[BACK]Return to dist.c CVS log [TXT][DIR] Up to [local] / OpenXM_contrib2 / asir2018 / engine

File: [local] / OpenXM_contrib2 / asir2018 / engine / dist.c (download)

Revision 1.1, Wed Sep 19 05:45:07 2018 UTC (3 years, 9 months ago) by noro
Branch: MAIN

Added asir2018 for implementing full-gmp asir.

/*
 * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED 
 * All rights reserved.
 * 
 * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
 * non-exclusive and royalty-free license to use, copy, modify and
 * redistribute, solely for non-commercial and non-profit purposes, the
 * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
 * conditions of this Agreement. For the avoidance of doubt, you acquire
 * only a limited right to use the SOFTWARE hereunder, and FLL or any
 * third party developer retains all rights, including but not limited to
 * copyrights, in and to the SOFTWARE.
 * 
 * (1) FLL does not grant you a license in any way for commercial
 * purposes. You may use the SOFTWARE only for non-commercial and
 * non-profit purposes only, such as academic, research and internal
 * business use.
 * (2) The SOFTWARE is protected by the Copyright Law of Japan and
 * international copyright treaties. If you make copies of the SOFTWARE,
 * with or without modification, as permitted hereunder, you shall affix
 * to all such copies of the SOFTWARE the above copyright notice.
 * (3) An explicit reference to this SOFTWARE and its copyright owner
 * shall be made on your publication or presentation in any form of the
 * results obtained by use of the SOFTWARE.
 * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
 * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
 * for such modification or the source code of the modified part of the
 * SOFTWARE.
 * 
 * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
 * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
 * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
 * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
 * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
 * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
 * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
 * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
 * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
 * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
 * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
 * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
 * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
 * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
 * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
 * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
 * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
 *
 * $OpenXM: OpenXM_contrib2/asir2018/engine/dist.c,v 1.1 2018/09/19 05:45:07 noro Exp $
*/
#include "ca.h"

#define ORD_REVGRADLEX 0
#define ORD_GRADLEX 1
#define ORD_LEX 2
#define ORD_BREVGRADLEX 3
#define ORD_BGRADLEX 4
#define ORD_BLEX 5
#define ORD_BREVREV 6
#define ORD_BGRADREV 7
#define ORD_BLEXREV 8
#define ORD_ELIM 9
#define ORD_WEYL_ELIM 10
#define ORD_HOMO_WW_DRL 11
#define ORD_DRL_ZIGZAG 12
#define ORD_HOMO_WW_DRL_ZIGZAG 13

int cmpdl_drl_zigzag(), cmpdl_homo_ww_drl_zigzag();
int cmpdl_top_weight();

int (*cmpdl)()=cmpdl_revgradlex;
int (*cmpdl_tie_breaker)();
int (*primitive_cmpdl[3])() = {cmpdl_revgradlex,cmpdl_gradlex,cmpdl_lex};

Obj current_top_weight;
int current_top_weight_len;

int do_weyl;

int dp_nelim,dp_fcoeffs;
struct order_spec *dp_current_spec;
struct modorder_spec *dp_current_modspec;
int *dp_dl_work;

void comm_muld_trunc(VL vl,DP p1,DP p2,DL dl,DP *pr);
void comm_quod(VL vl,DP p1,DP p2,DP *pr);
void muldm_trunc(VL vl,DP p,MP m0,DL dl,DP *pr);
void muldc_trunc(VL vl,DP p,Obj c,DL dl,DP *pr);
int create_order_spec(VL vl,Obj obj,struct order_spec **specp);
void create_modorder_spec(int id,LIST shift,struct modorder_spec **s);

void order_init()
{
  struct order_spec *spec;

  create_order_spec(0,0,&spec);
  initd(spec);
  create_modorder_spec(0,0,&dp_current_modspec);
}

int has_sfcoef_p(Obj f);

int has_sfcoef(DP f)
{
  MP t;

  if ( !f )
    return 0;
  for ( t = BDY(f); t; t = NEXT(t) )
    if ( has_sfcoef_p(t->c) )
      break;
  return t ? 1 : 0;
}

int has_sfcoef_p(Obj f)
{
  DCP dc;

  if ( !f )
    return 0;
  else if ( NUM(f) )
    return (NID((Num)f) == N_GFS) ? 1 : 0;
  else if ( POLY(f) ) {
    for ( dc = DC((P)f); dc; dc = NEXT(dc) )
      if ( has_sfcoef_p((Obj)COEF(dc)) )
        return 1;
    return 0;
  } else
    return 0;
}

extern Obj nd_top_weight;

void reset_top_weight()
{
  cmpdl = cmpdl_tie_breaker;
  cmpdl_tie_breaker = 0;
  nd_top_weight = 0;
  current_top_weight = 0;
  current_top_weight_len = 0;
}

void initd(struct order_spec *spec)
{
  int len,i,k,row;
  Q **mat;

  switch ( spec->id ) {
    case 3:
      cmpdl = cmpdl_composite;
      dp_dl_work = (int *)MALLOC_ATOMIC(spec->nv*sizeof(int));  
      break;
    case 2:
      cmpdl = cmpdl_matrix;
      dp_dl_work = (int *)MALLOC_ATOMIC(spec->nv*sizeof(int));  
      break;
    case 1:
      cmpdl = cmpdl_order_pair;
      break;
    default:
      switch ( spec->ord.simple ) {
        case ORD_REVGRADLEX:
          cmpdl = cmpdl_revgradlex; break;
        case ORD_GRADLEX:
          cmpdl = cmpdl_gradlex; break;
        case ORD_BREVGRADLEX:
          cmpdl = cmpdl_brevgradlex; break;
        case ORD_BGRADLEX:
          cmpdl = cmpdl_bgradlex; break;
        case ORD_BLEX:
          cmpdl = cmpdl_blex; break;
        case ORD_BREVREV:
          cmpdl = cmpdl_brevrev; break;
        case ORD_BGRADREV:
          cmpdl = cmpdl_bgradrev; break;
        case ORD_BLEXREV:
          cmpdl = cmpdl_blexrev; break;
        case ORD_ELIM:
          cmpdl = cmpdl_elim; break;
        case ORD_WEYL_ELIM:
          cmpdl = cmpdl_weyl_elim; break;
        case ORD_HOMO_WW_DRL:
          cmpdl = cmpdl_homo_ww_drl; break;
        case ORD_DRL_ZIGZAG:
          cmpdl = cmpdl_drl_zigzag; break;
        case ORD_HOMO_WW_DRL_ZIGZAG:
          cmpdl = cmpdl_homo_ww_drl_zigzag; break;
        case ORD_LEX: default:
          cmpdl = cmpdl_lex; break;
      }
      break;
  }
  if ( current_top_weight ) {
    cmpdl_tie_breaker = cmpdl;
    cmpdl = cmpdl_top_weight;
    if ( OID(current_top_weight) == O_VECT ) {
       mat = (Q **)&BDY((VECT)current_top_weight);
       row = 1;
    } else {
       mat = (Q **)BDY((MAT)current_top_weight);
       row = ((MAT)current_top_weight)->row;
    }
    for ( k = 0, len = 0; k < row; k++ )
      for ( i = 0; i < spec->nv; i++ )
        if ( mat[k][i] )
          len = MAX(mpz_size(BDY((Z)mat[k][i])),len);
    current_top_weight_len = len;
  }
  dp_current_spec = spec;
}

int dpm_ispot;

