < 0 ) {
-			if ( d )
-				SG(d) = sugar;
-			*rp = d;
-			return 1;
-		}
-		g = bucket->body[hindex];
-		index = nd_find_reducer(g);
-		if ( index >= 0 ) {
-			h = nd_psh[index];
-			ndl_sub(HDL(g),DL(h),DL(mul));
-			TD(mul) = HTD(g)-TD(h);
-			if ( ndl_check_bound2(index,DL(mul)) ) {
-				nd_free(d);
-				free_pbucket(bucket);
-				*rp = 0;
-				return 0;
-			}
- 			if ( mod ) {
-				p = nd_ps[index];
-				c1 = invm(HCM(p),mod); c2 = mod-HCM(g);
-				DMAR(c1,c2,0,mod,c); CM(mul) = c;
-			} else {
-				p = nd_psq[index];
-				igcd_cofactor(HCQ(g),HCQ(p),&gcd,&cg,&cred);
-				chsgnq(cg,&CQ(mul));
-				nd_mul_c_q(d,cred);
-				mulq_pbucket(bucket,cred);
-				g = bucket->body[hindex];
-				gmag = (double)p_mag((P)HCQ(g));
-			}
-			red = ndv_mul_nm(mod,p,mul);
-			bucket->body[hindex] = nd_remove_head(g);
-			red = nd_remove_head(red);
-			add_pbucket(mod,bucket,red);
-			sugar = MAX(sugar,SG(p)+TD(mul));
-			if ( !mod && hmag && (gmag > hmag) ) {
-				g = normalize_pbucket(mod,bucket);
-				if ( !g ) {
-					if ( d )
-						SG(d) = sugar;
-					*rp = d;
-					return 1;
-				}
-				nd_removecont2(d,g);
-				hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
-				add_pbucket(mod,bucket,g);
-			}
-		} else if ( !full ) {
-			g = normalize_pbucket(mod,bucket);
-			if ( g )
-				SG(g) = sugar;
-			*rp = g;
-			return 1;
-		} else {
-			m = BDY(g); 
-			if ( NEXT(m) ) {
-				BDY(g) = NEXT(m); NEXT(m) = 0;
-				LEN(g)--;
-			} else {
-				FREEND(g); g = 0;
-			}
-			bucket->body[hindex] = g;
-			NEXT(m) = 0;
-			if ( d ) {
-				NEXT(tail)=m;
-				tail=m;
-				LEN(d)++;
-			} else {
-				MKND(n,m,1,d);
-				tail = BDY(d);
-			}
-		}
-	}
+    if ( !p1 ) return p2;
+    else if ( !p2 ) return p1;
+    else {
+        can = 0;
+        for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
+            c = DL_COMPARE(DL(m1),DL(m2));
+            switch ( c ) {
+                case 0:
+                    t = _addsf(CM(m1),CM(m2));
+                    s = m1; m1 = NEXT(m1);
+                    if ( t ) {
+                        can++; NEXTNM2(mr0,mr,s); CM(mr) = (t);
+                    } else {
+                        can += 2; FREENM(s);
+                    }
+                    s = m2; m2 = NEXT(m2); FREENM(s);
+                    break;
+                case 1:
+                    s = m1; m1 = NEXT(m1); NEXTNM2(mr0,mr,s);
+                    break;
+                case -1:
+                    s = m2; m2 = NEXT(m2); NEXTNM2(mr0,mr,s);
+                    break;
+            }
+        }
+        if ( !mr0 )
+            if ( m1 ) mr0 = m1;
+            else if ( m2 ) mr0 = m2;
+            else return 0;
+        else if ( m1 ) NEXT(mr) = m1;
+        else if ( m2 ) NEXT(mr) = m2;
+        else NEXT(mr) = 0;
+        BDY(p1) = mr0;
+        SG(p1) = MAX(SG(p1),SG(p2));
+        LEN(p1) = LEN(p1)+LEN(p2)-can;
+        FREEND(p2);
+        return p1;
+    }
 }
 
-int nd_nf_direct(int mod,ND g,NDV *ps,int len,int full,ND *rp)
+ND nd_reduce2(int mod,ND d,ND g,NDV p,NM mul,NDC dn,Obj *divp)
 {
-	ND d;
-	NM m,mrd,tail;
-	NM mul;
-	int n,sugar,psugar,sugar0,stat,index;
-	int c,c1,c2;
-	RHist h;
-	NDV p,red;
-	Q cg,cred,gcd;
-	double hmag;
+    int c,c1,c2;
+    Q cg,cred,gcd,tq;
+    P cgp,credp,gcdp;
+    Obj tr,tr1;
 
-	if ( !g ) {
-		*rp = 0;
-		return 1;
-	}
-#if 0
-	if ( !mod )
-		hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
-#else
-	/* XXX */
-	hmag = 0;
-#endif
+    if ( mod == -1 ) {
+        CM(mul) = _mulsf(_invsf(HCM(p)),_chsgnsf(HCM(g)));
+        *divp = (Obj)ONE;
+    } else if ( mod ) {
+        c1 = invm(HCM(p),mod); c2 = mod-HCM(g);
+        DMAR(c1,c2,0,mod,c); CM(mul) = c;
+        *divp = (Obj)ONE;
+    } else if ( nd_vc ) {
+        ezgcdpz(nd_vc,HCP(g),HCP(p),&gcdp);
+        divsp(nd_vc,HCP(g),gcdp,&cgp); divsp(nd_vc,HCP(p),gcdp,&credp);
+        chsgnp(cgp,&CP(mul));
+        nd_mul_c_q(d,credp); nd_mul_c_q(g,credp);
+        if ( dn ) {
+            mulr(nd_vc,(Obj)dn->r,(Obj)credp,&tr);
+            reductr(nd_vc,tr,&tr1); dn->r = (R)tr1;
+        }
+        *divp = (Obj)credp;
+    } else {
+        igcd_cofactor(HCQ(g),HCQ(p),&gcd,&cg,&cred);
+        chsgnq(cg,&CQ(mul));
+        nd_mul_c_q(d,(P)cred); nd_mul_c_q(g,(P)cred);
+        if ( dn ) {
+            mulq(dn->z,cred,&tq); dn->z = tq;
+        }
+        *divp = (Obj)cred;
+    }
+    return nd_add(mod,g,ndv_mul_nm(mod,mul,p));
+}
 
-	sugar0 = sugar = SG(g);
-	n = NV(g);
-	mul = (NM)ALLOCA(sizeof(struct oNM)+(nd_wpd-1)*sizeof(unsigned int));
-	for ( d = 0; g; ) {
-		index = nd_find_reducer_direct(g,ps,len);
-		if ( index >= 0 ) {
-			p = ps[index];
-			ndl_sub(HDL(g),HDL(p),DL(mul));
-			TD(mul) = HTD(g)-HTD(p);
-			if ( ndl_check_bound2_direct(HDL(p),DL(mul)) ) {
-				nd_free(g); nd_free(d);
-				return 0;
-			}
-			if ( mod ) {
-				c1 = invm(HCM(p),mod); c2 = mod-HCM(g);
-				DMAR(c1,c2,0,mod,c); CM(mul) = c;
-			} else {
-				igcd_cofactor(HCQ(g),HCQ(p),&gcd,&cg,&cred);
-				chsgnq(cg,&CQ(mul));
-				nd_mul_c_q(d,cred); nd_mul_c_q(g,cred);
-			}
-			g = nd_add(mod,g,ndv_mul_nm(mod,p,mul));
-			sugar = MAX(sugar,SG(p)+TD(mul));
-			if ( !mod && hmag && g && ((double)(p_mag((P)HCQ(g))) > hmag) ) {
-				nd_removecont2(d,g);
-				hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
-			}
-		} else if ( !full ) {
-			*rp = g;
-			return 1;
-		} else {
-			m = BDY(g); 
-			if ( NEXT(m) ) {
-				BDY(g) = NEXT(m); NEXT(m) = 0;
-				LEN(g)--;
-			} else {
-				FREEND(g); g = 0;
-			}
-			if ( d ) {
-				NEXT(tail)=m;
-				tail=m;
-				LEN(d)++;
-			} else {
-				MKND(n,m,1,d);
-				tail = BDY(d);
-			}
-		}
-	}
-	if ( d )
-		SG(d) = sugar;
-	*rp = d;
-	return 1;
+/* ret=1 : success, ret=0 : overflow */
+int nd_nf(int mod,ND d,ND g,NDV *ps,int full,NDC dn,ND *rp)
+{
+    NM m,mrd,tail;
+    NM mul;
+    int n,sugar,psugar,sugar0,stat,index;
+    int c,c1,c2,dummy;
+    RHist h;
+    NDV p,red;
+    Q cg,cred,gcd,tq,qq,iq;
+    DP dmul;
+    NODE node;
+    LIST hist;
+    double hmag;
+    P tp,tp1;
+    Obj tr,tr1,div;
+    union oNDC hg;
+    P cont;
+
+    if ( dn ) {
+        if ( mod )
+            dn->m = 1;
+        else if ( nd_vc )
+            dn->r = (R)ONE;
+        else
+            dn->z = ONE;
+    }
+    if ( !g ) {
+        *rp = d;
+        return 1;
+    }
+    if ( !mod ) hmag = ((double)p_mag(HCP(g)))*nd_scale;
+
+    sugar0 = sugar = SG(g);
+    n = NV(g);
+    mul = (NM)ALLOCA(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT));
+    if ( d )
+        for ( tail = BDY(d); NEXT(tail); tail = NEXT(tail) );
+    for ( ; g; ) {
+        index = ndl_find_reducer(HDL(g));
+        if ( index >= 0 ) {
+            h = nd_psh[index];
+            ndl_sub(HDL(g),DL(h),DL(mul));
+            if ( ndl_check_bound2(index,DL(mul)) ) {
+                nd_free(g); nd_free(d);
+                return 0;
+            }
+            p = nd_demand ? ndv_load(index) : ps[index];
+            /* d+g -> div*(d+g)+mul*p */
+            g = nd_reduce2(mod,d,g,p,mul,dn,&div);
+            if ( nd_gentrace ) {
+                /* Trace=[div,index,mul,ONE] */
+                STOQ(index,iq);
+                nmtodp(mod,mul,&dmul);
+                node = mknode(4,div,iq,dmul,ONE);
+            }
+            sugar = MAX(sugar,SG(p)+TD(DL(mul)));
+            if ( !mod && g && !nd_vc && ((double)(p_mag(HCP(g))) > hmag) ) {
+                hg = HCU(g);
+                nd_removecont2(d,g);
+                if ( dn || nd_gentrace ) {
+                    /* overwrite cont : Trace=[div,index,mul,cont] */
+                    cont = ndc_div(mod,hg,HCU(g));
+                    if ( dn ) {
+                        if ( nd_vc ) {
+                            divr(nd_vc,(Obj)dn->r,(Obj)cont,&tr);
+                            reductr(nd_vc,(Obj)tr,&tr1); dn->r = (R)tr1;
+                        } else divq(dn->z,(Q)cont,&dn->z);
+                    }
+                    if ( nd_gentrace && !UNIQ(cont) ) ARG3(node) = (pointer)cont;
+                }
+                hmag = ((double)p_mag(HCP(g)))*nd_scale;
+            }
+            MKLIST(hist,node);
+            MKNODE(node,hist,nd_tracelist); nd_tracelist = node;
+        } else if ( !full ) {
+            *rp = g;
+            return 1;
+        } else {
+            m = BDY(g); 
+            if ( NEXT(m) ) {
+                BDY(g) = NEXT(m); NEXT(m) = 0; LEN(g)--;
+            } else {
+                FREEND(g); g = 0;
+            }
+            if ( d ) {
+                NEXT(tail)=m; tail=m; LEN(d)++;
+            } else {
+                MKND(n,m,1,d); tail = BDY(d);
+            }
+        }
+    }
+    if ( d ) SG(d) = sugar;
+    *rp = d;
+    return 1;
 }
 
-int nd_nf_direct_pbucket(int mod,ND g,NDV *ps,int len,int full,ND *rp)
+int nd_nf_pbucket(int mod,ND g,NDV *ps,int full,ND *rp)
 {
-	int hindex,index;
-	NDV p;
-	ND u,d,red;
-	NODE l;
-	NM mul,m,mrd,tail;
-	int sugar,psugar,n,h_reducible;
-	PGeoBucket bucket;
-	int c,c1,c2;
-	Q cg,cred,gcd,zzz;
-	RHist h;
-	double hmag,gmag;
+    int hindex,index;
+    NDV p;
+    ND u,d,red;
+    NODE l;
+    NM mul,m,mrd,tail;
+    int sugar,psugar,n,h_reducible;
+    PGeoBucket bucket;
+    int c,c1,c2;
+    Q cg,cred,gcd,zzz;
+    RHist h;
+    double hmag,gmag;
+    int count = 0;
+    int hcount = 0;
 
-	if ( !g ) {
-		*rp = 0;
-		return 1;
-	}
-	sugar = SG(g);
-	n = NV(g);
-#if 0
-	if ( !mod )
-		hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
-#else
-	/* XXX */
-	hmag = 0;
-#endif
-	bucket = create_pbucket();
-	add_pbucket(mod,bucket,g);
-	d = 0;
-	mul = (NM)ALLOCA(sizeof(struct oNM)+(nd_wpd-1)*sizeof(unsigned int));
-	while ( 1 ) {
-		hindex = mod?head_pbucket(mod,bucket):head_pbucket_q(bucket);
-		if ( hindex < 0 ) {
-			if ( d )
-				SG(d) = sugar;
-			*rp = d;
-			return 1;
-		}
-		g = bucket->body[hindex];
-		index = nd_find_reducer_direct(g,ps,len);
-		if ( index >= 0 ) {
-			p = ps[index];
-			ndl_sub(HDL(g),HDL(p),DL(mul));
-			TD(mul) = HTD(g)-HTD(p);
-			if ( ndl_check_bound2_direct(HDL(p),DL(mul)) ) {
-				nd_free(d);
-				free_pbucket(bucket);
-				*rp = 0;
-				return 0;
-			}
- 			if ( mod ) {
-				c1 = invm(HCM(p),mod); c2 = mod-HCM(g);
-				DMAR(c1,c2,0,mod,c); CM(mul) = c;
-			} else {
-				igcd_cofactor(HCQ(g),HCQ(p),&gcd,&cg,&cred);
-				chsgnq(cg,&CQ(mul));
-				nd_mul_c_q(d,cred);
-				mulq_pbucket(bucket,cred);
-				g = bucket->body[hindex];
-				gmag = (double)p_mag((P)HCQ(g));
-			}
-			red = ndv_mul_nm(mod,p,mul);
-			bucket->body[hindex] = nd_remove_head(g);
-			red = nd_remove_head(red);
-			add_pbucket(mod,bucket,red);
-			sugar = MAX(sugar,SG(p)+TD(mul));
-			if ( !mod && hmag && (gmag > hmag) ) {
-				g = normalize_pbucket(mod,bucket);
-				if ( !g ) {
-					if ( d )
-						SG(d) = sugar;
-					*rp = d;
-					return 1;
-				}
-				nd_removecont2(d,g);
-				hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
-				add_pbucket(mod,bucket,g);
-			}
-		} else if ( !full ) {
-			g = normalize_pbucket(mod,bucket);
-			if ( g )
-				SG(g) = sugar;
-			*rp = g;
-			return 1;
-		} else {
-			m = BDY(g); 
-			if ( NEXT(m) ) {
-				BDY(g) = NEXT(m); NEXT(m) = 0;
-				LEN(g)--;
-			} else {
-				FREEND(g); g = 0;
-			}
-			bucket->body[hindex] = g;
-			NEXT(m) = 0;
-			if ( d ) {
-				NEXT(tail)=m;
-				tail=m;
-				LEN(d)++;
-			} else {
-				MKND(n,m,1,d);
-				tail = BDY(d);
-			}
-		}
-	}
+    if ( !g ) {
+        *rp = 0;
+        return 1;
+    }
+    sugar = SG(g);
+    n = NV(g);
+    if ( !mod ) hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
+    bucket = create_pbucket();
+    add_pbucket(mod,bucket,g);
+    d = 0;
+    mul = (NM)ALLOCA(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT));
+    while ( 1 ) {
+        hindex = mod?head_pbucket(mod,bucket):head_pbucket_q(bucket);
+        if ( hindex < 0 ) {
+            if ( DP_Print > 3 ) printf("(%d %d)",count,hcount);
+            if ( d ) SG(d) = sugar;
+            *rp = d;
+            return 1;
+        }
+        g = bucket->body[hindex];
+        index = ndl_find_reducer(HDL(g));
+        if ( index >= 0 ) {
+            count++;
+            if ( !d ) hcount++;
+            h = nd_psh[index];
+            ndl_sub(HDL(g),DL(h),DL(mul));
+            if ( ndl_check_bound2(index,DL(mul)) ) {
+                nd_free(d);
+                free_pbucket(bucket);
+                *rp = 0;
+                return 0;
+            }
+            p = ps[index];
+            if ( mod == -1 )
+                CM(mul) = _mulsf(_invsf(HCM(p)),_chsgnsf(HCM(g)));
+             else if ( mod ) {
+                c1 = invm(HCM(p),mod); c2 = mod-HCM(g);
+                DMAR(c1,c2,0,mod,c); CM(mul) = c;
+            } else {
+                igcd_cofactor(HCQ(g),HCQ(p),&gcd,&cg,&cred);
+                chsgnq(cg,&CQ(mul));
+                nd_mul_c_q(d,(P)cred);
+                mulq_pbucket(bucket,cred);
+                g = bucket->body[hindex];
+                gmag = (double)p_mag((P)HCQ(g));
+            }
+            red = ndv_mul_nm(mod,mul,p);
+            bucket->body[hindex] = nd_remove_head(g);
+            red = nd_remove_head(red);
+            add_pbucket(mod,bucket,red);
+            psugar = SG(p)+TD(DL(mul));
+            sugar = MAX(sugar,psugar);
+            if ( !mod && hmag && (gmag > hmag) ) {
+                g = normalize_pbucket(mod,bucket);
+                if ( !g ) {
+                    if ( d ) SG(d) = sugar;
+                    *rp = d;
+                    return 1;
+                }
+                nd_removecont2(d,g);
+                hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
+                add_pbucket(mod,bucket,g);
+            }
+        } else if ( !full ) {
+            g = normalize_pbucket(mod,bucket);
+            if ( g ) SG(g) = sugar;
+            *rp = g;
+            return 1;
+        } else {
+            m = BDY(g); 
+            if ( NEXT(m) ) {
+                BDY(g) = NEXT(m); NEXT(m) = 0; LEN(g)--;
+            } else {
+                FREEND(g); g = 0;
+            }
+            bucket->body[hindex] = g;
+            NEXT(m) = 0;
+            if ( d ) {
+                NEXT(tail)=m; tail=m; LEN(d)++;
+            } else {
+                MKND(n,m,1,d); tail = BDY(d);
+            }
+        }
+    }
 }
 
-/* input : list of DP, cand : list of DP */
+/* input : list of NDV, cand : list of NDV */
 
-int nd_check_candidate(NODE input,NODE cand)
+int ndv_check_membership(int m,NODE input,int obpe,int oadv,EPOS oepos,NODE cand)
 {
-	int n,i,stat;
-	ND nf,d;
-	NODE t;
+    int n,i,stat;
+    ND nf,d;
+    NDV r;
+    NODE t,s;
+    union oNDC dn;
+    Q q;
+    LIST list;
 
-	nd_setup(0,cand);
-	n = length(cand);
+    ndv_setup(m,0,cand,nd_gentrace?1:0,1);
+    n = length(cand);
 
-	/* membercheck : list is a subset of Id(cand) ? */
-	for ( t = input; t; t = NEXT(t) ) {
-		d = dptond(0,(DP)BDY(t));
-		stat = nd_nf_direct(0,d,nd_psq,n,0,&nf);
-		if ( !stat )
-			nd_reconstruct_direct(0,nd_psq,n);
-		else if ( nf )
-			return 0;
-	}
-	/* gbcheck : cand is a GB of Id(cand) ? */
-	if ( !nd_gb(0,1) )
-		return 0;
-	/* XXX */
-	return 1;
+	if ( nd_gentrace ) { nd_alltracelist = 0; nd_tracelist = 0; }
+    /* membercheck : list is a subset of Id(cand) ? */
+    for ( t = input, i = 0; t; t = NEXT(t), i++ ) {
+again:
+		nd_tracelist = 0;
+        if ( nd_bpe > obpe )
+            r = ndv_dup_realloc((NDV)BDY(t),obpe,oadv,oepos);
+        else
+            r = (NDV)BDY(t);
+        d = ndvtond(m,r);
+        stat = nd_nf(m,0,d,nd_ps,0,0,&nf);
+        if ( !stat ) {
+            nd_reconstruct(0,0);
+            goto again;
+        } else if ( nf ) return 0;
+		if ( nd_gentrace ) {
+			nd_tracelist = reverse_node(nd_tracelist);
+			MKLIST(list,nd_tracelist);
+			STOQ(i,q); s = mknode(2,q,list); MKLIST(list,s);
+			MKNODE(s,list,nd_alltracelist);
+			nd_alltracelist = s; nd_tracelist = 0;
+		}
+        if ( DP_Print ) { printf("."); fflush(stdout); }
+    }
+    if ( DP_Print ) { printf("\n"); }
+    return 1;
 }
 
 ND nd_remove_head(ND p)
 {
-	NM m;
+    NM m;
 
-	m = BDY(p);
-	if ( !NEXT(m) ) {
-		FREEND(p);
-		p = 0;
-	} else {
-		BDY(p) = NEXT(m);
-		LEN(p)--;
-	}
-	FREENM(m);
-	return p;
+    m = BDY(p);
+    if ( !NEXT(m) ) {
+        FREEND(p); p = 0;
+    } else {
+        BDY(p) = NEXT(m); LEN(p)--;
+    }
+    FREENM(m);
+    return p;
 }
 
+ND nd_separate_head(ND p,ND *head)
+{
+    NM m,m0;
+    ND r;
+
+    m = BDY(p);
+    if ( !NEXT(m) ) {
+        *head = p; p = 0;
+    } else {
+        m0 = m;
+        BDY(p) = NEXT(m); LEN(p)--;
+        NEXT(m0) = 0;
+        MKND(NV(p),m0,1,r);
+        *head = r;
+    }
+    return p;
+}
+
 PGeoBucket create_pbucket()
 {
     PGeoBucket g;
-	 
-	g = CALLOC(1,sizeof(struct oPGeoBucket));
-	g->m = -1;
-	return g;
+     
+    g = CALLOC(1,sizeof(struct oPGeoBucket));
+    g->m = -1;
+    return g;
 }
 
 void free_pbucket(PGeoBucket b) {
-	int i;
+    int i;
 
-	for ( i = 0; i <= b->m; i++ )
-		if ( b->body[i] ) {
-			nd_free(b->body[i]);
-			b->body[i] = 0;
-		}
-	GC_free(b);
+    for ( i = 0; i <= b->m; i++ )
+        if ( b->body[i] ) {
+            nd_free(b->body[i]);
+            b->body[i] = 0;
+        }
+    GCFREE(b);
 }
 
+void add_pbucket_symbolic(PGeoBucket g,ND d)
+{
+    int l,i,k,m;
+
+    if ( !d )
+        return;
+    l = LEN(d);
+    for ( k = 0, m = 1; l > m; k++, m <<= 1 );
+    /* 2^(k-1) < l <= 2^k (=m) */
+    d = nd_merge(g->body[k],d);
+    for ( ; d && LEN(d) > m; k++, m <<= 1 ) {
+        g->body[k] = 0;
+        d = nd_merge(g->body[k+1],d);
+    }
+    g->body[k] = d;
+    g->m = MAX(g->m,k);
+}
+
 void add_pbucket(int mod,PGeoBucket g,ND d)
 {
-	int l,i,k,m;
+    int l,i,k,m;
 
-	if ( !d )
-		return;
-	l = LEN(d);
-	for ( k = 0, m = 1; l > m; k++, m <<= 1 );
-	/* 2^(k-1) < l <= 2^k (=m) */
-	d = nd_add(mod,g->body[k],d);
-	for ( ; d && LEN(d) > m; k++, m <<= 1 ) {
-		g->body[k] = 0;
-		d = nd_add(mod,g->body[k+1],d);
-	}
-	g->body[k] = d;
-	g->m = MAX(g->m,k);
+    if ( !d )
+        return;
+    l = LEN(d);
+    for ( k = 0, m = 1; l > m; k++, m <<= 1 );
+    /* 2^(k-1) < l <= 2^k (=m) */
+    d = nd_add(mod,g->body[k],d);
+    for ( ; d && LEN(d) > m; k++, m <<= 1 ) {
+        g->body[k] = 0;
+        d = nd_add(mod,g->body[k+1],d);
+    }
+    g->body[k] = d;
+    g->m = MAX(g->m,k);
 }
 
 void mulq_pbucket(PGeoBucket g,Q c)
 {
-	int k;
+    int k;
 
-	for ( k = 0; k <= g->m; k++ )
-		nd_mul_c_q(g->body[k],c);
+    for ( k = 0; k <= g->m; k++ )
+        nd_mul_c_q(g->body[k],(P)c);
 }
 
-/* XXX not completed */
+NM remove_head_pbucket_symbolic(PGeoBucket g)
+{
+    int j,i,k,c;
+    NM head;
+    
+    k = g->m;
+    j = -1;
+    for ( i = 0; i <= k; i++ ) {
+        if ( !g->body[i] ) continue;
+        if ( j < 0 ) j = i;
+        else {
+            c = DL_COMPARE(HDL(g->body[i]),HDL(g->body[j]));
+            if ( c > 0 )
+                j = i;
+            else if ( c == 0 )
+                g->body[i] = nd_remove_head(g->body[i]);
+        }
+    }
+    if ( j < 0 ) return 0;
+    else {
+        head = BDY(g->body[j]);
+        if ( !NEXT(head) ) {
+            FREEND(g->body[j]);
+            g->body[j] = 0;
+        } else {
+            BDY(g->body[j]) = NEXT(head);
+            LEN(g->body[j])--;
+        }
+        return head;
+    }
+}
+
 int head_pbucket(int mod,PGeoBucket g)
 {
-	int j,i,c,k,nv,sum;
-	unsigned int *di,*dj;
-	ND gi,gj;
+    int j,i,c,k,nv,sum;
+    UINT *di,*dj;
+    ND gi,gj;
 
-	k = g->m;
-	while ( 1 ) {
-		j = -1;
-		for ( i = 0; i <= k; i++ ) {
-			if ( !(gi = g->body[i]) )
-				continue;
-			if ( j < 0 ) {
-				j = i;
-				gj = g->body[j];
-				dj = HDL(gj);
-				sum = HCM(gj);
-			} else {
-				di = HDL(gi);
-				nv = NV(gi);
-				c = NM_COMPARE(BDY(gi),BDY(gj));
-				if ( c > 0 ) {
-					if ( sum )
-						HCM(gj) = sum;
-					else
-						g->body[j] = nd_remove_head(gj);
-					j = i;
-					gj = g->body[j];
-					dj = HDL(gj);
-					sum = HCM(gj);
-				} else if ( c == 0 ) {
-					sum = sum+HCM(gi)-mod;
-					if ( sum < 0 )
-						sum += mod;
-					g->body[i] = nd_remove_head(gi);
-				}
-			}
-		}
-		if ( j < 0 )
-			return -1;
-		else if ( sum ) {
-			HCM(gj) = sum;
-			return j;
-		} else
-			g->body[j] = nd_remove_head(gj);
-	}
+    k = g->m;
+    while ( 1 ) {
+        j = -1;
+        for ( i = 0; i <= k; i++ ) {
+            if ( !(gi = g->body[i]) )
+                continue;
+            if ( j < 0 ) {
+                j = i;
+                gj = g->body[j];
+                dj = HDL(gj);
+                sum = HCM(gj);
+            } else {
+                c = DL_COMPARE(HDL(gi),dj);
+                if ( c > 0 ) {
+                    if ( sum ) HCM(gj) = sum;
+                    else g->body[j] = nd_remove_head(gj);
+                    j = i;
+                    gj = g->body[j];
+                    dj = HDL(gj);
+                    sum = HCM(gj);
+                } else if ( c == 0 ) {
+                    if ( mod == -1 )
+                        sum = _addsf(sum,HCM(gi));
+                    else {
+                        sum = sum+HCM(gi)-mod;
+                        if ( sum < 0 ) sum += mod;
+                    }
+                    g->body[i] = nd_remove_head(gi);
+                }
+            }
+        }
+        if ( j < 0 ) return -1;
+        else if ( sum ) {
+            HCM(gj) = sum;
+            return j;
+        } else
+            g->body[j] = nd_remove_head(gj);
+    }
 }
 
 int head_pbucket_q(PGeoBucket g)
 {
-	int j,i,c,k,nv;
-	Q sum,t;
-	unsigned int *di,*dj;
-	ND gi,gj;
+    int j,i,c,k,nv;
+    Q sum,t;
+    ND gi,gj;
 
-	k = g->m;
-	while ( 1 ) {
-		j = -1;
-		for ( i = 0; i <= k; i++ ) {
-			if ( !(gi = g->body[i]) )
-				continue;
-			if ( j < 0 ) {
-				j = i;
-				gj = g->body[j];
-				dj = HDL(gj);
-				sum = HCQ(gj);
-			} else {
-				di = HDL(gi);
-				nv = NV(gi);
-				c = NM_COMPARE(BDY(gi),BDY(gj));
-				if ( c > 0 ) {
-					if ( sum )
-						HCQ(gj) = sum;
-					else
-						g->body[j] = nd_remove_head(gj);
-					j = i;
-					gj = g->body[j];
-					dj = HDL(gj);
-					sum = HCQ(gj);
-				} else if ( c == 0 ) {
-					addq(sum,HCQ(gi),&t);
-					sum = t;
-					g->body[i] = nd_remove_head(gi);
-				}
-			}
-		}
-		if ( j < 0 )
-			return -1;
-		else if ( sum ) {
-			HCQ(gj) = sum;
-			return j;
-		} else
-			g->body[j] = nd_remove_head(gj);
-	}
+    k = g->m;
+    while ( 1 ) {
+        j = -1;
+        for ( i = 0; i <= k; i++ ) {
+            if ( !(gi = g->body[i]) ) continue;
+            if ( j < 0 ) {
+                j = i;
+                gj = g->body[j];
+                sum = HCQ(gj);
+            } else {
+                nv = NV(gi);
+                c = DL_COMPARE(HDL(gi),HDL(gj));
+                if ( c > 0 ) {
+                    if ( sum ) HCQ(gj) = sum;
+                    else g->body[j] = nd_remove_head(gj);
+                    j = i;
+                    gj = g->body[j];
+                    sum = HCQ(gj);
+                } else if ( c == 0 ) {
+                    addq(sum,HCQ(gi),&t);
+                    sum = t;
+                    g->body[i] = nd_remove_head(gi);
+                }
+            }
+        }
+        if ( j < 0 ) return -1;
+        else if ( sum ) {
+            HCQ(gj) = sum;
+            return j;
+        } else
+            g->body[j] = nd_remove_head(gj);
+    }
 }
 
 ND normalize_pbucket(int mod,PGeoBucket g)
 {
-	int i;
-	ND r,t;
+    int i;
+    ND r,t;
 
-	r = 0;
-	for ( i = 0; i <= g->m; i++ ) {
-		r = nd_add(mod,r,g->body[i]);
-		g->body[i] = 0;
-	}
-	g->m = -1;
-	return r;
+    r = 0;
+    for ( i = 0; i <= g->m; i++ ) {
+        r = nd_add(mod,r,g->body[i]);
+        g->body[i] = 0;
+    }
+    g->m = -1;
+    return r;
 }
 
+#if 0
+void register_hcf(NDV p)
+{
+    DCP dc,t;
+    P hc,h;
+    int c;
+    NODE l,l1,prev;
+
+    hc = p->body->c.p;
+    if ( !nd_vc || NUM(hc) ) return;
+    fctrp(nd_vc,hc,&dc);
+    for ( t = dc; t; t = NEXT(t) ) {
+        h = t->c;
+        if ( NUM(h) ) continue;
+        for ( prev = 0, l = nd_hcf; l; prev = l, l = NEXT(l) ) {
+            c = compp(nd_vc,h,(P)BDY(l));
+            if ( c >= 0 ) break;
+        }
+        if ( !l || c > 0  ) {
+            MKNODE(l1,h,l);
+            if ( !prev )
+                nd_hcf = l1;
+            else
+                NEXT(prev) = l1;
+        }
+    }
+}
+#else
+void register_hcf(NDV p)
+{
+    DCP dc,t;
+    P hc,h,q;
+    Q dmy;
+    int c;
+    NODE l,l1,prev;
+
+    hc = p->body->c.p;
+    if ( NUM(hc) ) return;
+    ptozp(hc,1,&dmy,&h);
+#if 1
+    for ( l = nd_hcf; l; l = NEXT(l) ) {
+        while ( 1 ) {
+            if ( divtpz(nd_vc,h,(P)BDY(l),&q) ) h = q;
+            else break;
+        }
+    }
+    if ( NUM(h) ) return;
+#endif
+    for ( prev = 0, l = nd_hcf; l; prev = l, l = NEXT(l) ) {
+        c = compp(nd_vc,h,(P)BDY(l));
+        if ( c >= 0 ) break;
+    }
+    if ( !l || c > 0  ) {
+        MKNODE(l1,h,l);
+        if ( !prev )
+            nd_hcf = l1;
+        else
+            NEXT(prev) = l1;
+    }
+}
+#endif
+
+int do_diagonalize(int sugar,int m)
+{
+    int i,nh,stat;
+    NODE r,g,t;
+    ND h,nf,s,head;
+    NDV nfv;
+    Q q,num,den;
+    P nm,nmp,dn,mnp,dnp,cont,cont1;
+    union oNDC hc;
+    NODE node;
+    LIST l;
+    Q iq;
+
+    for ( i = nd_psn-1; i >= 0 && SG(nd_psh[i]) == sugar; i-- ) {
+        if ( nd_gentrace ) {
+            /* Trace = [1,index,1,1] */
+            STOQ(i,iq); node = mknode(4,ONE,iq,ONE,ONE);
+            MKLIST(l,node); MKNODE(nd_tracelist,l,0);
+        }
+        if ( nd_demand )
+            nfv = ndv_load(i);
+        else
+            nfv = nd_ps[i];
+        s = ndvtond(m,nfv);
+        s = nd_separate_head(s,&head);
+        stat = nd_nf(m,head,s,nd_ps,1,0,&nf);
+        if ( !stat ) return 0;
+        ndv_free(nfv);
+        hc = HCU(nf); nd_removecont(m,nf);
+        cont = ndc_div(m,hc,HCU(nf));
+		if ( nd_gentrace ) finalize_tracelist(i,cont);
+        nfv = ndtondv(m,nf);
+        nd_free(nf);
+        nd_bound[i] = ndv_compute_bound(nfv);
+        if ( !m ) register_hcf(nfv);
+        if ( nd_demand ) {
+            ndv_save(nfv,i);
+            ndv_free(nfv);
+        } else
+            nd_ps[i] = nfv;
+    }
+    return 1;
+}
+
 /* return value = 0 => input is not a GB */
 
-NODE nd_gb(int m,int checkonly)
+NODE nd_gb(int m,int ishomo,int checkonly,int gensyz,int **indp)
 {
-	int i,nh,sugar,stat;
-	NODE r,g,t;
-	ND_pairs d;
-	ND_pairs l;
-	ND h,nf;
+    int i,nh,sugar,stat;
+    NODE r,g,t;
+    ND_pairs d;
+    ND_pairs l;
+    ND h,nf,s,head,nf1;
+    NDV nfv;
+    Q q,num,den;
+    union oNDC dn,hc;
+    int diag_count = 0;
+    P cont;
+    LIST list;
 