/* type=0 => TOP, type=1 => POT */
void initdpm(struct order_spec *spec,int type)
{
  int len,i,k,row;
    Q **mat;

  initd(spec);
  dpm_ispot = type;
}

void ptod(VL vl,VL dvl,P p,DP *pr)
{
  int n,i,j,k;
  VL tvl;
  V v;
  DL d;
  MP m;
  DCP dc;
  DCP *w;
  DP r,s,t,u;
  P x,c;

  if ( !p )
    *pr = 0;
  else if ( OID(p) > O_P )
    error("ptod : only polynomials can be converted.");
  else {
    for ( n = 0, tvl = dvl; tvl; tvl = NEXT(tvl), n++ );
    if ( NUM(p) ) {
      NEWDL(d,n);
      NEWMP(m); m->dl = d; C(m) = (Obj)p; NEXT(m) = 0; MKDP(n,m,*pr); (*pr)->sugar = 0;
    } else {
      for ( i = 0, tvl = dvl, v = VR(p);
        tvl && tvl->v != v; tvl = NEXT(tvl), i++ );
      if ( !tvl ) {
        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 ( j = k-1, s = 0, MKV(v,x); j >= 0; j-- ) {
          ptod(vl,dvl,COEF(w[j]),&t); pwrp(vl,x,DEG(w[j]),&c);
          muldc(vl,t,(Obj)c,&r); addd(vl,r,s,&t); s = t;
        }
        *pr = s;
      } 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 ( j = k-1, s = 0; j >= 0; j-- ) {
          ptod(vl,dvl,COEF(w[j]),&t);
          NEWDL(d,n); d->d[i] = QTOS(DEG(w[j]));
          d->td = MUL_WEIGHT(d->d[i],i);
          NEWMP(m); m->dl = d; C(m) = (Obj)ONE; NEXT(m) = 0; MKDP(n,m,u); u->sugar = d->td;
          comm_muld(vl,t,u,&r); addd(vl,r,s,&t); s = t;
        }
        *pr = s;
      }
    }
  }
#if 0
  if ( !dp_fcoeffs && has_sfcoef(*pr) )
    dp_fcoeffs = N_GFS;
#endif
}

void dtop(VL vl,VL dvl,DP p,Obj *pr)
{
  int n,i,j,k;
  DL d;
  MP m;
  MP *a;
  P r;
  Obj t,w,s,u;
  Z q;
  VL tvl;

  if ( !p )
    *pr = 0;
  else {
    for ( k = 0, m = BDY(p); m; m = NEXT(m), k++ );
    a = (MP *)ALLOCA(k*sizeof(MP));
    for ( j = 0, m = BDY(p); j < k; m = NEXT(m), j++ )
      a[j] = m;

    for ( n = p->nv, j = k-1, s = 0; j >= 0; j-- ) {
      m = a[j];
      t = C(m);
      if ( NUM(t) && NID((Num)t) == N_M ) {
        mptop((P)t,(P *)&u); t = u;
      }
      for ( i = 0, d = m->dl, tvl = dvl;
        i < n; tvl = NEXT(tvl), i++ ) {
        MKV(tvl->v,r); STOQ(d->d[i],q); pwrp(vl,r,q,(P *)&u);
        arf_mul(vl,t,(Obj)u,&w); t = w;
      }
      arf_add(vl,s,t,&u); s = u;
    }
    *pr = s;
  }
}

void nodetod(NODE node,DP *dp)
{
  NODE t;
  int len,i,td;
  Q e;
  DL d;
  MP m;
  DP u;

  for ( t = node, len = 0; t; t = NEXT(t), len++ );
  NEWDL(d,len);
  for ( t = node, i = 0, td = 0; i < len; t = NEXT(t), i++ ) {
    e = (Q)BDY(t);
    if ( !e )
      d->d[i] = 0;
    else if ( !NUM(e) || !RATN(e) || !INT(e) )
      error("nodetod : invalid input");
    else {
      d->d[i] = QTOS((Q)e); td += MUL_WEIGHT(d->d[i],i);
    }
  }
  d->td = td;
  NEWMP(m); m->dl = d; C(m) = (Obj)ONE; NEXT(m) = 0;
  MKDP(len,m,u); u->sugar = td; *dp = u;
}

void nodetodpm(NODE node,Obj pos,DPM *dp)
{
  NODE t;
  int len,i,td;
  Q e;
  DL d;
  DMM m;
  DPM u;

  for ( t = node, len = 0; t; t = NEXT(t), len++ );
  NEWDL(d,len);
  for ( t = node, i = 0, td = 0; i < len; t = NEXT(t), i++ ) {
    e = (Q)BDY(t);
    if ( !e )
      d->d[i] = 0;
    else if ( !NUM(e) || !RATN(e) || !INT(e) )
      error("nodetodpm : invalid input");
    else {
      d->d[i] = QTOS((Q)e); td += MUL_WEIGHT(d->d[i],i);
    }
  }
  d->td = td;
  NEWDMM(m); m->dl = d; m->pos = QTOS((Q)pos); C(m) = (Obj)ONE; NEXT(m) = 0;
  MKDPM(len,m,u); u->sugar = td; *dp = u;
}

void dtodpm(DP d,int pos,DPM *dp)
{
  DMM mr0,mr;
  MP m;

  if ( !d ) *dp = 0;
  else {
    for ( m = BDY(d), mr0 = 0; m; m = NEXT(m) ) {
      NEXTDMM(mr0,mr);
      mr->dl = m->dl;
      mr->pos = pos;
      C(mr) = C(m);
    }
    MKDPM(d->nv,mr0,*dp); (*dp)->sugar = d->sugar;
  }
}

int sugard(MP m)
{
  int s;

  for ( s = 0; m; m = NEXT(m) )
    s = MAX(s,m->dl->td);
  return s;
}

void addd(VL vl,DP p1,DP p2,DP *pr)
{
  int n;
  MP m1,m2,mr=0,mr0;
  Obj t;
  DL d;

  if ( !p1 )
    *pr = p2;
  else if ( !p2 )
    *pr = p1;
  else {
    if ( OID(p1) <= O_R ) {
      n = NV(p2);  NEWDL(d,n);
      NEWMP(m1); m1->dl = d; C(m1) = (Obj)p1; NEXT(m1) = 0;
      MKDP(n,m1,p1); (p1)->sugar = 0;
    }
    if ( OID(p2) <= O_R ) {
      n = NV(p1);  NEWDL(d,n);
      NEWMP(m2); m2->dl = d; C(m2) = (Obj)p2; NEXT(m2) = 0;
      MKDP(n,m2,p2); (p2)->sugar = 0;
    }
    for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; )
      switch ( (*cmpdl)(n,m1->dl,m2->dl) ) {
        case 0:
          arf_add(vl,C(m1),C(m2),&t);
          if ( t ) {
            NEXTMP(mr0,mr); mr->dl = m1->dl; C(mr) = t;
          }
          m1 = NEXT(m1); m2 = NEXT(m2); break;
        case 1:
          NEXTMP(mr0,mr); mr->dl = m1->dl; C(mr) = C(m1);
          m1 = NEXT(m1); break;
        case -1:
          NEXTMP(mr0,mr); mr->dl = m2->dl; C(mr) = C(m2);
          m2 = NEXT(m2); break;
      }
    if ( !mr0 )
      if ( m1 )
        mr0 = m1;
      else if ( m2 )
        mr0 = m2;
      else {
        *pr = 0;
        return;
      }
    else if ( m1 )
      NEXT(mr) = m1;
    else if ( m2 )
      NEXT(mr) = m2;
    else
      NEXT(mr) = 0;
    MKDP(NV(p1),mr0,*pr);
    if ( *pr )
      (*pr)->sugar = MAX(p1->sugar,p2->sugar);
  }
}

/* for F4 symbolic reduction */

void symb_addd(DP p1,DP p2,DP *pr)
{
  int n;
  MP m1,m2,mr=0,mr0;

  if ( !p1 )
    *pr = p2;
  else if ( !p2 )
    *pr = p1;
  else {
    for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
      NEXTMP(mr0,mr); C(mr) = (Obj)ONE;
      switch ( (*cmpdl)(n,m1->dl,m2->dl) ) {
        case 0:
          mr->dl = m1->dl;
          m1 = NEXT(m1); m2 = NEXT(m2); break;
        case 1:
          mr->dl = m1->dl;
          m1 = NEXT(m1); break;
        case -1:
          mr->dl = m2->dl;
          m2 = NEXT(m2); break;
      }
    }
    if ( !mr0 )
      if ( m1 )
        mr0 = m1;
      else if ( m2 )
        mr0 = m2;
      else {
        *pr = 0;
        return;
      }
    else if ( m1 )
      NEXT(mr) = m1;
    else if ( m2 )
      NEXT(mr) = m2;
    else
      NEXT(mr) = 0;
    MKDP(NV(p1),mr0,*pr);
    if ( *pr )
      (*pr)->sugar = MAX(p1->sugar,p2->sugar);
  }
}

/* 
 * destructive merge of two list
 *
 * p1, p2 : list of DL
 * return : a merged list
 */

NODE symb_merge(NODE m1,NODE m2,int n)
{
  NODE top=0,prev,cur,m=0,t;
  DL d1,d2;

  if ( !m1 )
    return m2;
  else if ( !m2 )
    return m1;
  else {
    switch ( (*cmpdl)(n,(DL)BDY(m1),(DL)BDY(m2)) ) {
      case 0:
        top = m1; m = NEXT(m2);
        break;
      case 1:
        top = m1; m = m2;
        break;
      case -1:
        top = m2; m = m1;
        break;
    }
    prev = top; cur = NEXT(top);
    /* BDY(prev) > BDY(m) always holds */
    while ( cur && m ) {
      d1 = (DL)BDY(cur);
      d2 = (DL)BDY(m);
#if 1
      switch ( (*cmpdl)(n,(DL)BDY(cur),(DL)BDY(m)) ) {
#else
      /* XXX only valid for DRL */
      if ( d1->td > d2->td )
        c = 1;
      else if ( d1->td < d2->td )
        c = -1;
      else {
        for ( i = n-1; i >= 0 && d1->d[i] == d2->d[i]; i-- );
        if ( i < 0 )
          c = 0;
        else if ( d1->d[i] < d2->d[i] )
          c = 1;
        else
          c = -1;
      }
      switch ( c ) {
#endif
        case 0:
          m = NEXT(m);
          prev = cur; cur = NEXT(cur);
          break;
        case 1:
          t = NEXT(cur); NEXT(cur) = m; m = t;
          prev = cur; cur = NEXT(cur);
          break;
        case -1:
          NEXT(prev) = m; m = cur;
          prev = NEXT(prev); cur = NEXT(prev);
          break;
      }
    }
    if ( !cur )
      NEXT(prev) = m;
    return top;
  }
}

void _adddl(int n,DL d1,DL d2,DL d3)
{
  int i;

  d3->td = d1->td+d2->td;
  for ( i = 0; i < n; i++ )
    d3->d[i] = d1->d[i]+d2->d[i];
}

/* m1 <- m1 U dl*f, destructive */

NODE mul_dllist(DL dl,DP f);

NODE symb_mul_merge(NODE m1,DL dl,DP f,int n)
{
  NODE top,prev,cur,n1;
  DP g;
  DL t,s;
  MP m;

  if ( !m1 )
    return mul_dllist(dl,f);
  else if ( !f )
    return m1;
  else {
    m = BDY(f);
    NEWDL_NOINIT(t,n);
    _adddl(n,m->dl,dl,t);
    top = m1; prev = 0; cur = m1;
    while ( m ) {
      switch ( (*cmpdl)(n,(DL)BDY(cur),t) ) {
        case 0:
          prev = cur; cur = NEXT(cur);
          if ( !cur ) {
            MKDP(n,m,g);
            NEXT(prev) = mul_dllist(dl,g);
            return top;
          }
          m = NEXT(m);
          if ( m ) _adddl(n,m->dl,dl,t);
          break;
        case 1:
          prev = cur; cur = NEXT(cur); 
          if ( !cur ) {
            MKDP(n,m,g);
            NEXT(prev) = mul_dllist(dl,g);
            return top;
          }
          break;
        case -1:
          NEWDL_NOINIT(s,n);
          s->td = t->td;
          bcopy(t->d,s->d,n*sizeof(int));
          NEWNODE(n1);
          n1->body = (pointer)s;
          NEXT(n1) = cur;
          if ( !prev ) {
            top = n1; cur = n1;
          } else {
            NEXT(prev) = n1; prev = n1;
          }
          m = NEXT(m);
          if ( m ) _adddl(n,m->dl,dl,t);
          break;
      }
    }
    return top;
  }
}

DLBUCKET symb_merge_bucket(DLBUCKET m1,DLBUCKET m2,int n)
{
  DLBUCKET top,prev,cur,m,t;

  if ( !m1 )
    return m2;
  else if ( !m2 )
    return m1;
  else {
    if ( m1->td == m2->td ) {
      top = m1;
      BDY(top) = symb_merge(BDY(top),BDY(m2),n);
      m = NEXT(m2);
    } else if ( m1->td > m2->td ) {
      top = m1; m = m2;
    } else {
      top = m2; m = m1;
    }
    prev = top; cur = NEXT(top);
    /* prev->td > m->td always holds */
    while ( cur && m ) {
      if ( cur->td == m->td ) {
        BDY(cur) = symb_merge(BDY(cur),BDY(m),n);
        m = NEXT(m);
        prev = cur; cur = NEXT(cur);
      } else if ( cur->td > m->td ) {
        t = NEXT(cur); NEXT(cur) = m; m = t;
        prev = cur; cur = NEXT(cur);
      } else {
        NEXT(prev) = m; m = cur;
        prev = NEXT(prev); cur = NEXT(prev);
      }
    }
    if ( !cur )
      NEXT(prev) = m;
    return top;
  }
}

void subd(VL vl,DP p1,DP p2,DP *pr)
{
  DP t;

  if ( !p2 )
    *pr = p1;
  else {
    chsgnd(p2,&t); addd(vl,p1,t,pr);
  }
}

void chsgnd(DP p,DP *pr)
{
  MP m,mr=0,mr0;
  Obj r;

  if ( !p )
    *pr = 0;
  else if ( OID(p) <= O_R ) {
    arf_chsgn((Obj)p,&r); *pr = (DP)r;
  } else {
    for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
      NEXTMP(mr0,mr); arf_chsgn(C(m),&C(mr)); mr->dl = m->dl;
    }
    NEXT(mr) = 0; MKDP(NV(p),mr0,*pr);
    if ( *pr )
      (*pr)->sugar = p->sugar;
  }
}

void muld(VL vl,DP p1,DP p2,DP *pr)
{
  if ( ! do_weyl )
    comm_muld(vl,p1,p2,pr);
  else
    weyl_muld(vl,p1,p2,pr);
}

void comm_muld(VL vl,DP p1,DP p2,DP *pr)
{
  MP m;
  DP s,t,u;
  int i,l,l1;
  static MP *w;
  static int wlen;

  if ( !p1 || !p2 )
    *pr = 0;
  else if ( OID(p1) != O_DP )
    muldc(vl,p2,(Obj)p1,pr);
  else if ( OID(p2) != O_DP )
    muldc(vl,p1,(Obj)p2,pr);
  else {
    for ( m = BDY(p1), l1 = 0; m; m = NEXT(m), l1++ );
    for ( m = BDY(p2), l = 0; m; m = NEXT(m), l++ );
    if ( l1 < l ) {
      t = p1; p1 = p2; p2 = t;
      l = l1;
    }
    if ( l > wlen ) {
      if ( w ) GCFREE(w);
      w = (MP *)MALLOC(l*sizeof(MP));
      wlen = l;
    }
    for ( m = BDY(p2), i = 0; i < l; m = NEXT(m), i++ )
      w[i] = m;
    for ( s = 0, i = l-1; i >= 0; i-- ) {
      muldm(vl,p1,w[i],&t); addd(vl,s,t,&u); s = u;
    }
    bzero(w,l*sizeof(MP));
    *pr = s;
  }
}

/* discard terms which is not a multiple of dl */

void comm_muld_trunc(VL vl,DP p1,DP p2,DL dl,DP *pr)
{
  MP m;
  DP s,t,u;
  int i,l,l1;
  static MP *w;
  static int wlen;

  if ( !p1 || !p2 )
    *pr = 0;
  else if ( OID(p1) != O_DP )
    muldc_trunc(vl,p2,(Obj)p1,dl,pr);
  else if ( OID(p2) != O_DP )
    muldc_trunc(vl,p1,(Obj)p2,dl,pr);
  else {
    for ( m = BDY(p1), l1 = 0; m; m = NEXT(m), l1++ );
    for ( m = BDY(p2), l = 0; m; m = NEXT(m), l++ );
    if ( l1 < l ) {
      t = p1; p1 = p2; p2 = t;
      l = l1;
    }
    if ( l > wlen ) {
      if ( w ) GCFREE(w);
      w = (MP *)MALLOC(l*sizeof(MP));
      wlen = l;
    }
    for ( m = BDY(p2), i = 0; i < l; m = NEXT(m), i++ )
      w[i] = m;
    for ( s = 0, i = l-1; i >= 0; i-- ) {
      muldm_trunc(vl,p1,w[i],dl,&t); addd(vl,s,t,&u); s = u;
    }
    bzero(w,l*sizeof(MP));
    *pr = s;
  }
}

void comm_quod(VL vl,DP p1,DP p2,DP *pr)
{
  MP m=0,m0;
  DP s,t;
  int i,n,sugar;
  DL d1,d2,d;
  Q a,b;

  if ( !p2 )
    error("comm_quod : invalid input");
  if ( !p1 )
    *pr = 0;
  else {
    n = NV(p1);
    d2 = BDY(p2)->dl;
    m0 = 0;
    sugar = p1->sugar;
    while ( p1 ) {
      d1 = BDY(p1)->dl;
      NEWDL(d,n);
      d->td = d1->td - d2->td;
      for ( i = 0; i < n; i++ )
        d->d[i] = d1->d[i]-d2->d[i];
      NEXTMP(m0,m);
      m->dl = d;
      divq((Q)BDY(p1)->c,(Q)BDY(p2)->c,&a); chsgnq(a,&b);
      C(m) = (Obj)b;
      muldm_trunc(vl,p2,m,d2,&t);
      addd(vl,p1,t,&s); p1 = s;
      C(m) = (Obj)a;
    }
    if ( m0 ) {
      NEXT(m) = 0; MKDP(n,m0,*pr);
    } else
      *pr = 0;
    /* XXX */
    if ( *pr )
      (*pr)->sugar = sugar - d2->td;
  }
}