-	g = 0; d = 0;
-	for ( i = 0; i < nd_psn; i++ ) {
-		d = update_pairs(d,g,i);
-		g = update_base(g,i);
-	}
-	sugar = 0;
-	while ( d ) {
+    g = 0; d = 0;
+    for ( i = 0; i < nd_psn; i++ ) {
+        d = update_pairs(d,g,i,gensyz);
+        g = update_base(g,i);
+    }
+    sugar = 0;
+    while ( d ) {
 again:
-		l = nd_minp(d,&d);
-		if ( SG(l) != sugar ) {
-			sugar = SG(l);
-			fprintf(asir_out,"%d",sugar);
-		}
-		stat = nd_sp(m,l,&h);
-		if ( !stat ) {
-			NEXT(l) = d; d = l;
-			d = nd_reconstruct(m,0,d);
-			goto again;
-		}
-		stat = m?nd_nf_pbucket(m,h,!Top,&nf):nd_nf(m,h,!Top,&nf);
-		if ( !stat ) {
-			NEXT(l) = d; d = l;
-			d = nd_reconstruct(m,0,d);
-			goto again;
-		} else if ( nf ) {
-			if ( checkonly ) return 0;
-			printf("+"); fflush(stdout);
-			nh = nd_newps(m,nf);
-			d = update_pairs(d,g,nh);
-			g = update_base(g,nh);
-			FREENDP(l);
-		} else {
-			printf("."); fflush(stdout);
-			FREENDP(l);
-		}
-	}
-	if ( m )
-		for ( t = g; t; t = NEXT(t) )
-			BDY(t) = (pointer)nd_ps[(int)BDY(t)];
-	else
-		for ( t = g; t; t = NEXT(t) )
-			BDY(t) = (pointer)nd_psq[(int)BDY(t)];
-	return g;
+        l = nd_minp(d,&d);
+        if ( SG(l) != sugar ) {
+            if ( ishomo ) {
+                diag_count = 0;
+                stat = do_diagonalize(sugar,m);
+                if ( !stat ) {
+                    NEXT(l) = d; d = l;
+                    d = nd_reconstruct(0,d);
+                    goto again;
+                }
+            }
+            sugar = SG(l);
+            if ( DP_Print ) fprintf(asir_out,"%d",sugar);
+        }
+        stat = nd_sp(m,0,l,&h);
+        if ( !stat ) {
+            NEXT(l) = d; d = l;
+            d = nd_reconstruct(0,d);
+            goto again;
+        }
+#if USE_GEOBUCKET
+        stat = (m&&!nd_gentrace)?nd_nf_pbucket(m,h,nd_ps,!Top,&nf)
+               :nd_nf(m,0,h,nd_ps,!Top,0,&nf);
+#else
+        stat = nd_nf(m,0,h,nd_ps,!Top,0,&nf);
+#endif
+        if ( !stat ) {
+            NEXT(l) = d; d = l;
+            d = nd_reconstruct(0,d);
+            goto again;
+        } else if ( nf ) {
+            if ( checkonly || gensyz ) return 0;
+			if ( nd_newelim ) {
+				if ( nd_module ) {
+					if ( MPOS(HDL(nf)) > 1 ) return 0;
+				} else if ( !(HDL(nf)[nd_exporigin] & nd_mask[0]) ) return 0;
+			}
+            if ( DP_Print ) { printf("+"); fflush(stdout); }
+            hc = HCU(nf);
+            nd_removecont(m,nf);
+            if ( !m && nd_nalg ) {
+                nd_monic(0,&nf);
+                nd_removecont(m,nf);
+            }
+            if ( nd_gentrace ) {
+				cont = ndc_div(m,hc,HCU(nf));
+				if ( m || !UNIQ(cont) ) {
+                    t = mknode(4,NULLP,NULLP,NULLP,cont);
+                    MKLIST(list,t); MKNODE(t,list,nd_tracelist);
+					nd_tracelist = t;
+				}
+            }
+            nfv = ndtondv(m,nf); nd_free(nf);
+            nh = ndv_newps(m,nfv,0);
+            if ( !m && (ishomo && ++diag_count == diag_period) ) {
+                diag_count = 0;
+                stat = do_diagonalize(sugar,m);
+                if ( !stat ) {
+                    NEXT(l) = d; d = l;
+                    d = nd_reconstruct(1,d);
+                    goto again;
+                }
+            }
+            d = update_pairs(d,g,nh,0);
+            g = update_base(g,nh);
+            FREENDP(l);
+        } else {
+		    if ( nd_gentrace && gensyz ) {
+                nd_tracelist = reverse_node(nd_tracelist); 
+				MKLIST(list,nd_tracelist);
+                STOQ(-1,q); t = mknode(2,q,list); MKLIST(list,t);
+                MKNODE(t,list,nd_alltracelist); 
+				nd_alltracelist = t; nd_tracelist = 0;
+			}
+            if ( DP_Print ) { printf("."); fflush(stdout); }
+            FREENDP(l);
+        }
+    }
+	conv_ilist(nd_demand,0,g,indp);
+    if ( !checkonly && DP_Print ) { printf("nd_gb done.\n"); fflush(stdout); }
+    return g;
 }
 
-NODE nd_gb_trace(int m)
+int do_diagonalize_trace(int sugar,int m)
 {
-	int i,nh,sugar,stat;
-	NODE r,g,t;
-	ND_pairs d;
-	ND_pairs l;
-	ND h,nf,nfq;
+    int i,nh,stat;
+    NODE r,g,t;
+    ND h,nf,nfq,s,head;
+    NDV nfv,nfqv;
+    Q q,den,num;
+    union oNDC hc;
+    NODE node;
+    LIST l;
+    Q iq;
+    P cont,cont1;
 
-	g = 0; d = 0;
-	for ( i = 0; i < nd_psn; i++ ) {
-		d = update_pairs(d,g,i);
-		g = update_base(g,i);
-	}
-	sugar = 0;
-	while ( d ) {
+    for ( i = nd_psn-1; i >= 0 && SG(nd_psh[i]) == sugar; i-- ) {
+        if ( nd_gentrace ) {
+            /* Trace = [1,index,1,1] */
+            STOQ(i,iq); node = mknode(4,ONE,iq,ONE,ONE);
+            MKLIST(l,node); MKNODE(nd_tracelist,l,0);
+        }
+        /* for nd_ps */
+        s = ndvtond(m,nd_ps[i]);
+        s = nd_separate_head(s,&head);
+        stat = nd_nf_pbucket(m,s,nd_ps,1,&nf);
+        if ( !stat ) return 0;
+        nf = nd_add(m,head,nf);
+        ndv_free(nd_ps[i]);
+        nd_ps[i] = ndtondv(m,nf);
+        nd_free(nf);
+
+        /* for nd_ps_trace */
+        if ( nd_demand )
+            nfv = ndv_load(i);
+        else
+            nfv = nd_ps_trace[i];
+        s = ndvtond(0,nfv);
+        s = nd_separate_head(s,&head);
+        stat = nd_nf(0,head,s,nd_ps_trace,1,0,&nf);
+        if ( !stat ) return 0;
+        ndv_free(nfv);
+        hc = HCU(nf); nd_removecont(0,nf);
+		cont = ndc_div(0,hc,HCU(nf));
+        if ( nd_gentrace ) finalize_tracelist(i,cont);
+        nfv = ndtondv(0,nf);
+        nd_free(nf);
+        nd_bound[i] = ndv_compute_bound(nfv);
+        register_hcf(nfv);
+        if ( nd_demand ) {
+            ndv_save(nfv,i);
+            ndv_free(nfv);
+        } else
+            nd_ps_trace[i] = nfv;
+    }
+    return 1;
+}
+
+static struct oEGT eg_invdalg;
+struct oEGT eg_le;
+
+void nd_subst_vector(VL vl,P p,NODE subst,P *r)
+{
+    NODE tn;
+    P p1;
+
+    for ( tn = subst; tn; tn = NEXT(NEXT(tn)) ) {
+        substp(vl,p,BDY(tn),BDY(NEXT(tn)),&p1); p = p1;
+    }
+    *r = p;
+}
+
+NODE nd_gb_trace(int m,int ishomo,int **indp)
+{
+    int i,nh,sugar,stat;
+    NODE r,g,t;
+    ND_pairs d;
+    ND_pairs l;
+    ND h,nf,nfq,s,head;
+    NDV nfv,nfqv;
+    Q q,den,num;
+    P hc;
+    union oNDC dn,hnfq;
+    struct oEGT eg_monic,egm0,egm1;
+    int diag_count = 0;
+    P cont;
+    LIST list;
+
+    init_eg(&eg_monic);
+    init_eg(&eg_invdalg);
+    init_eg(&eg_le);
+    g = 0; d = 0;
+    for ( i = 0; i < nd_psn; i++ ) {
+        d = update_pairs(d,g,i,0);
+        g = update_base(g,i);
+    }
+    sugar = 0;
+    while ( d ) {
 again:
-		l = nd_minp(d,&d);
-		if ( SG(l) != sugar ) {
-			sugar = SG(l);
-			fprintf(asir_out,"%d",sugar);
-		}
-		stat = nd_sp(m,l,&h);
-		if ( !stat ) {
-			NEXT(l) = d; d = l;
-			d = nd_reconstruct(m,1,d);
-			goto again;
-		}
-		stat = nd_nf_pbucket(m,h,!Top,&nf);
-		if ( !stat ) {
-			NEXT(l) = d; d = l;
-			d = nd_reconstruct(m,1,d);
-			goto again;
-		} else if ( nf ) {
-			/* overflow does not occur */
-			nd_sp(0,l,&h);
-			nd_nf(0,h,!Top,&nfq);
-			if ( nfq ) {
-				printf("+"); fflush(stdout);
-				nh = nd_newps_trace(m,nf,nfq);
-				/* failure; m|HC(nfq) */
-				if ( nf < 0 ) return 0;
-				d = update_pairs(d,g,nh);
-				g = update_base(g,nh);
-			} else {
-				printf("*"); fflush(stdout);
-			}
-		} else {
-			printf("."); fflush(stdout);
-		}
-		FREENDP(l);
-	}
-	for ( t = g; t; t = NEXT(t) )
-		BDY(t) = (pointer)nd_psq[(int)BDY(t)];
-	return g;
+        l = nd_minp(d,&d);
+        if ( SG(l) != sugar ) {
+#if 1
+            if ( ishomo ) {
+                if ( DP_Print > 2 ) fprintf(asir_out,"|");
+                stat = do_diagonalize_trace(sugar,m);
+                if ( DP_Print > 2 ) fprintf(asir_out,"|");
+                diag_count = 0;
+                if ( !stat ) {
+                    NEXT(l) = d; d = l;
+                    d = nd_reconstruct(1,d);
+                    goto again;
+                }
+            }
+#endif
+            sugar = SG(l);
+            if ( DP_Print ) fprintf(asir_out,"%d",sugar);
+        }
+        stat = nd_sp(m,0,l,&h);
+        if ( !stat ) {
+            NEXT(l) = d; d = l;
+            d = nd_reconstruct(1,d);
+            goto again;
+        }
+#if USE_GEOBUCKET
+        stat = nd_nf_pbucket(m,h,nd_ps,!Top,&nf);
+#else
+        stat = nd_nf(m,0,h,nd_ps,!Top,0,&nf);
+#endif
+        if ( !stat ) {
+            NEXT(l) = d; d = l;
+            d = nd_reconstruct(1,d);
+            goto again;
+        } else if ( nf ) {
+            if ( nd_demand ) {
+                nfqv = ndv_load(nd_psn);
+                nfq = ndvtond(0,nfqv);
+            } else
+                nfq = 0;
+            if ( !nfq ) {
+                if ( !nd_sp(0,1,l,&h) || !nd_nf(0,0,h,nd_ps_trace,!Top,0,&nfq) ) {
+                    NEXT(l) = d; d = l;
+                    d = nd_reconstruct(1,d);
+                    goto again;
+                }
+            }
+            if ( nfq ) {
+                /* m|HC(nfq) => failure */
+                if ( nd_vc ) {
+                    nd_subst_vector(nd_vc,HCP(nfq),nd_subst,&hc); q = (Q)hc;
+                } else
+                    q = HCQ(nfq);
+                if ( !rem(NM(q),m) ) return 0;
+
+                if ( DP_Print ) { printf("+"); fflush(stdout); }
+                hnfq = HCU(nfq);
+                if ( nd_nalg ) {
+                    /* m|DN(HC(nf)^(-1)) => failure */
+                    get_eg(&egm0);
+                    if ( !nd_monic(m,&nfq) ) return 0;
+                    get_eg(&egm1); add_eg(&eg_monic,&egm0,&egm1);
+                    nd_removecont(0,nfq); nfqv = ndtondv(0,nfq); nd_free(nfq);
+                    nfv = ndv_dup(0,nfqv); ndv_mod(m,nfv); nd_free(nf);
+                } else {
+                    nd_removecont(0,nfq); nfqv = ndtondv(0,nfq); nd_free(nfq);
+                    nd_removecont(m,nf); nfv = ndtondv(m,nf); nd_free(nf);
+                }
+                if ( nd_gentrace ) {
+				   cont = ndc_div(0,hnfq,HCU(nfqv));
+				   if ( !UNIQ(cont) ) {
+                       t = mknode(4,NULLP,NULLP,NULLP,cont);
+                       MKLIST(list,t); MKNODE(t,list,nd_tracelist);
+					   nd_tracelist = t;
+				   }
+                }
+                nh = ndv_newps(0,nfv,nfqv);
+                if ( ishomo && ++diag_count == diag_period ) {
+                    diag_count = 0;
+                    if ( DP_Print > 2 ) fprintf(asir_out,"|");
+                    stat = do_diagonalize_trace(sugar,m);
+                    if ( DP_Print > 2 ) fprintf(asir_out,"|");
+                    if ( !stat ) {
+                        NEXT(l) = d; d = l;
+                        d = nd_reconstruct(1,d);
+                        goto again;
+                    }
+                }
+                d = update_pairs(d,g,nh,0);
+                g = update_base(g,nh);
+            } else {
+                if ( DP_Print ) { printf("*"); fflush(stdout); }
+            }
+        } else {
+            if ( DP_Print ) { printf("."); fflush(stdout); }
+        }
+        FREENDP(l);
+    }
+    if ( nd_nalg ) {
+        print_eg("monic",&eg_monic);
+        print_eg("invdalg",&eg_invdalg);
+        print_eg("le",&eg_le);
+    }
+	conv_ilist(nd_demand,1,g,indp);
+    if ( DP_Print ) { printf("nd_gb_trace done.\n"); fflush(stdout); }
+    return g;
 }
 
 int ndv_compare(NDV *p1,NDV *p2)
 {
-	int td1,td2;
-
-	if ( nd_degcompat ) {
-		td1 = HTD(*p1); td2 = HTD(*p2);
-		if ( td1 > td2 ) return 1;
-		else if ( td1 < td2 ) return -1;
-		else return ndl_compare(HDL(*p1),HDL(*p2));
-	} else
-		return (*nmv_compare_generic)(BDY(*p1),BDY(*p2));
+    return DL_COMPARE(HDL(*p1),HDL(*p2));
 }
 
 int ndv_compare_rev(NDV *p1,NDV *p2)
 {
-	return -ndv_compare(p1,p2);
+    return -DL_COMPARE(HDL(*p1),HDL(*p2));
 }
 
-NODE nd_reduceall(int m,NODE f)
+int ndvi_compare(NDVI p1,NDVI p2)
 {
-	int i,j,n,stat;
-	NDV *w,*ps;
-	ND nf,g;
-	NODE t,a0,a;
+    return DL_COMPARE(HDL(p1->p),HDL(p2->p));
+}
 
-	for ( n = 0, t = f; t; t = NEXT(t), n++ );
-	ps = (NDV *)ALLOCA(n*sizeof(NDV));
-	for ( i = 0, t = f; i < n; i++, t = NEXT(t) )
-		ps[i] = (NDV)BDY(t);
-	qsort(ps,n,sizeof(NDV),(int (*)(const void *,const void *))ndv_compare);
-	w = (NDV *)ALLOCA((n-1)*sizeof(NDV));
-	for ( i = 0; i < n; i++ ) {
-		for ( j = 0; j < i; j++ )
-			w[j] = (NDV)ps[j];
-		for ( j = i+1; j < n; j++ )
-			w[j-1] = ps[j];
-		g = ndvtond(m,ps[i]);
-		stat = nd_nf_direct(m,g,w,n-1,1,&nf);
-		if ( !stat )
-			nd_reconstruct_direct(m,ps,n);
-		else if ( !nf ) {
-			printf("."); fflush(stdout);
-			ndv_free(ps[i]);
-			for ( j = i+1; j < n; j++ )
-				ps[j-1] = ps[j];
-			n--;
-		} else {
-			printf("."); fflush(stdout);
-			ndv_free(ps[i]);
-			nd_removecont(m,nf);
-			ps[i] = ndtondv(m,nf);
-			nd_free(nf);
-		}
-	}
-	for ( a0 = 0, i = 0; i < n; i++ ) {
-		NEXTNODE(a0,a);
-		BDY(a) = (pointer)ps[i];
-	}
-	NEXT(a) = 0;
-	return a0;
+int ndvi_compare_rev(NDVI p1,NDVI p2)
+{
+    return -DL_COMPARE(HDL(p1->p),HDL(p2->p));
 }
 
-ND_pairs update_pairs( ND_pairs d, NODE /* of index */ g, int t)
+NODE ndv_reduceall(int m,NODE f)
 {
-	ND_pairs d1,nd,cur,head,prev,remove;
+    int i,j,n,stat;
+    ND nf,g,head;
+    NODE t,a0,a;
+    union oNDC dn;
+    Q q,num,den;
+    NODE node;
+	LIST l;
+	Q iq,jq;
+    int *perm;
+    union oNDC hc;
+    P cont,cont1;
 
-	if ( !g ) return d;
-	d = crit_B(d,t);
-	d1 = nd_newpairs(g,t);
-	d1 = crit_M(d1);
-	d1 = crit_F(d1);
-	prev = 0; cur = head = d1;
-	while ( cur ) {
-		if ( crit_2( cur->i1,cur->i2 ) ) {
-			remove = cur;
-			if ( !prev ) {
-				head = cur = NEXT(cur);
-			} else {
-				cur = NEXT(prev) = NEXT(cur);
-			}
-			FREENDP(remove);
-		} else {
-			prev = cur;
-			cur = NEXT(cur);
-		}
+    if ( nd_nora ) return f;
+    n = length(f);
+    ndv_setup(m,0,f,0,1);
+	perm = (int *)MALLOC(n*sizeof(int));
+	if ( nd_gentrace ) {
+	    for ( t = nd_tracelist, i = 0; i < n; i++, t = NEXT(t) )
+		    perm[i] = QTOS((Q)ARG1(BDY((LIST)BDY(t))));
 	}
-	if ( !d )
-		return head;
-	else {
-		nd = d;
-		while ( NEXT(nd) )
-			nd = NEXT(nd);
-		NEXT(nd) = head;
-		return d;
-	}
+    for ( i = 0; i < n; ) {
+        if ( nd_gentrace ) {
+            /* Trace = [1,index,1,1] */
+            STOQ(i,iq); node = mknode(4,ONE,iq,ONE,ONE);
+            MKLIST(l,node); MKNODE(nd_tracelist,l,0);
+        }
+        g = ndvtond(m,nd_ps[i]);
+        g = nd_separate_head(g,&head);
+        stat = nd_nf(m,head,g,nd_ps,1,0,&nf);
+        if ( !stat )
+            nd_reconstruct(0,0);
+        else {
+            if ( DP_Print ) { printf("."); fflush(stdout); }
+            ndv_free(nd_ps[i]);
+            hc = HCU(nf); nd_removecont(m,nf);
+            if ( nd_gentrace ) {
+				for ( t = nd_tracelist; t; t = NEXT(t) ) {
+                    jq = ARG1(BDY((LIST)BDY(t))); j = QTOS(jq);
+                    STOQ(perm[j],jq); ARG1(BDY((LIST)BDY(t))) = jq;
+                }
+                cont = ndc_div(m,hc,HCU(nf));
+                finalize_tracelist(perm[i],cont);
+            }
+            nd_ps[i] = ndtondv(m,nf); nd_free(nf);
+            nd_bound[i] = ndv_compute_bound(nd_ps[i]);
+            i++;
+        }
+    }
+    if ( DP_Print ) { printf("\n"); }
+    for ( a0 = 0, i = 0; i < n; i++ ) {
+        NEXTNODE(a0,a);
+		if ( !nd_gentrace ) BDY(a) = (pointer)nd_ps[i];
+		else {
+			for ( j = 0; j < n; j++ ) if ( perm[j] == i ) break;
+			BDY(a) = (pointer)nd_ps[j];
+		}
+    }
+    NEXT(a) = 0;
+    return a0;
 }
 
-ND_pairs nd_newpairs( NODE g, int t )
+ND_pairs update_pairs( ND_pairs d, NODE /* of index */ g, int t, int gensyz)
 {
-	NODE h;
-	unsigned int *dl;
-	int td,ts,s;
-	ND_pairs r,r0;
+    ND_pairs d1,nd,cur,head,prev,remove;
 
-	dl = DL(nd_psh[t]);
-	td = TD(nd_psh[t]);
-	ts = SG(nd_psh[t]) - td;
-	for ( r0 = 0, h = g; h; h = NEXT(h) ) {
-		NEXTND_pairs(r0,r);
-		r->i1 = (int)BDY(h);
-		r->i2 = t;
-		ndl_lcm(DL(nd_psh[r->i1]),dl,r->lcm);
-		TD(r) = ndl_td(r->lcm);
-		s = SG(nd_psh[r->i1])-TD(nd_psh[r->i1]);
-		SG(r) = MAX(s,ts) + TD(r);
+    if ( !g ) return d;
+	/* for testing */
+	if ( gensyz && nd_gensyz == 2 ) {
+    	d1 = nd_newpairs(g,t);
+    	if ( !d )
+       	 return d1;
+    	else {
+       	 nd = d;
+       	 while ( NEXT(nd) ) nd = NEXT(nd);
+       	 NEXT(nd) = d1;
+       	 return d;
+    	}
 	}
-	NEXT(r) = 0;
-	return r0;
+    d = crit_B(d,t);
+    d1 = nd_newpairs(g,t);
+    d1 = crit_M(d1);
+    d1 = crit_F(d1);
+    if ( gensyz || do_weyl )
+        head = d1;
+    else {
+        prev = 0; cur = head = d1;
+        while ( cur ) {
+            if ( crit_2( cur->i1,cur->i2 ) ) {
+                remove = cur;
+                if ( !prev ) head = cur = NEXT(cur);
+                else cur = NEXT(prev) = NEXT(cur);
+                FREENDP(remove);
+            } else {
+                prev = cur; cur = NEXT(cur);
+            }
+        }
+    }
+    if ( !d )
+        return head;
+    else {
+        nd = d;
+        while ( NEXT(nd) ) nd = NEXT(nd);
+        NEXT(nd) = head;
+        return d;
+    }
 }
 
-ND_pairs crit_B( ND_pairs d, int s )
+
+ND_pairs nd_newpairs( NODE g, int t )
 {
-	ND_pairs cur,head,prev,remove;
-	unsigned int *t,*tl,*lcm;
-	int td,tdl;
+    NODE h;
+    UINT *dl;
+    int ts,s,i,t0,min,max;
+    ND_pairs r,r0;
 
-	if ( !d ) return 0;
-	t = DL(nd_psh[s]);
-	prev = 0;
-	head = cur = d;
-	lcm = (unsigned int *)ALLOCA(nd_wpd*sizeof(unsigned int));
-	while ( cur ) {
-		tl = cur->lcm;
-		if ( ndl_reducible(tl,t)
-			&& (ndl_lcm(DL(nd_psh[cur->i1]),t,lcm),!ndl_equal(lcm,tl))
-			&& (ndl_lcm(DL(nd_psh[cur->i2]),t,lcm),!ndl_equal(lcm,tl)) ) {
-			remove = cur;
-			if ( !prev ) {
-				head = cur = NEXT(cur);
-			} else {
-				cur = NEXT(prev) = NEXT(cur);
+    dl = DL(nd_psh[t]);
+    ts = SG(nd_psh[t]) - TD(dl);
+	if ( nd_module && nd_intersect && (MPOS(dl) > 1) ) return 0;
+    for ( r0 = 0, h = g; h; h = NEXT(h) ) {
+        if ( nd_module && (MPOS(DL(nd_psh[(long)BDY(h)])) != MPOS(dl)) )
+                continue;
+		if ( nd_gbblock ) {
+			t0 = (long)BDY(h);
+			for ( i = 0; nd_gbblock[i] >= 0; i += 2 ) {
+				min = nd_gbblock[i]; max = nd_gbblock[i+1];
+				if ( t0 >= min && t0 <= max && t >= min && t <= max )
+					break;
 			}
-			FREENDP(remove);
-		} else {
-			prev = cur;
-			cur = NEXT(cur);
+			if ( nd_gbblock[i] >= 0 )
+				continue;
 		}
-	}
-	return head;
+        NEXTND_pairs(r0,r);
+        r->i1 = (long)BDY(h);
+        r->i2 = t;
+        ndl_lcm(DL(nd_psh[r->i1]),dl,r->lcm);
+        s = SG(nd_psh[r->i1])-TD(DL(nd_psh[r->i1]));
+        SG(r) = MAX(s,ts) + TD(LCM(r));
+    }
+    if ( r0 ) NEXT(r) = 0;
+    return r0;
 }
 
+/* kokokara */
+
+ND_pairs crit_B( ND_pairs d, int s )
+{
+    ND_pairs cur,head,prev,remove;
+    UINT *t,*tl,*lcm;
+    int td,tdl;
+
+    if ( !d ) return 0;
+    t = DL(nd_psh[s]);
+    prev = 0;
+    head = cur = d;
+    lcm = (UINT *)ALLOCA(nd_wpd*sizeof(UINT));
+    while ( cur ) {
+        tl = cur->lcm;
+        if ( ndl_reducible(tl,t) ) {
+            ndl_lcm(DL(nd_psh[cur->i1]),t,lcm);
+            if ( !ndl_equal(lcm,tl) ) {
+                ndl_lcm(DL(nd_psh[cur->i2]),t,lcm);
+                if (!ndl_equal(lcm,tl)) {
+                    remove = cur;
+                    if ( !prev ) {
+                        head = cur = NEXT(cur);
+                    } else {
+                        cur = NEXT(prev) = NEXT(cur);
+                    }
+                    FREENDP(remove);
+                } else {
+                    prev = cur; cur = NEXT(cur);
+                }
+            } else {
+                    prev = cur; cur = NEXT(cur);
+            }
+        } else {
+            prev = cur; cur = NEXT(cur);
+        }
+    }
+    return head;
+}
+
 ND_pairs crit_M( ND_pairs d1 )
 {
-	ND_pairs e,d2,d3,dd,p;
-	unsigned int *id,*jd;
-	int itd,jtd;
+    ND_pairs e,d2,d3,dd,p;
+    UINT *id,*jd;
 
-	for ( dd = 0, e = d1; e; e = d3 ) {
-		if ( !(d2 = NEXT(e)) ) {
-			NEXT(e) = dd;
-			return e;
-		}
-		id = e->lcm;
-		itd = TD(e);
-		for ( d3 = 0; d2; d2 = p ) {
-			p = NEXT(d2),
-			jd = d2->lcm;
-			jtd = TD(d2);
-			if ( jtd == itd  )
-				if ( id == jd );
-				else if ( ndl_reducible(jd,id) ) continue;
-				else if ( ndl_reducible(id,jd) ) goto delit;
-				else ;
-			else if ( jtd > itd )
-				if ( ndl_reducible(jd,id) ) continue;
-				else ;
-			else if ( ndl_reducible(id,jd ) ) goto delit;
-			NEXT(d2) = d3;
-			d3 = d2;
-		}
-		NEXT(e) = dd;
-		dd = e;
-		continue;
-		/**/
-	delit:	NEXT(d2) = d3;
-		d3 = d2;
-		for ( ; p; p = d2 ) {
-			d2 = NEXT(p);
-			NEXT(p) = d3;
-			d3 = p;
-		}
-		FREENDP(e);
-	}
-	return dd;
+    if ( !d1 ) return d1;
+    for ( dd = 0, e = d1; e; e = d3 ) {
+        if ( !(d2 = NEXT(e)) ) {
+            NEXT(e) = dd;
+            return e;
+        }
+        id = LCM(e);
+        for ( d3 = 0; d2; d2 = p ) {
+            p = NEXT(d2);
+            jd = LCM(d2);
+            if ( ndl_equal(jd,id) )
+                ;
+            else if ( TD(jd) > TD(id) )
+                if ( ndl_reducible(jd,id) ) continue;
+                else ;
+            else if ( ndl_reducible(id,jd) ) goto delit;
+            NEXT(d2) = d3;
+            d3 = d2;
+        }
+        NEXT(e) = dd;
+        dd = e;
+        continue;
+        /**/
+    delit:    NEXT(d2) = d3;
+        d3 = d2;
+        for ( ; p; p = d2 ) {
+            d2 = NEXT(p);
+            NEXT(p) = d3;
+            d3 = p;
+        }
+        FREENDP(e);
+    }
+    return dd;
 }
 
 ND_pairs crit_F( ND_pairs d1 )
 {
-	ND_pairs rest, head,remove;
-	ND_pairs last, p, r, w;
-	int s;
+    ND_pairs rest, head,remove;
+    ND_pairs last, p, r, w;
+    int s;
 
-	for ( head = last = 0, p = d1; NEXT(p); ) {
-		r = w = equivalent_pairs(p,&rest);
-		s = SG(r);
-		w = NEXT(w);
-		while ( w ) {
-			if ( crit_2(w->i1,w->i2) ) {
-				r = w;
-				w = NEXT(w);
-				while ( w ) {
-					remove = w;
-					w = NEXT(w);
-					FREENDP(remove);
-				}
-				break;
-			} else if ( SG(w) < s ) {
-				FREENDP(r);
-				r = w;
-				s = SG(r);
-				w = NEXT(w);
-			} else {
-				remove = w;
-				w = NEXT(w);
-				FREENDP(remove);
-			}
-		}
-		if ( last ) NEXT(last) = r;
-		else head = r;
-		NEXT(last = r) = 0;
-		p = rest;
-		if ( !p ) return head;
-	}
-	if ( !last ) return p;
-	NEXT(last) = p;
-	return head;
+    if ( !d1 ) return d1;
+    for ( head = last = 0, p = d1; NEXT(p); ) {
+        r = w = equivalent_pairs(p,&rest);
+        s = SG(r);
+        w = NEXT(w);
+        while ( w ) {
+            if ( crit_2(w->i1,w->i2) ) {
+                r = w;
+                w = NEXT(w);
+                while ( w ) {
+                    remove = w;
+                    w = NEXT(w);
+                    FREENDP(remove);
+                }
+                break;
+            } else if ( SG(w) < s ) {
+                FREENDP(r);
+                r = w;
+                s = SG(r);
+                w = NEXT(w);
+            } else {
+                remove = w;
+                w = NEXT(w);
+                FREENDP(remove);
+            }
+        }
+        if ( last ) NEXT(last) = r;
+        else head = r;
+        NEXT(last = r) = 0;
+        p = rest;
+        if ( !p ) return head;
+    }
+    if ( !last ) return p;
+    NEXT(last) = p;
+    return head;
 }
 
 int crit_2( int dp1, int dp2 )
 {
-	return ndl_disjoint(DL(nd_psh[dp1]),DL(nd_psh[dp2]));
+    return ndl_disjoint(DL(nd_psh[dp1]),DL(nd_psh[dp2]));
 }
 
-static ND_pairs equivalent_pairs( ND_pairs d1, ND_pairs *prest )
+ND_pairs equivalent_pairs( ND_pairs d1, ND_pairs *prest )
 {
-	ND_pairs w,p,r,s;
-	unsigned int *d;
-	int td;
+    ND_pairs w,p,r,s;
+    UINT *d;
 
-	w = d1;
-	d = w->lcm;
-	td = TD(w);
-	s = NEXT(w);
-	NEXT(w) = 0;
-	for ( r = 0; s; s = p ) {
-		p = NEXT(s);
-		if ( td == TD(s) && ndl_equal(d,s->lcm) ) {
-			NEXT(s) = w;
-			w = s;
-		} else {
-			NEXT(s) = r;
-			r = s;
-		}
-	}
-	*prest = r;
-	return w;
+    w = d1;
+    d = LCM(w);
+    s = NEXT(w);
+    NEXT(w) = 0;
+    for ( r = 0; s; s = p ) {
+        p = NEXT(s);
+        if ( ndl_equal(d,LCM(s)) ) {
+            NEXT(s) = w; w = s;
+        } else {
+            NEXT(s) = r; r = s;
+        }
+    }
+    *prest = r;
+    return w;
 }
 
 NODE update_base(NODE nd,int ndp)
 {
-	unsigned int *dl, *dln;
-	NODE last, p, head;
-	int td,tdn;
+    UINT *dl, *dln;
+    NODE last, p, head;
 
-	dl = DL(nd_psh[ndp]);
-	td = TD(nd_psh[ndp]);
-	for ( head = last = 0, p = nd; p; ) {
-		dln = DL(nd_psh[(int)BDY(p)]);
-		tdn = TD(nd_psh[(int)BDY(p)]);
-		if ( tdn >= td && ndl_reducible( dln, dl ) ) {
-			p = NEXT(p);
-			if ( last ) NEXT(last) = p;
-		} else {
-			if ( !last ) head = p;
-			p = NEXT(last = p);
-		}
-	}
-	head = append_one(head,ndp);
-	return head;
+    dl = DL(nd_psh[ndp]);
+    for ( head = last = 0, p = nd; p; ) {
+        dln = DL(nd_psh[(long)BDY(p)]);
+        if ( ndl_reducible( dln, dl ) ) {
+            p = NEXT(p);
+            if ( last ) NEXT(last) = p;
+        } else {
+            if ( !last ) head = p;
+            p = NEXT(last = p);
+        }
+    }
+    head = append_one(head,ndp);
+    return head;
 }
 
 ND_pairs nd_minp( ND_pairs d, ND_pairs *prest )
 {
-	ND_pairs m,ml,p,l;
-	unsigned int *lcm;
-	int s,td,len,tlen,c;
+    ND_pairs m,ml,p,l;
+    UINT *lcm;
+    int s,td,len,tlen,c,c1;
 
-	if ( !(p = NEXT(m = d)) ) {
-		*prest = p;
-		NEXT(m) = 0;
-		return m;
-	}
-	lcm = m->lcm;
-	s = SG(m);
-	td = TD(m);
-	len = nd_psl[m->i1]+nd_psl[m->i2];
-	for ( ml = 0, l = m; p; p = NEXT(l = p) ) {
-		if (SG(p) < s)
-			goto find;
-		else if ( SG(p) == s ) {
-			if ( TD(p) < td )
-				goto find;
-			else if ( TD(p) == td ) {
-				c = ndl_compare(p->lcm,lcm);
-				if ( c < 0 )
-					goto find;
-			}
-		}
-		continue;
-find:
-		ml = l;
-		m = p;
-		lcm = m->lcm;
-		s = SG(m);
-		td = TD(m);
-		len = tlen;
-	}
-	if ( !ml ) *prest = NEXT(m);
-	else {
-		NEXT(ml) = NEXT(m);
-		*prest = d;
-	}
-	NEXT(m) = 0;
-	return m;
+    if ( !(p = NEXT(m = d)) ) {
+        *prest = p;
+        NEXT(m) = 0;
+        return m;
+    }
+    s = SG(m);
+    if ( !NoSugar ) {
+        for ( ml = 0, l = m; p; p = NEXT(l = p) )
+            if ( (SG(p) < s) 
+                || ((SG(p) == s) && (DL_COMPARE(LCM(p),LCM(m)) < 0)) ) {
+                ml = l; m = p; s = SG(m);
+            }
+    } else {
+        for ( ml = 0, l = m; p; p = NEXT(l = p) )
+            if ( DL_COMPARE(LCM(p),LCM(m)) < 0 ) {
+                ml = l; m = p; s = SG(m);
+            }
+    }
+    if ( !ml ) *prest = NEXT(m);
+    else {
+        NEXT(ml) = NEXT(m);
+        *prest = d;
+    }
+    NEXT(m) = 0;
+    return m;
 }
 