void muldm(VL vl,DP p,MP m0,DP *pr)
{
  MP m,mr=0,mr0;
  Obj c;
  DL d;
  int n;

  if ( !p )
    *pr = 0;
  else {
    for ( mr0 = 0, m = BDY(p), c = C(m0), d = m0->dl, n = NV(p); 
      m; m = NEXT(m) ) {
      NEXTMP(mr0,mr);
      if ( NUM(C(m)) && RATN(C(m)) && NUM(c) && RATN(c) )
        mulq((Q)C(m),(Q)c,(Q *)&C(mr));
      else
        arf_mul(vl,C(m),c,&C(mr));
      adddl(n,m->dl,d,&mr->dl);
    }
    NEXT(mr) = 0; MKDP(NV(p),mr0,*pr);
    if ( *pr )
      (*pr)->sugar = p->sugar + m0->dl->td;
  }
}

void muldm_trunc(VL vl,DP p,MP m0,DL dl,DP *pr)
{
  MP m,mr=0,mr0;
  Obj c;
  DL d,tdl;
  int n,i;

  if ( !p )
    *pr = 0;
  else {
    n = NV(p);
    NEWDL(tdl,n);
    for ( mr0 = 0, m = BDY(p), c = C(m0), d = m0->dl; 
      m; m = NEXT(m) ) {
      _adddl(n,m->dl,d,tdl);
      for ( i = 0; i < n; i++ )
        if ( tdl->d[i] < dl->d[i] )
          break;
      if ( i < n )
        continue;
      NEXTMP(mr0,mr);
      mr->dl = tdl;
      NEWDL(tdl,n);
      if ( NUM(C(m)) && RATN(C(m)) && NUM(c) && RATN(c) )
        mulq((Q)C(m),(Q)c,(Q *)&C(mr));
      else
        arf_mul(vl,C(m),(Obj)c,&C(mr));
    }
    if ( mr0 ) {
      NEXT(mr) = 0; MKDP(NV(p),mr0,*pr);
    } else
      *pr = 0;
    if ( *pr )
      (*pr)->sugar = p->sugar + m0->dl->td;
  }
}

void weyl_muld(VL vl,DP p1,DP p2,DP *pr)
{
  MP m;
  DP s,t,u;
  int i,l;
  static MP *w;
  static int wlen;

  if ( !p1 || !p2 )
    *pr = 0;
  else if ( OID(p1) != O_DP )
    muldc(vl,p2,(Obj)p1,pr);
  else if ( OID(p2) != O_DP )
    muldc(vl,p1,(Obj)p2,pr);
  else {
    for ( m = BDY(p1), l = 0; m; m = NEXT(m), l++ );
    if ( l > wlen ) {
      if ( w ) GCFREE(w);
      w = (MP *)MALLOC(l*sizeof(MP));
      wlen = l;
    }
    for ( m = BDY(p1), i = 0; i < l; m = NEXT(m), i++ )
      w[i] = m;
    for ( s = 0, i = l-1; i >= 0; i-- ) {
      weyl_muldm(vl,w[i],p2,&t); addd(vl,s,t,&u); s = u;
    }
    bzero(w,l*sizeof(MP));
    *pr = s;
  }
}

void actm(VL vl,int nv,MP m1,MP m2,DP *pr)
{
  DL d1,d2,d;
  int n2,i,j,k;
  Z jq,c,c1;
  MP m;
  Obj t;

  d1 = m1->dl;
  d2 = m2->dl;
  for ( i = 0; i < nv; i++ )
    if ( d1->d[i] > d2->d[i] ) {
      *pr = 0; return;
    }
  NEWDL(d,nv);
  c = ONE;
  for ( i = 0; i < nv; i++ ) {
    for ( j = d2->d[i], k = d1->d[i]; k > 0; k--, j-- ) {
      STOQ(j,jq); mulz(c,jq,&c1); c = c1;
    }
    d->d[i] = d2->d[i]-d1->d[i];
  }
  arf_mul(vl,C(m1),C(m2),&t);
  NEWMP(m);
  arf_mul(vl,(Obj)c,t,&C(m));
  m->dl = d;
  MKDP(nv,m,*pr);
}

void weyl_actd(VL vl,DP p1,DP p2,DP *pr)
{
  int n;
  MP m1,m2;
  DP d,r,s;

  if ( !p1 || !p2 ) *pr = 0;
  else {
    n = NV(p1);
    r = 0;
    for ( m1 = BDY(p1); m1; m1 = NEXT(m1) )
      for ( m2 = BDY(p2); m2; m2 = NEXT(m2) ) {
        actm(vl,n,m1,m2,&d);
        addd(vl,r,d,&s); r = s;
      }
    *pr = r;
  }
}

/* monomial * polynomial */

void weyl_muldm(VL vl,MP m0,DP p,DP *pr)
{
  DP r,t,t1;
  MP m;
  DL d0;
  int n,n2,l,i,j,tlen;
  static MP *w,*psum;
  static struct cdl *tab;
  static int wlen;
  static int rtlen;

  if ( !p )
    *pr = 0;
  else {
    for ( m = BDY(p), l = 0; m; m = NEXT(m), l++ );
    if ( l > wlen ) {
      if ( w ) GCFREE(w);
      w = (MP *)MALLOC(l*sizeof(MP));
      wlen = l;
    }
    for ( m = BDY(p), i = 0; i < l; m = NEXT(m), i++ )
      w[i] = m;

    n = NV(p); n2 = n>>1;
    d0 = m0->dl;
    for ( i = 0, tlen = 1; i < n2; i++ )
      tlen *= d0->d[n2+i]+1;
    if ( tlen > rtlen ) {
      if ( tab ) GCFREE(tab);
      if ( psum ) GCFREE(psum);
      rtlen = tlen;
      tab = (struct cdl *)MALLOC(rtlen*sizeof(struct cdl));
      psum = (MP *)MALLOC(rtlen*sizeof(MP));
    }
    bzero(psum,tlen*sizeof(MP));
    for ( i = l-1; i >= 0; i-- ) {
      bzero(tab,tlen*sizeof(struct cdl));
      weyl_mulmm(vl,m0,w[i],n,tab,tlen);
      for ( j = 0; j < tlen; j++ ) {
        if ( tab[j].c ) {
          NEWMP(m); m->dl = tab[j].d; C(m) = (Obj)tab[j].c; NEXT(m) = psum[j];
          psum[j] = m;
        }
      }
    }
    for ( j = tlen-1, r = 0; j >= 0; j-- ) 
      if ( psum[j] ) {
        MKDP(n,psum[j],t); addd(vl,r,t,&t1); r = t1;
      }
    if ( r )
      r->sugar = p->sugar + m0->dl->td;
    *pr = r;
  }
}

/* m0 = x0^d0*x1^d1*... * dx0^e0*dx1^e1*... */
/* rtab : array of length (e0+1)*(e1+1)*... */

void weyl_mulmm(VL vl,MP m0,MP m1,int n,struct cdl *rtab,int rtablen)
{
  Obj c,c0,c1;
  DL d,d0,d1,dt;
  int i,j,a,b,k,l,n2,s,min,curlen;
  struct cdl *p;
  static Z *ctab;
  static struct cdl *tab;
  static int tablen;
  static struct cdl *tmptab;
  static int tmptablen;

  
  if ( !m0 || !m1 ) {
    rtab[0].c = 0;
    rtab[0].d = 0;
    return;
  }
  c0 = C(m0); c1 = C(m1);
  arf_mul(vl,c0,c1,&c);
  d0 = m0->dl; d1 = m1->dl;
  n2 = n>>1;
  curlen = 1;
  NEWDL(d,n);
  if ( n & 1 )
    /* offset of h-degree */
     d->td = d->d[n-1] = d0->d[n-1]+d1->d[n-1];
  else
    d->td = 0;
  rtab[0].c = c;
  rtab[0].d = d;

  if ( rtablen > tmptablen ) {
    if ( tmptab ) GCFREE(tmptab);
    tmptab = (struct cdl *)MALLOC(rtablen*sizeof(struct cdl));
    tmptablen = rtablen;
  }
  for ( i = 0; i < n2; i++ ) {
    a = d0->d[i]; b = d1->d[n2+i];
    k = d0->d[n2+i]; l = d1->d[i];

    /* degree of 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, p = rtab; j < curlen; j++, p++ ) {
        if ( p->c ) {
          dt = p->d;
          dt->d[i] = a;
          dt->d[n2+i] = b;
          dt->td += s;
        }
      }
      curlen *= k+1;
      continue;
    }
    if ( k+1 > tablen ) {
      if ( tab ) GCFREE(tab);
      if ( ctab ) GCFREE(ctab);
      tablen = k+1;
      tab = (struct cdl *)MALLOC(tablen*sizeof(struct cdl));
      ctab = (Z *)MALLOC(tablen*sizeof(Q));
    }
    /* compute xi^a*(Di^k*xi^l)*Di^b */
    min = MIN(k,l);
    mkwc(k,l,ctab);
    bzero(tab,(k+1)*sizeof(struct cdl));
    if ( n & 1 )
      for ( j = 0; j <= min; j++ ) {
        NEWDL(d,n);
        d->d[i] = a-j; d->d[n2+i] = b-j;
        d->td = s;
        d->d[n-1] = s-(MUL_WEIGHT(a-j,i)+MUL_WEIGHT(b-j,n2+i));
        tab[j].d = d;
        tab[j].c = (Obj)ctab[j];
      }
    else
      for ( j = 0; j <= min; j++ ) {
        NEWDL(d,n);
        d->d[i] = a-j; d->d[n2+i] = b-j;
        d->td = MUL_WEIGHT(a-j,i)+MUL_WEIGHT(b-j,n2+i); /* XXX */
        tab[j].d = d;
        tab[j].c = (Obj)ctab[j];
      }
    bzero(ctab,(min+1)*sizeof(Q));
    comm_muld_tab(vl,n,rtab,curlen,tab,k+1,tmptab);
    curlen *= k+1;
    bcopy(tmptab,rtab,curlen*sizeof(struct cdl));
  }
}

/* direct product of two cdl tables
  rt[] = [
    t[0]*t1[0],...,t[n-1]*t1[0],
    t[0]*t1[1],...,t[n-1]*t1[1],
    ...
    t[0]*t1[n1-1],...,t[n-1]*t1[n1-1]
  ]
*/

void comm_muld_tab(VL vl,int nv,struct cdl *t,int n,struct cdl *t1,int n1,struct cdl *rt)
{
  int i,j;
  struct cdl *p;
  Obj c;
  DL d;

  bzero(rt,n*n1*sizeof(struct cdl));
  for ( j = 0, p = rt; j < n1; j++ ) {
    c = (Obj)t1[j].c;
    d = t1[j].d;
    if ( !c )
      break;
    for ( i = 0; i < n; i++, p++ ) {
      if ( t[i].c ) {
        arf_mul(vl,(Obj)t[i].c,c,(Obj *)&p->c);
        adddl(nv,t[i].d,d,&p->d);
      }
    }
  }
}

void muldc(VL vl,DP p,Obj c,DP *pr)
{
  MP m,mr=0,mr0;

  if ( !p || !c )
    *pr = 0;
  else if ( NUM(c) && UNIQ((Q)c) )
    *pr = p;
  else if ( NUM(c) && MUNIQ((Q)c) )
    chsgnd(p,pr);
  else {
    for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
      NEXTMP(mr0,mr);
      if ( NUM(C(m)) && RATN(C(m)) && NUM(c) && RATN(c) )
        mulq((Q)C(m),(Q)c,(Q *)&C(mr));
      else
        arf_mul(vl,C(m),c,&C(mr));
      mr->dl = m->dl;
    }
    NEXT(mr) = 0; MKDP(NV(p),mr0,*pr);
    if ( *pr )
      (*pr)->sugar = p->sugar;
  }
}

void divdc(VL vl,DP p,Obj c,DP *pr)
{
  Obj inv;

  arf_div(vl,(Obj)ONE,c,&inv);
  muld(vl,p,(DP)inv,pr);
}

void muldc_trunc(VL vl,DP p,Obj c,DL dl,DP *pr)
{
  MP m,mr=0,mr0;
  DL mdl;
  int i,n;

  if ( !p || !c ) {
    *pr = 0; return;
  }
  n = NV(p);
  for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
    mdl = m->dl;
    for ( i = 0; i < n; i++ )
      if ( mdl->d[i] < dl->d[i] )
        break;
    if ( i < n )
      break;
    NEXTMP(mr0,mr);
    if ( NUM(C(m)) && RATN(C(m)) && NUM(c) && RATN(c) )
      mulq((Q)C(m),(Q)c,(Q *)&C(mr));
    else
      arf_mul(vl,C(m),c,&C(mr));
    mr->dl = m->dl;
  }
  NEXT(mr) = 0; MKDP(NV(p),mr0,*pr);
  if ( *pr )
    (*pr)->sugar = p->sugar;
}

void divsdc(VL vl,DP p,P c,DP *pr)
{
  MP m,mr=0,mr0;

  if ( !c )
    error("disvsdc : division by 0");
  else if ( !p )
    *pr = 0;
  else if ( OID(c) > O_P )
    error("divsdc : invalid argument");
  else {
    for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
      NEXTMP(mr0,mr); divsp(vl,(P)C(m),c,(P *)&C(mr)); mr->dl = m->dl;
    }
    NEXT(mr) = 0; MKDP(NV(p),mr0,*pr);
    if ( *pr )
      (*pr)->sugar = p->sugar;
  }
}

void adddl(int n,DL d1,DL d2,DL *dr)
{
  DL dt;
  int i;

  *dr = dt = (DL)MALLOC_ATOMIC((n+1)*sizeof(int));
  dt->td = d1->td + d2->td;
  for ( i = 0; i < n; i++ )
    dt->d[i] = d1->d[i]+d2->d[i];
}

/* d1 += d2 */

void adddl_destructive(int n,DL d1,DL d2)
{
  int i;

  d1->td += d2->td;
  for ( i = 0; i < n; i++ )
    d1->d[i] += d2->d[i];
}

int compd(VL vl,DP p1,DP p2)
{
  int n,t;
  MP m1,m2;

  if ( !p1 )
    return p2 ? -1 : 0;
  else if ( !p2 )
    return 1;
  else if ( NV(p1) != NV(p2) ) {
    error("compd : size mismatch");
    return 0; /* XXX */
  } else {
    for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2);
      m1 && m2; m1 = NEXT(m1), m2 = NEXT(m2) )
      if ( (t = (*cmpdl)(n,m1->dl,m2->dl)) ||
        (t = arf_comp(vl,C(m1),C(m2)) ) )
        return t;
    if ( m1 )
      return 1;
    else if ( m2 )
      return -1;
    else
      return 0;
  }
}

int cmpdl_lex(int n,DL d1,DL d2)
{
  int i;

  for ( i = 0; i < n && d1->d[i] == d2->d[i]; i++ );
  return i == n ? 0 : (d1->d[i] > d2->d[i] ? 1 : -1);
}

int cmpdl_revlex(int n,DL d1,DL d2)
{
  int i;

  for ( i = n - 1; i >= 0 && d1->d[i] == d2->d[i]; i-- );
  return i < 0 ? 0 : (d1->d[i] < d2->d[i] ? 1 : -1);
}

int cmpdl_gradlex(int n,DL d1,DL d2)
{
  if ( d1->td > d2->td )
    return 1;
  else if ( d1->td < d2->td )
    return -1;
  else
    return cmpdl_lex(n,d1,d2);
}

int cmpdl_revgradlex(int n,DL d1,DL d2)
{
  register int i,c;
  register int *p1,*p2;

  if ( d1->td > d2->td )
    return 1;
  else if ( d1->td < d2->td )
    return -1;
  else {
    i = n-1;
    p1 = d1->d+n-1;
    p2 = d2->d+n-1;
    while ( i >= 7 ) {
      c = (*p1--) - (*p2--); if ( c ) goto LAST;
      c = (*p1--) - (*p2--); if ( c ) goto LAST;
      c = (*p1--) - (*p2--); if ( c ) goto LAST;
      c = (*p1--) - (*p2--); if ( c ) goto LAST;
      c = (*p1--) - (*p2--); if ( c ) goto LAST;
      c = (*p1--) - (*p2--); if ( c ) goto LAST;
      c = (*p1--) - (*p2--); if ( c ) goto LAST;
      c = (*p1--) - (*p2--); if ( c ) goto LAST;
      i -= 8;
    }
    switch ( i ) {
      case 6:
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        return 0;
      case 5:
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        return 0;
      case 4:
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        return 0;
      case 3:
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        return 0;
      case 2:
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        return 0;
      case 1:
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        return 0;
      case 0:
        c = (*p1--) - (*p2--); if ( c ) goto LAST;
        return 0;
      default:
        return 0;
    }
LAST:
    if ( c > 0 ) return -1;
    else return 1;
  }
}