-int nd_newps(int mod,ND a)
+ND_pairs nd_minsugarp( ND_pairs d, ND_pairs *prest )
 {
-	int len;
-	RHist r;
-	NDV b;
+    int msugar,i;
+    ND_pairs t,dm0,dm,dr0,dr;
 
-	if ( nd_psn == nd_pslen ) {
-		nd_pslen *= 2;
-		nd_psl = (int *)REALLOC((char *)nd_psl,nd_pslen*sizeof(int));
-		nd_ps = (NDV *)REALLOC((char *)nd_ps,nd_pslen*sizeof(NDV));
-		nd_psq = (NDV *)REALLOC((char *)nd_psq,nd_pslen*sizeof(NDV));
-		nd_psh = (RHist *)REALLOC((char *)nd_psh,nd_pslen*sizeof(RHist));
-		nd_bound = (unsigned int **)
-			REALLOC((char *)nd_bound,nd_pslen*sizeof(unsigned int *));
-	}
-	nd_removecont(mod,a);
-	nd_bound[nd_psn] = nd_compute_bound(a);
-	NEWRHist(r); SG(r) = SG(a); TD(r) = HTD(a); ndl_copy(HDL(a),DL(r)); 
-	nd_psh[nd_psn] = r;
-	b = ndtondv(mod,a);
-	len = LEN(b);
-	if ( mod )
-		nd_ps[nd_psn] = b;
-	else
-		nd_psq[nd_psn] = b;
-	nd_psl[nd_psn] = len;
-	nd_free(a);
-	return nd_psn++;
+    for ( msugar = SG(d), t = NEXT(d); t; t = NEXT(t) )
+        if ( SG(t) < msugar ) msugar = SG(t);
+    dm0 = 0; dr0 = 0;
+    for ( i = 0, t = d; t; t = NEXT(t) )
+        if ( i < nd_f4_nsp && SG(t) == msugar ) {
+            if ( dm0 ) NEXT(dm) = t;
+            else dm0 = t;
+            dm = t;
+            i++;
+        } else {
+            if ( dr0 ) NEXT(dr) = t;
+            else dr0 = t;
+            dr = t;
+        }
+    NEXT(dm) = 0;
+    if ( dr0 ) NEXT(dr) = 0;
+    *prest = dr0;
+    return dm0;
 }
 
-int nd_newps_trace(int mod,ND nf,ND nfq)
+int ndv_newps(int m,NDV a,NDV aq)
 {
-	int len;
-	RHist r;
-	NDV b;
+    int len;
+    RHist r;
+    NDV b;
+    NODE tn;
+    LIST l;
+    Q iq;
 
-	if ( nd_psn == nd_pslen ) {
-		nd_pslen *= 2;
-		nd_psl = (int *)REALLOC((char *)nd_psl,nd_pslen*sizeof(int));
-		nd_ps = (NDV *)REALLOC((char *)nd_ps,nd_pslen*sizeof(NDV));
-		nd_psq = (NDV *)REALLOC((char *)nd_psq,nd_pslen*sizeof(NDV));
-		nd_psh = (RHist *)REALLOC((char *)nd_psh,nd_pslen*sizeof(RHist));
-		nd_bound = (unsigned int **)
-			REALLOC((char *)nd_bound,nd_pslen*sizeof(unsigned int *));
-	}
-	if ( !rem(NM(HCQ(nfq)),mod) ) return -1;
-	nd_removecont(mod,nf);
-	nd_ps[nd_psn] = ndtondv(mod,nf);
+    if ( nd_psn == nd_pslen ) {
+        nd_pslen *= 2;
+        nd_ps = (NDV *)REALLOC((char *)nd_ps,nd_pslen*sizeof(NDV));
+        nd_ps_trace = (NDV *)REALLOC((char *)nd_ps_trace,nd_pslen*sizeof(NDV));
+        nd_psh = (RHist *)REALLOC((char *)nd_psh,nd_pslen*sizeof(RHist));
+        nd_bound = (UINT **)
+            REALLOC((char *)nd_bound,nd_pslen*sizeof(UINT *));
+    }
+    NEWRHist(r); nd_psh[nd_psn] = r;
+    nd_ps[nd_psn] = a;
+    if ( aq ) {
+        nd_ps_trace[nd_psn] = aq;
+        register_hcf(aq);
+        nd_bound[nd_psn] = ndv_compute_bound(aq);
+        SG(r) = SG(aq); ndl_copy(HDL(aq),DL(r));
+    } else {
+        if ( !m ) register_hcf(a);
+        nd_bound[nd_psn] = ndv_compute_bound(a);
+        SG(r) = SG(a); ndl_copy(HDL(a),DL(r));
+    }
+    if ( nd_demand ) {
+        if ( aq ) {
+            ndv_save(nd_ps_trace[nd_psn],nd_psn);
+            nd_ps_trace[nd_psn] = 0;
+        } else {
+            ndv_save(nd_ps[nd_psn],nd_psn);
+            nd_ps[nd_psn] = 0;
+        }
+    }
+    if ( nd_gentrace ) {
+        /* reverse the tracelist and append it to alltracelist */
+        nd_tracelist = reverse_node(nd_tracelist); MKLIST(l,nd_tracelist);
+        STOQ(nd_psn,iq); tn = mknode(2,iq,l); MKLIST(l,tn);
+        MKNODE(tn,l,nd_alltracelist); nd_alltracelist = tn; nd_tracelist = 0;
+    }
+    return nd_psn++;
+}
 
-	nd_removecont(0,nfq);
-	nd_psq[nd_psn] = ndtondv(0,nfq);
+/* nd_tracelist = [[0,index,div],...,[nd_psn-1,index,div]] */
+/* return 1 if success, 0 if failure (HC(a mod p)) */
 
-	nd_bound[nd_psn] = nd_compute_bound(nfq);
-	NEWRHist(r); SG(r) = SG(nf); TD(r) = HTD(nf); ndl_copy(HDL(nf),DL(r)); 
-	nd_psh[nd_psn] = r;
+int ndv_setup(int mod,int trace,NODE f,int dont_sort,int dont_removecont)
+{
+    int i,j,td,len,max;
+    NODE s,s0,f0,tn;
+    UINT *d;
+    RHist r;
+    NDVI w;
+    NDV a,am;
+    union oNDC hc;
+    NODE node;
+    P hcp;
+    Q iq,jq,hcq;
+    LIST l;
 
-	len = LEN(nd_psq[nd_psn]);
-	nd_psl[nd_psn] = len;
+    nd_found = 0; nd_notfirst = 0; nd_create = 0;
+    /* initialize the tracelist */
+    nd_tracelist = 0;
 
-	nd_free(nf); nd_free(nfq);
-	return nd_psn++;
+    for ( nd_psn = 0, s = f; s; s = NEXT(s) ) if ( BDY(s) ) nd_psn++;
+    w = (NDVI)ALLOCA(nd_psn*sizeof(struct oNDVI));
+    for ( i = j = 0, s = f; s; s = NEXT(s), j++ ) 
+        if ( BDY(s) ) { w[i].p = BDY(s); w[i].i = j; i++; }
+    if ( !dont_sort ) {
+        /* XXX heuristic */
+        if ( !nd_ord->id && (nd_ord->ord.simple<2) )
+            qsort(w,nd_psn,sizeof(struct oNDVI),
+                (int (*)(const void *,const void *))ndvi_compare_rev);
+        else
+            qsort(w,nd_psn,sizeof(struct oNDVI),
+                (int (*)(const void *,const void *))ndvi_compare);
+    }
+    nd_pslen = 2*nd_psn;
+    nd_ps = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
+    nd_ps_trace = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
+    nd_psh = (RHist *)MALLOC(nd_pslen*sizeof(RHist));
+    nd_bound = (UINT **)MALLOC(nd_pslen*sizeof(UINT *));
+    nd_hcf = 0;
+
+    if ( trace && nd_vc )
+        makesubst(nd_vc,&nd_subst);
+    else
+        nd_subst = 0;
+
+    if ( !nd_red )
+        nd_red = (RHist *)MALLOC(REDTAB_LEN*sizeof(RHist));
+    for ( i = 0; i < REDTAB_LEN; i++ ) nd_red[i] = 0;
+    for ( i = 0; i < nd_psn; i++ ) {
+        hc = HCU(w[i].p);
+        if ( trace ) {
+            a = nd_ps_trace[i] = ndv_dup(0,w[i].p);
+            if ( !dont_removecont) ndv_removecont(0,a);
+            register_hcf(a);
+            am = nd_ps[i] = ndv_dup(mod,a);
+            ndv_mod(mod,am);
+	    if ( DL_COMPARE(HDL(am),HDL(a)) ) 
+	    	return 0;
+            ndv_removecont(mod,am);
+        } else {
+            a = nd_ps[i] = ndv_dup(mod,w[i].p);
+            if ( mod || !dont_removecont ) ndv_removecont(mod,a);
+            if ( !mod ) register_hcf(a);
+        }
+        if ( nd_gentrace ) {
+            STOQ(i,iq); STOQ(w[i].i,jq); node = mknode(3,iq,jq,ONE);
+			if ( !dont_removecont )
+                ARG2(node) = (pointer)ndc_div(trace?0:mod,hc,HCU(a));
+            MKLIST(l,node); NEXTNODE(nd_tracelist,tn); BDY(tn) = l;
+        }
+        NEWRHist(r); SG(r) = HTD(a); ndl_copy(HDL(a),DL(r));
+        nd_bound[i] = ndv_compute_bound(a);
+        nd_psh[i] = r;
+        if ( nd_demand ) {
+            if ( trace ) {
+                ndv_save(nd_ps_trace[i],i);
+                nd_ps_trace[i] = 0;
+            } else {
+                ndv_save(nd_ps[i],i);
+                nd_ps[i] = 0;
+            }
+        }
+    }
+    if ( nd_gentrace && nd_tracelist ) NEXT(tn) = 0;
+    return 1;
 }
 
-void nd_setup(int mod,NODE f)
+struct order_spec *append_block(struct order_spec *spec,
+    int nv,int nalg,int ord);
+
+extern VECT current_dl_weight_vector_obj;
+static VECT prev_weight_vector_obj;
+
+void preprocess_algcoef(VL vv,VL av,struct order_spec *ord,LIST f,
+    struct order_spec **ord1p,LIST *f1p,NODE *alistp)
 {
-	int i,j,td,len,max;
-	NODE s,s0,f0;
-	unsigned int *d;
-	RHist r;
-	NDV a;
+    NODE alist,t,s,r0,r,arg;
+    VL tv;
+    P poly;
+    DP d;
+    Alg alpha,dp;
+    DAlg inv,da,hc;
+    MP m;
+    int i,nvar,nalg,n;
+    NumberField nf;
+    LIST f1,f2;
+    struct order_spec *current_spec;
+    VECT obj,obj0;
+    Obj tmp;
 
-	nd_found = 0; nd_notfirst = 0; nd_create = 0;
+    for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++);
+    for ( nalg = 0, tv = av; tv; tv = NEXT(tv), nalg++);
 
-	nd_psn = length(f); nd_pslen = 2*nd_psn;
-	nd_psl = (int *)MALLOC(nd_pslen*sizeof(int));
-	nd_ps = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
-	nd_psq = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
-	nd_psh = (RHist *)MALLOC(nd_pslen*sizeof(RHist));
-	nd_bound = (unsigned int **)MALLOC(nd_pslen*sizeof(unsigned int *));
-	for ( max = 0, i = 0, s = f; i < nd_psn; i++, s = NEXT(s) ) {
-		nd_bound[i] = d = dp_compute_bound((DP)BDY(s));
-		for ( j = 0; j < nd_nvar; j++ )
-			max = MAX(d[j],max);
-	}
-	if ( !nd_red )
-		nd_red = (RHist *)MALLOC(REDTAB_LEN*sizeof(RHist));
-	bzero(nd_red,REDTAB_LEN*sizeof(RHist));
+    for ( alist = 0, tv = av; tv; tv = NEXT(tv) ) {
+        NEXTNODE(alist,t); MKV(tv->v,poly); 
+        MKAlg(poly,alpha); BDY(t) = (pointer)alpha;
+        tv->v = tv->v->priv;
+    }
+    NEXT(t) = 0;
 
-	if ( max < 2 )
-		nd_bpe = 2;
-	else if ( max < 4 )
-		nd_bpe = 4;
-	else if ( max < 64 )
-		nd_bpe = 6;
-	else if ( max < 256 )
-		nd_bpe = 8;
-	else if ( max < 65536 )
-		nd_bpe = 16;
-	else
-		nd_bpe = 32;
+    /* simplification, making polynomials monic */
+    setfield_dalg(alist);
+    obj_algtodalg(f,&f1);
+    for ( t = BDY(f); t; t = NEXT(t) ) {
+        initd(ord); ptod(vv,vv,(P)BDY(t),&d);            
+        hc = (DAlg)BDY(d)->c;
+        if ( NID(hc) == N_DA ) {
+            invdalg(hc,&inv);
+            for ( m = BDY(d); m; m = NEXT(m) ) {
+                muldalg(inv,(DAlg)m->c,&da); m->c = (P)da;
+            }
+        }
+        initd(ord); dtop(vv,vv,d,&poly); BDY(f) = (pointer)poly;
+    }
+    obj_dalgtoalg(f1,&f);
 
-	nd_setup_parameters();
-	nd_free_private_storage();
-	len = 0;
-	for ( i = 0; i < nd_psn; i++, f = NEXT(f) ) {
-		NEWRHist(r);
-		a = dptondv(mod,(DP)BDY(f));
-		ndv_removecont(mod,a);
-		len = MAX(len,LEN(a));
-		SG(r) = HTD(a); TD(r) = HTD(a); ndl_copy(HDL(a),DL(r));
-		if ( mod )
-			nd_ps[i] = a;
-		else
-			nd_psq[i] = a;
-		nd_psh[i] = r;
-	}
+    /* append alg vars to the var list */
+    for ( tv = vv; NEXT(tv); tv = NEXT(tv) );
+    NEXT(tv) = av;
+
+    /* append a block to ord */
+    *ord1p = append_block(ord,nvar,nalg,2);
+
+    /* create generator list */
+    nf = get_numberfield();
+    for ( i = nalg-1, t = BDY(f); i >= 0; i-- ) {
+        MKAlg(nf->defpoly[i],dp);
+        MKNODE(s,dp,t); t = s;
+    }
+    MKLIST(f1,t);
+    *alistp = alist;
+    algobjtorat(f1,f1p);
+
+    /* creating a new weight vector */
+    prev_weight_vector_obj = obj0 = current_dl_weight_vector_obj;
+    n = nvar+nalg+1;
+    MKVECT(obj,n);
+    if ( obj0 && obj0->len == nvar )
+        for ( i = 0; i < nvar; i++ ) BDY(obj)[i] = BDY(obj0)[i];
+    else
+        for ( i = 0; i < nvar; i++ ) BDY(obj)[i] = (pointer)ONE;
+    for ( i = 0; i < nalg; i++ ) BDY(obj)[i+nvar] = 0;
+    BDY(obj)[n-1] = (pointer)ONE;
+    arg = mknode(1,obj);
+    Pdp_set_weight(arg,&tmp);
 }
 
-void nd_setup_trace(int mod,NODE f)
+NODE postprocess_algcoef(VL av,NODE alist,NODE r)
 {
-	int i,j,td,len,max;
-	NODE s,s0,f0;
-	unsigned int *d;
-	RHist r;
-	NDV a;
+    NODE s,t,u0,u;
+    P p;
+    VL tv;
+    Obj obj,tmp;
+    NODE arg;
 
-	nd_found = 0; nd_notfirst = 0; nd_create = 0;
+    u0 = 0;
+    for ( t = r; t; t = NEXT(t) ) {
+        p = (P)BDY(t);
+        for ( tv = av, s = alist; tv; tv = NEXT(tv), s = NEXT(s) ) {
+            substr(CO,0,(Obj)p,tv->v,(Obj)BDY(s),&obj); p = (P)obj;
+        }
+        if ( OID(p) == O_P || (OID(p) == O_N && NID((Num)p) != N_A) ) {
+            NEXTNODE(u0,u);
+            BDY(u) = (pointer)p;
+        }
+    }    
+    arg = mknode(1,prev_weight_vector_obj);
+    Pdp_set_weight(arg,&tmp);
 
-	nd_psn = length(f); nd_pslen = 2*nd_psn;
-	nd_psl = (int *)MALLOC(nd_pslen*sizeof(int));
-	nd_ps = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
-	nd_psq = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
-	nd_psh = (RHist *)MALLOC(nd_pslen*sizeof(RHist));
-	nd_bound = (unsigned int **)MALLOC(nd_pslen*sizeof(unsigned int *));
-	for ( max = 0, i = 0, s = f; i < nd_psn; i++, s = NEXT(s) ) {
-		nd_bound[i] = d = dp_compute_bound((DP)BDY(s));
-		for ( j = 0; j < nd_nvar; j++ )
-			max = MAX(d[j],max);
-	}
-	if ( !nd_red )
-		nd_red = (RHist *)MALLOC(REDTAB_LEN*sizeof(RHist));
-	bzero(nd_red,REDTAB_LEN*sizeof(RHist));
+    return u0;
+}
 
-	if ( max < 2 )
-		nd_bpe = 2;
-	else if ( max < 4 )
-		nd_bpe = 4;
-	else if ( max < 64 )
-		nd_bpe = 6;
-	else if ( max < 256 )
-		nd_bpe = 8;
-	else if ( max < 65536 )
-		nd_bpe = 16;
-	else
-		nd_bpe = 32;
+void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int f4,struct order_spec *ord,LIST *rp)
+{
+    VL tv,fv,vv,vc,av;
+    NODE fd,fd0,r,r0,t,x,s,xx,alist;
+    int e,max,nvar,i;
+    NDV b;
+    int ishomo,nalg,mrank,trank,wmax,len;
+	NMV a;
+    Alg alpha,dp;
+    P p,zp;
+    Q dmy;
+    LIST f1,f2,zpl;
+    Obj obj;
+    NumberField nf;
+    struct order_spec *ord1;
+    NODE tr,tl1,tl2,tl3,tl4;
+    LIST l1,l2,l3,l4,l5;
+	int j;
+	Q jq,bpe;
+    int *perm;
+    EPOS oepos;
+    int obpe,oadv,ompos,cbpe;
 
-	nd_setup_parameters();
-	nd_free_private_storage();
-	len = 0;
-	for ( i = 0; i < nd_psn; i++, f = NEXT(f) ) {
-		a = dptondv(mod,(DP)BDY(f)); ndv_removecont(mod,a); nd_ps[i] = a;
-		a = dptondv(0,(DP)BDY(f)); ndv_removecont(0,a); nd_psq[i] = a;
-		NEWRHist(r);
-		len = MAX(len,LEN(a));
-		SG(r) = HTD(a); TD(r) = HTD(a); ndl_copy(HDL(a),DL(r));
-		nd_psh[i] = r;
+    nd_module = 0;
+    if ( !m && Demand ) nd_demand = 1;
+    else nd_demand = 0;
+    parse_nd_option(current_option);
+
+    if ( DP_Multiple )
+        nd_scale = ((double)DP_Multiple)/(double)(Denominator?Denominator:1);
+#if 0
+    ndv_alloc = 0;
+#endif
+    get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+    for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
+    switch ( ord->id ) {
+        case 1:
+            if ( ord->nv != nvar )
+                error("nd_{gr,f4} : invalid order specification");
+            break;
+        default:
+            break;
+    }
+    nd_nalg = 0;
+    av = 0;
+    if ( !m ) {
+        get_algtree((Obj)f,&av);
+        for ( nalg = 0, tv = av; tv; tv = NEXT(tv), nalg++ );
+        nd_ntrans = nvar;
+        nd_nalg = nalg;
+        /* #i -> t#i */
+        if ( nalg ) {
+            preprocess_algcoef(vv,av,ord,f,&ord1,&f1,&alist);
+            ord = ord1;
+            f = f1;
+        }
+        nvar += nalg;
+    }
+    nd_init_ord(ord);
+    mrank = 0;
+    for ( t = BDY(f), max = 1; t; t = NEXT(t) )
+        for ( tv = vv; tv; tv = NEXT(tv) ) {
+            if ( nd_module ) {
+                s = BDY((LIST)BDY(t));
+                trank = length(s);
+                mrank = MAX(mrank,trank);
+                for ( ; s; s = NEXT(s) ) {
+                    e = getdeg(tv->v,(P)BDY(s));
+                    max = MAX(e,max);
+                }
+            } else {
+                e = getdeg(tv->v,(P)BDY(t));
+                max = MAX(e,max);
+            }
+        }
+    nd_setup_parameters(nvar,max);
+    obpe = nd_bpe; oadv = nmv_adv; oepos = nd_epos; ompos = nd_mpos;
+    ishomo = 1;
+    for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
+        if ( nd_module ) {
+			if ( !m && !nd_gentrace ) pltozpl((LIST)BDY(t),&dmy,&zpl);
+			else zpl = (LIST)BDY(t);
+            b = (pointer)pltondv(CO,vv,zpl);
+        } else {
+			if ( !m && !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp);
+			else zp = (P)BDY(t);
+            b = (pointer)ptondv(CO,vv,zp);
+        }
+        if ( ishomo )
+            ishomo = ishomo && ndv_ishomo(b);
+        if ( m ) ndv_mod(m,b);
+        if ( b ) { NEXTNODE(fd0,fd); BDY(fd) = (pointer)b; }
+    }
+    if ( fd0 ) NEXT(fd) = 0;
+
+	if ( !ishomo && homo ) {
+        for ( t = fd0, wmax = max; t; t = NEXT(t) ) {
+            b = (NDV)BDY(t); len = LEN(b);
+            for ( a = BDY(b), i = 0; i < len; i++, NMV_ADV(a) )
+                wmax = MAX(TD(DL(a)),wmax);
+        }
+        homogenize_order(ord,nvar,&ord1);
+        nd_init_ord(ord1);
+        nd_setup_parameters(nvar+1,wmax);
+        for ( t = fd0; t; t = NEXT(t) )
+            ndv_homogenize((NDV)BDY(t),obpe,oadv,oepos,ompos);
+    }
+
+    ndv_setup(m,0,fd0,nd_gbblock?1:0,0);
+    if ( nd_gentrace ) {
+        MKLIST(l1,nd_tracelist); MKNODE(nd_alltracelist,l1,0);
+    }
+    x = f4?nd_f4(m,&perm):nd_gb(m,ishomo || homo,0,0,&perm);
+	if ( !x ) {
+		*rp = 0; return;
 	}
+	if ( !ishomo && homo ) {
+	   	/* dehomogenization */
+		for ( t = x; t; t = NEXT(t) ) ndv_dehomogenize((NDV)BDY(t),ord);
+		nd_init_ord(ord);
+		nd_setup_parameters(nvar,0);
+	}
+    nd_demand = 0;
+	if ( nd_module && nd_intersect ) {
+		for ( j = nd_psn-1, x = 0; j >= 0; j-- )
+			if ( MPOS(DL(nd_psh[j])) > 1 ) { 
+				MKNODE(xx,(pointer)j,x); x = xx; 
+			}
+	  conv_ilist(nd_demand,0,x,0);
+	  goto FINAL;
+	}
+    x = ndv_reducebase(x,perm);
+    if ( nd_gentrace ) { tl1 = nd_alltracelist; nd_alltracelist = 0; }
+    x = ndv_reduceall(m,x);
+    cbpe = nd_bpe;
+    if ( nd_gentrace ) { 
+        tl2 = nd_alltracelist; nd_alltracelist = 0;
+        ndv_check_membership(m,fd0,obpe,oadv,oepos,x);
+        tl3 = nd_alltracelist; nd_alltracelist = 0; 
+        if ( nd_gensyz ) { 
+        	nd_gb(m,0,1,1,0);
+            tl4 = nd_alltracelist; nd_alltracelist = 0; 
+        } else tl4 = 0;
+    }
+    nd_bpe = cbpe;
+    nd_setup_parameters(nd_nvar,0);
+FINAL:
+    for ( r0 = 0, t = x; t; t = NEXT(t) ) {
+        NEXTNODE(r0,r); 
+        if ( nd_module ) BDY(r) = ndvtopl(m,CO,vv,BDY(t),mrank);
+        else if ( retdp ) BDY(r) = ndvtodp(m,BDY(t));
+		else BDY(r) = ndvtop(m,CO,vv,BDY(t));
+    }
+    if ( r0 ) NEXT(r) = 0;
+    if ( nalg )
+        r0 = postprocess_algcoef(av,alist,r0);
+    MKLIST(*rp,r0);
+    if ( nd_gentrace ) {
+        tl1 = reverse_node(tl1); tl2 = reverse_node(tl2);
+	tl3 = reverse_node(tl3);
+		/* tl2 = [[i,[[*,j,*,*],...]],...] */
+        for ( t = tl2; t; t = NEXT(t) ) {
+			/* s = [i,[*,j,*,*],...] */
+            s = BDY((LIST)BDY(t));
+            j = perm[QTOS((Q)ARG0(s))]; STOQ(j,jq); ARG0(s) = (pointer)jq;
+			for ( s = BDY((LIST)ARG1(s)); s; s = NEXT(s) ) {
+                j = perm[QTOS((Q)ARG1(BDY((LIST)BDY(s))))]; STOQ(j,jq); 
+				ARG1(BDY((LIST)BDY(s))) = (pointer)jq;
+            }
+		}
+		for ( j = length(x)-1, t = 0; j >= 0; j-- ) {
+		    STOQ(perm[j],jq); MKNODE(s,jq,t); t = s;
+		}
+      MKLIST(l1,tl1); MKLIST(l2,tl2); MKLIST(l3,t); MKLIST(l4,tl3);
+      MKLIST(l5,tl4);
+	  STOQ(nd_bpe,bpe);
+      tr = mknode(8,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe); MKLIST(*rp,tr);
+    }
+#if 0
+    fprintf(asir_out,"ndv_alloc=%d\n",ndv_alloc);
+#endif
 }
 
-void nd_gr(LIST f,LIST v,int m,struct order_spec *ord,LIST *rp)
+void nd_gr_postproc(LIST f,LIST v,int m,struct order_spec *ord,int do_check,LIST *rp)
 {
-	struct order_spec ord1;
-	VL fv,vv,vc;
-	NODE fd,fd0,r,r0,t,x,s,xx;
-	DP a,b,c;
+    VL tv,fv,vv,vc,av;
+    NODE fd,fd0,r,r0,t,x,s,xx,alist;
+    int e,max,nvar,i;
+    NDV b;
+    int ishomo,nalg;
+    Alg alpha,dp;
+    P p,zp;
+    Q dmy;
+    LIST f1,f2;
+    Obj obj;
+    NumberField nf;
+    struct order_spec *ord1;
+    int *perm;
 
-	get_vars((Obj)f,&fv); pltovl(v,&vv);
-	nd_nvar = length(vv);
-	nd_init_ord(ord);
-	/* XXX for DP */
-	initd(ord);
-	for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
-		ptod(CO,vv,(P)BDY(t),&b);
-		NEXTNODE(fd0,fd); BDY(fd) = (pointer)b;
-	}
-	if ( fd0 ) NEXT(fd) = 0;
-	nd_setup(m,fd0);
-	x = nd_gb(m,0);
-	fprintf(asir_out,"found=%d,notfirst=%d,create=%d\n",
-		nd_found,nd_notfirst,nd_create);
-	x = nd_reduceall(m,x);
-	for ( r0 = 0, t = x; t; t = NEXT(t) ) {
-		NEXTNODE(r0,r); 
-		if ( m ) {
-			a = ndvtodp(m,BDY(t));
-			_dtop_mod(CO,vv,a,(P *)&BDY(r));
-		} else {
-			a = ndvtodp(m,BDY(t));
-			dtop(CO,vv,a,(P *)&BDY(r));
-		}
-	}
-	if ( r0 ) NEXT(r) = 0;
-	MKLIST(*rp,r0);
+    parse_nd_option(current_option);
+    get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+    for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
+    switch ( ord->id ) {
+        case 1:
+            if ( ord->nv != nvar )
+                error("nd_check : invalid order specification");
+            break;
+        default:
+            break;
+    }
+    nd_nalg = 0;
+    av = 0;
+    if ( !m ) {
+        get_algtree((Obj)f,&av);
+        for ( nalg = 0, tv = av; tv; tv = NEXT(tv), nalg++ );
+        nd_ntrans = nvar;
+        nd_nalg = nalg;
+        /* #i -> t#i */
+        if ( nalg ) {
+            preprocess_algcoef(vv,av,ord,f,&ord1,&f1,&alist);
+            ord = ord1;
+            f = f1;
+        }
+        nvar += nalg;
+    }
+    nd_init_ord(ord);
+    for ( t = BDY(f), max = 1; t; t = NEXT(t) )
+        for ( tv = vv; tv; tv = NEXT(tv) ) {
+            e = getdeg(tv->v,(P)BDY(t));
+            max = MAX(e,max);
+        }
+    nd_setup_parameters(nvar,max);
+    ishomo = 1;
+    for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
+        ptozp((P)BDY(t),1,&dmy,&zp);
+        b = (pointer)ptondv(CO,vv,zp);
+        if ( ishomo )
+            ishomo = ishomo && ndv_ishomo(b);
+        if ( m ) ndv_mod(m,b);
+        if ( b ) { NEXTNODE(fd0,fd); BDY(fd) = (pointer)b; }
+    }
+    if ( fd0 ) NEXT(fd) = 0;
+    ndv_setup(m,0,fd0,0,1);
+    for ( x = 0, i = 0; i < nd_psn; i++ )
+        x = update_base(x,i);
+    if ( do_check ) {
+        x = nd_gb(m,ishomo,1,0,&perm);
+        if ( !x ) {
+            *rp = 0;
+            return;
+        }
+    } else {
+#if 0
+		/* bug ? */
+        for ( t = x; t; t = NEXT(t) )
+            BDY(t) = (pointer)nd_ps[(long)BDY(t)];
+#else
+		conv_ilist(0,0,x,&perm);
+#endif
+    }
+    x = ndv_reducebase(x,perm);
+    x = ndv_reduceall(m,x);
+    for ( r0 = 0, t = x; t; t = NEXT(t) ) {
+        NEXTNODE(r0,r); 
+        BDY(r) = ndvtop(m,CO,vv,BDY(t));
+    }
+    if ( r0 ) NEXT(r) = 0;
+    if ( nalg )
+        r0 = postprocess_algcoef(av,alist,r0);
+    MKLIST(*rp,r0);
 }
 
-void nd_gr_trace(LIST f,LIST v,int m,int homo,struct order_spec *ord,LIST *rp)
+NDV recompute_trace(NODE trace,NDV *p,int m);
+void nd_gr_recompute_trace(LIST f,LIST v,int m,struct order_spec *ord,LIST tlist,LIST *rp);
+
+NDV recompute_trace(NODE ti,NDV *p,int mod)
 {
-	struct order_spec ord1;
-	VL fv,vv,vc;
-	NODE fd,fd0,in0,in,r,r0,t,s,cand;
-	DP a,b,c,h;
-	P p;
+	int c,c1,c2,i;
+	NM mul,m,tail;
+	ND d,r,rm;
+	NODE sj;
+	NDV red;
+	Obj mj;
+	static int afo=0;
 
-	get_vars((Obj)f,&fv); pltovl(v,&vv);
-	nd_nvar = length(vv);
-	initd(ord);
-	if ( homo ) {
-		homogenize_order(ord,nd_nvar,&ord1);
-		for ( fd0 = 0, in0 = 0, t = BDY(f); t; t = NEXT(t) ) {
-			ptod(CO,vv,(P)BDY(t),&c);
-			if ( c ) {
-				dp_homo(c,&h); NEXTNODE(fd0,fd); BDY(fd) = (pointer)h;
-				NEXTNODE(in0,in); BDY(in) = (pointer)c;
+	afo++;
+	mul = (NM)ALLOCA(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT));
+	CM(mul) = 1;
+	tail = 0;
+	for ( i = 0, d = r = 0; ti; ti = NEXT(ti), i++ ) {
+		sj = BDY((LIST)BDY(ti));
+		if ( ARG0(sj) ) {
+			red = p[QTOS((Q)ARG1(sj))];
+			mj = (Obj)ARG2(sj);
+			if ( OID(mj) != O_DP ) ndl_zero(DL(mul));
+			else dltondl(nd_nvar,BDY((DP)mj)->dl,DL(mul));
+			rm = ndv_mul_nm(mod,mul,red);
+			if ( !r ) r = rm;
+			else {
+				for ( m = BDY(r); m && !ndl_equal(m->dl,BDY(rm)->dl); m = NEXT(m), LEN(r)-- ) {
+					if ( d ) {
+						NEXT(tail) = m; tail = m; LEN(d)++;
+					} else {
+						MKND(nd_nvar,m,1,d); tail = BDY(d);
+					}
+				}
+				if ( !m ) return 0; /* failure */
+				else {
+					BDY(r) = m;
+					c1 = invm(HCM(rm),mod); c2 = mod-HCM(r);
+					DMAR(c1,c2,0,mod,c);
+					nd_mul_c(mod,rm,c);
+					r = nd_add(mod,r,rm);
+				}
 			}
 		}
-		if ( fd0 ) NEXT(fd) = 0;
-		if ( in0 ) NEXT(in) = 0;
-		nd_init_ord(&ord1);
-		initd(&ord1);
-		nd_nvar++;
-	} else {
-		switch ( ord->ord.simple ) {
-			case 0: nd_isrlex = 1; nd_degcompat = 1; break;
-			case 1: nd_isrlex = 0; nd_degcompat = 1; break;
-			default: error("nd_gr : unsupported order");
-		}
-		for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
-			ptod(CO,vv,(P)BDY(t),&c);
-			if ( c ) {
-				NEXTNODE(fd0,fd); BDY(fd) = (pointer)c;
-			}
-		}
-		if ( fd0 ) NEXT(fd) = 0;
-		in0 = fd0;
 	}
-	do {
-		nd_setup_trace(m,fd0);
-		cand = nd_gb_trace(m);
-		if ( !cand ) continue;
-		if ( homo ) {
-			/* dehomogenization */
-			for ( t = cand; t; t = NEXT(t) )
-				ndv_dehomogenize((NDV)BDY(t));
-			nd_nvar--;
-			nd_setup_parameters();
-			initd(ord);
-			cand = nd_reducebase(cand);
-		}
-		fprintf(asir_out,"found=%d,notfirst=%d,create=%d\n",
-			nd_found,nd_notfirst,nd_create);
-		cand = nd_reduceall(0,cand);
-		initd(ord);
-		for ( r0 = 0; cand; cand = NEXT(cand) ) {
-			NEXTNODE(r0,r); 
-			BDY(r) = (pointer)ndvtodp(0,(NDV)BDY(cand));
-		}
-		if ( r0 ) NEXT(r) = 0;
-		cand = r0;
-	} while ( !nd_check_candidate(in0,cand) );
-	/* dp->p */
-	for ( r = cand; r; r = NEXT(r) ) {
-		dtop(CO,vv,BDY(r),&p);
-		BDY(r) = (pointer)p;
+	if ( tail ) NEXT(tail) = 0;
+	d = nd_add(mod,d,r);
+	nd_mul_c(mod,d,invm(HCM(d),mod));
+	return ndtondv(mod,d);
+}
+
+void nd_gr_recompute_trace(LIST f,LIST v,int m,struct order_spec *ord,LIST tlist,LIST *rp)
+{
+    VL tv,fv,vv,vc,av;
+    NODE fd,fd0,r,r0,t,x,s,xx,alist;
+    int e,max,nvar,i;
+    NDV b;
+    int ishomo,nalg;
+    Alg alpha,dp;
+    P p,zp;
+    Q dmy;
+    LIST f1,f2;
+    Obj obj;
+    NumberField nf;
+    struct order_spec *ord1;
+	NODE permtrace,intred,ind,perm,trace,ti;
+	int len,n,j;
+	NDV *db,*pb;
+
+    parse_nd_option(current_option);
+    get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+    for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
+    switch ( ord->id ) {
+        case 1:
+            if ( ord->nv != nvar )
+                error("nd_check : invalid order specification");
+            break;
+        default:
+            break;
+    }
+    nd_init_ord(ord);
+	nd_bpe = QTOS((Q)ARG7(BDY(tlist)));
+    nd_setup_parameters(nvar,0);
+
+	len = length(BDY(f));
+	db = (NDV *)MALLOC(len*sizeof(NDV *));
+	for ( i = 0, t = BDY(f); t; i++, t = NEXT(t) ) {
+	    ptozp((P)BDY(t),1,&dmy,&zp);
+	    b = ptondv(CO,vv,zp);
+        ndv_mod(m,b);
+		ndv_mul_c(m,b,invm(HCM(b),m));
+		db[i] = b;
+    }
+
+	permtrace = BDY((LIST)ARG2(BDY(tlist))); 
+	intred = BDY((LIST)ARG3(BDY(tlist))); 
+	ind = BDY((LIST)ARG4(BDY(tlist)));
+	perm = BDY((LIST)ARG0(permtrace));
+	trace = NEXT(permtrace);
+
+	for ( i = length(perm)-1, t = trace; t; t = NEXT(t) ) {
+		j = QTOS((Q)ARG0(BDY((LIST)BDY(t))));
+		if ( j > i ) i = j;
 	}
-	MKLIST(*rp,cand);
+	n = i+1;
+	pb = (NDV *)MALLOC(n*sizeof(NDV *));
+	for ( t = perm, i = 0; t; t = NEXT(t), i++ ) {
+		ti = BDY((LIST)BDY(t));
+		pb[QTOS((Q)ARG0(ti))] = db[QTOS((Q)ARG1(ti))];
+	}
+	for ( t = trace; t; t = NEXT(t) ) {
+		ti = BDY((LIST)BDY(t));
+		pb[QTOS((Q)ARG0(ti))] = recompute_trace(BDY((LIST)ARG1(ti)),pb,m);
+		if ( !pb[QTOS((Q)ARG0(ti))] ) { *rp = 0; return; }
+    	if ( DP_Print ) { 
+       		fprintf(asir_out,"."); fflush(asir_out);
+    	}
+	}
+	for ( t = intred; t; t = NEXT(t) ) {
+		ti = BDY((LIST)BDY(t));
+		pb[QTOS((Q)ARG0(ti))] = recompute_trace(BDY((LIST)ARG1(ti)),pb,m);
+		if ( !pb[QTOS((Q)ARG0(ti))] ) { *rp = 0; return; }
+    	if ( DP_Print ) { 
+       		fprintf(asir_out,"*"); fflush(asir_out);
+    	}
+	}
+    for ( r0 = 0, t = ind; t; t = NEXT(t) ) {
+        NEXTNODE(r0,r); 
+		b = pb[QTOS((Q)BDY(t))];
+        ndv_mul_c(m,b,invm(HCM(b),m));
+#if 0
+        BDY(r) = ndvtop(m,CO,vv,pb[QTOS((Q)BDY(t))]);
+#else
+        BDY(r) = ndvtodp(m,pb[QTOS((Q)BDY(t))]);
+#endif
+    }
+    if ( r0 ) NEXT(r) = 0;
+    MKLIST(*rp,r0);
+    if ( DP_Print ) fprintf(asir_out,"\n");
 }
 
-void dltondl(int n,DL dl,unsigned int *r)
+void nd_gr_trace(LIST f,LIST v,int trace,int homo,int f4,struct order_spec *ord,LIST *rp)
 {
-	unsigned int *d;
-	int i;
+    VL tv,fv,vv,vc,av;
+    NODE fd,fd0,in0,in,r,r0,t,s,cand,alist;
+    int m,nocheck,nvar,mindex,e,max;
+    NDV c;
+    NMV a;
+    P p,zp;
+    Q dmy;
+    EPOS oepos;
+    int obpe,oadv,wmax,i,len,cbpe,ishomo,nalg,mrank,trank,ompos;
+    Alg alpha,dp;
+    P poly;
+    LIST f1,f2,zpl;
+    Obj obj;
+    NumberField nf;
+    struct order_spec *ord1;
+    struct oEGT eg_check,eg0,eg1;
+    NODE tr,tl1,tl2,tl3,tl4;
+    LIST l1,l2,l3,l4,l5;
+    int *perm;
+    int j,ret;
+    Q jq,bpe;
 
-	d = dl->d;
-	bzero(r,nd_wpd*sizeof(unsigned int));
-	if ( nd_isrlex )
-		for ( i = 0; i < n; i++ )
-			r[(n-1-i)/nd_epw] |= (d[i]<<((nd_epw-((n-1-i)%nd_epw)-1)*nd_bpe));
-	else
-		for ( i = 0; i < n; i++ )
-			r[i/nd_epw] |= d[i]<<((nd_epw-(i%nd_epw)-1)*nd_bpe);
+    nd_module = 0;
+    parse_nd_option(current_option);
+    if ( DP_Multiple )
+        nd_scale = ((double)DP_Multiple)/(double)(Denominator?Denominator:1);
+
+    get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc);
+    for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
+    switch ( ord->id ) {
+        case 1:
+            if ( ord->nv != nvar )
+                error("nd_gr_trace : invalid order specification");
+            break;
+        default:
+            break;
+    }
+
+    get_algtree((Obj)f,&av);
+    for ( nalg = 0, tv = av; tv; tv = NEXT(tv), nalg++ );
+    nd_ntrans = nvar;
+    nd_nalg = nalg;
+    /* #i -> t#i */
+    if ( nalg ) {
+        preprocess_algcoef(vv,av,ord,f,&ord1,&f1,&alist);
+        ord = ord1;
+        f = f1;
+    }
+    nvar += nalg;
+
+    nocheck = 0;
+    mindex = 0;
+
+    if ( Demand ) nd_demand = 1;
+    else nd_demand = 0;
+
+    /* setup modulus */
+    if ( trace < 0 ) {
+        trace = -trace;
+        nocheck = 1;
+    }
+    m = trace > 1 ? trace : get_lprime(mindex);
+    nd_init_ord(ord);
+    mrank = 0;
+    for ( t = BDY(f), max = 1; t; t = NEXT(t) )
+        for ( tv = vv; tv; tv = NEXT(tv) ) {
+            if ( nd_module ) {
+                s = BDY((LIST)BDY(t));
+                trank = length(s);
+                mrank = MAX(mrank,trank);
+                for ( ; s; s = NEXT(s) ) {
+                    e = getdeg(tv->v,(P)BDY(s));
+                    max = MAX(e,max);
+                }
+            } else {
+                e = getdeg(tv->v,(P)BDY(t));
+                max = MAX(e,max);
+            }
+        }
+    nd_setup_parameters(nvar,max);
+    obpe = nd_bpe; oadv = nmv_adv; oepos = nd_epos; ompos = nd_mpos;
+    ishomo = 1;
+    for ( in0 = 0, fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
+        if ( nd_module ) {
+			if ( !nd_gentrace ) pltozpl((LIST)BDY(t),&dmy,&zpl);
+			else zpl = (LIST)BDY(t);
+            c = (pointer)pltondv(CO,vv,zpl);
+        } else {
+			if ( !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp);
+			else zp = (P)BDY(t);
+            c = (pointer)ptondv(CO,vv,zp);
+        }
+        if ( ishomo )
+            ishomo = ishomo && ndv_ishomo(c);
+        if ( c ) { 
+            NEXTNODE(in0,in); BDY(in) = (pointer)c;
+            NEXTNODE(fd0,fd); BDY(fd) = (pointer)ndv_dup(0,c);
+        }
+    }
+    if ( in0 ) NEXT(in) = 0;
+    if ( fd0 ) NEXT(fd) = 0;
+    if ( !ishomo && homo ) {
+        for ( t = in0, wmax = max; t; t = NEXT(t) ) {
+            c = (NDV)BDY(t); len = LEN(c);
+            for ( a = BDY(c), i = 0; i < len; i++, NMV_ADV(a) )
+                wmax = MAX(TD(DL(a)),wmax);
+        }
+        homogenize_order(ord,nvar,&ord1);
+        nd_init_ord(ord1);
+        nd_setup_parameters(nvar+1,wmax);
+        for ( t = fd0; t; t = NEXT(t) )
+            ndv_homogenize((NDV)BDY(t),obpe,oadv,oepos,ompos);
+    }
+    while ( 1 ) {
+		tl1 = tl2 = tl3 = tl4 = 0;
+        if ( Demand )
+            nd_demand = 1;
+        ret = ndv_setup(m,1,fd0,nd_gbblock?1:0,0);
+        if ( nd_gentrace ) {
+            MKLIST(l1,nd_tracelist); MKNODE(nd_alltracelist,l1,0);
+        }
+        if ( ret )
+            cand = f4?nd_f4_trace(m,&perm):nd_gb_trace(m,ishomo || homo,&perm);
+        if ( !ret || !cand ) {
+            /* failure */
+            if ( trace > 1 ) { *rp = 0; return; }
+            else m = get_lprime(++mindex);
+            continue;
+        }
+        if ( !ishomo && homo ) {
+            /* dehomogenization */
+            for ( t = cand; t; t = NEXT(t) ) ndv_dehomogenize((NDV)BDY(t),ord);
+            nd_init_ord(ord);
+            nd_setup_parameters(nvar,0);
+        }
+        nd_demand = 0;
+        cand = ndv_reducebase(cand,perm);
+        if ( nd_gentrace ) { tl1 = nd_alltracelist; nd_alltracelist = 0; }
+        cand = ndv_reduceall(0,cand);
+        cbpe = nd_bpe;
+        if ( nd_gentrace ) { tl2 = nd_alltracelist; nd_alltracelist = 0; }
+        get_eg(&eg0);
+        if ( nocheck )
+            break;
+        if ( ret = ndv_check_membership(0,in0,obpe,oadv,oepos,cand) ) {
+            if ( nd_gentrace ) { 
+			    tl3 = nd_alltracelist; nd_alltracelist = 0; 
+		    } else tl3 = 0;
+            /* gbcheck : cand is a GB of Id(cand) ? */
+            ret = nd_gb(0,0,1,nd_gensyz?1:0,0)!=0;
+            if ( nd_gentrace && nd_gensyz ) { 
+			    tl4 = nd_alltracelist; nd_alltracelist = 0; 
+		    } else tl4 = 0;
+		}
+		if ( ret ) break;
+        else if ( trace > 1 ) {
+            /* failure */
+            *rp = 0; return;    
+        } else {
+            /* try the next modulus */
+            m = get_lprime(++mindex);
+            /* reset the parameters */
+            if ( !ishomo && homo ) {
+                nd_init_ord(ord1);
+                nd_setup_parameters(nvar+1,wmax);
+            } else {
+                nd_init_ord(ord);
+                nd_setup_parameters(nvar,max);
+            }
+        }
+    }
+    get_eg(&eg1); init_eg(&eg_check); add_eg(&eg_check,&eg0,&eg1);
+    if ( DP_Print )
+        fprintf(asir_out,"check=%fsec\n",eg_check.exectime+eg_check.gctime);
+    /* dp->p */
+    nd_bpe = cbpe;
+    nd_setup_parameters(nd_nvar,0);
+    for ( r = cand; r; r = NEXT(r) ) {
+    if ( nd_module ) BDY(r) = ndvtopl(0,CO,vv,BDY(r),mrank);
+        else BDY(r) = (pointer)ndvtop(0,CO,vv,BDY(r));
+    }
+    if ( nalg )
+        cand = postprocess_algcoef(av,alist,cand);
+    MKLIST(*rp,cand);
+    if ( nd_gentrace ) {
+        tl1 = reverse_node(tl1); tl2 = reverse_node(tl2);
+		tl3 = reverse_node(tl3);
+		/* tl2 = [[i,[[*,j,*,*],...]],...] */
+        for ( t = tl2; t; t = NEXT(t) ) {
+			/* s = [i,[*,j,*,*],...] */
+            s = BDY((LIST)BDY(t));
+            j = perm[QTOS((Q)ARG0(s))]; STOQ(j,jq); ARG0(s) = (pointer)jq;
+			for ( s = BDY((LIST)ARG1(s)); s; s = NEXT(s) ) {
+                j = perm[QTOS((Q)ARG1(BDY((LIST)BDY(s))))]; STOQ(j,jq); 
+				ARG1(BDY((LIST)BDY(s))) = (pointer)jq;
+            }
+		}
+		for ( j = length(cand)-1, t = 0; j >= 0; j-- ) {
+		    STOQ(perm[j],jq); MKNODE(s,jq,t); t = s;
+		}
+        MKLIST(l1,tl1); MKLIST(l2,tl2); MKLIST(l3,t); MKLIST(l4,tl3);
+		MKLIST(l5,tl4);
+	  	STOQ(nd_bpe,bpe);
+        tr = mknode(8,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe); MKLIST(*rp,tr);
+    }
 }
 
-DL ndltodl(int n,int td,unsigned int *ndl)
+/* XXX : module element is not considered  */
+
+void dltondl(int n,DL dl,UINT *r)
 {
-	DL dl;
-	int *d;
-	int i;
+    UINT *d;
+    int i,j,l,s,ord_l;
+    struct order_pair *op;
 
-	NEWDL(dl,n);
-	TD(dl) = td;
-	d = dl->d;
-	if ( nd_isrlex )
-		for ( i = 0; i < n; i++ )
-			d[i] = (ndl[(n-1-i)/nd_epw]>>((nd_epw-((n-1-i)%nd_epw)-1)*nd_bpe))
-				&((1<<nd_bpe)-1);
-	else
-		for ( i = 0; i < n; i++ )
-			d[i] = (ndl[i/nd_epw]>>((nd_epw-(i%nd_epw)-1)*nd_bpe))
-				&((1<<nd_bpe)-1);
-	return dl;
+    d = dl->d;
+    for ( i = 0; i < nd_wpd; i++ ) r[i] = 0;
+    if ( nd_blockmask ) {
+        l = nd_blockmask->n;
+        op = nd_blockmask->order_pair;
+        for ( j = 0, s = 0; j < l; j++ ) {
+            ord_l = op[j].length;
+            for ( i = 0; i < ord_l; i++, s++ ) PUT_EXP(r,s,d[s]);
+        }
+        TD(r) = ndl_weight(r);
+        ndl_weight_mask(r);
+    } else {
+        for ( i = 0; i < n; i++ ) PUT_EXP(r,i,d[i]);
+        TD(r) = ndl_weight(r);
+    }
 }
 
-ND dptond(int mod,DP p)
+DL ndltodl(int n,UINT *ndl)
 {
-	ND d;
-	NM m0,m;
-	MP t;
-	int n,l;
+    DL dl;
+    int *d;
+    int i,j,l,s,ord_l;
+    struct order_pair *op;
 
-	if ( !p )
-		return 0;
-	n = NV(p);
-	m0 = 0;
-	for ( t = BDY(p), l = 0; t; t = NEXT(t), l++ ) {
-		NEXTNM(m0,m);
-		if ( mod )
-			CM(m) = ITOS(C(t));
-		else
-			CQ(m) = (Q)C(t);
-		TD(m) = TD(DL(t));
-		dltondl(n,DL(t),DL(m));
-	}
-	NEXT(m) = 0;
-	MKND(n,m0,l,d);
-	SG(d) = SG(p);
-	return d;
+    NEWDL(dl,n);
+    dl->td = TD(ndl);
+    d = dl->d;
+    if ( nd_blockmask ) {
+        l = nd_blockmask->n;
+        op = nd_blockmask->order_pair;
+        for ( j = 0, s = 0; j < l; j++ ) {
+            ord_l = op[j].length;
+            for ( i = 0; i < ord_l; i++, s++ ) d[s] = GET_EXP(ndl,s);
+        }
+    } else {
+        for ( i = 0; i < n; i++ ) d[i] = GET_EXP(ndl,i);
+    }
+    return dl;
 }
 
-DP ndtodp(int mod,ND p)
+void nmtodp(int mod,NM m,DP *r)
 {
-	DP d;
-	MP m0,m;
-	NM t;
-	int n;
+    DP dp;
+    MP mr;
 
-	if ( !p )
-		return 0;
-	n = NV(p);
-	m0 = 0;
-	for ( t = BDY(p); t; t = NEXT(t) ) {
-		NEXTMP(m0,m);
-		if ( mod )
-			C(m) = STOI(CM(t));
-		else
-			C(m) = (P)CQ(t);
-		DL(m) = ndltodl(n,TD(t),DL(t));
-	}
-	NEXT(m) = 0;
-	MKDP(n,m0,d);
-	SG(d) = SG(p);
-	return d;
+    NEWMP(mr); 
+    mr->dl = ndltodl(nd_nvar,DL(m));
+    mr->c = ndctop(mod,m->c);
+    NEXT(mr) = 0; MKDP(nd_nvar,mr,dp); dp->sugar = mr->dl->td;
+    *r = dp;
 }
 
-void ndl_print(unsigned int *dl)
+void ndl_print(UINT *dl)
 {
-	int n;
-	int i;
+    int n;
+    int i,j,l,ord_l,s,s0;
+    struct order_pair *op;
 
-	n = nd_nvar;
-	printf("<<");
-	if ( nd_isrlex )
-		for ( i = 0; i < n; i++ )
-			printf(i==n-1?"%d":"%d,",
-				(dl[(n-1-i)/nd_epw]>>((nd_epw-((n-1-i)%nd_epw)-1)*nd_bpe))
-					&((1<<nd_bpe)-1));
-	else
-		for ( i = 0; i < n; i++ )
-			printf(i==n-1?"%d":"%d,",
-				(dl[i/nd_epw]>>((nd_epw-(i%nd_epw)-1)*nd_bpe))
-					&((1<<nd_bpe)-1));
-	printf(">>");
+    n = nd_nvar;
+    printf("<<");
+    if ( nd_blockmask ) {
+        l = nd_blockmask->n;
+        op = nd_blockmask->order_pair;
+        for ( j = 0, s = s0 = 0; j < l; j++ ) {
+            ord_l = op[j].length;
+            for ( i = 0; i < ord_l; i++, s++ )
+                printf(s==n-1?"%d":"%d,",GET_EXP(dl,s));
+        }
+    } else {
+        for ( i = 0; i < n; i++ ) printf(i==n-1?"%d":"%d,",GET_EXP(dl,i));
+    }
+    printf(">>");
+    if ( MPOS(dl) )
+        printf("*e%d",MPOS(dl));
 }
 
 void nd_print(ND p)
 {
-	NM m;
+    NM m;
 
-	if ( !p )
-		printf("0\n");
-	else {
-		for ( m = BDY(p); m; m = NEXT(m) ) {
-			printf("+%d*",CM(m));
-			ndl_print(DL(m));
-		}
-		printf("\n");
-	}
+    if ( !p )
+        printf("0\n");
+    else {
+        for ( m = BDY(p); m; m = NEXT(m) ) {
+            if ( CM(m) & 0x80000000 ) printf("+@_%d*",IFTOF(CM(m)));
+            else printf("+%d*",CM(m));
+            ndl_print(DL(m));
+        }
+        printf("\n");
+    }
 }
 
 void nd_print_q(ND p)
 {
-	NM m;
+    NM m;
 
-	if ( !p )
-		printf("0\n");
-	else {
-		for ( m = BDY(p); m; m = NEXT(m) ) {
-			printf("+");
-			printexpr(CO,CQ(m));
-			printf("*");
-			ndl_print(DL(m));
-		}
-		printf("\n");
-	}
+    if ( !p )
+        printf("0\n");
+    else {
+        for ( m = BDY(p); m; m = NEXT(m) ) {
+            printf("+");
+            printexpr(CO,(Obj)CQ(m));
+            printf("*");
+            ndl_print(DL(m));
+        }
+        printf("\n");
+    }
 }
 
 void ndp_print(ND_pairs d)
 {
-	ND_pairs t;
+    ND_pairs t;
 
-	for ( t = d; t; t = NEXT(t) ) {
-		printf("%d,%d ",t->i1,t->i2);
-	}
-	printf("\n");
+    for ( t = d; t; t = NEXT(t) ) printf("%d,%d ",t->i1,t->i2);
+    printf("\n");
 }
 
 void nd_removecont(int mod,ND p)
 {
-	int i,n;
-	Q *w;
-	Q dvr,t;
-	NM m;
-	struct oVECT v;
-	N q,r;
+    int i,n;
+    Q *w;
+    Q dvr,t;
+    NM m;
+    struct oVECT v;
+    N q,r;
 
-	if ( mod )
-		nd_mul_c(mod,p,invm(HCM(p),mod));
-	else {
-		for ( m = BDY(p), n = 0; m; m = NEXT(m), n++ );
-		w = (Q *)ALLOCA(n*sizeof(Q));
-		v.len = n;
-		v.body = (pointer *)w;
-		for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ )
-			w[i] = CQ(m);
-		removecont_array(w,n);
-		for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) CQ(m) = w[i];	
-	}
+    if ( mod == -1 ) nd_mul_c(mod,p,_invsf(HCM(p)));
+    else if ( mod ) nd_mul_c(mod,p,invm(HCM(p),mod));
+    else {
+        for ( m = BDY(p), n = 0; m; m = NEXT(m), n++ );
+        w = (Q *)ALLOCA(n*sizeof(Q));
+        v.len = n;
+        v.body = (pointer *)w;
+        for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) w[i] = CQ(m);
+        removecont_array((P *)w,n,1);
+        for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) CQ(m) = w[i];    
+    }
 }
 
 void nd_removecont2(ND p1,ND p2)
 {
-	int i,n1,n2,n;
-	Q *w;
-	Q dvr,t;
-	NM m;
-	struct oVECT v;
-	N q,r;
+    int i,n1,n2,n;
+    Q *w;
+    Q dvr,t;
+    NM m;
+    struct oVECT v;
+    N q,r;
 
-	if ( !p1 ) {
-		nd_removecont(0,p2); return;
-	} else if ( !p2 ) {
-		nd_removecont(0,p1); return;
-	}
-	n1 = nd_length(p1);
-	n2 = nd_length(p2);
-	n = n1+n2;
-	w = (Q *)ALLOCA(n*sizeof(Q));
-	v.len = n;
-	v.body = (pointer *)w;
-	for ( m = BDY(p1), i = 0; i < n1; m = NEXT(m), i++ )
-		w[i] = CQ(m);
-	for ( m = BDY(p2); i < n; m = NEXT(m), i++ )
-		w[i] = CQ(m);
-	removecont_array(w,n);
-	for ( m = BDY(p1), i = 0; i < n1; m = NEXT(m), i++ ) CQ(m) = w[i];	
-	for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) CQ(m) = w[i];	
+    n1 = nd_length(p1);
+    n2 = nd_length(p2);
+    n = n1+n2;
+    w = (Q *)ALLOCA(n*sizeof(Q));
+    v.len = n;
+    v.body = (pointer *)w;
+    i = 0;
+    if ( p1 )
+        for ( m = BDY(p1); i < n1; m = NEXT(m), i++ ) w[i] = CQ(m);
+    if ( p2 )
+        for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) w[i] = CQ(m);
+    removecont_array((P *)w,n,1);
+    i = 0;
+    if ( p1 )
+        for ( m = BDY(p1); i < n1; m = NEXT(m), i++ ) CQ(m) = w[i];    
+    if ( p2 )
+        for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) CQ(m) = w[i];    
 }
 
 void ndv_removecont(int mod,NDV p)
 {
-	int i,len;
-	Q *w;
-	Q dvr,t;
-	NMV m;
+    int i,len,all_p;
+    Q *c;
+    P *w;
+    Q dvr,t;
+    P g,cont,tp;
+    NMV m;
 
-	if ( mod )
-		ndv_mul_c(mod,p,invm(HCM(p),mod));
-	else {
-		len = p->len;
-		w = (Q *)ALLOCA(len*sizeof(Q));
-		for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ )
-			w[i] = CQ(m);
-		sortbynm(w,len);
-		qltozl(w,len,&dvr);
-		for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ ) {
-			divq(CQ(m),dvr,&t); CQ(m) = t;
-		}
-	}
+    if ( mod == -1 )
+        ndv_mul_c(mod,p,_invsf(HCM(p)));
+    else if ( mod )
+        ndv_mul_c(mod,p,invm(HCM(p),mod));
+    else {
+        len = p->len;
+        w = (P *)ALLOCA(len*sizeof(P));
+        c = (Q *)ALLOCA(len*sizeof(Q));
+        for ( m = BDY(p), all_p = 1, i = 0; i < len; NMV_ADV(m), i++ ) {
+            ptozp(CP(m),1,&c[i],&w[i]);
+            all_p = all_p && !NUM(w[i]);
+        }
+        if ( all_p ) {
+            qltozl(c,len,&dvr); nd_heu_nezgcdnpz(nd_vc,w,len,1,&g);
+            mulp(nd_vc,(P)dvr,g,&cont);
+            for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ ) {
+                divsp(nd_vc,CP(m),cont,&tp); CP(m) = tp;
+            }
+        } else {
+            sortbynm((Q *)c,len);
+            qltozl((Q *)c,len,&dvr);
+            for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ ) {
+                divsp(nd_vc,CP(m),(P)dvr,&tp); CP(m) = tp;
+            }
+        }
+    }
 }
 
-void ndv_dehomogenize(NDV p)
+/* koko */
+
+void ndv_homogenize(NDV p,int obpe,int oadv,EPOS oepos,int ompos)
 {
-	int i,len,newnvar,newwpd,newadv;
-	Q *w;
-	Q dvr,t;
-	NMV m,r;
-	unsigned int *d;
-#define NEWADV(m) (m = (NMV)(((char *)m)+newadv))
+    int len,i,max;
+    NMV m,mr0,mr,t;
 
-	len = p->len;
-	newnvar = nd_nvar-1;
-	newwpd = newnvar/nd_epw+(newnvar%nd_epw?1:0);
-	for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ )
-		TD(m) -= ndl_dehomogenize(DL(m));
-	if ( newwpd != nd_wpd ) {
-		d = (unsigned int *)ALLOCA(newwpd*sizeof(unsigned int));
-		newadv = sizeof(struct oNMV)+(newwpd-1)*sizeof(unsigned int);
-		for ( m = r = BDY(p), i = 0; i < len; NMV_ADV(m), NEWADV(r), i++ ) {
-			CQ(r) = CQ(m); TD(r) = TD(m); ndl_copy(DL(m),d); ndl_copy(d,DL(r));
-		}
-	}
-	NV(p)--;
+    len = p->len;
+    for ( m = BDY(p), i = 0, max = 1; i < len; NMV_OADV(m), i++ )
+        max = MAX(max,TD(DL(m)));
+    mr0 = nmv_adv>oadv?(NMV)REALLOC(BDY(p),len*nmv_adv):BDY(p);
+    m = (NMV)((char *)mr0+(len-1)*oadv);
+    mr = (NMV)((char *)mr0+(len-1)*nmv_adv);
+    t = (NMV)ALLOCA(nmv_adv);
+    for ( i = 0; i < len; i++, NMV_OPREV(m), NMV_PREV(mr) ) {
+        ndl_homogenize(DL(m),DL(t),obpe,oepos,ompos,max);
+        CQ(mr) = CQ(m);
+        ndl_copy(DL(t),DL(mr));
+    }
+    NV(p)++;
+    BDY(p) = mr0;
 }
 
-void removecont_array(Q *c,int n)
+void ndv_dehomogenize(NDV p,struct order_spec *ord)
 {
-	struct oVECT v;
-	Q d0,d1,a,u,u1,gcd;
-	int i;
-	N qn,rn,gn;
-	Q *q,*r;
+    int i,j,adj,len,newnvar,newwpd,newadv,newexporigin,newmpos;
+    int pos;
+    Q *w;
+    Q dvr,t;
+    NMV m,r;
 
-	q = (Q *)ALLOCA(n*sizeof(Q));
-	r = (Q *)ALLOCA(n*sizeof(Q));
-	v.id = O_VECT; v.len = n; v.body = (pointer *)c;
-	igcdv_estimate(&v,&d0);
-	for ( i = 0; i < n; i++ ) {
-		divn(NM(c[i]),NM(d0),&qn,&rn);
-		NTOQ(qn,SGN(c[i])*SGN(d0),q[i]);
-		NTOQ(rn,SGN(c[i]),r[i]);
-	}
-	for ( i = 0; i < n; i++ )
-		if ( r[i] )
-			break;
-	if ( i < n ) {
-		v.id = O_VECT; v.len = n; v.body = (pointer *)r;
-		igcdv(&v,&d1);
-		gcdn(NM(d0),NM(d1),&gn); NTOQ(gn,1,gcd);
-		divsn(NM(d0),gn,&qn); NTOQ(qn,1,a);
-		for ( i = 0; i < n; i++ ) {
-			mulq(a,q[i],&u);
-			if ( r[i] ) {
-				divsn(NM(r[i]),gn,&qn); NTOQ(qn,SGN(r[i]),u1);
-				addq(u,u1,&q[i]);
-			} else
-				q[i] = u;
-		}
-	}
-	for ( i = 0; i < n; i++ )
-		c[i] = q[i];
+    len = p->len;
+    newnvar = nd_nvar-1;
+    newexporigin = nd_get_exporigin(ord);
+    if ( nd_module ) newmpos = newexporigin-1;
+    newwpd = newnvar/nd_epw+(newnvar%nd_epw?1:0)+newexporigin;
+    for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ )
+        ndl_dehomogenize(DL(m));
+    if ( newwpd != nd_wpd ) {
+        newadv = ROUND_FOR_ALIGN(sizeof(struct oNMV)+(newwpd-1)*sizeof(UINT));
+        for ( m = r = BDY(p), i = 0; i < len; NMV_ADV(m), NDV_NADV(r), i++ ) {
+            CQ(r) = CQ(m);
+            if ( nd_module ) pos = MPOS(DL(m));
+            for ( j = 0; j < newexporigin; j++ ) DL(r)[j] = DL(m)[j];
+            adj = nd_exporigin-newexporigin;
+            for ( ; j < newwpd; j++ ) DL(r)[j] = DL(m)[j+adj];
+            if ( nd_module ) {
+                DL(r)[newmpos] = pos;
+            }
+        }
+    }
+    NV(p)--;
 }
 
+void nd_heu_nezgcdnpz(VL vl,P *pl,int m,int full,P *pr)
+{
+    int i;
+    P *tpl,*tpl1;
+    NODE l;
+    P h,gcd,t;
+
+    tpl = (P *)ALLOCA(m*sizeof(P));
+    tpl1 = (P *)ALLOCA(m*sizeof(P));
+    bcopy(pl,tpl,m*sizeof(P));
+    gcd = (P)ONE;
+    for ( l = nd_hcf; l; l = NEXT(l) ) {
+        h = (P)BDY(l);
+        while ( 1 ) {
+            for ( i = 0; i < m; i++ )
+                if ( !divtpz(vl,tpl[i],h,&tpl1[i]) )
+                    break;
+            if ( i == m ) {
+                bcopy(tpl1,tpl,m*sizeof(P));
+                mulp(vl,gcd,h,&t); gcd = t;
+            } else
+                break;
+        }
+    }
+    if ( DP_Print > 2 ){fprintf(asir_out,"[%d]",nmonop(gcd)); fflush(asir_out);}
+    if ( full ) {
+        heu_nezgcdnpz(vl,tpl,m,&t);
+        mulp(vl,gcd,t,pr);
+    } else
+        *pr = gcd;
+}
+
+void removecont_array(P *p,int n,int full)
+{
+    int all_p,all_q,i;
+    Q *c;
+    P *w;
+    P t,s;
+
+    for ( all_q = 1, i = 0; i < n; i++ )
+        all_q = all_q && NUM(p[i]);
+    if ( all_q ) {
+        removecont_array_q((Q *)p,n);
+    } else {
+        c = (Q *)ALLOCA(n*sizeof(Q));
+        w = (P *)ALLOCA(n*sizeof(P));
+        for ( i = 0; i < n; i++ ) {
+            ptozp(p[i],1,&c[i],&w[i]);
+        }
+        removecont_array_q(c,n);
+        nd_heu_nezgcdnpz(nd_vc,w,n,full,&t);
+        for ( i = 0; i < n; i++ ) {
+            divsp(nd_vc,w[i],t,&s); mulp(nd_vc,s,(P)c[i],&p[i]);
+        }
+    }
+}
+
+void removecont_array_q(Q *c,int n)
+{
+    struct oVECT v;
+    Q d0,d1,a,u,u1,gcd;
+    int i,j;
+    N qn,rn,gn;
+    Q *q,*r;
+
+    q = (Q *)ALLOCA(n*sizeof(Q));
+    r = (Q *)ALLOCA(n*sizeof(Q));
+    v.id = O_VECT; v.len = n; v.body = (pointer *)c;
+    igcdv_estimate(&v,&d0);
+    for ( i = 0; i < n; i++ ) {
+        divn(NM(c[i]),NM(d0),&qn,&rn);
+        NTOQ(qn,SGN(c[i])*SGN(d0),q[i]);
+        NTOQ(rn,SGN(c[i]),r[i]);
+    }
+    for ( i = 0; i < n; i++ ) if ( r[i] ) break;
+    if ( i < n ) {
+        v.id = O_VECT; v.len = n; v.body = (pointer *)r;
+        igcdv(&v,&d1);
+        gcdn(NM(d0),NM(d1),&gn); NTOQ(gn,1,gcd);
+        divsn(NM(d0),gn,&qn); NTOQ(qn,1,a);
+        for ( i = 0; i < n; i++ ) {
+            mulq(a,q[i],&u);
+            if ( r[i] ) {
+                divsn(NM(r[i]),gn,&qn); NTOQ(qn,SGN(r[i]),u1);
+                addq(u,u1,&q[i]);
+            } else
+                q[i] = u;
+        }
+    }
+    for ( i = 0; i < n; i++ ) c[i] = q[i];
+}
+
 void nd_mul_c(int mod,ND p,int mul)
 {
-	NM m;
-	int c,c1;
+    NM m;
+    int c,c1;
 
-	if ( !p )
-		return;
-	for ( m = BDY(p); m; m = NEXT(m) ) {
-		c1 = CM(m);
-		DMAR(c1,mul,0,mod,c);
-		CM(m) = c;
-	}
+    if ( !p ) return;
+    if ( mul == 1 ) return;
+    if ( mod == -1 )
+        for ( m = BDY(p); m; m = NEXT(m) )
+            CM(m) = _mulsf(CM(m),mul);
+    else
+        for ( m = BDY(p); m; m = NEXT(m) ) {
+            c1 = CM(m); DMAR(c1,mul,0,mod,c); CM(m) = c;
+        }
 }
 
-void nd_mul_c_q(ND p,Q mul)
+void nd_mul_c_q(ND p,P mul)
 {
-	NM m;
-	Q c;
+    NM m;
+    P c;
 
-	if ( !p )
-		return;
-	for ( m = BDY(p); m; m = NEXT(m) ) {
-		mulq(CQ(m),mul,&c); CQ(m) = c;
-	}
+    if ( !p ) return;
+    if ( UNIQ(mul) ) return;
+    for ( m = BDY(p); m; m = NEXT(m) ) {
+        mulp(nd_vc,CP(m),mul,&c); CP(m) = c;
+    }
 }
 
+void nd_mul_c_p(VL vl,ND p,P mul)
+{
+    NM m;
+    P c;
+
+    if ( !p ) return;
+    for ( m = BDY(p); m; m = NEXT(m) ) {
+        mulp(vl,CP(m),mul,&c); CP(m) = c;
+    }
+}
+
 void nd_free(ND p)
 {
-	NM t,s;
+    NM t,s;
 
-	if ( !p )
-		return;
-	t = BDY(p);
-	while ( t ) {
-		s = NEXT(t);
-		FREENM(t);
-		t = s;
-	}
-	FREEND(p);
+    if ( !p ) return;
+    t = BDY(p);
+    while ( t ) {
+        s = NEXT(t);
+        FREENM(t);
+        t = s;
+    }
+    FREEND(p);
 }
 
 void ndv_free(NDV p)
 {
-	GC_free(BDY(p));
+    GCFREE(BDY(p));
 }
 
-void nd_append_red(unsigned int *d,int td,int i)
+void nd_append_red(UINT *d,int i)
 {
-	RHist m,m0;
-	int h;
+    RHist m,m0;
+    int h;
 