int cmpdl_blex(int n,DL d1,DL d2)
{
  int c;

  if ( (c = cmpdl_lex(n-1,d1,d2)) )
    return c;
  else {
    c = d1->d[n-1] - d2->d[n-1];
    return c > 0 ? 1 : c < 0 ? -1 : 0;
  }
}

int cmpdl_bgradlex(int n,DL d1,DL d2)
{
  int e1,e2,c;

  e1 = d1->td - d1->d[n-1]; e2 = d2->td - d2->d[n-1];
  if ( e1 > e2 )
    return 1;
  else if ( e1 < e2 )
    return -1;
  else {
    c = cmpdl_lex(n-1,d1,d2);
    if ( c )
      return c;
    else
      return d1->td > d2->td ? 1 : d1->td < d2->td ? -1 : 0;
  }
}

int cmpdl_brevgradlex(int n,DL d1,DL d2)
{
  int e1,e2,c;

  e1 = d1->td - d1->d[n-1]; e2 = d2->td - d2->d[n-1];
  if ( e1 > e2 )
    return 1;
  else if ( e1 < e2 )
    return -1;
  else {
    c = cmpdl_revlex(n-1,d1,d2);
    if ( c )
      return c;
    else
      return d1->td > d2->td ? 1 : d1->td < d2->td ? -1 : 0;
  }
}

int cmpdl_brevrev(int n,DL d1,DL d2)
{
  int e1,e2,f1,f2,c,i;

  for ( i = 0, e1 = 0, e2 = 0; i < dp_nelim; i++ ) {
    e1 += d1->d[i]; e2 += d2->d[i];
  }
  f1 = d1->td - e1; f2 = d2->td - e2;
  if ( e1 > e2 )
    return 1;
  else if ( e1 < e2 )
    return -1;
  else {
    c = cmpdl_revlex(dp_nelim,d1,d2);
    if ( c )
      return c;
    else if ( f1 > f2 )
      return 1;
    else if ( f1 < f2 )
      return -1;
    else {
      for ( i = n - 1; i >= dp_nelim && d1->d[i] == d2->d[i]; i-- );
      return i < dp_nelim ? 0 : (d1->d[i] < d2->d[i] ? 1 : -1);
    }
  }
}

int cmpdl_bgradrev(int n,DL d1,DL d2)
{
  int e1,e2,f1,f2,c,i;

  for ( i = 0, e1 = 0, e2 = 0; i < dp_nelim; i++ ) {
    e1 += d1->d[i]; e2 += d2->d[i];
  }
  f1 = d1->td - e1; f2 = d2->td - e2;
  if ( e1 > e2 )
    return 1;
  else if ( e1 < e2 )
    return -1;
  else {
    c = cmpdl_lex(dp_nelim,d1,d2);
    if ( c )
      return c;
    else if ( f1 > f2 )
      return 1;
    else if ( f1 < f2 )
      return -1;
    else {
      for ( i = n - 1; i >= dp_nelim && d1->d[i] == d2->d[i]; i-- );
      return i < dp_nelim ? 0 : (d1->d[i] < d2->d[i] ? 1 : -1);
    }
  }
}

int cmpdl_blexrev(int n,DL d1,DL d2)
{
  int e1,e2,f1,f2,c,i;

  for ( i = 0, e1 = 0, e2 = 0; i < dp_nelim; i++ ) {
    e1 += d1->d[i]; e2 += d2->d[i];
  }
  f1 = d1->td - e1; f2 = d2->td - e2;
  c = cmpdl_lex(dp_nelim,d1,d2);
  if ( c )
    return c;
  else if ( f1 > f2 )
    return 1;
  else if ( f1 < f2 )
    return -1;
  else {
    for ( i = n - 1; i >= dp_nelim && d1->d[i] == d2->d[i]; i-- );
    return i < dp_nelim ? 0 : (d1->d[i] < d2->d[i] ? 1 : -1);
  }
}

int cmpdl_elim(int n,DL d1,DL d2)
{
  int e1,e2,i;

  for ( i = 0, e1 = 0, e2 = 0; i < dp_nelim; i++ ) {
    e1 += d1->d[i]; e2 += d2->d[i];
  }
  if ( e1 > e2 )
    return 1;
  else if ( e1 < e2 )
    return -1;
  else 
    return cmpdl_revgradlex(n,d1,d2);
}

int cmpdl_weyl_elim(int n,DL d1,DL d2)
{
  int e1,e2,i;

  for ( i = 1, e1 = 0, e2 = 0; i <= dp_nelim; i++ ) {
    e1 += d1->d[n-i]; e2 += d2->d[n-i];
  }
  if ( e1 > e2 )
    return 1;
  else if ( e1 < e2 )
    return -1;
  else if ( d1->td > d2->td )
    return 1;
  else if ( d1->td < d2->td )
    return -1;
  else return -cmpdl_revlex(n,d1,d2);
}

/*
  a special ordering
  1. total order
  2. (-w,w) for the first 2*m variables
  3. DRL for the first 2*m variables
*/

extern int *current_weyl_weight_vector;

int cmpdl_homo_ww_drl(int n,DL d1,DL d2)
{
  int e1,e2,m,i;
  int *p1,*p2;

  if ( d1->td > d2->td )
    return 1;
  else if ( d1->td < d2->td )
    return -1;

  m = n>>1;
  for ( i = 0, e1 = e2 = 0, p1 = d1->d, p2 = d2->d; i < m; i++ ) {
    e1 += current_weyl_weight_vector[i]*(p1[m+i] - p1[i]);
    e2 += current_weyl_weight_vector[i]*(p2[m+i] - p2[i]);
  }
  if ( e1 > e2 )
    return 1;
  else if ( e1 < e2 )
    return -1;

  e1 = d1->td - d1->d[n-1];
  e2 = d2->td - d2->d[n-1];
  if ( e1 > e2 )
    return 1;
  else if ( e1 < e2 )
    return -1;

  for ( i= n - 1, p1 = d1->d+n-1, p2 = d2->d+n-1;
    i >= 0 && *p1 == *p2; i--, p1--, p2-- );
  return i < 0 ? 0 : (*p1 < *p2 ? 1 : -1);
}

int cmpdl_drl_zigzag(int n,DL d1,DL d2)
{
  int i,t,m;
  int *p1,*p2;

  if ( d1->td > d2->td )
    return 1;
  else if ( d1->td < d2->td )
    return -1;
  else {
    m = n>>1;
    for ( i= m - 1, p1 = d1->d, p2 = d2->d; i >= 0; i-- ) {
      if ( (t = p1[m+i] - p2[m+i]) ) return t > 0 ? -1 : 1;
      if ( (t = p1[i] - p2[i]) ) return t > 0 ? -1 : 1;
    }
    return 0;
  }
}

int cmpdl_homo_ww_drl_zigzag(int n,DL d1,DL d2)
{
  int e1,e2,m,i,t;
  int *p1,*p2;

  if ( d1->td > d2->td )
    return 1;
  else if ( d1->td < d2->td )
    return -1;

  m = n>>1;
  for ( i = 0, e1 = e2 = 0, p1 = d1->d, p2 = d2->d; i < m; i++ ) {
    e1 += current_weyl_weight_vector[i]*(p1[m+i] - p1[i]);
    e2 += current_weyl_weight_vector[i]*(p2[m+i] - p2[i]);
  }
  if ( e1 > e2 )
    return 1;
  else if ( e1 < e2 )
    return -1;

  e1 = d1->td - d1->d[n-1];
  e2 = d2->td - d2->d[n-1];
  if ( e1 > e2 )
    return 1;
  else if ( e1 < e2 )
    return -1;

  for ( i= m - 1, p1 = d1->d, p2 = d2->d; i >= 0; i-- ) {
    if ( (t = p1[m+i] - p2[m+i]) ) return t > 0 ? -1 : 1;
    if ( (t = p1[i] - p2[i]) ) return t > 0 ? -1 : 1;
  }
  return 0;
}

int cmpdl_order_pair(int n,DL d1,DL d2)
{
  int e1,e2,i,j,l;
  int *t1,*t2;
  int len,head;
  struct order_pair *pair;

  len = dp_current_spec->ord.block.length;
  if ( n != dp_current_spec->nv )
    error("cmpdl_order_pair : incompatible order specification");
  pair = dp_current_spec->ord.block.order_pair;