-	NEWRHist(m);
-	h = ndl_hash_value(td,d);
-	m->index = i;
-	TD(m) = td;
-	ndl_copy(d,DL(m));
-	NEXT(m) = nd_red[h];
-	nd_red[h] = m;
+    NEWRHist(m);
+    h = ndl_hash_value(d);
+    m->index = i;
+    ndl_copy(d,DL(m));
+    NEXT(m) = nd_red[h];
+    nd_red[h] = m;
 }
 
-unsigned int *dp_compute_bound(DP p)
+UINT *ndv_compute_bound(NDV p)
 {
-	unsigned int *d,*d1,*d2,*t;
-	MP m;
-	int i,l;
+    UINT *d1,*d2,*t;
+    UINT u;
+    int i,j,k,l,len,ind;
+    NMV m;
 
-	if ( !p )
-		return 0;
-	d1 = (unsigned int *)ALLOCA(nd_nvar*sizeof(unsigned int));
-	d2 = (unsigned int *)ALLOCA(nd_nvar*sizeof(unsigned int));
-	m = BDY(p);
-	bcopy(DL(m)->d,d1,nd_nvar*sizeof(unsigned int));
-	for ( m = NEXT(BDY(p)); m; m = NEXT(m) ) {
-		d = DL(m)->d;
-		for ( i = 0; i < nd_nvar; i++ )
-			d2[i] = d[i] > d1[i] ? d[i] : d1[i];
-		t = d1; d1 = d2; d2 = t;
-	}
-	l = (nd_nvar+31);
-	t = (unsigned int *)MALLOC_ATOMIC(l*sizeof(unsigned int));
-	bzero(t,l*sizeof(unsigned int));
-	bcopy(d1,t,nd_nvar*sizeof(unsigned int));
-	return t;
+    if ( !p )
+        return 0;
+    d1 = (UINT *)ALLOCA(nd_wpd*sizeof(UINT));
+    d2 = (UINT *)ALLOCA(nd_wpd*sizeof(UINT));
+    len = LEN(p);
+    m = BDY(p); ndl_copy(DL(m),d1); NMV_ADV(m);
+    for ( i = 1; i < len; i++, NMV_ADV(m) ) {
+        ndl_max(DL(m),d1,d2);
+        t = d1; d1 = d2; d2 = t;
+    }
+    l = nd_nvar+31;
+    t = (UINT *)MALLOC_ATOMIC(l*sizeof(UINT));
+    for ( i = nd_exporigin, ind = 0; i < nd_wpd; i++ ) {
+        u = d1[i];
+        k = (nd_epw-1)*nd_bpe;
+        for ( j = 0; j < nd_epw; j++, k -= nd_bpe, ind++ )
+            t[ind] = (u>>k)&nd_mask0;
+    }
+    for ( ; ind < l; ind++ ) t[ind] = 0;
+    return t;
 }
 
-unsigned int *nd_compute_bound(ND p)
+UINT *nd_compute_bound(ND p)
 {
-	unsigned int *d1,*d2,*t;
-	int i,l;
-	NM m;
+    UINT *d1,*d2,*t;
+    UINT u;
+    int i,j,k,l,len,ind;
+    NM m;
 
-	if ( !p )
-		return 0;
-	d1 = (unsigned int *)ALLOCA(nd_wpd*sizeof(unsigned int));
-	d2 = (unsigned int *)ALLOCA(nd_wpd*sizeof(unsigned int));
-	bcopy(HDL(p),d1,nd_wpd*sizeof(unsigned int));
-	for ( m = NEXT(BDY(p)); m; m = NEXT(m) ) {
-		ndl_lcm(DL(m),d1,d2);
-		t = d1; d1 = d2; d2 = t;
-	}
-	l = nd_nvar+31;
-	t = (unsigned int *)MALLOC_ATOMIC(l*sizeof(unsigned int));
-	bzero(t,l*sizeof(unsigned int));
-	for ( i = 0; i < nd_nvar; i++ )
-		t[i] = (d1[i/nd_epw]>>((nd_epw-(i%nd_epw)-1)*nd_bpe))&nd_mask0;
-	return t;
+    if ( !p )
+        return 0;
+    d1 = (UINT *)ALLOCA(nd_wpd*sizeof(UINT));
+    d2 = (UINT *)ALLOCA(nd_wpd*sizeof(UINT));
+    len = LEN(p);
+    m = BDY(p); ndl_copy(DL(m),d1); m = NEXT(m);
+    for ( m = NEXT(m); m; m = NEXT(m) ) {
+        ndl_lcm(DL(m),d1,d2);
+        t = d1; d1 = d2; d2 = t;
+    }
+    l = nd_nvar+31;
+    t = (UINT *)MALLOC_ATOMIC(l*sizeof(UINT));
+    for ( i = nd_exporigin, ind = 0; i < nd_wpd; i++ ) {
+        u = d1[i];
+        k = (nd_epw-1)*nd_bpe;
+        for ( j = 0; j < nd_epw; j++, k -= nd_bpe, ind++ )
+            t[ind] = (u>>k)&nd_mask0;
+    }
+    for ( ; ind < l; ind++ ) t[ind] = 0;
+    return t;
 }
 
-void nd_setup_parameters() {
-	int i;
+/* if nd_module == 1 then d[nd_exporigin-1] indicates the position */
+/* of a term. In this case we need additional 1 word. */
 
-	nd_epw = (sizeof(unsigned int)*8)/nd_bpe;
-	nd_wpd = nd_nvar/nd_epw+(nd_nvar%nd_epw?1:0);
-	if ( nd_bpe < 32 ) {
-		nd_mask0 = (1<<nd_bpe)-1;
-	} else {
-		nd_mask0 = 0xffffffff;
+int nd_get_exporigin(struct order_spec *ord)
+{
+    switch ( ord->id ) {
+        case 0: case 2: case 256: case 258:
+            return 1+nd_module;
+        case 1: case 257:
+            /* block order */
+            /* poly ring d[0]:weight d[1]:w0,...,d[nd_exporigin-1]:w(n-1) */
+            /* module d[0]:weight d[1]:w0,...,d[nd_exporigin-2]:w(n-1) */
+            return ord->ord.block.length+1+nd_module;
+        case 3: case 259:
+            error("nd_get_exporigin : composite order is not supported yet.");
+    }
+}
+
+void nd_setup_parameters(int nvar,int max) {
+    int i,j,n,elen,ord_o,ord_l,l,s,wpd;
+    struct order_pair *op;
+
+    nd_nvar = nvar;
+    if ( max ) {
+        /* XXX */
+        if ( do_weyl ) nd_bpe = 32;
+        else if ( max < 2 ) nd_bpe = 1;
+        else if ( max < 4 ) nd_bpe = 2;
+        else if ( max < 8 ) nd_bpe = 3;
+        else if ( max < 16 ) nd_bpe = 4;
+        else if ( max < 32 ) nd_bpe = 5;
+        else if ( max < 64 ) nd_bpe = 6;
+        else if ( max < 256 ) nd_bpe = 8;
+        else if ( max < 1024 ) nd_bpe = 10;
+        else if ( max < 65536 ) nd_bpe = 16;
+        else nd_bpe = 32;
+    }
+    if ( !do_weyl && current_dl_weight_vector ) {
+        UINT t;
+		/* t = max(weights) */
+        for ( i = 0, t = 0; i < nd_nvar; i++ )
+			if ( t < current_dl_weight_vector[i] )
+				t = current_dl_weight_vector[i];
+		/* i = bitsize of t */
+		for ( i = 0; t; t >>=1, i++ );
+		/* i += bitsize of nd_nvar */
+		for ( t = nd_nvar; t; t >>=1, i++);
+		/* nd_bpe+i = bitsize of max(weights)*max(exp)*nd_nvar */
+		if ( (nd_bpe+i) >= 31 )
+			error("nd_setup_parameters : too large weight");
 	}
-	bzero(nd_mask,sizeof(nd_mask));
-	nd_mask1 = 0;
-	for ( i = 0; i < nd_epw; i++ ) {
-		nd_mask[nd_epw-i-1] = (nd_mask0<<(i*nd_bpe));
-		nd_mask1 |= (1<<(nd_bpe-1))<<(i*nd_bpe);
-	}
-	nm_adv = sizeof(struct oNM)+(nd_wpd-1)*sizeof(unsigned int);
-	nmv_adv = sizeof(struct oNMV)+(nd_wpd-1)*sizeof(unsigned int);
+    nd_epw = (sizeof(UINT)*8)/nd_bpe;
+    elen = nd_nvar/nd_epw+(nd_nvar%nd_epw?1:0);
+    nd_exporigin = nd_get_exporigin(nd_ord);
+    wpd = nd_exporigin+elen;
+    if ( nd_module )
+        nd_mpos = nd_exporigin-1;
+    else
+        nd_mpos = -1;
+    if ( wpd != nd_wpd ) {
+        nd_free_private_storage();
+        nd_wpd = wpd;
+    }
+    if ( nd_bpe < 32 ) {
+        nd_mask0 = (1<<nd_bpe)-1;
+    } else {
+        nd_mask0 = 0xffffffff;
+    }
+    bzero(nd_mask,sizeof(nd_mask));
+    nd_mask1 = 0;
+    for ( i = 0; i < nd_epw; i++ ) {
+        nd_mask[nd_epw-i-1] = (nd_mask0<<(i*nd_bpe));
+        nd_mask1 |= (1<<(nd_bpe-1))<<(i*nd_bpe);
+    }
+    nmv_adv = ROUND_FOR_ALIGN(sizeof(struct oNMV)+(nd_wpd-1)*sizeof(UINT));
+    nd_epos = nd_create_epos(nd_ord);
+    nd_blockmask = nd_create_blockmask(nd_ord);
+    nd_work_vector = (int *)REALLOC(nd_work_vector,nd_nvar*sizeof(int));
 }
 
-/* mod < 0 => realloc nd_ps and pd_psq */
+ND_pairs nd_reconstruct(int trace,ND_pairs d)
+{
+    int i,obpe,oadv,h;
+    static NM prev_nm_free_list;
+    static ND_pairs prev_ndp_free_list;
+    RHist mr0,mr;
+    RHist r;
+    RHist *old_red;
+    ND_pairs s0,s,t;
+    EPOS oepos;
 
-ND_pairs nd_reconstruct(int mod,int trace,ND_pairs d)
+    obpe = nd_bpe;
+    oadv = nmv_adv;
+    oepos = nd_epos;
+    if ( obpe < 2 ) nd_bpe = 2;
+    else if ( obpe < 3 ) nd_bpe = 3;
+    else if ( obpe < 4 ) nd_bpe = 4;
+    else if ( obpe < 5 ) nd_bpe = 5;
+    else if ( obpe < 6 ) nd_bpe = 6;
+    else if ( obpe < 8 ) nd_bpe = 8;
+    else if ( obpe < 10 ) nd_bpe = 10;
+    else if ( obpe < 16 ) nd_bpe = 16;
+    else if ( obpe < 32 ) nd_bpe = 32;
+    else error("nd_reconstruct : exponent too large");
+
+    nd_setup_parameters(nd_nvar,0);
+    prev_nm_free_list = _nm_free_list;
+    prev_ndp_free_list = _ndp_free_list;
+    _nm_free_list = 0;
+    _ndp_free_list = 0;
+    for ( i = nd_psn-1; i >= 0; i-- ) ndv_realloc(nd_ps[i],obpe,oadv,oepos);
+    if ( trace )
+        for ( i = nd_psn-1; i >= 0; i-- )
+            ndv_realloc(nd_ps_trace[i],obpe,oadv,oepos);
+    s0 = 0;
+    for ( t = d; t; t = NEXT(t) ) {
+        NEXTND_pairs(s0,s);
+        s->i1 = t->i1;
+        s->i2 = t->i2;
+        SG(s) = SG(t);
+        ndl_reconstruct(LCM(t),LCM(s),obpe,oepos);
+    }
+    
+    old_red = (RHist *)ALLOCA(REDTAB_LEN*sizeof(RHist));
+    for ( i = 0; i < REDTAB_LEN; i++ ) {
+        old_red[i] = nd_red[i];
+        nd_red[i] = 0;
+    }
+    for ( i = 0; i < REDTAB_LEN; i++ )
+        for ( r = old_red[i]; r; r = NEXT(r) ) {
+            NEWRHist(mr);
+            mr->index = r->index;
+            SG(mr) = SG(r);
+            ndl_reconstruct(DL(r),DL(mr),obpe,oepos);
+            h = ndl_hash_value(DL(mr));
+            NEXT(mr) = nd_red[h];
+            nd_red[h] = mr;
+        }
+    for ( i = 0; i < REDTAB_LEN; i++ ) old_red[i] = 0;
+    old_red = 0;
+    for ( i = 0; i < nd_psn; i++ ) {
+        NEWRHist(r); SG(r) = SG(nd_psh[i]);
+        ndl_reconstruct(DL(nd_psh[i]),DL(r),obpe,oepos);
+        nd_psh[i] = r;
+    }
+    if ( s0 ) NEXT(s) = 0;
+    prev_nm_free_list = 0;
+    prev_ndp_free_list = 0;
+#if 0
+    GC_gcollect();
+#endif
+    return s0;
+}
+
+void ndl_reconstruct(UINT *d,UINT *r,int obpe,EPOS oepos)
 {
-	int i,obpe,oadv;
-	NM prev_nm_free_list;
-	RHist mr0,mr;
-	RHist r;
-	ND_pairs s0,s,t,prev_ndp_free_list;
+    int n,i,ei,oepw,omask0,j,s,ord_l,l;
+    struct order_pair *op;
 
-	obpe = nd_bpe;
-	oadv = nmv_adv;
-	if ( obpe < 4 )
-		nd_bpe = 4;
-	else if ( obpe < 6 )
-		nd_bpe = 6;
-	else if ( obpe < 8 )
-		nd_bpe = 8;
-	else if ( obpe < 16 )
-		nd_bpe = 16;
-	else if ( obpe < 32 )
-		nd_bpe = 32;
-	else
-		error("nd_reconstruct : exponent too large");
+    n = nd_nvar;
+    oepw = (sizeof(UINT)*8)/obpe;
+    omask0 = (1<<obpe)-1;
+    TD(r) = TD(d);
+    for ( i = nd_exporigin; i < nd_wpd; i++ ) r[i] = 0;
+    if ( nd_blockmask ) {
+        l = nd_blockmask->n;
+        op = nd_blockmask->order_pair;
+        for ( i = 1; i < nd_exporigin; i++ )
+            r[i] = d[i];
+        for ( j = 0, s = 0; j < l; j++ ) {
+            ord_l = op[j].length;
+            for ( i = 0; i < ord_l; i++, s++ ) {
+                ei =  GET_EXP_OLD(d,s);
+                PUT_EXP(r,s,ei);
+            }
+        }
+    } else {
+        for ( i = 0; i < n; i++ ) {
+            ei = GET_EXP_OLD(d,i);
+            PUT_EXP(r,i,ei);
+        }
+    }
+    if ( nd_module ) MPOS(r) = MPOS(d);
+}
 
-	nd_setup_parameters();
-	prev_nm_free_list = _nm_free_list;
-	prev_ndp_free_list = _ndp_free_list;
-	_nm_free_list = 0;
-	_ndp_free_list = 0;
-	if ( mod != 0 )
-		for ( i = nd_psn-1; i >= 0; i-- )
-			ndv_realloc(nd_ps[i],obpe,oadv);
-	if ( !mod || trace )
-		for ( i = nd_psn-1; i >= 0; i-- )
-			ndv_realloc(nd_psq[i],obpe,oadv);
-	s0 = 0;
-	for ( t = d; t; t = NEXT(t) ) {
-		NEXTND_pairs(s0,s);
-		s->i1 = t->i1;
-		s->i2 = t->i2;
-		TD(s) = TD(t);
-		SG(s) = SG(t);
-		ndl_dup(obpe,t->lcm,s->lcm);
-	}
-	for ( i = 0; i < REDTAB_LEN; i++ ) {
-		for ( mr0 = 0, r = nd_red[i]; r; r = NEXT(r) ) {
-			NEXTRHist(mr0,mr);
-			mr->index = r->index;
-			SG(mr) = SG(r);
-			TD(mr) = TD(r);
-			ndl_dup(obpe,DL(r),DL(mr));
-		}
-		if ( mr0 ) NEXT(mr) = 0;
-		nd_red[i] = mr0;
-	}
-	for ( i = 0; i < nd_psn; i++ ) {
-		NEWRHist(r); SG(r) = SG(nd_psh[i]);
-		TD(r) = TD(nd_psh[i]); ndl_dup(obpe,DL(nd_psh[i]),DL(r));
-		nd_psh[i] = r;
-	}
-	if ( s0 ) NEXT(s) = 0;
-	prev_nm_free_list = 0;
-	prev_ndp_free_list = 0;
-	GC_gcollect();
-	return s0;
+ND nd_copy(ND p)
+{
+    NM m,mr,mr0;
+    int c,n;
+    ND r;
+
+    if ( !p )
+        return 0;
+    else {
+        for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
+            NEXTNM(mr0,mr);
+            CM(mr) = CM(m);
+            ndl_copy(DL(m),DL(mr));
+        }
+        NEXT(mr) = 0; 
+        MKND(NV(p),mr0,LEN(p),r);
+        SG(r) = SG(p);
+        return r;
+    }
 }
 
-void nd_reconstruct_direct(int mod,NDV *ps,int len)
+int nd_sp(int mod,int trace,ND_pairs p,ND *rp)
 {
-	int i,obpe,oadv;
-	NM prev_nm_free_list;
-	RHist mr0,mr;
-	RHist r;
-	ND_pairs s0,s,t,prev_ndp_free_list;
+    NM m1,m2;
+    NDV p1,p2;
+    ND t1,t2;
+    UINT *lcm;
+    P gp,tp;
+    Q g,t,iq;
+    int td;
+    LIST hist;
+    NODE node;
+    DP d;
 
-	obpe = nd_bpe;
-	oadv = nmv_adv;
-	if ( obpe < 4 )
-		nd_bpe = 4;
-	else if ( obpe < 6 )
-		nd_bpe = 6;
-	else if ( obpe < 8 )
-		nd_bpe = 8;
-	else if ( obpe < 16 )
-		nd_bpe = 16;
-	else if ( obpe < 32 )
-		nd_bpe = 32;
-	else
-		error("nd_reconstruct_direct : exponent too large");
+    if ( !mod && nd_demand ) {
+        p1 = ndv_load(p->i1); p2 = ndv_load(p->i2);
+    } else {
+        if ( trace ) {
+            p1 = nd_ps_trace[p->i1]; p2 = nd_ps_trace[p->i2];
+        } else {
+            p1 = nd_ps[p->i1]; p2 = nd_ps[p->i2];
+        }
+    }
+    lcm = LCM(p);
+    NEWNM(m1); ndl_sub(lcm,HDL(p1),DL(m1));
+    if ( ndl_check_bound2(p->i1,DL(m1)) ) {
+        FREENM(m1); return 0;
+    }
+    NEWNM(m2); ndl_sub(lcm,HDL(p2),DL(m2));
+    if ( ndl_check_bound2(p->i2,DL(m2)) ) {
+        FREENM(m1); FREENM(m2); return 0;
+    }
 
-	nd_setup_parameters();
-	prev_nm_free_list = _nm_free_list;
-	prev_ndp_free_list = _ndp_free_list;
-	_nm_free_list = 0;
-	_ndp_free_list = 0;
-	if ( mod != 0 )
-		for ( i = len-1; i >= 0; i-- )
-			ndv_realloc(ps[i],obpe,oadv);
-	for ( i = 0; i < REDTAB_LEN; i++ ) {
-		for ( mr0 = 0, r = nd_red[i]; r; r = NEXT(r) ) {
-			NEXTRHist(mr0,mr);
-			mr->index = r->index;
-			SG(mr) = SG(r);
-			TD(mr) = TD(r);
-			ndl_dup(obpe,DL(r),DL(mr));
-		}
-		if ( mr0 ) NEXT(mr) = 0;
-		nd_red[i] = mr0;
-	}
-	prev_nm_free_list = 0;
-	prev_ndp_free_list = 0;
-	GC_gcollect();
+    if ( mod == -1 ) {
+        CM(m1) = HCM(p2); CM(m2) = _chsgnsf(HCM(p1));
+    } else if ( mod ) {
+        CM(m1) = HCM(p2); CM(m2) = mod-HCM(p1); 
+    } else if ( nd_vc ) {
+        ezgcdpz(nd_vc,HCP(p1),HCP(p2),&gp);
+        divsp(nd_vc,HCP(p2),gp,&CP(m1));
+        divsp(nd_vc,HCP(p1),gp,&tp); chsgnp(tp,&CP(m2));
+    } else {
+        igcd_cofactor(HCQ(p1),HCQ(p2),&g,&t,&CQ(m1)); chsgnq(t,&CQ(m2));
+    }
+    t1 = ndv_mul_nm(mod,m1,p1); t2 = ndv_mul_nm(mod,m2,p2);
+    *rp = nd_add(mod,t1,t2);
+    if ( nd_gentrace ) {
+        /* nd_tracelist is initialized */
+        STOQ(p->i1,iq); nmtodp(mod,m1,&d); node = mknode(4,ONE,iq,d,ONE);
+        MKLIST(hist,node); MKNODE(nd_tracelist,hist,0);
+        STOQ(p->i2,iq); nmtodp(mod,m2,&d); node = mknode(4,ONE,iq,d,ONE);
+        MKLIST(hist,node); MKNODE(node,hist,nd_tracelist);
+        nd_tracelist = node;
+    }
+    FREENM(m1); FREENM(m2);
+    return 1;
 }
 
-void ndl_dup(int obpe,unsigned int *d,unsigned int *r)
+void ndv_mul_c(int mod,NDV p,int mul)
 {
-	int n,i,ei,oepw,cepw,cbpe;
+    NMV m;
+    int c,c1,len,i;
 
-	n = nd_nvar;
-	oepw = (sizeof(unsigned int)*8)/obpe;
-	cepw = nd_epw;
-	cbpe = nd_bpe;
-	for ( i = 0; i < nd_wpd; i++ )
-		r[i] = 0;
-	if ( nd_isrlex )
-		for ( i = 0; i < n; i++ ) {
-			ei = (d[(n-1-i)/oepw]>>((oepw-((n-1-i)%oepw)-1)*obpe))
-				&((1<<obpe)-1);
-			r[(n-1-i)/cepw] |= (ei<<((cepw-((n-1-i)%cepw)-1)*cbpe));
-		}
+    if ( !p ) return;
+    len = LEN(p);
+    if ( mod == -1 )
+        for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) 
+            CM(m) = _mulsf(CM(m),mul);
+    else
+        for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
+            c1 = CM(m); DMAR(c1,mul,0,mod,c); CM(m) = c;
+        }
+}
+
+void ndv_mul_c_q(NDV p,Q mul)
+{
+    NMV m;
+    Q c;
+    int len,i;
+
+    if ( !p ) return;
+    len = LEN(p);
+    for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
+        mulq(CQ(m),mul,&c); CQ(m) = c;
+    }
+}
+
+ND weyl_ndv_mul_nm(int mod,NM m0,NDV p) {
+    int n2,i,j,l,n,tlen;
+    UINT *d0;
+    NM *tab,*psum;
+    ND s,r;
+    NM t;
+    NMV m1;
+
+    if ( !p ) return 0;
+    n = NV(p); n2 = n>>1;
+    d0 = DL(m0);
+    l = LEN(p);
+    for ( i = 0, tlen = 1; i < n2; i++ ) tlen *= (GET_EXP(d0,n2+i)+1);
+    tab = (NM *)ALLOCA(tlen*sizeof(NM));
+    psum = (NM *)ALLOCA(tlen*sizeof(NM));
+    for ( i = 0; i < tlen; i++ ) psum[i] = 0;
+    m1 = (NMV)(((char *)BDY(p))+nmv_adv*(l-1));
+    for ( i = l-1; i >= 0; i--, NMV_PREV(m1) ) {
+        /* m0(NM) * m1(NMV) => tab(NM) */
+        weyl_mul_nm_nmv(n,mod,m0,m1,tab,tlen);
+        for ( j = 0; j < tlen; j++ ) {
+            if ( tab[j] ) {
+                NEXT(tab[j]) = psum[j];    psum[j] = tab[j];
+            }
+        }        
+    }
+    for ( i = tlen-1, r = 0; i >= 0; i-- )
+        if ( psum[i] ) {
+            for ( j = 0, t = psum[i]; t; t = NEXT(t), j++ );
+            MKND(n,psum[i],j,s);
+            r = nd_add(mod,r,s);
+        }
+    if ( r ) SG(r) = SG(p)+TD(d0);
+    return r;
+}
+
+/* product of monomials */
+/* XXX block order is not handled correctly */
+
+void weyl_mul_nm_nmv(int n,int mod,NM m0,NMV m1,NM *tab,int tlen)
+{
+    int i,n2,j,s,curlen,homo,h,a,b,k,l,u,min;
+    UINT *d0,*d1,*d,*dt,*ctab;
+    Q *ctab_q;
+    Q q,q1;
+    UINT c0,c1,c;
+    NM *p;
+    NM m,t;
+    int mpos;
+
+    for ( i = 0; i < tlen; i++ ) tab[i] = 0;
+    if ( !m0 || !m1 ) return;
+    d0 = DL(m0); d1 = DL(m1); n2 = n>>1;
+    if ( nd_module )
+        if ( MPOS(d0) ) error("weyl_mul_nm_nmv : invalid operation");
+
+    NEWNM(m); d = DL(m);
+    if ( mod ) {
+        c0 = CM(m0); c1 = CM(m1); DMAR(c0,c1,0,mod,c); CM(m) = c;
+    } else if ( nd_vc )
+        mulp(nd_vc,CP(m0),CP(m1),&CP(m));
 	else
-		for ( i = 0; i < n; i++ ) {
-			ei = (d[i/oepw]>>((oepw-(i%oepw)-1)*obpe))
-				&((1<<obpe)-1);
-			r[i/cepw] |= (ei<<((cepw-(i%cepw)-1)*cbpe));
-		}
+        mulq(CQ(m0),CQ(m1),&CQ(m));
+    for ( i = 0; i < nd_wpd; i++ ) d[i] = 0;
+    homo = n&1 ? 1 : 0;
+    if ( homo ) {
+        /* offset of h-degree */
+        h = GET_EXP(d0,n-1)+GET_EXP(d1,n-1);
+        PUT_EXP(DL(m),n-1,h);
+        TD(DL(m)) = h;
+        if ( nd_blockmask ) ndl_weight_mask(DL(m));
+    }
+    tab[0] = m;
+    NEWNM(m); d = DL(m);
+    for ( i = 0, curlen = 1; i < n2; i++ ) {
+        a = GET_EXP(d0,i); b = GET_EXP(d1,n2+i);
+        k = GET_EXP(d0,n2+i); l = GET_EXP(d1,i);
+        /* xi^a*(Di^k*xi^l)*Di^b */
+        a += l; b += k;
+        s = MUL_WEIGHT(a,i)+MUL_WEIGHT(b,n2+i);
+        if ( !k || !l ) {
+            for ( j = 0; j < curlen; j++ )
+                if ( t = tab[j] ) {
+                    dt = DL(t);
+                    PUT_EXP(dt,i,a); PUT_EXP(dt,n2+i,b); TD(dt) += s;
+                    if ( nd_blockmask ) ndl_weight_mask(dt);
+                }
+            curlen *= k+1;
+            continue;
+        }
+        min = MIN(k,l);
+        if ( mod ) {
+            ctab = (UINT *)ALLOCA((min+1)*sizeof(UINT));
+            mkwcm(k,l,mod,ctab);
+        } else {
+            ctab_q = (Q *)ALLOCA((min+1)*sizeof(Q));
+            mkwc(k,l,ctab_q);
+        }
+        for ( j = min; j >= 0; j-- ) {
+            for ( u = 0; u < nd_wpd; u++ ) d[u] = 0;
+            PUT_EXP(d,i,a-j); PUT_EXP(d,n2+i,b-j);
+            h = MUL_WEIGHT(a-j,i)+MUL_WEIGHT(b-j,n2+i);
+            if ( homo ) {
+                TD(d) = s;
+                PUT_EXP(d,n-1,s-h);
+            } else TD(d) = h;
+            if ( nd_blockmask ) ndl_weight_mask(d);
+            if ( mod ) c = ctab[j];
+            else q = ctab_q[j];
+            p = tab+curlen*j;
+            if ( j == 0 ) {
+                for ( u = 0; u < curlen; u++, p++ ) {
+                    if ( tab[u] ) {
+                        ndl_addto(DL(tab[u]),d);
+                        if ( mod ) {
+                            c0 = CM(tab[u]); DMAR(c0,c,0,mod,c1); CM(tab[u]) = c1;
+                        } else if ( nd_vc )
+                            mulp(nd_vc,CP(tab[u]),(P)q,&CP(tab[u]));
+						else {
+                            mulq(CQ(tab[u]),q,&q1); CQ(tab[u]) = q1;
+                        }
+                    }
+                }
+            } else {
+                for ( u = 0; u < curlen; u++, p++ ) {
+                    if ( tab[u] ) {
+                        NEWNM(t);
+                        ndl_add(DL(tab[u]),d,DL(t));
+                        if ( mod ) {
+                            c0 = CM(tab[u]); DMAR(c0,c,0,mod,c1); CM(t) = c1;
+                        } else if ( nd_vc )
+                            mulp(nd_vc,CP(tab[u]),(P)q,&CP(t));
+						else
+                            mulq(CQ(tab[u]),q,&CQ(t));
+                        *p = t;
+                    }
+                }
+            }
+        }
+        curlen *= k+1;
+    }
+    FREENM(m);
+    if ( nd_module ) {
+        mpos = MPOS(d1);
+        for ( i = 0; i < tlen; i++ )
+            if ( tab[i] ) {
+                d = DL(tab[i]);
+                MPOS(d) = mpos;
+                TD(d) = ndl_weight(d);
+            }
+    }
 }
 
-void nd_realloc(ND p,int obpe)
+ND ndv_mul_nm_symbolic(NM m0,NDV p)
 {
-	NM m,mr,mr0;
+    NM mr,mr0;
+    NMV m;
+    UINT *d,*dt,*dm;
+    int c,n,td,i,c1,c2,len;
+    Q q;
+    ND r;
 
-	if ( p ) {
-		m = BDY(p);
-		for ( mr0 = 0; m; m = NEXT(m) ) {
-			NEXTNM(mr0,mr);
-			CM(mr) = CM(m);
-			TD(mr) = TD(m);
-			ndl_dup(obpe,DL(m),DL(mr));
-		}
-		NEXT(mr) = 0; 
-		BDY(p) = mr0;
-	}
+    if ( !p ) return 0;
+    else {
+        n = NV(p); m = BDY(p);
+        d = DL(m0);
+        len = LEN(p);
+        mr0 = 0;
+        td = TD(d);
+        c = CM(m0);
+        for ( i = 0; i < len; i++, NMV_ADV(m) ) {
+            NEXTNM(mr0,mr);
+            CM(mr) = 1;
+            ndl_add(DL(m),d,DL(mr));
+        }
+        NEXT(mr) = 0; 
+        MKND(NV(p),mr0,len,r);
+        SG(r) = SG(p) + TD(d);
+        return r;
+    }
 }
 
-ND nd_copy(ND p)
+ND ndv_mul_nm(int mod,NM m0,NDV p)
 {
-	NM m,mr,mr0;
-	int c,n,s;
-	ND r;
+    NM mr,mr0;
+    NMV m;
+    UINT *d,*dt,*dm;
+    int c,n,td,i,c1,c2,len;
+    P q;
+    ND r;
 
-	if ( !p )
-		return 0;
-	else {
-		s = sizeof(struct oNM)+(nd_wpd-1)*sizeof(unsigned int);
-		for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
-			NEXTNM(mr0,mr);
-			CM(mr) = CM(m);
-			TD(mr) = TD(m);
-			ndl_copy(DL(m),DL(mr));
-		}
-		NEXT(mr) = 0; 
-		MKND(NV(p),mr0,LEN(p),r);
-		SG(r) = SG(p);
-		return r;
-	}
+    if ( !p ) return 0;
+    else if ( do_weyl )
+        if ( mod == -1 )
+            error("ndv_mul_nm : not implemented (weyl)");
+        else
+            return weyl_ndv_mul_nm(mod,m0,p);
+    else {
+        n = NV(p); m = BDY(p);
+        d = DL(m0);
+        len = LEN(p);
+        mr0 = 0;
+        td = TD(d);
+        if ( mod == -1 ) {
+            c = CM(m0);
+            for ( i = 0; i < len; i++, NMV_ADV(m) ) {
+                NEXTNM(mr0,mr);
+                CM(mr) = _mulsf(CM(m),c);
+                ndl_add(DL(m),d,DL(mr));
+            }
+        } else if ( mod ) {
+            c = CM(m0);
+            for ( i = 0; i < len; i++, NMV_ADV(m) ) {
+                NEXTNM(mr0,mr);
+                c1 = CM(m);
+                DMAR(c1,c,0,mod,c2);
+                CM(mr) = c2;
+                ndl_add(DL(m),d,DL(mr));
+            }
+        } else {
+            q = CP(m0);
+            for ( i = 0; i < len; i++, NMV_ADV(m) ) {
+                NEXTNM(mr0,mr);
+                mulp(nd_vc,CP(m),q,&CP(mr));
+                ndl_add(DL(m),d,DL(mr));
+            }
+        }
+        NEXT(mr) = 0; 
+        MKND(NV(p),mr0,len,r);
+        SG(r) = SG(p) + TD(d);
+        return r;
+    }
 }
 
-int nd_sp(int mod,ND_pairs p,ND *rp)
+ND nd_quo(int mod,PGeoBucket bucket,NDV d)
 {
-	NM m;
-	NDV p1,p2;
-	ND t1,t2;
-	unsigned int *lcm;
-	int td;
+    NM mq0,mq;
+    NMV tm;
+    Q q;
+    int i,nv,sg,c,c1,c2,hindex;
+    ND p,t,r;
+    N tnm;
 
-	if ( mod ) {
-		p1 = nd_ps[p->i1]; p2 = nd_ps[p->i2];
-	} else {
-		p1 = nd_psq[p->i1]; p2 = nd_psq[p->i2];
-	}
-	lcm = p->lcm;
-	td = TD(p);
-	NEWNM(m);
-	CQ(m) = HCQ(p2);
-	TD(m) = td-HTD(p1); ndl_sub(lcm,HDL(p1),DL(m));
-	if ( ndl_check_bound2(p->i1,DL(m)) )
-		return 0;
-	t1 = ndv_mul_nm(mod,p1,m);
-	if ( mod )
-		CM(m) = mod-HCM(p1); 
-	else
-		chsgnq(HCQ(p1),&CQ(m));
-	TD(m) = td-HTD(p2); ndl_sub(lcm,HDL(p2),DL(m));
-	if ( ndl_check_bound2(p->i2,DL(m)) ) {
-		nd_free(t1);
-		return 0;
-	}
-	t2 = ndv_mul_nm(mod,p2,m);
-	*rp = nd_add(mod,t1,t2);
-	FREENM(m);
-	return 1;
+    if ( bucket->m < 0 ) return 0;
+    else {
+        nv = NV(d);
+        mq0 = 0;
+        tm = (NMV)ALLOCA(nmv_adv);
+        while ( 1 ) {
+            hindex = mod?head_pbucket(mod,bucket):head_pbucket_q(bucket);
+            if ( hindex < 0 ) break;
+            p = bucket->body[hindex];
+            NEXTNM(mq0,mq);
+            ndl_sub(HDL(p),HDL(d),DL(mq));
+            ndl_copy(DL(mq),DL(tm));
+            if ( mod ) {
+                c1 = invm(HCM(d),mod); c2 = HCM(p);
+                DMAR(c1,c2,0,mod,c); CM(mq) = c;
+                CM(tm) = mod-c;
+            } else {
+                divsn(NM(HCQ(p)),NM(HCQ(d)),&tnm);
+                NTOQ(tnm,SGN(HCQ(p))*SGN(HCQ(d)),CQ(mq));
+                chsgnq(CQ(mq),&CQ(tm));
+            }
+            t = ndv_mul_nmv_trunc(mod,tm,d,HDL(d));
+            bucket->body[hindex] = nd_remove_head(p);
+            t = nd_remove_head(t);
+            add_pbucket(mod,bucket,t);
+        }
+        if ( !mq0 )
+            r = 0;
+        else {
+            NEXT(mq) = 0;
+            for ( i = 0, mq = mq0; mq; mq = NEXT(mq), i++ );
+            MKND(nv,mq0,i,r);
+            /* XXX */
+            SG(r) = HTD(r);
+        }
+        return r;
+    }
 }
 
-void ndv_mul_c(int mod,NDV p,int mul)
+void ndv_realloc(NDV p,int obpe,int oadv,EPOS oepos)
 {
-	NMV m;
-	int c,c1,len,i;
+    NMV m,mr,mr0,t;
+    int len,i,k;
 
-	if ( !p )
-		return;
-	len = LEN(p);
-	for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
-		c1 = CM(m);
-		DMAR(c1,mul,0,mod,c);
-		CM(m) = c;
-	}
+    if ( !p ) return;
+    m = BDY(p); len = LEN(p);
+    mr0 = nmv_adv>oadv?(NMV)REALLOC(BDY(p),len*nmv_adv):BDY(p);
+    m = (NMV)((char *)mr0+(len-1)*oadv);
+    mr = (NMV)((char *)mr0+(len-1)*nmv_adv);
+    t = (NMV)ALLOCA(nmv_adv);
+    for ( i = 0; i < len; i++, NMV_OPREV(m), NMV_PREV(mr) ) {
+        CQ(t) = CQ(m);
+        for ( k = 0; k < nd_wpd; k++ ) DL(t)[k] = 0;
+        ndl_reconstruct(DL(m),DL(t),obpe,oepos);
+        CQ(mr) = CQ(t);
+        ndl_copy(DL(t),DL(mr));
+    }
+    BDY(p) = mr0;
 }
 
-void ndv_mul_c_q(NDV p,Q mul)
+NDV ndv_dup_realloc(NDV p,int obpe,int oadv,EPOS oepos)
 {
-	NMV m;
-	Q c;
-	int len,i;
+    NMV m,mr,mr0;
+    int len,i;
+    NDV r;
 
-	if ( !p )
-		return;
-	len = LEN(p);
-	for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
-		mulq(CQ(m),mul,&c); CQ(m) = c;
-	}
+    if ( !p ) return 0;
+    m = BDY(p); len = LEN(p);
+    mr0 = mr = (NMV)MALLOC(len*nmv_adv);
+    for ( i = 0; i < len; i++, NMV_OADV(m), NMV_ADV(mr) ) {
+        ndl_zero(DL(mr));
+        ndl_reconstruct(DL(m),DL(mr),obpe,oepos);
+        CQ(mr) = CQ(m);
+    }
+    MKNDV(NV(p),mr0,len,r);
+    SG(r) = SG(p);
+    return r;
 }
 
-ND ndv_mul_nm(int mod,NDV p,NM m0)
+/* duplicate p */
+
+NDV ndv_dup(int mod,NDV p)
 {
-	NM mr,mr0;
-	NMV m;
-	unsigned int *d,*dt,*dm;
-	int c,n,td,i,c1,c2,len;
-	Q q;
-	ND r;
+    NDV d;
+    NMV t,m,m0;
+    int i,len;
 
-	if ( !p )
-		return 0;
-	else {
-		n = NV(p); m = BDY(p);
-		d = DL(m0); td = TD(m0); 
-		len = LEN(p);
-		mr0 = 0;
-		if ( mod ) {
-			c = CM(m0);
-			for ( i = 0; i < len; i++, NMV_ADV(m) ) {
-				NEXTNM(mr0,mr);
-				c1 = CM(m);
-				DMAR(c1,c,0,mod,c2);
-				CM(mr) = c2;
-				TD(mr) = TD(m)+td;
-				ndl_add(DL(m),d,DL(mr));
-			}
-		} else {
-			q = CQ(m0);
-			for ( i = 0; i < len; i++, NMV_ADV(m) ) {
-				NEXTNM(mr0,mr);
-				mulq(CQ(m),q,&CQ(mr));
-				TD(mr) = TD(m)+td;
-				ndl_add(DL(m),d,DL(mr));
-			}
-		}
-		NEXT(mr) = 0; 
-		MKND(NV(p),mr0,len,r);
-		SG(r) = SG(p) + td;
-		return r;
-	}
+    if ( !p ) return 0;
+    len = LEN(p);
+    m0 = m = (NMV)(mod?MALLOC_ATOMIC(len*nmv_adv):MALLOC(len*nmv_adv));
+    for ( t = BDY(p), i = 0; i < len; i++, NMV_ADV(t), NMV_ADV(m) ) {
+        ndl_copy(DL(t),DL(m));
+        CQ(m) = CQ(t);
+    }
+    MKNDV(NV(p),m0,len,d);
+    SG(d) = SG(p);
+    return d;
 }
 
-void ndv_realloc(NDV p,int obpe,int oadv)
+ND nd_dup(ND p)
 {
-	NMV m,mr,mr0,t;
-	int len,i,k;
+    ND d;
+    NM t,m,m0;
 
-#define NMV_OPREV(m) (m = (NMV)(((char *)m)-oadv))
-#define NMV_PREV(m) (m = (NMV)(((char *)m)-nmv_adv))
+    if ( !p ) return 0;
+    for ( m0 = 0, t = BDY(p); t; t = NEXT(t) ) {
+        NEXTNM(m0,m);
+        ndl_copy(DL(t),DL(m));
+        CQ(m) = CQ(t);
+    }
+    if ( m0 ) NEXT(m) = 0;
+    MKND(NV(p),m0,LEN(p),d);
+    SG(d) = SG(p);
+    return d;
+}
 
-	if ( p ) {
-		m = BDY(p); len = LEN(p);
-		if ( nmv_adv > oadv )
-			mr0 = (NMV)REALLOC(BDY(p),len*nmv_adv);
-		else
-			mr0 = BDY(p);
-		m = (NMV)((char *)mr0+(len-1)*oadv);
-		mr = (NMV)((char *)mr0+(len-1)*nmv_adv);
-		t = (NMV)ALLOCA(nmv_adv);
-		for ( i = 0; i < len; i++, NMV_OPREV(m), NMV_PREV(mr) ) {
-			CQ(t) = CQ(m);
-			TD(t) = TD(m);
-			for ( k = 0; k < nd_wpd; k++ ) DL(t)[k] = 0;
-			ndl_dup(obpe,DL(m),DL(t));
-			CQ(mr) = CQ(t);
-			TD(mr) = TD(t);
-			ndl_copy(DL(t),DL(mr));
-		}
-		BDY(p) = mr0;
-	}
+/* XXX if p->len == 0 then it represents 0 */
+
+void ndv_mod(int mod,NDV p)
+{
+    NMV t,d;
+    int r,s,u;
+    int i,len,dlen;
+    P cp;
+    Q c;
+    Obj gfs;
+
+    if ( !p ) return;
+    len = LEN(p);
+    dlen = 0;
+    if ( mod == -1 )
+        for ( t = d = BDY(p), i = 0; i < len; i++, NMV_ADV(t) ) {
+            simp_ff((Obj)CP(t),&gfs);
+            r = FTOIF(CONT((GFS)gfs));
+            CM(d) = r;
+            ndl_copy(DL(t),DL(d));
+            NMV_ADV(d);
+            dlen++;    
+        }
+    else
+        for ( t = d = BDY(p), i = 0; i < len; i++, NMV_ADV(t) ) {
+            if ( nd_vc ) {
+                nd_subst_vector(nd_vc,CP(t),nd_subst,&cp);
+                c = (Q)cp;
+            } else
+                c = CQ(t);
+            r = rem(NM(c),mod);
+            if ( r ) {
+                if ( SGN(c) < 0 )
+                    r = mod-r;
+                if ( DN(c) ) {
+                    s = rem(DN(c),mod);
+                    if ( !s )
+                        error("ndv_mod : division by 0");
+                    s = invm(s,mod);
+                    DMAR(r,s,0,mod,u); r = u;
+                }
+                CM(d) = r;
+                ndl_copy(DL(t),DL(d));
+                NMV_ADV(d);
+                dlen++;    
+            }
+        }
+    LEN(p) = dlen;
 }
 
-NDV ndtondv(int mod,ND p)
+NDV ptondv(VL vl,VL dvl,P p)
 {
-	NDV d;
-	NMV m,m0;
-	NM t;
-	int i,len;
+    ND nd;
 
-	if ( !p )
-		return 0;
-	len = LEN(p);
-	if ( mod )
-		m0 = m = (NMV)MALLOC_ATOMIC(len*nmv_adv);
-	else
-		m0 = m = (NMV)MALLOC(len*nmv_adv);
-	for ( t = BDY(p), i = 0; t; t = NEXT(t), i++, NMV_ADV(m) ) {
-		TD(m) = TD(t);
-		ndl_copy(DL(t),DL(m));
-		CQ(m) = CQ(t);
-	}
-	MKNDV(NV(p),m0,len,d);
-	SG(d) = SG(p);
-	return d;
+    nd = ptond(vl,dvl,p);
+    return ndtondv(0,nd);
 }
 
-ND ndvtond(int mod,NDV p)
+void pltozpl(LIST l,Q *cont,LIST *pp)
 {
-	ND d;
-	NM m,m0;
-	NMV t;
-	int i,len;
+    NODE nd,nd1;
+    int n;
+    P *pl;
+    Q *cl;
+    int i;
+    P dmy;
+    Q dvr;
+    LIST r;
 
-	if ( !p )
-		return 0;
-	m0 = 0;
-	len = p->len;
-	for ( t = BDY(p), i = 0; i < len; NMV_ADV(t), i++ ) {
-		NEXTNM(m0,m);
-		TD(m) = TD(t);
-		ndl_copy(DL(t),DL(m));
-		CQ(m) = CQ(t);
-	}
-	NEXT(m) = 0;
-	MKND(NV(p),m0,len,d);
-	SG(d) = SG(p);
-	return d;
+    nd = BDY(l); n = length(nd);
+    pl = (P *)ALLOCA(n*sizeof(P));
+    cl = (Q *)ALLOCA(n*sizeof(P));
+    for ( i = 0; i < n; i++, nd = NEXT(nd) )
+        ptozp((P)BDY(nd),1,&cl[i],&dmy);
+    qltozl(cl,n,&dvr);
+    nd = BDY(l);
+    for ( i = 0; i < n; i++, nd = NEXT(nd) ) {
+        divsp(CO,(P)BDY(nd),(P)dvr,&pl[i]);
+    }
+    nd = 0;
+    for ( i = n-1; i >= 0; i-- ) {
+        MKNODE(nd1,pl[i],nd); nd = nd1;
+    }
+    MKLIST(r,nd);
+    *pp = r;
 }
 
-NDV dptondv(int mod,DP p)
+/* (a1,a2,...,an) -> a1*e(1)+...+an*e(n) */
+
+NDV pltondv(VL vl,VL dvl,LIST p)
 {
-	NDV d;
-	NMV m0,m;
-	MP t;
-	DP q;
-	int l,i,n;
+    int i;
+    NODE t;
+    ND r,ri;
+    NM m;
 
-	if ( !p )
-		return 0;
-	for ( t = BDY(p), l = 0; t; t = NEXT(t), l++ );
-	if ( mod ) {
-		_dp_mod(p,mod,0,&q); p = q;
-		m0 = m = (NMV)MALLOC_ATOMIC(l*nmv_adv);
-	} else
-		m0 = m = (NMV)MALLOC(l*nmv_adv);
-	n = NV(p);
-	for ( t = BDY(p), i = 0; i < l; i++, t = NEXT(t), NMV_ADV(m) ) {
-		if ( mod )
-			CM(m) = ITOS(C(t));
-		else
-			CQ(m) = (Q)C(t);
-		TD(m) = TD(DL(t));
-		dltondl(n,DL(t),DL(m));
-	}
-	MKNDV(n,m0,l,d);
-	SG(d) = SG(p);
-	return d;
+    if ( !nd_module ) error("pltond : module order must be set");
+    r = 0;
+    for ( i = 1, t = BDY(p); t; t = NEXT(t), i++ ) {
+        ri = ptond(vl,dvl,(P)BDY(t));
+        if ( ri ) 
+            for ( m = BDY(ri); m; m = NEXT(m) ) {
+                MPOS(DL(m)) = i;
+                TD(DL(m)) = ndl_weight(DL(m));
+                if ( nd_blockmask ) ndl_weight_mask(DL(m));
+            }
+        r = nd_add(0,r,ri);
+    }
+    return ndtondv(0,r);
 }
 
+ND ptond(VL vl,VL dvl,P p)
+{
+    int n,i,j,k,e;
+    VL tvl;
+    V v;
+    DCP dc;
+    DCP *w;
+    ND r,s,t,u;
+    P x;
+    int c;
+    UINT *d;
+    NM m,m0;
+
+    if ( !p )
+        return 0;
+    else if ( NUM(p) ) {
+        NEWNM(m);
+        ndl_zero(DL(m));
+        CQ(m) = (Q)p;
+        NEXT(m) = 0;
+        MKND(nd_nvar,m,1,r);
+        SG(r) = 0;
+        return r;
+    } else {
+        for ( dc = DC(p), k = 0; dc; dc = NEXT(dc), k++ );
+        w = (DCP *)ALLOCA(k*sizeof(DCP));
+        for ( dc = DC(p), j = 0; j < k; dc = NEXT(dc), j++ ) w[j] = dc;
+        for ( i = 0, tvl = dvl, v = VR(p);
+            tvl && tvl->v != v; tvl = NEXT(tvl), i++ );
+        if ( !tvl ) {
+            for ( j = k-1, s = 0, MKV(v,x); j >= 0; j-- ) {
+                t = ptond(vl,dvl,COEF(w[j]));
+                pwrp(vl,x,DEG(w[j]),&p);
+                nd_mul_c_p(CO,t,p); s = nd_add(0,s,t);
+            }
+            return s;
+        } else {
+            NEWNM(m0); d = DL(m0);
+            for ( j = k-1, s = 0; j >= 0; j-- ) {
+                ndl_zero(d); e = QTOS(DEG(w[j])); PUT_EXP(d,i,e);
+                TD(d) = MUL_WEIGHT(e,i);
+                if ( nd_blockmask) ndl_weight_mask(d);
+                if ( nd_module ) MPOS(d) = 0;
+                t = ptond(vl,dvl,COEF(w[j]));
+                for ( m = BDY(t); m; m = NEXT(m) )
+                    ndl_addto(DL(m),d);
+                SG(t) += TD(d);
+                s = nd_add(0,s,t);
+            }
+            FREENM(m0);
+            return s;
+        }
+    }
+}
+
+P ndvtop(int mod,VL vl,VL dvl,NDV p)
+{
+    VL tvl;
+    int len,n,j,i,e;
+    NMV m;
+    Q q;
+    P c;
+    UINT *d;
+    P s,r,u,t,w;
+    GFS gfs;
+
+    if ( !p ) return 0;
+    else {
+        len = LEN(p);
+        n = NV(p);
+        m = (NMV)(((char *)BDY(p))+nmv_adv*(len-1));
+        for ( j = len-1, s = 0; j >= 0; j--, NMV_PREV(m) ) {
+            if ( mod == -1 ) {
+                e = IFTOF(CM(m)); MKGFS(e,gfs); c = (P)gfs;
+            } else if ( mod ) {
+                STOQ(CM(m),q); c = (P)q;
+            } else
+                c = CP(m);
+            d = DL(m);
+            for ( i = 0, t = c, tvl = dvl; i < n; tvl = NEXT(tvl), i++ ) {
+                MKV(tvl->v,r); e = GET_EXP(d,i); STOQ(e,q);
+                pwrp(vl,r,q,&u); mulp(vl,t,u,&w); t = w;
+            }
+            addp(vl,s,t,&u); s = u;
+        }
+        return s;
+    }
+}
+
+LIST ndvtopl(int mod,VL vl,VL dvl,NDV p,int rank)
+{
+    VL tvl;
+    int len,n,j,i,e;
+    NMV m;
+    Q q;
+    P c;
+    UINT *d;
+    P s,r,u,t,w;
+    GFS gfs;
+    P *a;
+    LIST l;
+    NODE nd,nd1;
+
+    if ( !p ) return 0;
+    else {
+        a = (P *)ALLOCA((rank+1)*sizeof(P));
+        for ( i = 0; i <= rank; i++ ) a[i] = 0;
+        len = LEN(p);
+        n = NV(p);
+        m = (NMV)(((char *)BDY(p))+nmv_adv*(len-1));
+        for ( j = len-1; j >= 0; j--, NMV_PREV(m) ) {
+            if ( mod == -1 ) {
+                e = IFTOF(CM(m)); MKGFS(e,gfs); c = (P)gfs;
+            } else if ( mod ) {
+                STOQ(CM(m),q); c = (P)q;
+            } else
+                c = CP(m);
+            d = DL(m);
+            for ( i = 0, t = c, tvl = dvl; i < n; tvl = NEXT(tvl), i++ ) {
+                MKV(tvl->v,r); e = GET_EXP(d,i); STOQ(e,q);
+                pwrp(vl,r,q,&u); mulp(vl,t,u,&w); t = w;
+            }
+            addp(vl,a[MPOS(d)],t,&u); a[MPOS(d)] = u;
+        }
+        nd = 0;
+        for ( i = rank; i > 0; i-- ) {
+            MKNODE(nd1,a[i],nd); nd = nd1;
+        }
+        MKLIST(l,nd);
+        return l;
+    }
+}
+
+NDV ndtondv(int mod,ND p)
+{
+    NDV d;
+    NMV m,m0;
+    NM t;
+    int i,len;
+
+    if ( !p ) return 0;
+    len = LEN(p);
+    if ( mod )
+        m0 = m = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(len*nmv_adv);
+    else
+        m0 = m = MALLOC(len*nmv_adv);
+#if 0
+    ndv_alloc += nmv_adv*len;
+#endif
+    for ( t = BDY(p), i = 0; t; t = NEXT(t), i++, NMV_ADV(m) ) {
+        ndl_copy(DL(t),DL(m));
+        CQ(m) = CQ(t);
+    }
+    MKNDV(NV(p),m0,len,d);
+    SG(d) = SG(p);
+    return d;
+}
+
+ND ndvtond(int mod,NDV p)
+{
+    ND d;
+    NM m,m0;
+    NMV t;
+    int i,len;
+
+    if ( !p ) return 0;
+    m0 = 0;
+    len = p->len;
+    for ( t = BDY(p), i = 0; i < len; NMV_ADV(t), i++ ) {
+        NEXTNM(m0,m);
+        ndl_copy(DL(t),DL(m));
+        CQ(m) = CQ(t);
+    }
+    NEXT(m) = 0;
+    MKND(NV(p),m0,len,d);
+    SG(d) = SG(p);
+    return d;
+}
+
 DP ndvtodp(int mod,NDV p)
 {
+    MP m,m0;
 	DP d;
-	MP m0,m;
-	NMV t;
-	int len,i,n;
+    NMV t;
+    int i,len;
 
-	if ( !p )
-		return 0;
-	m0 = 0;
-	len = LEN(p);
-	n = NV(p);
-	for ( t = BDY(p), i = 0; i < len; i++, NMV_ADV(t) ) {
-		NEXTMP(m0,m);
-		if ( mod ) 
-			C(m) = STOI(CM(t));
-		else
-			C(m) = (P)CQ(t);
-		DL(m) = ndltodl(n,TD(t),DL(t));
-	}
-	NEXT(m) = 0;
-	MKDP(NV(p),m0,d);
-	SG(d) = SG(p);
-	return d;
+    if ( !p ) return 0;
+    m0 = 0;
+    len = p->len;
+    for ( t = BDY(p), i = 0; i < len; NMV_ADV(t), i++ ) {
+        NEXTMP(m0,m);
+    	m->dl = ndltodl(nd_nvar,DL(t));
+    	m->c = ndctop(mod,t->c);
+    }
+    NEXT(m) = 0;
+	MKDP(nd_nvar,m0,d);
+    SG(d) = SG(p);
+    return d;
 }
 
 void ndv_print(NDV p)
 {
-	NMV m;
-	int i,len;
+    NMV m;
+    int i,len;
     
-	if ( !p )
-		printf("0\n");
-	else {
-		len = LEN(p);
-		for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
-			printf("+%d*",CM(m));
-			ndl_print(DL(m));
-		}
-		printf("\n");
-	}
+    if ( !p ) printf("0\n");
+    else {
+        len = LEN(p);
+        for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
+            if ( CM(m) & 0x80000000 ) printf("+@_%d*",IFTOF(CM(m)));
+            else printf("+%d*",CM(m));
+            ndl_print(DL(m));
+        }
+        printf("\n");
+    }
 }
 
 void ndv_print_q(NDV p)
 {
-	NMV m;
-	int i,len;
+    NMV m;
+    int i,len;
     
-	if ( !p )
-		printf("0\n");
-	else {
-		len = LEN(p);
-		for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
-			printf("+");
-			printexpr(CO,CQ(m));
-			printf("*");
-			ndl_print(DL(m));
-		}
-		printf("\n");
-	}
+    if ( !p ) printf("0\n");
+    else {
+        len = LEN(p);
+        for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
+            printf("+");
+            printexpr(CO,(Obj)CQ(m));
+            printf("*");
+            ndl_print(DL(m));
+        }
+        printf("\n");
+    }
 }
 
-int nd_equal(ND a,ND b)
+NODE ndv_reducebase(NODE x,int *perm)
 {
-	NM ma,mb;
+    int len,i,j;
+    NDVI w;
+    NODE t,t0;
 
-	if ( (!a && b)||(a&& !b)||(NV(a) != NV(b))||(SG(a) != SG(b)) ) return 0;
-	for ( ma = BDY(a), mb = BDY(b); ma && mb; ma = NEXT(ma), mb = NEXT(mb) ) {
-		if ( (TD(ma) != TD(mb)) || !ndl_equal(DL(ma),DL(mb)) ) return 0;
-	}
-	if ( !ma && !mb ) return 1;
-	else return 0;
+    len = length(x);
+    w = (NDVI)ALLOCA(len*sizeof(struct oNDVI));
+    for ( i = 0, t = x; i < len; i++, t = NEXT(t) ) {
+        w[i].p = BDY(t); w[i].i = perm[i];
+    }
+    for ( i = 0; i < len; i++ ) {
+        for ( j = 0; j < i; j++ ) {
+            if ( w[i].p && w[j].p )
+                if ( ndl_reducible(HDL(w[i].p),HDL(w[j].p)) ) w[i].p = 0;
+                else if ( ndl_reducible(HDL(w[j].p),HDL(w[i].p)) ) w[j].p = 0;
+        }
+    }
+    for ( i = j = 0, t0 = 0; i < len; i++ ) {
+        if ( w[i].p ) { 
+            NEXTNODE(t0,t); BDY(t) = (pointer)w[i].p; 
+            perm[j++] = w[i].i;
+        }
+    }
+    NEXT(t) = 0; x = t0;
+    return x;
 }
 
-NODE nd_reducebase(NODE x)
+/* XXX incomplete */
+
+void nd_init_ord(struct order_spec *ord)
 {
-	int len,i,j;
-	NDV *w;
-	NODE t,t0;
+    nd_module = (ord->id >= 256);
+    switch ( ord->id ) {
+        case 0:
+            switch ( ord->ord.simple ) {
+                case 0:
+                    nd_dcomp = 1;
+                    nd_isrlex = 1;
+                    break;
+                case 1:
+                    nd_dcomp = 1;
+                    nd_isrlex = 0;
+                    break;
+                case 2:
+                    nd_dcomp = 0;
+                    nd_isrlex = 0;
+                    ndl_compare_function = ndl_lex_compare;
+                    break;
+                case 11:
+                    /* XXX */
+                    nd_dcomp = 0;
+                    nd_isrlex = 1;
+                    ndl_compare_function = ndl_ww_lex_compare;
+                    break;
+                default:
+                    error("nd_gr : unsupported order");
+            }
+            break;
+        case 1:
+            /* block order */
+            /* XXX */
+            nd_dcomp = -1;
+            nd_isrlex = 0;
+            ndl_compare_function = ndl_block_compare;
+            break;
+        case 2:
+            /* matrix order */
+            /* XXX */
+            nd_dcomp = -1;
+            nd_isrlex = 0;
+            nd_matrix_len = ord->ord.matrix.row;
+            nd_matrix = ord->ord.matrix.matrix;
+            ndl_compare_function = ndl_matrix_compare;
+            break;
+        case 3:
+            /* composite order */
+            nd_dcomp = -1;
+            nd_isrlex = 0;
+            nd_worb_len = ord->ord.composite.length;
+            nd_worb = ord->ord.composite.w_or_b;
+            ndl_compare_function = ndl_composite_compare;
+            break;
 