  head = 0;
  for ( i = 0, t1 = d1->d, t2 = d2->d; i < len; i++ ) {
    l = pair[i].length;
    switch ( pair[i].order ) {
      case 0:
        for ( j = 0, e1 = e2 = 0; j < l; j++ ) {
          e1 += MUL_WEIGHT(t1[j],head+j);
          e2 += MUL_WEIGHT(t2[j],head+j);
        }
        if ( e1 > e2 )
          return 1;
        else if ( e1 < e2 )
          return -1;
        else {
          for ( j = l - 1; j >= 0 && t1[j] == t2[j]; j-- );
          if ( j >= 0 )
            return t1[j] < t2[j] ? 1 : -1;
        }
        break;
      case 1:
        for ( j = 0, e1 = e2 = 0; j < l; j++ ) {
          e1 += MUL_WEIGHT(t1[j],head+j);
          e2 += MUL_WEIGHT(t2[j],head+j);
        }
        if ( e1 > e2 )
          return 1;
        else if ( e1 < e2 )
          return -1;
        else {
          for ( j = 0; j < l && t1[j] == t2[j]; j++ );
          if ( j < l )
            return t1[j] > t2[j] ? 1 : -1;
        }
        break;
      case 2:
        for ( j = 0; j < l && t1[j] == t2[j]; j++ );
        if ( j < l )
          return t1[j] > t2[j] ? 1 : -1;
        break;
      default:
        error("cmpdl_order_pair : invalid order"); break;
    }
    t1 += l; t2 += l; head += l;
  }
  return 0;
}

int cmpdl_composite(int nv,DL d1,DL d2)
{
  int n,i,j,k,start,s,len;
  int *dw;
  struct sparse_weight *sw;
  struct weight_or_block *worb;
  int *w,*t1,*t2;

  n = dp_current_spec->ord.composite.length;
  worb = dp_current_spec->ord.composite.w_or_b;
  w = dp_dl_work;
  for ( i = 0, t1 = d1->d, t2 = d2->d; i < nv; i++ )
    w[i] = t1[i]-t2[i];
  for ( i = 0; i < n; i++, worb++ ) {
    len = worb->length;
    switch ( worb->type ) {
      case IS_DENSE_WEIGHT:
        dw = worb->body.dense_weight;
        for ( j = 0, s = 0; j < len; j++ )
          s += dw[j]*w[j];
        if ( s > 0 ) return 1;
        else if ( s < 0 ) return -1;
        break;
      case IS_SPARSE_WEIGHT:
        sw = worb->body.sparse_weight;
        for ( j = 0, s = 0; j < len; j++ )
          s += sw[j].value*w[sw[j].pos];
        if ( s > 0 ) return 1;
        else if ( s < 0 ) return -1;
        break;
      case IS_BLOCK:
        start = worb->body.block.start;
        switch ( worb->body.block.order ) {
          case 0:
            for ( j = 0, k = start, s = 0; j < len; j++, k++ ) {
              s += MUL_WEIGHT(w[k],k);
            }
            if ( s > 0 ) return 1;
            else if ( s < 0 ) return -1;
            else {
              for ( j = k-1; j >= start && w[j] == 0; j-- );
              if ( j >= start )
                return w[j] < 0 ? 1 : -1;
            }
            break;
          case 1:
            for ( j = 0, k = start, s = 0; j < len; j++, k++ ) {
              s += MUL_WEIGHT(w[k],k);
            }
            if ( s > 0 ) return 1;
            else if ( s < 0 ) return -1;
            else {
              for ( j = 0, k = start;  j < len && w[j] == 0; j++, k++ );
              if ( j < len )
                return w[j] > 0 ? 1 : -1;
            }
            break;
          case 2:
            for ( j = 0, k = start;  j < len && w[j] == 0; j++, k++ );
            if ( j < len )
              return w[j] > 0 ? 1 : -1;
            break;
        }
        break;
    }
  }
  return 0;
}

int cmpdl_matrix(int n,DL d1,DL d2)
{
  int *v,*w,*t1,*t2;
  int s,i,j,len;
  int **matrix;

  for ( i = 0, t1 = d1->d, t2 = d2->d, w = dp_dl_work; i < n; i++ )
    w[i] = t1[i]-t2[i];
  len = dp_current_spec->ord.matrix.row;
  matrix = dp_current_spec->ord.matrix.matrix;
  for ( j = 0; j < len; j++ ) {
    v = matrix[j];
    for ( i = 0, s = 0; i < n; i++ )
      s += v[i]*w[i];  
    if ( s > 0 )
      return 1;
    else if ( s < 0 )
      return -1;
  }
  return 0;
}

int cmpdl_top_weight(int n,DL d1,DL d2)
{
  int *w;
  Z **mat;
  Z *a;
  mpz_t sum;
  int len,i,sgn,tsgn,row,k;
  int *t1,*t2;

  w = (int *)ALLOCA(n*sizeof(int));
  len = current_top_weight_len+3;
  t1 = d1->d; t2 = d2->d;
  for ( i = 0; i < n; i++ ) w[i] = t1[i]-t2[i];
  mpz_init_set_ui(sum,0);
  if ( OID(current_top_weight) == O_VECT ) {
      mat = (Z **)&BDY((VECT)current_top_weight);
    row = 1;
  } else {
      mat = (Z **)BDY((MAT)current_top_weight);
    row = ((MAT)current_top_weight)->row;
  }
  for ( k = 0; k < row; k++ ) {
    a = mat[k];
    for ( i = 0; i < n; i++ ) {
      if ( !a[i] || !w[i] ) continue;
      if ( w[i] > 0 )
        mpz_addmul_ui(sum,BDY(a[i]),(unsigned int)w[i]);
      else
        mpz_submul_ui(sum,BDY(a[i]),(unsigned int)(-w[i]));
    }
    sgn = mpz_sgn(sum);
    if ( sgn > 0 ) return 1;
    else if ( sgn < 0 ) return -1;
  }
  return (*cmpdl_tie_breaker)(n,d1,d2);
}

GeoBucket create_bucket()
{
  GeoBucket g;

  g = CALLOC(1,sizeof(struct oGeoBucket));
  g->m = 32;
  return g;
}

int length(NODE d);

void add_bucket(GeoBucket g,NODE d,int nv)
{
  int l,k,m;

  l = length(d);
  for ( k = 0, m = 1; l > m; k++, m <<= 1 );
  /* 2^(k-1) < l <= 2^k */
  d = symb_merge(g->body[k],d,nv);
  for ( ; length(d) > (1<<(k)); k++ ) {
    g->body[k] = 0;
    d = symb_merge(g->body[k+1],d,nv);
  }
  g->body[k] = d;
  g->m = MAX(g->m,k);
}

DL remove_head_bucket(GeoBucket g,int nv)
{
  int j,i,c,m;
  DL d;

  j = -1;
  m = g->m;
  for ( i = 0; i <= m; i++ ) {
    if ( !g->body[i] )
      continue;
    if ( j < 0 ) j = i;
    else {
      c = (*cmpdl)(nv,g->body[i]->body,g->body[j]->body);
      if ( c > 0 )
        j = i;
      else if ( c == 0 )
        g->body[i] = NEXT(g->body[i]);  
    }
  }
  if ( j < 0 )
    return 0;
  else {
    d = g->body[j]->body;
    g->body[j] = NEXT(g->body[j]);
    return d;
  }
}

/*  DPV functions */

void adddv(VL vl,DPV p1,DPV p2,DPV *pr)
{
  int i,len;
  DP *e;

  if ( !p1 || !p2 )
    error("adddv : invalid argument");
  else if ( p1->len != p2->len )
    error("adddv : size mismatch");
  else {
    len = p1->len;
    e = (DP *)MALLOC(p1->len*sizeof(DP));
    for ( i = 0; i < len; i++ )
      addd(vl,p1->body[i],p2->body[i],&e[i]);
    MKDPV(len,e,*pr);
    (*pr)->sugar = MAX(p1->sugar,p2->sugar);
  }
}

void subdv(VL vl,DPV p1,DPV p2,DPV *pr)
{
  int i,len;
  DP *e;

  if ( !p1 || !p2 )
    error("subdv : invalid argument");
  else if ( p1->len != p2->len )
    error("subdv : size mismatch");
  else {
    len = p1->len;
    e = (DP *)MALLOC(p1->len*sizeof(DP));
    for ( i = 0; i < len; i++ )
      subd(vl,p1->body[i],p2->body[i],&e[i]);
    MKDPV(len,e,*pr);
    (*pr)->sugar = MAX(p1->sugar,p2->sugar);
  }
}

void chsgndv(DPV p1,DPV *pr)
{
  int i,len;
  DP *e;

  if ( !p1 )
    error("subdv : invalid argument");
  else {
    len = p1->len;
    e = (DP *)MALLOC(p1->len*sizeof(DP));
    for ( i = 0; i < len; i++ )
      chsgnd(p1->body[i],&e[i]);
    MKDPV(len,e,*pr);
    (*pr)->sugar = p1->sugar;
  }
}

void muldv(VL vl,DP p1,DPV p2,DPV *pr)
{
  int i,len;
  DP *e;

  len = p2->len;
  e = (DP *)MALLOC(p2->len*sizeof(DP));
  if ( !p1 ) {
    MKDPV(len,e,*pr);
    (*pr)->sugar = 0;
  } else {
    for ( i = 0; i < len; i++ )
      muld(vl,p1,p2->body[i],&e[i]);
    MKDPV(len,e,*pr);
    (*pr)->sugar = p1->sugar + p2->sugar;  
  }
}

int compdv(VL vl,DPV p1,DPV p2)
{
  int i,t,len;

  if ( p1->len != p2->len ) {
    error("compdv : size mismatch");
    return 0; /* XXX */
  } else {
    len = p1->len;
    for ( i = 0; i < len; i++ )
      if ( (t = compd(vl,p1->body[i],p2->body[i])) )
        return t;
    return 0;
  }
}

int ni_next(int *a,int n)
{
  int i,j,k,kj;