-	len = length(x);
-	w = (NDV *)ALLOCA(len*sizeof(NDV));
-	for ( i = 0, t = x; i < len; i++, t = NEXT(t) ) w[i] = BDY(t);
-	for ( i = 0; i < len; i++ ) {
-		for ( j = 0; j < i; j++ ) {
-			if ( w[i] && w[j] )
-				if ( ndl_reducible(HDL(w[i]),HDL(w[j])) ) w[i] = 0;
-				else if ( ndl_reducible(HDL(w[j]),HDL(w[i])) ) w[j] = 0;
+        /* module order */
+        case 256:
+            nd_ispot = ord->ispot;
+            nd_pot_nelim = ord->pot_nelim;
+            nd_dcomp = -1;
+            switch ( ord->ord.simple ) {
+                case 0:
+                    nd_isrlex = 1;
+                    ndl_compare_function = ndl_module_grlex_compare;
+                    break;
+                case 1:
+                    nd_isrlex = 0;
+                    ndl_compare_function = ndl_module_glex_compare;
+                    break;
+                case 2:
+                    nd_isrlex = 0;
+                    ndl_compare_function = ndl_module_lex_compare;
+                    break;
+                default:
+                    error("nd_gr : unsupported order");
+            }
+            break;
+        case 257:
+            /* block order */
+            nd_ispot = ord->ispot;
+            nd_pot_nelim = ord->pot_nelim;
+            nd_dcomp = -1;
+            nd_isrlex = 0;
+            ndl_compare_function = ndl_module_block_compare;
+            break;
+        case 258:
+            /* matrix order */
+            nd_ispot = ord->ispot;
+            nd_pot_nelim = ord->pot_nelim;
+            nd_dcomp = -1;
+            nd_isrlex = 0;
+            nd_matrix_len = ord->ord.matrix.row;
+            nd_matrix = ord->ord.matrix.matrix;
+            ndl_compare_function = ndl_module_matrix_compare;
+            break;
+        case 259:
+            /* composite order */
+            nd_ispot = ord->ispot;
+            nd_pot_nelim = ord->pot_nelim;
+            nd_dcomp = -1;
+            nd_isrlex = 0;
+            nd_worb_len = ord->ord.composite.length;
+            nd_worb = ord->ord.composite.w_or_b;
+            ndl_compare_function = ndl_module_composite_compare;
+            break;
+    }
+    nd_ord = ord;
+}
+
+BlockMask nd_create_blockmask(struct order_spec *ord)
+{
+    int n,i,j,s,l;
+    UINT *t;
+    BlockMask bm;
+
+    /* we only create mask table for block order */
+    if ( ord->id != 1 && ord->id != 257 )
+        return 0;
+    n = ord->ord.block.length;
+    bm = (BlockMask)MALLOC(sizeof(struct oBlockMask));
+    bm->n = n;
+    bm->order_pair = ord->ord.block.order_pair;
+    bm->mask = (UINT **)MALLOC(n*sizeof(UINT *));
+    for ( i = 0, s = 0; i < n; i++ ) {
+        bm->mask[i] = t = (UINT *)MALLOC_ATOMIC(nd_wpd*sizeof(UINT));
+        for ( j = 0; j < nd_wpd; j++ ) t[j] = 0;
+        l = bm->order_pair[i].length;
+        for ( j = 0; j < l; j++, s++ ) PUT_EXP(t,s,nd_mask0);        
+    }
+    return bm;
+}
+
+EPOS nd_create_epos(struct order_spec *ord)
+{
+    int i,j,l,s,ord_l,ord_o;
+    EPOS epos;
+    struct order_pair *op;
+
+    epos = (EPOS)MALLOC_ATOMIC(nd_nvar*sizeof(struct oEPOS));
+    switch ( ord->id ) {
+        case 0: case 256:
+            if ( nd_isrlex ) {
+                for ( i = 0; i < nd_nvar; i++ ) {
+                    epos[i].i = nd_exporigin + (nd_nvar-1-i)/nd_epw;
+                    epos[i].s = (nd_epw-((nd_nvar-1-i)%nd_epw)-1)*nd_bpe;
+                }
+            } else {
+                for ( i = 0; i < nd_nvar; i++ ) {
+                    epos[i].i = nd_exporigin + i/nd_epw;
+                    epos[i].s = (nd_epw-(i%nd_epw)-1)*nd_bpe;
+                }
+            }
+            break;
+        case 1: case 257:
+            /* block order */
+            l = ord->ord.block.length;
+            op = ord->ord.block.order_pair;
+            for ( j = 0, s = 0; j < l; j++ ) {
+                ord_o = op[j].order;
+                ord_l = op[j].length;
+                if ( !ord_o )
+                    for ( i = 0; i < ord_l; i++ ) {
+                        epos[s+i].i = nd_exporigin + (s+ord_l-i-1)/nd_epw;
+                        epos[s+i].s = (nd_epw-((s+ord_l-i-1)%nd_epw)-1)*nd_bpe;
+                    }
+                else
+                    for ( i = 0; i < ord_l; i++ ) {
+                        epos[s+i].i = nd_exporigin + (s+i)/nd_epw;
+                        epos[s+i].s = (nd_epw-((s+i)%nd_epw)-1)*nd_bpe;
+                    }
+                s += ord_l;
+            }
+            break;
+        case 2:
+            /* matrix order */
+        case 3:
+            /* composite order */
+        default:
+            for ( i = 0; i < nd_nvar; i++ ) {
+                epos[i].i = nd_exporigin + i/nd_epw;
+                epos[i].s = (nd_epw-(i%nd_epw)-1)*nd_bpe;
+            }
+            break;
+    }
+    return epos;
+}
+
+/* external interface */
+
+void nd_nf_p(Obj f,LIST g,LIST v,int m,struct order_spec *ord,Obj *rp)
+{
+    NODE t,in0,in;
+    ND ndf,nf;
+    NDV ndvf;
+    VL vv,tv;
+    int stat,nvar,max,mrank;
+    union oNDC dn;
+    Q cont;
+    P pp;
+    LIST ppl;
+
+    if ( !f ) {
+        *rp = 0;
+        return;
+    }
+    pltovl(v,&vv);
+    for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ );
+
+    /* max=65536 implies nd_bpe=32 */
+    max = 65536; 
+
+	nd_module = 0;
+	/* nd_module will be set if ord is a module ordering */
+    nd_init_ord(ord);
+    nd_setup_parameters(nvar,max);
+    if ( nd_module && OID(f) != O_LIST )
+        error("nd_nf_p : the first argument must be a list");
+	if ( nd_module ) mrank = length(BDY((LIST)f));
+    /* conversion to ndv */
+    for ( in0 = 0, t = BDY(g); t; t = NEXT(t) ) {
+        NEXTNODE(in0,in);
+        if ( nd_module ) {
+          if ( !BDY(t) || OID(BDY(t)) != O_LIST 
+               || length(BDY((LIST)BDY(t))) != mrank )
+              error("nd_nf_p : inconsistent basis element");
+          if ( !m ) pltozpl((LIST)BDY(t),&cont,&ppl);
+          else ppl = (LIST)BDY(t);
+          BDY(in) = (pointer)pltondv(CO,vv,ppl);
+        } else {
+          if ( !m ) ptozp((P)BDY(t),1,&cont,&pp);
+          else pp = (P)BDY(t);
+          BDY(in) = (pointer)ptondv(CO,vv,pp);
+        }
+        if ( m ) ndv_mod(m,(NDV)BDY(in));
+    }
+    if ( in0 ) NEXT(in) = 0;
+
+    if ( nd_module ) ndvf = pltondv(CO,vv,(LIST)f);
+    else ndvf = ptondv(CO,vv,(P)f);
+    if ( m ) ndv_mod(m,ndvf);
+    ndf = (pointer)ndvtond(m,ndvf);
+
+    /* dont sort, dont removecont */
+    ndv_setup(m,0,in0,1,1);
+    nd_scale=2;
+    stat = nd_nf(m,0,ndf,nd_ps,1,0,&nf);
+    if ( !stat )
+        error("nd_nf_p : exponent too large");
+    if ( nd_module ) *rp = (Obj)ndvtopl(m,CO,vv,ndtondv(m,nf),mrank);
+    else *rp = (Obj)ndvtop(m,CO,vv,ndtondv(m,nf));
+}
+
+int nd_to_vect(int mod,UINT *s0,int n,ND d,UINT *r)
+{
+    NM m;
+    UINT *t,*s;
+    int i;
+
+    for ( i = 0; i < n; i++ ) r[i] = 0;
+    for ( i = 0, s = s0, m = BDY(d); m; m = NEXT(m) ) {
+        t = DL(m);
+        for ( ; !ndl_equal(t,s); s += nd_wpd, i++ );
+        r[i] = CM(m);
+    }
+    for ( i = 0; !r[i]; i++ );
+    return i;
+}
+
+int nd_to_vect_q(UINT *s0,int n,ND d,Q *r)
+{
+    NM m;
+    UINT *t,*s;
+    int i;
+
+    for ( i = 0; i < n; i++ ) r[i] = 0;
+    for ( i = 0, s = s0, m = BDY(d); m; m = NEXT(m) ) {
+        t = DL(m);
+        for ( ; !ndl_equal(t,s); s += nd_wpd, i++ );
+        r[i] = CQ(m);
+    }
+    for ( i = 0; !r[i]; i++ );
+    return i;
+}
+
+Q *nm_ind_pair_to_vect(int mod,UINT *s0,int n,NM_ind_pair pair)
+{
+    NM m;
+    NMV mr;
+    UINT *d,*t,*s;
+    NDV p;
+    int i,j,len;
+    Q *r;
+
+    m = pair->mul;
+    d = DL(m);
+    p = nd_ps[pair->index];
+    len = LEN(p);
+    r = (Q *)CALLOC(n,sizeof(Q));
+    t = (UINT *)ALLOCA(nd_wpd*sizeof(UINT));
+    for ( i = j = 0, s = s0, mr = BDY(p); j < len; j++, NMV_ADV(mr) ) {
+        ndl_add(d,DL(mr),t);    
+        for ( ; !ndl_equal(t,s); s += nd_wpd, i++ );
+        r[i] = CQ(mr);
+    }
+    return r;
+}
+
+IndArray nm_ind_pair_to_vect_compress(int mod,UINT *s0,int n,NM_ind_pair pair)
+{
+    NM m;
+    NMV mr;
+    UINT *d,*t,*s;
+    NDV p;
+    unsigned char *ivc;
+    unsigned short *ivs;
+    UINT *v,*ivi,*s0v;
+    int i,j,len,prev,diff,cdiff;
+    IndArray r;
+struct oEGT eg0,eg1;
+
+    m = pair->mul;
+    d = DL(m);
+    p = nd_ps[pair->index];
+    len = LEN(p);
+    t = (UINT *)ALLOCA(nd_wpd*sizeof(UINT));
+    v = (unsigned int *)ALLOCA(len*sizeof(unsigned int));
+get_eg(&eg0);
+    for ( i = j = 0, s = s0, mr = BDY(p); j < len; j++, NMV_ADV(mr) ) {
+        ndl_add(d,DL(mr),t);    
+        for ( ; !ndl_equal(t,s); s += nd_wpd, i++ );
+        v[j] = i;
+    }
+get_eg(&eg1); add_eg(&eg_search,&eg0,&eg1);
+    r = (IndArray)MALLOC(sizeof(struct oIndArray));
+    r->head = v[0];
+    diff = 0;
+    for ( i = 1; i < len; i++ ) {
+        cdiff = v[i]-v[i-1]; diff = MAX(cdiff,diff);
+    }
+    if ( diff < 256 ) {
+        r->width = 1;
+        ivc = (unsigned char *)MALLOC_ATOMIC(len*sizeof(unsigned char));
+        r->index.c = ivc;
+        for ( i = 1, ivc[0] = 0; i < len; i++ ) ivc[i] = v[i]-v[i-1];
+    } else if ( diff < 65536 ) {
+        r->width = 2;
+        ivs = (unsigned short *)MALLOC_ATOMIC(len*sizeof(unsigned short));
+        r->index.s = ivs;
+        for ( i = 1, ivs[0] = 0; i < len; i++ ) ivs[i] = v[i]-v[i-1];
+    } else {
+        r->width = 4;
+        ivi = (unsigned int *)MALLOC_ATOMIC(len*sizeof(unsigned int));
+        r->index.i = ivi;
+        for ( i = 1, ivi[0] = 0; i < len; i++ ) ivi[i] = v[i]-v[i-1];
+    }
+    return r;
+}
+
+int compress_array(Q *svect,Q *cvect,int n)
+{
+    int i,j;
+
+    for ( i = j = 0; i < n; i++ )
+        if ( svect[i] ) cvect[j++] = svect[i];
+    return j;
+}
+
+void expand_array(Q *svect,Q *cvect,int n)
+{
+    int i,j;
+
+    for ( i = j = 0; j < n;  i++  )
+        if ( svect[i] ) svect[i] = cvect[j++];
+}
+
+int ndv_reduce_vect_q(Q *svect,int trace,int col,IndArray *imat,NM_ind_pair *rp0,int nred)
+{
+    int i,j,k,len,pos,prev,nz;
+    Q cs,mcs,c1,c2,cr,gcd,t;
+    IndArray ivect;
+    unsigned char *ivc;
+    unsigned short *ivs;
+    unsigned int *ivi;
+    NDV redv;
+    NMV mr;
+    NODE rp;
+    int maxrs;
+    double hmag;
+    Q *cvect;
+
+    maxrs = 0;
+    for ( i = 0; i < col && !svect[i]; i++ );
+    if ( i == col ) return maxrs;
+    hmag = p_mag((P)svect[i])*nd_scale;
+    cvect = (Q *)ALLOCA(col*sizeof(Q));
+    for ( i = 0; i < nred; i++ ) {
+        ivect = imat[i];
+        k = ivect->head;
+        if ( svect[k] ) {
+            maxrs = MAX(maxrs,rp0[i]->sugar);
+            redv = trace?nd_ps_trace[rp0[i]->index]:nd_ps[rp0[i]->index];
+            len = LEN(redv); mr = BDY(redv);
+            igcd_cofactor(svect[k],CQ(mr),&gcd,&cs,&cr);
+            chsgnq(cs,&mcs);
+            if ( !UNIQ(cr) ) {
+                for ( j = 0; j < col; j++ ) {
+                    mulq(svect[j],cr,&c1); svect[j] = c1;
+                }
+            }
+            svect[k] = 0; prev = k;
+            switch ( ivect->width ) {
+                case 1:
+                    ivc = ivect->index.c;
+                    for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
+                        pos = prev+ivc[j]; prev = pos;
+                        mulq(CQ(mr),mcs,&c2); addq(svect[pos],c2,&t); svect[pos] = t;
+                    }
+                    break;
+                case 2:
+                    ivs = ivect->index.s; 
+                    for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
+                        pos = prev+ivs[j]; prev = pos;
+                        mulq(CQ(mr),mcs,&c2); addq(svect[pos],c2,&t); svect[pos] = t;
+                    }
+                    break;
+                case 4:
+                    ivi = ivect->index.i;
+                    for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
+                        pos = prev+ivi[j]; prev = pos;
+                        mulq(CQ(mr),mcs,&c2); addq(svect[pos],c2,&t); svect[pos] = t;
+                    }
+                    break;
+            }
+            for ( j = k+1; j < col && !svect[j]; j++ );
+            if ( j == col ) break;
+            if ( hmag && ((double)p_mag((P)svect[j]) > hmag) ) {
+                nz = compress_array(svect,cvect,col);
+                removecont_array((P *)cvect,nz,1);
+                expand_array(svect,cvect,nz);
+                hmag = ((double)p_mag((P)svect[j]))*nd_scale;
+            }
+        }
+    }
+    nz = compress_array(svect,cvect,col);
+    removecont_array((P *)cvect,nz,1);
+    expand_array(svect,cvect,nz);
+    if ( DP_Print ) { 
+        fprintf(asir_out,"-"); fflush(asir_out);
+    }
+    return maxrs;
+}
+
+int ndv_reduce_vect(int m,UINT *svect,int col,IndArray *imat,NM_ind_pair *rp0,int nred)
+{
+    int i,j,k,len,pos,prev;
+    UINT c,c1,c2,c3,up,lo,dmy;
+    IndArray ivect;
+    unsigned char *ivc;
+    unsigned short *ivs;
+    unsigned int *ivi;
+    NDV redv;
+    NMV mr;
+    NODE rp;
+    int maxrs;
+
+    maxrs = 0;
+    for ( i = 0; i < nred; i++ ) {
+        ivect = imat[i];
+        k = ivect->head; svect[k] %= m;
+        if ( c = svect[k] ) {
+            maxrs = MAX(maxrs,rp0[i]->sugar);
+            c = m-c; redv = nd_ps[rp0[i]->index];
+            len = LEN(redv); mr = BDY(redv);
+            svect[k] = 0; prev = k;
+            switch ( ivect->width ) {
+                case 1:
+                    ivc = ivect->index.c;
+                    for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
+                        pos = prev+ivc[j]; c1 = CM(mr); c2 = svect[pos];
+                        prev = pos;
+                        DMA(c1,c,c2,up,lo);
+                        if ( up ) { DSAB(m,up,lo,dmy,c3); svect[pos] = c3;
+                        } else svect[pos] = lo;
+                    }
+                    break;
+                case 2:
+                    ivs = ivect->index.s; 
+                    for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
+                        pos = prev+ivs[j]; c1 = CM(mr); c2 = svect[pos];
+                        prev = pos;
+                        DMA(c1,c,c2,up,lo);
+                        if ( up ) { DSAB(m,up,lo,dmy,c3); svect[pos] = c3;
+                        } else svect[pos] = lo;
+                    }
+                    break;
+                case 4:
+                    ivi = ivect->index.i;
+                    for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
+                        pos = prev+ivi[j]; c1 = CM(mr); c2 = svect[pos];
+                        prev = pos;
+                        DMA(c1,c,c2,up,lo);
+                        if ( up ) { DSAB(m,up,lo,dmy,c3); svect[pos] = c3;
+                        } else svect[pos] = lo;
+                    }
+                    break;
+            }
+        }
+    }
+    for ( i = 0; i < col; i++ )
+        if ( svect[i] >= (UINT)m ) svect[i] %= m;
+    return maxrs;
+}
+
+int ndv_reduce_vect_sf(int m,UINT *svect,int col,IndArray *imat,NM_ind_pair *rp0,int nred)
+{
+    int i,j,k,len,pos,prev;
+    UINT c,c1,c2,c3,up,lo,dmy;
+    IndArray ivect;
+    unsigned char *ivc;
+    unsigned short *ivs;
+    unsigned int *ivi;
+    NDV redv;
+    NMV mr;
+    NODE rp;
+    int maxrs;
+
+    maxrs = 0;
+    for ( i = 0; i < nred; i++ ) {
+        ivect = imat[i];
+        k = ivect->head; svect[k] %= m;
+        if ( c = svect[k] ) {
+            maxrs = MAX(maxrs,rp0[i]->sugar);
+            c = _chsgnsf(c); redv = nd_ps[rp0[i]->index];
+            len = LEN(redv); mr = BDY(redv);
+            svect[k] = 0; prev = k;
+            switch ( ivect->width ) {
+                case 1:
+                    ivc = ivect->index.c;
+                    for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
+                        pos = prev+ivc[j]; prev = pos;
+                        svect[pos] = _addsf(_mulsf(CM(mr),c),svect[pos]);
+                    }
+                    break;
+                case 2:
+                    ivs = ivect->index.s; 
+                    for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
+                        pos = prev+ivs[j]; prev = pos;
+                        svect[pos] = _addsf(_mulsf(CM(mr),c),svect[pos]);
+                    }
+                    break;
+                case 4:
+                    ivi = ivect->index.i;
+                    for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
+                        pos = prev+ivi[j]; prev = pos;
+                        svect[pos] = _addsf(_mulsf(CM(mr),c),svect[pos]);
+                    }
+                    break;
+            }
+        }
+    }
+    return maxrs;
+}
+
+NDV vect_to_ndv(UINT *vect,int spcol,int col,int *rhead,UINT *s0vect)
+{
+    int j,k,len;
+    UINT *p;
+    UINT c;
+    NDV r;
+    NMV mr0,mr;
+
+    for ( j = 0, len = 0; j < spcol; j++ ) if ( vect[j] ) len++;
+    if ( !len ) return 0;
+    else {
+        mr0 = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(nmv_adv*len);
+#if 0
+        ndv_alloc += nmv_adv*len;
+#endif
+        mr = mr0; 
+        p = s0vect;
+        for ( j = k = 0; j < col; j++, p += nd_wpd )
+            if ( !rhead[j] ) {
+                if ( c = vect[k++] ) {
+                    ndl_copy(p,DL(mr)); CM(mr) = c; NMV_ADV(mr);
+                }
+            }
+        MKNDV(nd_nvar,mr0,len,r);
+        return r;
+    }
+}
+
+/* for preprocessed vector */
+
+NDV vect_to_ndv_q(Q *vect,int spcol,int col,int *rhead,UINT *s0vect)
+{
+    int j,k,len;
+    UINT *p;
+    Q c;
+    NDV r;
+    NMV mr0,mr;
+
+    for ( j = 0, len = 0; j < spcol; j++ ) if ( vect[j] ) len++;
+    if ( !len ) return 0;
+    else {
+        mr0 = (NMV)MALLOC(nmv_adv*len);
+#if 0
+        ndv_alloc += nmv_adv*len;
+#endif
+        mr = mr0; 
+        p = s0vect;
+        for ( j = k = 0; j < col; j++, p += nd_wpd )
+            if ( !rhead[j] ) {
+                if ( c = vect[k++] ) {
+                    if ( DN(c) )
+                        error("afo");
+                    ndl_copy(p,DL(mr)); CQ(mr) = c; NMV_ADV(mr);
+                }
+            }
+        MKNDV(nd_nvar,mr0,len,r);
+        return r;
+    }
+}
+
+/* for plain vector */
+
+NDV plain_vect_to_ndv_q(Q *vect,int col,UINT *s0vect)
+{
+    int j,k,len;
+    UINT *p;
+    Q c;
+    NDV r;
+    NMV mr0,mr;
+
+    for ( j = 0, len = 0; j < col; j++ ) if ( vect[j] ) len++;
+    if ( !len ) return 0;
+    else {
+        mr0 = (NMV)MALLOC(nmv_adv*len);
+#if 0
+        ndv_alloc += nmv_adv*len;
+#endif
+        mr = mr0; 
+        p = s0vect;
+        for ( j = k = 0; j < col; j++, p += nd_wpd, k++ )
+            if ( c = vect[k] ) {
+                if ( DN(c) )
+                    error("afo");
+                ndl_copy(p,DL(mr)); CQ(mr) = c; NMV_ADV(mr);
+            }
+        MKNDV(nd_nvar,mr0,len,r);
+        return r;
+    }
+}
+
+int nd_sp_f4(int m,int trace,ND_pairs l,PGeoBucket bucket)
+{
+    ND_pairs t;
+    NODE sp0,sp;
+    int stat;
+    ND spol;
+
+    for ( t = l; t; t = NEXT(t) ) {
+        stat = nd_sp(m,trace,t,&spol);
+        if ( !stat ) return 0;
+        if ( spol ) {
+            add_pbucket_symbolic(bucket,spol);
+        }
+    }
+    return 1;
+}
+
+int nd_symbolic_preproc(PGeoBucket bucket,int trace,UINT **s0vect,NODE *r)
+{
+    NODE rp0,rp;
+    NM mul,head,s0,s;
+    int index,col,i,sugar;
+    RHist h;
+    UINT *s0v,*p;
+    NM_ind_pair pair;
+    ND red;
+    NDV *ps;
+
+    s0 = 0; rp0 = 0; col = 0;
+    ps = trace?nd_ps_trace:nd_ps;
+    while ( 1 ) {
+        head = remove_head_pbucket_symbolic(bucket);
+        if ( !head ) break;
+        if ( !s0 ) s0 = head;
+        else NEXT(s) = head;
+        s = head;
+        index = ndl_find_reducer(DL(head));
+        if ( index >= 0 ) {
+            h = nd_psh[index];
+            NEWNM(mul);
+            ndl_sub(DL(head),DL(h),DL(mul));
+            if ( ndl_check_bound2(index,DL(mul)) ) return 0;
+            sugar = TD(DL(mul))+SG(ps[index]);
+            MKNM_ind_pair(pair,mul,index,sugar);
+            red = ndv_mul_nm_symbolic(mul,ps[index]);
+            add_pbucket_symbolic(bucket,nd_remove_head(red));
+            NEXTNODE(rp0,rp); BDY(rp) = (pointer)pair;
+        }
+        col++;
+    }
+    if ( rp0 ) NEXT(rp) = 0;
+    NEXT(s) = 0;
+    s0v = (UINT *)MALLOC_ATOMIC(col*nd_wpd*sizeof(UINT));
+    for ( i = 0, p = s0v, s = s0; i < col;
+        i++, p += nd_wpd, s = NEXT(s) ) ndl_copy(DL(s),p);
+    *s0vect = s0v;        
+    *r = rp0;
+    return col;
+}
+
+
+NODE nd_f4(int m,int **indp)
+{
+    int i,nh,stat,index;
+    NODE r,g;
+    ND_pairs d,l,t;
+    ND spol,red;
+    NDV nf,redv;
+    NM s0,s;
+    NODE rp0,srp0,nflist;
+    int nsp,nred,col,rank,len,k,j,a;
+    UINT c;
+    UINT **spmat;
+    UINT *s0vect,*svect,*p,*v;
+    int *colstat;
+    IndArray *imat;
+    int *rhead;
+    int spcol,sprow;
+    int sugar;
+    PGeoBucket bucket;
+    struct oEGT eg0,eg1,eg_f4;
+
+#if 0
+    ndv_alloc = 0;
+#endif
+    g = 0; d = 0;
+    for ( i = 0; i < nd_psn; i++ ) {
+        d = update_pairs(d,g,i,0);
+        g = update_base(g,i);
+    }
+    while ( d ) {
+        get_eg(&eg0);
+        l = nd_minsugarp(d,&d);
+        sugar = SG(l);
+        bucket = create_pbucket();
+        stat = nd_sp_f4(m,0,l,bucket);
+        if ( !stat ) {
+            for ( t = l; NEXT(t); t = NEXT(t) );
+            NEXT(t) = d; d = l;
+            d = nd_reconstruct(0,d);
+            continue;
+        }
+        if ( bucket->m < 0 ) continue;
+        col = nd_symbolic_preproc(bucket,0,&s0vect,&rp0);
+        if ( !col ) {
+            for ( t = l; NEXT(t); t = NEXT(t) );
+            NEXT(t) = d; d = l;
+            d = nd_reconstruct(0,d);
+            continue;
+        }
+        get_eg(&eg1); init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg1);
+        if ( DP_Print )
+            fprintf(asir_out,"sugar=%d,symb=%fsec,",
+                sugar,eg_f4.exectime+eg_f4.gctime);
+        if ( 1 )
+            nflist = nd_f4_red(m,l,0,s0vect,col,rp0,0);
+        else
+            nflist = nd_f4_red_dist(m,l,s0vect,col,rp0,0);
+        /* adding new bases */
+        for ( r = nflist; r; r = NEXT(r) ) {
+            nf = (NDV)BDY(r);
+            ndv_removecont(m,nf);
+            if ( !m && nd_nalg ) {
+                ND nf1;
+
+                nf1 = ndvtond(m,nf);
+                nd_monic(0,&nf1);
+                nd_removecont(m,nf1);
+                nf = ndtondv(m,nf1);
+            }
+            nh = ndv_newps(m,nf,0);
+            d = update_pairs(d,g,nh,0);
+            g = update_base(g,nh);
+        }
+    }
+#if 0
+    fprintf(asir_out,"ndv_alloc=%d\n",ndv_alloc);
+#endif
+	conv_ilist(0,0,g,indp);
+    return g;
+}
+
+NODE nd_f4_trace(int m,int **indp)
+{
+    int i,nh,stat,index;
+    NODE r,g;
+    ND_pairs d,l,l0,t;
+    ND spol,red;
+    NDV nf,redv,nfqv,nfv;
+    NM s0,s;
+    NODE rp0,srp0,nflist;
+    int nsp,nred,col,rank,len,k,j,a;
+    UINT c;
+    UINT **spmat;
+    UINT *s0vect,*svect,*p,*v;
+    int *colstat;
+    IndArray *imat;
+    int *rhead;
+    int spcol,sprow;
+    int sugar;
+    PGeoBucket bucket;
+    struct oEGT eg0,eg1,eg_f4;
+
+    g = 0; d = 0;
+    for ( i = 0; i < nd_psn; i++ ) {
+        d = update_pairs(d,g,i,0);
+        g = update_base(g,i);
+    }
+    while ( d ) {
+        get_eg(&eg0);
+        l = nd_minsugarp(d,&d);
+        sugar = SG(l);
+        bucket = create_pbucket();
+        stat = nd_sp_f4(m,0,l,bucket);
+        if ( !stat ) {
+            for ( t = l; NEXT(t); t = NEXT(t) );
+            NEXT(t) = d; d = l;
+            d = nd_reconstruct(1,d);
+            continue;
+        }
+        if ( bucket->m < 0 ) continue;
+        col = nd_symbolic_preproc(bucket,0,&s0vect,&rp0);
+        if ( !col ) {
+            for ( t = l; NEXT(t); t = NEXT(t) );
+            NEXT(t) = d; d = l;
+            d = nd_reconstruct(1,d);
+            continue;
+        }
+        get_eg(&eg1); init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg1);
+        if ( DP_Print )
+            fprintf(asir_out,"sugar=%d,symb=%fsec,",
+                sugar,eg_f4.exectime+eg_f4.gctime);
+        nflist = nd_f4_red(m,l,0,s0vect,col,rp0,&l0);
+        if ( !l0 ) continue;
+        l = l0;
+
+        /* over Q */
+        bucket = create_pbucket();
+        stat = nd_sp_f4(0,1,l,bucket);
+        if ( !stat ) {
+            for ( t = l; NEXT(t); t = NEXT(t) );
+            NEXT(t) = d; d = l;
+            d = nd_reconstruct(1,d);
+            continue;
+        }
+        if ( bucket->m < 0 ) continue;
+        col = nd_symbolic_preproc(bucket,1,&s0vect,&rp0);
+        if ( !col ) {
+            for ( t = l; NEXT(t); t = NEXT(t) );
+            NEXT(t) = d; d = l;
+            d = nd_reconstruct(1,d);
+            continue;
+        }
+        nflist = nd_f4_red(0,l,1,s0vect,col,rp0,0);
+        /* adding new bases */
+        for ( r = nflist; r; r = NEXT(r) ) {
+            nfqv = (NDV)BDY(r);
+            ndv_removecont(0,nfqv);
+            if ( !rem(NM(HCQ(nfqv)),m) ) return 0;
+            if ( nd_nalg ) {
+                ND nf1;
+
+                nf1 = ndvtond(m,nfqv);
+                nd_monic(0,&nf1);
+                nd_removecont(0,nf1);
+                nfqv = ndtondv(0,nf1); nd_free(nf1);
+            }
+            nfv = ndv_dup(0,nfqv);
+            ndv_mod(m,nfv);
+            ndv_removecont(m,nfv);
+            nh = ndv_newps(0,nfv,nfqv);
+            d = update_pairs(d,g,nh,0);
+            g = update_base(g,nh);
+        }
+    }
+#if 0
+    fprintf(asir_out,"ndv_alloc=%d\n",ndv_alloc);
+#endif
+	conv_ilist(0,1,g,indp);
+    return g;
+}
+
+NODE nd_f4_pseudo_trace(int m,int **indp)
+{
+    int i,nh,stat,index;
+    NODE r,g;
+    ND_pairs d,l,l0,t;
+    ND spol,red;
+    NDV nf,redv,nfqv,nfv;
+    NM s0,s;
+    NODE rp0,srp0,nflist;
+    int nsp,nred,col,rank,len,k,j,a;
+    UINT c;
+    UINT **spmat;
+    UINT *s0vect,*svect,*p,*v;
+    int *colstat;
+    IndArray *imat;
+    int *rhead;
+    int spcol,sprow;
+    int sugar;
+    PGeoBucket bucket;
+    struct oEGT eg0,eg1,eg_f4;
+
+    g = 0; d = 0;
+    for ( i = 0; i < nd_psn; i++ ) {
+        d = update_pairs(d,g,i,0);
+        g = update_base(g,i);
+    }
+    while ( d ) {
+        get_eg(&eg0);
+        l = nd_minsugarp(d,&d);
+        sugar = SG(l);
+        bucket = create_pbucket();
+        stat = nd_sp_f4(m,0,l,bucket);
+        if ( !stat ) {
+            for ( t = l; NEXT(t); t = NEXT(t) );
+            NEXT(t) = d; d = l;
+            d = nd_reconstruct(1,d);
+            continue;
+        }
+        if ( bucket->m < 0 ) continue;
+        col = nd_symbolic_preproc(bucket,0,&s0vect,&rp0);
+        if ( !col ) {
+            for ( t = l; NEXT(t); t = NEXT(t) );
+            NEXT(t) = d; d = l;
+            d = nd_reconstruct(1,d);
+            continue;
+        }
+        get_eg(&eg1); init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg1);
+        if ( DP_Print )
+            fprintf(asir_out,"sugar=%d,symb=%fsec,",
+                sugar,eg_f4.exectime+eg_f4.gctime);
+        nflist = nd_f4_red(m,l,0,s0vect,col,rp0,&l0);
+        if ( !l0 ) continue;
+        l = l0;
+
+        /* over Q */
+		while ( 1 ) {
+        	bucket = create_pbucket();
+        	stat = nd_sp_f4(0,1,l,bucket);
+        	if ( !stat ) {
+            	for ( t = l; NEXT(t); t = NEXT(t) );
+            	NEXT(t) = d; d = l;
+            	d = nd_reconstruct(1,d);
+            	continue;
+        	}
+        	if ( bucket->m < 0 ) continue;
+        	col = nd_symbolic_preproc(bucket,1,&s0vect,&rp0);
+        	if ( !col ) {
+            	for ( t = l; NEXT(t); t = NEXT(t) );
+            	NEXT(t) = d; d = l;
+            	d = nd_reconstruct(1,d);
+            	continue;
+        	}
+        	nflist = nd_f4_red(0,l,1,s0vect,col,rp0,0);
 		}
-	}
-	for ( i = len-1, t0 = 0; i >= 0; i-- ) {
-		if ( w[i] ) { NEXTNODE(t0,t); BDY(t) = (pointer)w[i]; }
-	}
-	NEXT(t) = 0; x = t0;
-	return x;
+
+        /* adding new bases */
+        for ( r = nflist; r; r = NEXT(r) ) {
+            nfqv = (NDV)BDY(r);
+            ndv_removecont(0,nfqv);
+            if ( !rem(NM(HCQ(nfqv)),m) ) return 0;
+            if ( nd_nalg ) {
+                ND nf1;
+
+                nf1 = ndvtond(m,nfqv);
+                nd_monic(0,&nf1);
+                nd_removecont(0,nf1);
+                nfqv = ndtondv(0,nf1); nd_free(nf1);
+            }
+            nfv = ndv_dup(0,nfqv);
+            ndv_mod(m,nfv);
+            ndv_removecont(m,nfv);
+            nh = ndv_newps(0,nfv,nfqv);
+            d = update_pairs(d,g,nh,0);
+            g = update_base(g,nh);
+        }
+    }
+#if 0
+    fprintf(asir_out,"ndv_alloc=%d\n",ndv_alloc);
+#endif
+	conv_ilist(0,1,g,indp);
+    return g;
 }
 
-void nd_init_ord(struct order_spec *ord)
+NODE nd_f4_red(int m,ND_pairs sp0,int trace,UINT *s0vect,int col,NODE rp0,ND_pairs *nz)
 {
-	if ( ord->id )
-		error("nd_gr : unsupported order");
-	nd_degcompat = 0;
-	switch ( ord->ord.simple ) {
-		case 0:
-			nd_degcompat = 1;
-			nd_isrlex = 1;
-			break;
-		case 1:
-			nd_degcompat = 1;
-			nd_isrlex = 0;
-			break;
-		default:
-			error("nd_gr : unsupported order");
+    IndArray *imat;
+    int nsp,nred,i;
+    int *rhead;
+    NODE r0,rp;
+    ND_pairs sp;
+    NM_ind_pair *rvect;
+init_eg(&eg_search);
+    for ( sp = sp0, nsp = 0; sp; sp = NEXT(sp), nsp++ );
+    nred = length(rp0);
+    imat = (IndArray *)ALLOCA(nred*sizeof(IndArray));
+    rhead = (int *)ALLOCA(col*sizeof(int));
+    for ( i = 0; i < col; i++ ) rhead[i] = 0;
+
+    /* construction of index arrays */
+    rvect = (NM_ind_pair *)ALLOCA(nred*sizeof(NM_ind_pair));
+    for ( rp = rp0, i = 0; rp; i++, rp = NEXT(rp) ) {
+        rvect[i] = (NM_ind_pair)BDY(rp);
+        imat[i] = nm_ind_pair_to_vect_compress(m,s0vect,col,rvect[i]);
+        rhead[imat[i]->head] = 1;
+    }
+    if ( m )
+        r0 = nd_f4_red_main(m,sp0,nsp,s0vect,col,rvect,rhead,imat,nred,nz);
+    else
+        r0 = nd_f4_red_q_main(sp0,nsp,trace,s0vect,col,rvect,rhead,imat,nred);
+print_eg("search",&eg_search);
+    return r0;
+}
+
+NODE nd_f4_red_main(int m,ND_pairs sp0,int nsp,UINT *s0vect,int col,
+        NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred,ND_pairs *nz)
+{
+    int spcol,sprow,a;
+    int i,j,k,l,rank;
+    NODE r0,r;
+    ND_pairs sp;
+    ND spol;
+    int **spmat;
+    UINT *svect,*v;
+    int *colstat;
+    struct oEGT eg0,eg1,eg2,eg_f4,eg_f4_1,eg_f4_2;
+    int maxrs;
+    int *spsugar;
+    ND_pairs *spactive;
+
+    spcol = col-nred;
+    get_eg(&eg0);
+    /* elimination (1st step) */
+    spmat = (int **)ALLOCA(nsp*sizeof(UINT *));
+    svect = (UINT *)ALLOCA(col*sizeof(UINT));
+    spsugar = (int *)ALLOCA(nsp*sizeof(UINT));
+    spactive = !nz?0:(ND_pairs *)ALLOCA(nsp*sizeof(ND_pairs));
+    for ( a = sprow = 0, sp = sp0; a < nsp; a++, sp = NEXT(sp) ) {
+        nd_sp(m,0,sp,&spol);
+        if ( !spol ) continue;
+        nd_to_vect(m,s0vect,col,spol,svect);
+        if ( m == -1 ) 
+            maxrs = ndv_reduce_vect_sf(m,svect,col,imat,rvect,nred);
+        else
+            maxrs = ndv_reduce_vect(m,svect,col,imat,rvect,nred);
+        for ( i = 0; i < col; i++ ) if ( svect[i] ) break;
+        if ( i < col ) {
+            spmat[sprow] = v = (UINT *)MALLOC_ATOMIC(spcol*sizeof(UINT));
+            for ( j = k = 0; j < col; j++ )
+                if ( !rhead[j] ) v[k++] = svect[j];
+            spsugar[sprow] = MAX(maxrs,SG(spol));
+            if ( nz )
+            spactive[sprow] = sp;
+            sprow++;
+        }
+        nd_free(spol);
+    }
+    get_eg(&eg1); init_eg(&eg_f4_1); add_eg(&eg_f4_1,&eg0,&eg1);
+    if ( DP_Print ) {
+        fprintf(asir_out,"elim1=%fsec,",eg_f4_1.exectime+eg_f4_1.gctime);
+        fflush(asir_out);
+    }
+    /* free index arrays */
+    for ( i = 0; i < nred; i++ ) GCFREE(imat[i]->index.c);
+
+    /* elimination (2nd step) */
+    colstat = (int *)ALLOCA(spcol*sizeof(int));
+    if ( m == -1 )
+        rank = nd_gauss_elim_sf(spmat,spsugar,sprow,spcol,m,colstat);
+    else
+        rank = nd_gauss_elim_mod(spmat,spsugar,spactive,sprow,spcol,m,colstat);
+    r0 = 0;
+    for ( i = 0; i < rank; i++ ) {
+        NEXTNODE(r0,r); BDY(r) = 
+            (pointer)vect_to_ndv(spmat[i],spcol,col,rhead,s0vect);
+        SG((NDV)BDY(r)) = spsugar[i];
+        GCFREE(spmat[i]);
+    }
+    if ( r0 ) NEXT(r) = 0;
+
+    for ( ; i < sprow; i++ ) GCFREE(spmat[i]);
+    get_eg(&eg2); init_eg(&eg_f4_2); add_eg(&eg_f4_2,&eg1,&eg2);
+    init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg2);
+    if ( DP_Print ) {
+        fprintf(asir_out,"elim2=%fsec\n",eg_f4_2.exectime+eg_f4_2.gctime);
+        fprintf(asir_out,"nsp=%d,nred=%d,spmat=(%d,%d),rank=%d  ",
+            nsp,nred,sprow,spcol,rank);
+        fprintf(asir_out,"%fsec\n",eg_f4.exectime+eg_f4.gctime);
+    }
+    if ( nz ) {
+        for ( i = 0; i < rank-1; i++ ) NEXT(spactive[i]) = spactive[i+1];
+        if ( rank > 0 ) {
+            NEXT(spactive[rank-1]) = 0;
+            *nz = spactive[0];
+        } else
+            *nz = 0;
+    }
+    return r0;
+}
+
+#if 1
+NODE nd_f4_red_q_main(ND_pairs sp0,int nsp,int trace,UINT *s0vect,int col,
+        NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred)
+{
+    int spcol,sprow,a;
+    int i,j,k,l,rank;
+    NODE r0,r;
+    ND_pairs sp;
+    ND spol;
+    Q **spmat;
+    Q *svect,*v;
+    int *colstat;
+    struct oEGT eg0,eg1,eg2,eg_f4,eg_f4_1,eg_f4_2;
+    int maxrs;
+    int *spsugar;
+    pointer *w;
+
+    spcol = col-nred;
+    get_eg(&eg0);
+    /* elimination (1st step) */
+    spmat = (Q **)ALLOCA(nsp*sizeof(Q *));
+    svect = (Q *)ALLOCA(col*sizeof(Q));
+    spsugar = (int *)ALLOCA(nsp*sizeof(Q));
+    for ( a = sprow = 0, sp = sp0; a < nsp; a++, sp = NEXT(sp) ) {
+        nd_sp(0,trace,sp,&spol);
+        if ( !spol ) continue;
+        nd_to_vect_q(s0vect,col,spol,svect);
+        maxrs = ndv_reduce_vect_q(svect,trace,col,imat,rvect,nred);
+        for ( i = 0; i < col; i++ ) if ( svect[i] ) break;
+        if ( i < col ) {
+            spmat[sprow] = v = (Q *)MALLOC(spcol*sizeof(Q));
+            for ( j = k = 0; j < col; j++ )
+                if ( !rhead[j] ) v[k++] = svect[j];
+            spsugar[sprow] = MAX(maxrs,SG(spol));
+            sprow++;
+        }
+/*        nd_free(spol); */
+    }
+    get_eg(&eg1); init_eg(&eg_f4_1); add_eg(&eg_f4_1,&eg0,&eg1);
+    if ( DP_Print ) {
+        fprintf(asir_out,"elim1=%fsec,",eg_f4_1.exectime+eg_f4_1.gctime);
+        fflush(asir_out);
+    }
+    /* free index arrays */
+/*    for ( i = 0; i < nred; i++ ) GCFREE(imat[i]->index.c); */
+
+    /* elimination (2nd step) */
+    colstat = (int *)ALLOCA(spcol*sizeof(int));
+    rank = nd_gauss_elim_q(spmat,spsugar,sprow,spcol,colstat);
+    w = (pointer *)ALLOCA(rank*sizeof(pointer));
+    for ( i = 0; i < rank; i++ ) {
+        w[rank-i-1] = (pointer)vect_to_ndv_q(spmat[i],spcol,col,rhead,s0vect);
+        SG((NDV)w[rank-i-1]) = spsugar[i];
+/*        GCFREE(spmat[i]); */
+    }
+#if 0
+    qsort(w,rank,sizeof(NDV),
+        (int (*)(const void *,const void *))ndv_compare);
+#endif
+    r0 = 0;
+    for ( i = 0; i < rank; i++ ) {
+        NEXTNODE(r0,r); BDY(r) = w[i];
+    }
+    if ( r0 ) NEXT(r) = 0;
+
+/*    for ( ; i < sprow; i++ ) GCFREE(spmat[i]); */
+    get_eg(&eg2); init_eg(&eg_f4_2); add_eg(&eg_f4_2,&eg1,&eg2);
+    init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg2);
+    if ( DP_Print ) {
+        fprintf(asir_out,"elim2=%fsec\n",eg_f4_2.exectime+eg_f4_2.gctime);
+        fprintf(asir_out,"nsp=%d,nred=%d,spmat=(%d,%d),rank=%d  ",
+            nsp,nred,sprow,spcol,rank);
+        fprintf(asir_out,"%fsec\n",eg_f4.exectime+eg_f4.gctime);
+    }
+    return r0;
+}
+#else
+void printm(Q **mat,int row,int col)
+{
+    int i,j;
+    printf("[");
+    for ( i = 0; i < row; i++ ) {
+        for ( j = 0; j < col; j++ ) {
+            printexpr(CO,mat[i][j]); printf(" ");
+        }
+        printf("]\n");
+    }
+}
+
+NODE nd_f4_red_q_main(ND_pairs sp0,int nsp,UINT *s0vect,int col,
+        NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred)
+{
+    int row,a;
+    int i,j,rank;
+    NODE r0,r;
+    ND_pairs sp;
+    ND spol;
+    Q **mat;
+    int *colstat;
+    int *sugar;
+
+    row = nsp+nred;
+    /* make the matrix */
+    mat = (Q **)ALLOCA(row*sizeof(Q *));
+    sugar = (int *)ALLOCA(row*sizeof(int));
+    for ( row = a = 0, sp = sp0; a < nsp; a++, sp = NEXT(sp) ) {
+        nd_sp(0,0,sp,&spol);
+        if ( !spol ) continue;
+        mat[row] = (Q *)MALLOC(col*sizeof(Q));
+        nd_to_vect_q(s0vect,col,spol,mat[row]);
+        sugar[row] = SG(spol);
+        row++;
+    }
+    for ( i = 0; i < nred; i++, row++ ) {
+        mat[row] = nm_ind_pair_to_vect(0,s0vect,col,rvect[i]);
+        sugar[row] = rvect[i]->sugar;
+    }
+    /* elimination */
+    colstat = (int *)ALLOCA(col*sizeof(int));
+    rank = nd_gauss_elim_q(mat,sugar,row,col,colstat);
+    r0 = 0;
+    for ( i = 0; i < rank; i++ ) {
+        for ( j = 0; j < col; j++ ) if ( mat[i][j] ) break;
+        if ( j == col ) error("nd_f4_red_q_main : cannot happen");
+        if ( rhead[j] ) continue;
+        NEXTNODE(r0,r); BDY(r) = 
+            (pointer)plain_vect_to_ndv_q(mat[i],col,s0vect);
+        SG((NDV)BDY(r)) = sugar[i];
+    }
+    if ( r0 ) NEXT(r) = 0;
+    printf("\n");
+    return r0;
+}
+#endif
+
+FILE *nd_write,*nd_read;
+
+void nd_send_int(int a) {
+    write_int(nd_write,&a);
+}
+
+void nd_send_intarray(int *p,int len) {
+    write_intarray(nd_write,p,len);
+}
+
+int nd_recv_int() {
+    int a;
+
+    read_int(nd_read,&a);
+    return a;
+}
+
+void nd_recv_intarray(int *p,int len) {
+    read_intarray(nd_read,p,len);
+}
+
+void nd_send_ndv(NDV p) {
+    int len,i;
+    NMV m;
+
+    if ( !p ) nd_send_int(0);
+    else {
+        len = LEN(p);
+        nd_send_int(len);
+        m = BDY(p);
+        for ( i = 0; i < len; i++, NMV_ADV(m) ) {
+            nd_send_int(CM(m));    
+            nd_send_intarray(DL(m),nd_wpd);
+        }
+    }
+}
+
+void nd_send_nd(ND p) {
+    int len,i;
+    NM m;
+
+    if ( !p ) nd_send_int(0);
+    else {
+        len = LEN(p);
+        nd_send_int(len);
+        m = BDY(p);
+        for ( i = 0; i < len; i++, m = NEXT(m) ) {
+            nd_send_int(CM(m));    
+            nd_send_intarray(DL(m),nd_wpd);
+        }
+    }
+}
+
+NDV nd_recv_ndv()
+{
+    int len,i;
+    NMV m,m0;
+    NDV r;
+
+    len = nd_recv_int();
+    if ( !len ) return 0;
+    else {
+        m0 = m = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(nmv_adv*len);
+#if 0
+        ndv_alloc += len*nmv_adv;
+#endif
+        for ( i = 0; i < len; i++, NMV_ADV(m) ) {
+            CM(m) = nd_recv_int();    
+            nd_recv_intarray(DL(m),nd_wpd);
+        }
+        MKNDV(nd_nvar,m0,len,r);
+        return r;    
+    }
+}
+
+int ox_exec_f4_red(Q proc)
+{
+    Obj obj;
+    STRING fname;
+    NODE arg;
+    int s;
+    extern int ox_need_conv,ox_file_io;
+
+    MKSTR(fname,"nd_exec_f4_red");
+    arg = mknode(2,proc,fname);
+    Pox_cmo_rpc(arg,&obj);
+    s = get_ox_server_id(QTOS(proc));
+    nd_write = iofp[s].out;
+    nd_read = iofp[s].in;
+    ox_need_conv = ox_file_io = 0;
+    return s;
+}
+
+NODE nd_f4_red_dist(int m,ND_pairs sp0,UINT *s0vect,int col,NODE rp0,ND_pairs *nz)
+{
+    int nsp,nred;
+    int i,rank,s;
+    NODE rp,r0,r;
+    ND_pairs sp;
+    NM_ind_pair pair;
+    NMV nmv;
+    NM nm;
+    NDV nf;
+    Obj proc,dmy;
+
+    ox_launch_main(0,0,&proc);
+    s = ox_exec_f4_red((Q)proc);
+
+    nd_send_int(m);
+    nd_send_int(nd_nvar);
+    nd_send_int(nd_bpe);
+    nd_send_int(nd_wpd);
+    nd_send_int(nmv_adv);
+
+    saveobj(nd_write,dp_current_spec->obj); fflush(nd_write);
+
+    nd_send_int(nd_psn);
+    for ( i = 0; i < nd_psn; i++ ) nd_send_ndv(nd_ps[i]);
+
+    for ( sp = sp0, nsp = 0; sp; sp = NEXT(sp), nsp++ );
+    nd_send_int(nsp);
+    for ( i = 0, sp = sp0; i < nsp; i++, sp = NEXT(sp) ) {
+        nd_send_int(sp->i1); nd_send_int(sp->i2);
+    }
+
+    nd_send_int(col); nd_send_intarray(s0vect,col*nd_wpd);
+
+    nred = length(rp0); nd_send_int(nred);
+    for ( i = 0, rp = rp0; i < nred; i++, rp = NEXT(rp) ) {
+        pair = (NM_ind_pair)BDY(rp);
+        nd_send_int(pair->index);
+        nd_send_intarray(pair->mul->dl,nd_wpd);
+    }
+    fflush(nd_write);
+    rank = nd_recv_int();
+    fprintf(asir_out,"rank=%d\n",rank);
+    r0 = 0;
+    for ( i = 0; i < rank; i++ ) {
+        nf = nd_recv_ndv();
+        NEXTNODE(r0,r); BDY(r) = (pointer)nf;
+    }
+    Pox_shutdown(mknode(1,proc),&dmy);
+    return r0;
+}
+
+/* server side */
+
+void nd_exec_f4_red_dist()
+{
+    int m,i,nsp,col,s0size,nred,spcol,j,k;
+    NM_ind_pair *rp0;
+    NDV nf;
+    UINT *s0vect;
+    IndArray *imat;
+    int *rhead;
+    int **spmat;
+    UINT *svect,*v;
+    ND_pairs *sp0;
+    int *colstat;
+    int a,sprow,rank;
+    struct order_spec *ord;
+    Obj ordspec;
+    ND spol;
+    int maxrs;
+    int *spsugar;
+
+    nd_read = iofp[0].in;
+    nd_write = iofp[0].out;
+    m = nd_recv_int();
+    nd_nvar = nd_recv_int();
+    nd_bpe = nd_recv_int();
+    nd_wpd = nd_recv_int();
+    nmv_adv = nd_recv_int();
+
+    loadobj(nd_read,&ordspec);
+    create_order_spec(0,ordspec,&ord);
+    nd_init_ord(ord);
+    nd_setup_parameters(nd_nvar,0);
+
+    nd_psn = nd_recv_int();
+    nd_ps = (NDV *)MALLOC(nd_psn*sizeof(NDV));
+    nd_bound = (UINT **)MALLOC(nd_psn*sizeof(UINT *));
+    for ( i = 0; i < nd_psn; i++ ) {
+        nd_ps[i] = nd_recv_ndv();
+        nd_bound[i] = ndv_compute_bound(nd_ps[i]);
+    }
+
+    nsp = nd_recv_int();
+    sp0 = (ND_pairs *)MALLOC(nsp*sizeof(ND_pairs));
+    for ( i = 0; i < nsp; i++ ) {
+        NEWND_pairs(sp0[i]);
+        sp0[i]->i1 = nd_recv_int(); sp0[i]->i2 = nd_recv_int();
+        ndl_lcm(HDL(nd_ps[sp0[i]->i1]),HDL(nd_ps[sp0[i]->i2]),LCM(sp0[i]));
+    }
+
+    col = nd_recv_int();
+    s0size = col*nd_wpd;
+    s0vect = (UINT *)MALLOC(s0size*sizeof(UINT));
+    nd_recv_intarray(s0vect,s0size);
+
+    nred = nd_recv_int();
+    rp0 = (NM_ind_pair *)MALLOC(nred*sizeof(NM_ind_pair));
+    for ( i = 0; i < nred; i++ ) {
+        rp0[i] = (NM_ind_pair)MALLOC(sizeof(struct oNM_ind_pair));
+        rp0[i]->index = nd_recv_int();
+        rp0[i]->mul = (NM)MALLOC(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT));
+        nd_recv_intarray(rp0[i]->mul->dl,nd_wpd);
+    }
+
+    spcol = col-nred;
+    imat = (IndArray *)MALLOC(nred*sizeof(IndArray));
+    rhead = (int *)MALLOC(col*sizeof(int));
+    for ( i = 0; i < col; i++ ) rhead[i] = 0;
+
+    /* construction of index arrays */
+    for ( i = 0; i < nred; i++ ) {
+        imat[i] = nm_ind_pair_to_vect_compress(m,s0vect,col,rp0[i]);
+        rhead[imat[i]->head] = 1;
+    }
+
+    /* elimination (1st step) */
+    spmat = (int **)MALLOC(nsp*sizeof(UINT *));
+    svect = (UINT *)MALLOC(col*sizeof(UINT));
+    spsugar = (int *)ALLOCA(nsp*sizeof(UINT));
+    for ( a = sprow = 0; a < nsp; a++ ) {
+        nd_sp(m,0,sp0[a],&spol);
+        if ( !spol ) continue;
+        nd_to_vect(m,s0vect,col,spol,svect);
+        if ( m == -1 ) 
+            maxrs = ndv_reduce_vect_sf(m,svect,col,imat,rp0,nred);
+        else 
+            maxrs = ndv_reduce_vect(m,svect,col,imat,rp0,nred);
+        for ( i = 0; i < col; i++ ) if ( svect[i] ) break;
+        if ( i < col ) {
+            spmat[sprow] = v = (UINT *)MALLOC(spcol*sizeof(UINT));
+            for ( j = k = 0; j < col; j++ )
+                if ( !rhead[j] ) v[k++] = svect[j];
+            spsugar[sprow] = MAX(maxrs,SG(spol));
+            sprow++;
+        }
+        nd_free(spol);
+    }
+    /* elimination (2nd step) */
+    colstat = (int *)ALLOCA(spcol*sizeof(int));
+    if ( m == -1 )
+        rank = nd_gauss_elim_sf(spmat,spsugar,sprow,spcol,m,colstat);
+    else
+        rank = nd_gauss_elim_mod(spmat,spsugar,0,sprow,spcol,m,colstat);
+    nd_send_int(rank);
+    for ( i = 0; i < rank; i++ ) {
+        nf = vect_to_ndv(spmat[i],spcol,col,rhead,s0vect);
+        nd_send_ndv(nf);
+    }
+    fflush(nd_write);
+}
+
+int nd_gauss_elim_q(Q **mat0,int *sugar,int row,int col,int *colstat)
+{
+    int i,j,t,c,rank,inv;
+    int *ci,*ri;
+    Q dn;
+    MAT m,nm;
+
+    NEWMAT(m); m->row = row; m->col = col; m->body = (pointer **)mat0;
+    rank = generic_gauss_elim(m,&nm,&dn,&ri,&ci);
+    for ( i = 0; i < row; i++ )
+        for ( j = 0; j < col; j++ )
+            mat0[i][j] = 0;
+    c = col-rank;
+    for ( i = 0; i < rank; i++ ) {
+        mat0[i][ri[i]] = dn;    
+        for ( j = 0; j < c; j++ )
+            mat0[i][ci[j]] = (Q)BDY(nm)[i][j];
+    }
+    return rank;
+}
+
+int nd_gauss_elim_mod(int **mat0,int *sugar,ND_pairs *spactive,int row,int col,int md,int *colstat)
+{
+    int i,j,k,l,inv,a,rank,s;
+    unsigned int *t,*pivot,*pk;
+    unsigned int **mat;
+    ND_pairs pair;
+
+    mat = (unsigned int **)mat0;
+    for ( rank = 0, j = 0; j < col; j++ ) {
+        for ( i = rank; i < row; i++ )
+            mat[i][j] %= md;
+        for ( i = rank; i < row; i++ )
+            if ( mat[i][j] )
+                break;
+        if ( i == row ) {
+            colstat[j] = 0;
+            continue;
+        } else
+            colstat[j] = 1;
+        if ( i != rank ) {
+            t = mat[i]; mat[i] = mat[rank]; mat[rank] = t;
+            s = sugar[i]; sugar[i] = sugar[rank]; sugar[rank] = s;
+            if ( spactive ) {
+                pair = spactive[i]; spactive[i] = spactive[rank]; 
+                spactive[rank] = pair;
+            }
+        }
+        pivot = mat[rank];
+        s = sugar[rank];
+        inv = invm(pivot[j],md);
+        for ( k = j, pk = pivot+k; k < col; k++, pk++ )
+            if ( *pk ) {
+                if ( *pk >= (unsigned int)md )
+                    *pk %= md;
+                DMAR(*pk,inv,0,md,*pk)
+            }
+        for ( i = rank+1; i < row; i++ ) {
+            t = mat[i];
+            if ( a = t[j] ) {
+                sugar[i] = MAX(sugar[i],s);
+                red_by_vect(md,t+j,pivot+j,md-a,col-j);
+            }
+        }
+        rank++;
+    }
+    for ( j = col-1, l = rank-1; j >= 0; j-- )
+        if ( colstat[j] ) {
+            pivot = mat[l];
+            s = sugar[l];
+            for ( i = 0; i < l; i++ ) {
+                t = mat[i];
+                t[j] %= md;
+                if ( a = t[j] ) {
+                    sugar[i] = MAX(sugar[i],s);
+                    red_by_vect(md,t+j,pivot+j,md-a,col-j);
+                }
+            }
+            l--;
+        }
+    for ( j = 0, l = 0; l < rank; j++ )
+        if ( colstat[j] ) {
+            t = mat[l];
+            for ( k = j; k < col; k++ )
+                if ( t[k] >= (unsigned int)md )
+                    t[k] %= md;
+            l++;
+        }
+    return rank;
+}
+
+int nd_gauss_elim_sf(int **mat0,int *sugar,int row,int col,int md,int *colstat)
+{
+    int i,j,k,l,inv,a,rank,s;
+    unsigned int *t,*pivot,*pk;
+    unsigned int **mat;
+
+    mat = (unsigned int **)mat0;
+    for ( rank = 0, j = 0; j < col; j++ ) {
+        for ( i = rank; i < row; i++ )
+            if ( mat[i][j] )
+                break;
+        if ( i == row ) {
+            colstat[j] = 0;
+            continue;
+        } else
+            colstat[j] = 1;
+        if ( i != rank ) {
+            t = mat[i]; mat[i] = mat[rank]; mat[rank] = t;
+            s = sugar[i]; sugar[i] = sugar[rank]; sugar[rank] = s;
+        }
+        pivot = mat[rank];
+        s = sugar[rank];
+        inv = _invsf(pivot[j]);
+        for ( k = j, pk = pivot+k; k < col; k++, pk++ )
+            if ( *pk )
+                *pk = _mulsf(*pk,inv);
+        for ( i = rank+1; i < row; i++ ) {
+            t = mat[i];
+            if ( a = t[j] ) {
+                sugar[i] = MAX(sugar[i],s);
+                red_by_vect_sf(md,t+j,pivot+j,_chsgnsf(a),col-j);
+            }
+        }
+        rank++;
+    }
+    for ( j = col-1, l = rank-1; j >= 0; j-- )
+        if ( colstat[j] ) {
+            pivot = mat[l];
+            s = sugar[l];
+            for ( i = 0; i < l; i++ ) {
+                t = mat[i];
+                if ( a = t[j] ) {
+                    sugar[i] = MAX(sugar[i],s);
+                    red_by_vect_sf(md,t+j,pivot+j,_chsgnsf(a),col-j);
+                }
+            }
+            l--;
+        }
+    return rank;
+}
+
+int ndv_ishomo(NDV p)
+{
+    NMV m;
+    int len,h;
+
+    if ( !p ) return 1;
+    len = LEN(p);
+    m = BDY(p);
+    h = TD(DL(m));
+    NMV_ADV(m);
+    for ( len--; len; len--, NMV_ADV(m) )
+        if ( TD(DL(m)) != h ) return 0;
+    return 1;
+}
+
+void ndv_save(NDV p,int index)
+{
+    FILE *s;
+    char name[BUFSIZ];
+    short id;
+    int nv,sugar,len,n,i,td,e,j;
+    NMV m;
+    unsigned int *dl;
+    int mpos;
+
+    sprintf(name,"%s/%d",Demand,index);
+    s = fopen(name,"w");
+    savevl(s,0);
+    if ( !p ) { 
+        saveobj(s,0);
+        return;
+    }
+    id = O_DP;
+    nv = NV(p);
+    sugar = SG(p);
+    len = LEN(p);
+    write_short(s,&id); write_int(s,&nv); write_int(s,&sugar);
+    write_int(s,&len);
+
+    for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
+        saveobj(s,(Obj)CQ(m));
+        dl = DL(m);
+        td = TD(dl);
+        write_int(s,&td);
+        for ( j = 0; j < nv; j++ ) {
+            e = GET_EXP(dl,j);    
+            write_int(s,&e);
+        }
+        if ( nd_module ) {
+            mpos = MPOS(dl); write_int(s,&mpos);
+        }
+    }
+    fclose(s);
+}
+
+NDV ndv_load(int index)
+{
+    FILE *s;
+    char name[BUFSIZ];
+    short id;
+    int nv,sugar,len,n,i,td,e,j;
+    NDV d;
+    NMV m0,m;
+    unsigned int *dl;
+    Obj obj;
+    int mpos;
+
+    sprintf(name,"%s/%d",Demand,index);
+    s = fopen(name,"r");
+    if ( !s ) return 0;
+
+    skipvl(s);
+    read_short(s,&id);
+    if ( !id ) return 0;
+    read_int(s,&nv);
+    read_int(s,&sugar);
+    read_int(s,&len);
+
+    m0 = m = MALLOC(len*nmv_adv);
+    for ( i = 0; i < len; i++, NMV_ADV(m) ) {
+        loadobj(s,&obj); CQ(m) = (Q)obj;
+        dl = DL(m);
+        ndl_zero(dl);
+        read_int(s,&td); TD(dl) = td;
+        for ( j = 0; j < nv; j++ ) {
+            read_int(s,&e);
+            PUT_EXP(dl,j,e);    
+        }
+        if ( nd_module ) {
+            read_int(s,&mpos); MPOS(dl) = mpos;
+        }
+        if ( nd_blockmask ) ndl_weight_mask(dl);
+    }
+    fclose(s);
+    MKNDV(nv,m0,len,d);
+    SG(d) = sugar;
+    return d;
+}
+
+void nd_det(int mod,MAT f,P *rp)
+{
+    VL fv,tv;
+    int n,i,j,max,e,nvar,sgn,k0,l0,len0,len,k,l,a;
+    pointer **m;
+    Q mone;
+    P **w;
+    P mp,r;
+    NDV **dm;
+    NDV *t,*mi,*mj;
+    NDV d,s,mij,mjj;
+    ND u;
+    NMV nmv;
+    UINT *bound;
+    PGeoBucket bucket;
+    struct order_spec *ord;
+    Q dq,dt,ds;
+    N gn,qn,dn0,nm,dn;
+
+    create_order_spec(0,0,&ord);
+    nd_init_ord(ord);
+    get_vars((Obj)f,&fv);
+    if ( f->row != f->col )
+        error("nd_det : non-square matrix");
+    n = f->row;
+    m = f->body;
+    for ( nvar = 0, tv = fv; tv; tv = NEXT(tv), nvar++ );
+
+    if ( !nvar ) {
+        if ( !mod )
+            detp(CO,(P **)m,n,rp);
+        else {
+            w = (P **)almat_pointer(n,n);
+            for ( i = 0; i < n; i++ )
+                for ( j = 0; j < n; j++ )
+                    ptomp(mod,(P)m[i][j],&w[i][j]);
+            detmp(CO,mod,w,n,&mp);
+            mptop(mp,rp);
+        }
+        return;
+    }
+    
+    if ( !mod ) {
+        w = (P **)almat_pointer(n,n);
+        dq = ONE;
+        for ( i = 0; i < n; i++ ) {
+            dn0 = ONEN;
+            for ( j = 0; j < n; j++ ) {
+                if ( !m[i][j] ) continue;
+                lgp(m[i][j],&nm,&dn);
+                gcdn(dn0,dn,&gn); divsn(dn0,gn,&qn); muln(qn,dn,&dn0);
+            }
+            if ( !UNIN(dn0) ) {
+                NTOQ(dn0,1,ds);
+                for ( j = 0; j < n; j++ )
+                    mulp(CO,(P)m[i][j],(P)ds,&w[i][j]);
+                mulq(dq,ds,&dt); dq = dt;
+            } else
+                for ( j = 0; j < n; j++ )
+                    w[i][j] = (P)m[i][j];
+        }
+        m = (pointer **)w;
+    }
+
+    for ( i = 0, max = 1; i < n; i++ )
+        for ( j = 0; j < n; j++ )
+            for ( tv = fv; tv; tv = NEXT(tv) ) {
+                e = getdeg(tv->v,(P)m[i][j]);
+                max = MAX(e,max);
+            }
+    nd_setup_parameters(nvar,max);
+    dm = (NDV **)almat_pointer(n,n);
+    for ( i = 0, max = 1; i < n; i++ )
+        for ( j = 0; j < n; j++ ) {
+            dm[i][j] = ptondv(CO,fv,m[i][j]);
+            if ( mod ) ndv_mod(mod,dm[i][j]);
+            if ( dm[i][j] && !LEN(dm[i][j]) ) dm[i][j] = 0;
+        }
+    d = ptondv(CO,fv,(P)ONE);
+    if ( mod ) ndv_mod(mod,d);
+    chsgnq(ONE,&mone);
+    for ( j = 0, sgn = 1; j < n; j++ ) {
+        if ( DP_Print ) fprintf(stderr,".",j);
+        for ( i = j; i < n && !dm[i][j]; i++ );
+        if ( i == n ) {
+            *rp = 0;
+            return;
+        }
+        k0 = i; l0 = j; len0 = LEN(dm[k0][l0]);
+        for ( k = j; k < n; k++ )
+            for ( l = j; l < n; l++ )
+                if ( dm[k][l] && LEN(dm[k][l]) < len0 ) {
+                    k0 = k; l0 = l; len0 = LEN(dm[k][l]);
+                }
+        if ( k0 != j ) {
+            t = dm[j]; dm[j] = dm[k0]; dm[k0] = t;
+            sgn = -sgn;
+        }
+        if ( l0 != j ) {
+            for ( k = j; k < n; k++ ) {
+                s = dm[k][j]; dm[k][j] = dm[k][l0]; dm[k][l0] = s;
+            }
+            sgn = -sgn;
+        }
+        bound = nd_det_compute_bound(dm,n,j);
+        for ( k = 0; k < nd_nvar; k++ )
+            if ( bound[k]*2 > nd_mask0 ) break;
+        if ( k < nd_nvar )
+            nd_det_reconstruct(dm,n,j,d);
+
+        for ( i = j+1, mj = dm[j], mjj = mj[j]; i < n; i++ ) {
+/*            if ( DP_Print ) fprintf(stderr,"    i=%d\n        ",i); */
+            mi = dm[i]; mij = mi[j];
+            if ( mod )
+                ndv_mul_c(mod,mij,mod-1);
+            else
+                ndv_mul_c_q(mij,mone);
+            for ( k = j+1; k < n; k++ ) {
+/*                if ( DP_Print ) fprintf(stderr,"k=%d ",k); */
+                bucket = create_pbucket();
+                if ( mi[k] ) {
+                    nmv = BDY(mjj); len = LEN(mjj);
+                    for ( a = 0; a < len; a++, NMV_ADV(nmv) ) {
+                        u = ndv_mul_nmv_trunc(mod,nmv,mi[k],DL(BDY(d)));
+                        add_pbucket(mod,bucket,u);
+                    }
+                }
+                if ( mj[k] && mij ) {
+                    nmv = BDY(mij); len = LEN(mij);
+                    for ( a = 0; a < len; a++, NMV_ADV(nmv) ) {
+                        u = ndv_mul_nmv_trunc(mod,nmv,mj[k],DL(BDY(d)));
+                        add_pbucket(mod,bucket,u);
+                    }
+                }
+                u = nd_quo(mod,bucket,d);
+                mi[k] = ndtondv(mod,u);
+            }
+/*            if ( DP_Print ) fprintf(stderr,"\n",k); */
+        }
+        d = mjj;
+    }
+    if ( DP_Print ) fprintf(stderr,"\n",k);
+    if ( sgn < 0 )
+        if ( mod )
+            ndv_mul_c(mod,d,mod-1);
+        else
+            ndv_mul_c_q(d,mone);
+    r = ndvtop(mod,CO,fv,d);
+    if ( !mod && !UNIQ(dq) )
+        divsp(CO,r,(P)dq,rp);
+    else
+        *rp = r;
+}
+
+ND ndv_mul_nmv_trunc(int mod,NMV m0,NDV p,UINT *d)
+{
+    NM mr,mr0;
+    NM tnm;
+    NMV m;
+    UINT *d0,*dt,*dm;
+    int c,n,td,i,c1,c2,len;
+    Q q;
+    ND r;
+
+    if ( !p ) return 0;
+    else {
+        n = NV(p); m = BDY(p); len = LEN(p);
+        d0 = DL(m0);
+        td = TD(d);
+        mr0 = 0;
+        NEWNM(tnm);
+        if ( mod ) {
+            c = CM(m0);
+            for ( i = 0; i < len; i++, NMV_ADV(m) ) {
+                ndl_add(DL(m),d0,DL(tnm));
+                if ( ndl_reducible(DL(tnm),d) ) {
+                    NEXTNM(mr0,mr);
+                    c1 = CM(m); DMAR(c1,c,0,mod,c2); CM(mr) = c2;
+                    ndl_copy(DL(tnm),DL(mr));
+                }
+            }
+        } else {
+            q = CQ(m0);
+            for ( i = 0; i < len; i++, NMV_ADV(m) ) {
+                ndl_add(DL(m),d0,DL(tnm));
+                if ( ndl_reducible(DL(tnm),d) ) {
+                    NEXTNM(mr0,mr);
+                    mulq(CQ(m),q,&CQ(mr));
+                    ndl_copy(DL(tnm),DL(mr));
+                }
+            }
+        }
+        if ( !mr0 )
+            return 0;
+        else {
+            NEXT(mr) = 0; 
+            for ( len = 0, mr = mr0; mr; mr = NEXT(mr), len++ );
+            MKND(NV(p),mr0,len,r);
+            SG(r) = SG(p) + TD(d0);
+            return r;
+        }
+    }
+}
+
+void nd_det_reconstruct(NDV **dm,int n,int j,NDV d)
+{
+    int i,obpe,oadv,h,k,l;
+    static NM prev_nm_free_list;
+    EPOS oepos;
+
+    obpe = nd_bpe;
+    oadv = nmv_adv;
+    oepos = nd_epos;
+    if ( obpe < 2 ) nd_bpe = 2;
+    else if ( obpe < 3 ) nd_bpe = 3;
+    else if ( obpe < 4 ) nd_bpe = 4;
+    else if ( obpe < 5 ) nd_bpe = 5;
+    else if ( obpe < 6 ) nd_bpe = 6;
+    else if ( obpe < 8 ) nd_bpe = 8;
+    else if ( obpe < 10 ) nd_bpe = 10;
+    else if ( obpe < 16 ) nd_bpe = 16;
+    else if ( obpe < 32 ) nd_bpe = 32;
+    else error("nd_det_reconstruct : exponent too large");
+
+    nd_setup_parameters(nd_nvar,0);
+    prev_nm_free_list = _nm_free_list;
+    _nm_free_list = 0;
+    for ( k = j; k < n; k++ )
+        for (l = j; l < n; l++ )
+            ndv_realloc(dm[k][l],obpe,oadv,oepos);
+    ndv_realloc(d,obpe,oadv,oepos);
+    prev_nm_free_list = 0;
+#if 0
+    GC_gcollect();
+#endif
+}
+
+/* returns a UINT array containing degree bounds */
+
+UINT *nd_det_compute_bound(NDV **dm,int n,int j)
+{
+    UINT *d0,*d1,*d,*t,*r;
+    int k,l,i;
+
+    d0 = (UINT *)MALLOC(nd_nvar*sizeof(UINT));
+    for ( k = 0; k < nd_nvar; k++ ) d0[k] = 0;
+    for ( k = j; k < n; k++ )
+        for ( l = j; l < n; l++ )
+            if ( dm[k][l] ) {
+                d = ndv_compute_bound(dm[k][l]);
+                for ( i = 0; i < nd_nvar; i++ )
+                    d0[i] = MAX(d0[i],d[i]);
+            }
+    return d0;
+}
+
+DL nd_separate_d(UINT *d,UINT *trans)
+{
+    int n,td,i,e,j;
+    DL a;
+
+    ndl_zero(trans);
+    td = 0;
+    for ( i = 0; i < nd_ntrans; i++ ) {
+        e = GET_EXP(d,i);
+        PUT_EXP(trans,i,e);
+        td += MUL_WEIGHT(e,i);
+    }
+    if ( nd_ntrans+nd_nalg < nd_nvar ) {
+        /* homogenized */
+        i = nd_nvar-1;
+        e = GET_EXP(d,i);
+        PUT_EXP(trans,i,e);
+        td += MUL_WEIGHT(e,i);
+    }
+    TD(trans) = td;
+    if ( nd_blockmask) ndl_weight_mask(trans);
+    NEWDL(a,nd_nalg);
+    td = 0;
+    for ( i = 0; i < nd_nalg; i++ ) {
+        j = nd_ntrans+i;
+        e = GET_EXP(d,j);
+        a->d[i] = e;
+        td += e;
+    }
+    a->td = td;
+    return a;
+}
+
+int nd_monic(int mod,ND *p)
+{
+    UINT *trans,*t;
+    DL alg;
+    MP mp0,mp;
+    NM m,m0,m1,ma0,ma,mb,mr0,mr;
+    ND r;
+    DL dl;
+    DP nm;
+    NDV ndv;
+    DAlg inv,cd;
+    ND s,c;
+    Q l,mul;
+    N ln;
+    int n,ntrans,i,e,td,is_lc,len;
+    NumberField nf;
+    struct oEGT eg0,eg1;
+
+    if ( !(nf = get_numberfield()) )
+        error("nd_monic : current_numberfield is not set");
+
+    /* Q coef -> DAlg coef */
+    NEWNM(ma0); ma = ma0;
+    m = BDY(*p); 
+    is_lc = 1;
+    while ( 1 ) {
+        NEWMP(mp0); mp = mp0;
+        mp->c = (P)CQ(m);
+        mp->dl = nd_separate_d(DL(m),DL(ma));
+        NEWNM(mb);
+        for ( m = NEXT(m); m; m = NEXT(m) ) {
+            alg = nd_separate_d(DL(m),DL(mb));
+            if ( !ndl_equal(DL(ma),DL(mb)) )
+                break;
+            NEXTMP(mp0,mp); mp->c = (P)CQ(m); mp->dl = alg;
+        }
+        NEXT(mp) = 0;
+        MKDP(nd_nalg,mp0,nm);
+        MKDAlg(nm,ONE,cd);
+        if ( is_lc == 1 ) {
+            /* if the lc is a rational number, we have nothing to do */
+            if ( !mp0->dl->td )
+                return 1;
+
+            get_eg(&eg0);
+            invdalg(cd,&inv);
+            get_eg(&eg1); add_eg(&eg_invdalg,&eg0,&eg1);
+            /* check the validity of inv */
+            if ( mod && !rem(NM(inv->dn),mod) )
+                return 0;
+            CA(ma) = nf->one;
+            is_lc = 0;
+            ln = ONEN;
+        } else {
+            muldalg(cd,inv,&CA(ma));    
+            lcmn(ln,NM(CA(ma)->dn),&ln);
+        }
+        if ( m ) {
+            NEXT(ma) = mb; ma = mb;
+        } else {
+            NEXT(ma) = 0;
+            break;
+        }
+    }
+    /* l = lcm(denoms) */
+    NTOQ(ln,1,l);
+    for ( mr0 = 0, m = ma0; m; m = NEXT(m) ) {
+        divq(l,CA(m)->dn,&mul);
+        for ( mp = BDY(CA(m)->nm); mp; mp = NEXT(mp) ) {
+            NEXTNM(mr0,mr);
+            mulq((Q)mp->c,mul,&CQ(mr));
+            dl = mp->dl;
+            td = TD(DL(m));
+            ndl_copy(DL(m),DL(mr));
+            for ( i = 0; i < nd_nalg; i++ ) {
+                e = dl->d[i];
+                PUT_EXP(DL(mr),i+nd_ntrans,e);
+                td += MUL_WEIGHT(e,i+nd_ntrans);
+            }
+            if ( nd_module ) MPOS(DL(mr)) = MPOS(DL(m));
+            TD(DL(mr)) = td;
+            if ( nd_blockmask) ndl_weight_mask(DL(mr));
+        }
+    }
+    NEXT(mr) = 0;
+    for ( len = 0, mr = mr0; mr; mr = NEXT(mr), len++ );
+    MKND(NV(*p),mr0,len,r);
+    /* XXX */
+    SG(r) = SG(*p);
+    nd_free(*p);
+    *p = r;
+    return 1;
+}
+
+NODE reverse_node(NODE n)
+{
+    NODE t,t1;
+
+    for ( t = 0; n; n = NEXT(n) ) {
+        MKNODE(t1,BDY(n),t); t = t1;
+    }
+    return t;
+}
+
+P ndc_div(int mod,union oNDC a,union oNDC b)
+{
+    union oNDC c;
+    int inv,t;
+
+    if ( mod == -1 ) c.m = _mulsf(a.m,_invsf(b.m));
+    else if ( mod ) {
+        inv = invm(b.m,mod);
+        DMAR(a.m,inv,0,mod,t); c.m = t;
+    } else if ( nd_vc )
+       divsp(nd_vc,a.p,b.p,&c.p);
+    else
+       divq(a.z,b.z,&c.z);
+    return ndctop(mod,c);
+}
+
+P ndctop(int mod,union oNDC c)
+{
+    Q q;
+    int e;
+    GFS gfs;
+
+    if ( mod == -1 ) {
+        e = IFTOF(c.m); MKGFS(e,gfs); return (P)gfs;
+    } else if ( mod ) {
+        STOQ(c.m,q); return (P)q;
+    } else
+        return (P)c.p;
+}
+
+/* [0,0,0,cont] = p -> p/cont */
+
+void finalize_tracelist(int i,P cont)
+{
+	 LIST l;
+	 NODE node;
+     Q iq;
+
+	 if ( !UNIQ(cont) ) {
+         node = mknode(4,NULLP,NULLP,NULLP,cont);
+         MKLIST(l,node); MKNODE(node,l,nd_tracelist);
+		 nd_tracelist = node;
+	 }
+     STOQ(i,iq);
+     nd_tracelist = reverse_node(nd_tracelist);
+     MKLIST(l,nd_tracelist);
+     node = mknode(2,iq,l); MKLIST(l,node);
+     MKNODE(node,l,nd_alltracelist); MKLIST(l,node);
+     nd_alltracelist = node; nd_tracelist = 0;
+}
+
+void conv_ilist(int demand,int trace,NODE g,int **indp)
+{
+    int n,i,j;
+	int *ind;
+	NODE t;
+
+    n = length(g);
+	ind = (int *)MALLOC(n*sizeof(int));
+	for ( i = 0, t = g; i < n; i++, t = NEXT(t) ) {
+		j = (long)BDY(t); ind[i] = j;
+		BDY(t) = (pointer)(demand?ndv_load(j):(trace?nd_ps_trace[j]:nd_ps[j]));
 	}
+	if ( indp ) *indp = ind;
 }
 
+void parse_nd_option(NODE opt)
+{
+    NODE t,p,u;
+	int i,s;
+    char *key;
+    Obj value;
+
+    nd_gentrace = 0; nd_gensyz = 0; nd_nora = 0; nd_gbblock = 0;
+	nd_newelim = 0; nd_intersect = 0;
+    for ( t = opt; t; t = NEXT(t) ) {
+        p = BDY((LIST)BDY(t));
+        key = BDY((STRING)BDY(p));
+        value = (Obj)BDY(NEXT(p));
+        if ( !strcmp(key,"gentrace") )
+            nd_gentrace = value?1:0;
+        else if ( !strcmp(key,"gensyz") )
+            nd_gensyz = value?1:0;
+        else if ( !strcmp(key,"nora") )
+            nd_nora = value?1:0;
+        else if ( !strcmp(key,"gbblock") ) {
+			if ( !value || OID(value) != O_LIST )
+				error("nd_* : invalid value for gbblock option");
+			u = BDY((LIST)value);
+            nd_gbblock = MALLOC((2*length(u)+1)*sizeof(int));
+			for ( i = 0; u; u = NEXT(u) ) {
+				p = BDY((LIST)BDY(u));
+				s = nd_gbblock[i++] = QTOS((Q)BDY(p));
+				nd_gbblock[i++] = s+QTOS((Q)BDY(NEXT(p)))-1;
+			}
+			nd_gbblock[i] = -1;
+		} else if ( !strcmp(key,"newelim") )
+            nd_newelim = value?1:0;
+		else if ( !strcmp(key,"intersect") )
+            nd_intersect = value?1:0;
+    }
+}