  /* find the first nonzero a[j] */
  for ( j = 0; j < n && a[j] == 0; j++ );
  /* find the first zero a[k] after a[j] */
  for ( k = j; k < n && a[k] == 1; k++ );
  if ( k == n ) return 0;
  /* a[0] = 0, ... , a[j-1] = 0, a[j] = 1, ..., a[k-1] = 1, a[k] = 0 */
  /* a[0] = 1,..., a[k-j-2] = 1, a[k-j-1] = 0, ..., a[k-1] = 0, a[k] = 1 */
  kj = k-j-1;
  for ( i = 0; i < kj; i++ ) a[i] = 1;
  for ( ; i < k; i++ ) a[i] = 0;
  a[k] = 1;
  return 1;
}

int comp_nbm(NBM a,NBM b)
{
  int d,i,ai,bi;
  unsigned int *ab,*bb;

  if ( a->d > b->d ) return 1;
  else if ( a->d < b->d ) return -1;
  else {
    d = a->d; ab = a->b; bb = b->b;
#if 0
    w = (d+31)/32;
    for ( i = 0; i < w; i++ ) 
      if ( ab[i] > bb[i] ) return 1;
      else if ( ab[i] < bb[i] ) return -1;
#else
    for ( i = 0; i < d; i++ ) {
      ai = NBM_GET(ab,i);
      bi = NBM_GET(bb,i);
      if ( ai > bi ) return 1;
      else if ( ai < bi ) return -1;
    }
#endif
    return 0;
  }
}

NBM mul_nbm(NBM a,NBM b)
{
  int ad,bd,d,i,j;
  unsigned int *ab,*bb,*mb;
  NBM m;

  ad = a->d; bd = b->d; ab = a->b; bb = b->b;
  d = ad + bd;
  NEWNBM(m); NEWNBMBDY(m,d);
  m->d = d; mulp(CO,a->c,b->c,&m->c); mb = m->b; 
  j = 0;
  for ( i = 0; i < ad; i++, j++ )
    if ( NBM_GET(ab,i) ) NBM_SET(mb,j);
    else NBM_CLR(mb,j);
  for ( i = 0; i < bd; i++, j++ )
    if ( NBM_GET(bb,i) ) NBM_SET(mb,j);
    else NBM_CLR(mb,j);
  return m;
}

NBP nbmtonbp(NBM m)
{
  NODE n;
  NBP u;

  MKNODE(n,m,0);
  MKNBP(u,n);
  return u;
}

/* a=c*x*rest -> a0= x*rest, ah=x, ar=rest */

P separate_nbm(NBM a,NBP *a0,NBP *ah,NBP *ar)
{
  int i,d1;
  NBM t;

  if ( !a->d ) error("separate_nbm : invalid argument");

  if ( a0 ) {
    NEWNBM(t); t->d = a->d; t->b = a->b; t->c = (P)ONE;
    *a0 = nbmtonbp(t);
  }

  if ( ah ) {
    NEWNBM(t); NEWNBMBDY(t,1); t->d = 1; t->c = (P)ONE;
    if ( NBM_GET(a->b,0) ) NBM_SET(t->b,0);
    else NBM_CLR(t->b,0);
    *ah = nbmtonbp(t);
  }

  if ( ar ) {
    d1 = a->d-1;
    NEWNBM(t); NEWNBMBDY(t,d1); t->d = d1; t->c = (P)ONE;
    for ( i = 0; i < d1; i++ ) {
      if ( NBM_GET(a->b,i+1) ) NBM_SET(t->b,i);
      else NBM_CLR(t->b,i);
    }
    *ar = nbmtonbp(t);
  }

  return a->c;
}

/* a=c*rest*x -> a0= rest*x, ar=rest, at=x */

P separate_tail_nbm(NBM a,NBP *a0,NBP *ar,NBP *at)
{
  int i,d,d1;
  NBM t;

  if ( !(d=a->d) ) error("separate_tail_nbm : invalid argument");

  if ( a0 ) {
    NEWNBM(t); t->d = a->d; t->b = a->b; t->c = (P)ONE;
    *a0 = nbmtonbp(t);
  }

  d1 = a->d-1;
  if ( at ) {
    NEWNBM(t); NEWNBMBDY(t,1); t->d = 1; t->c = (P)ONE;
    if ( NBM_GET(a->b,d1) ) NBM_SET(t->b,0);
    else NBM_CLR(t->b,0);
    *at = nbmtonbp(t);
  }

  if ( ar ) {
    NEWNBM(t); NEWNBMBDY(t,d1); t->d = d1; t->c = (P)ONE;
    for ( i = 0; i < d1; i++ ) {
      if ( NBM_GET(a->b,i) ) NBM_SET(t->b,i);
      else NBM_CLR(t->b,i);
    }
    *ar = nbmtonbp(t);
  }

  return a->c;
}

NBP make_xky(int k)
{
  int k1,i;
  NBM t;

  NEWNBM(t); NEWNBMBDY(t,k); t->d = k; t->c = (P)ONE;
  k1 = k-1;
  for ( i = 0; i < k1; i++ ) NBM_SET(t->b,i);
  NBM_CLR(t->b,i);
  return nbmtonbp(t);
}

/* a=c*x^(k-1)*y*rest -> a0= x^(k-1)*y*rest, ah=x^(k-1)*y, ar=rest */

P separate_xky_nbm(NBM a,NBP *a0,NBP *ah,NBP *ar)
{
  int i,d1,k,k1;
  NBM t;

  if ( !a->d )
    error("separate_nbm : invalid argument");
  for ( i = 0; i < a->d && NBM_GET(a->b,i); i++ );
  if ( i == a->d )
    error("separate_nbm : invalid argument");
  k1 = i;
  k = i+1;

  if ( a0 ) {
    NEWNBM(t); t->d = a->d; t->b = a->b; t->c = (P)ONE;
    *a0 = nbmtonbp(t);
  }

  if ( ah ) {
    NEWNBM(t); NEWNBMBDY(t,k); t->d = k; t->c = (P)ONE;
    for ( i = 0; i < k1; i++ ) NBM_SET(t->b,i);
    NBM_CLR(t->b,i);
    *ah = nbmtonbp(t);
  }

  if ( ar ) {
    d1 = a->d-k;
    NEWNBM(t); NEWNBMBDY(t,d1); t->d = d1; t->c = (P)ONE;
    for ( i = 0; i < d1; i++ ) {
      if ( NBM_GET(a->b,i+k) ) NBM_SET(t->b,i);
      else NBM_CLR(t->b,i);
    }
    *ar = nbmtonbp(t);
  }

  return a->c;
}

void shuffle_mulnbp(VL vl,NBP p1,NBP p2, NBP *rp);
void harmonic_mulnbp(VL vl,NBP p1,NBP p2, NBP *rp);
void mulnbmnbp(VL vl,NBM m,NBP p, NBP *rp);
void mulnbpnbm(VL vl,NBP p,NBM m, NBP *rp);

NBP shuffle_mul_nbm(NBM a,NBM b)
{
  NBP u,a0,ah,ar,b0,bh,br,a1,b1,t;
  P ac,bc,c;

  if ( !a->d || !b->d )
    u = nbmtonbp(mul_nbm(a,b));
  else {
    ac = separate_nbm(a,&a0,&ah,&ar);
    bc = separate_nbm(b,&b0,&bh,&br);
    mulp(CO,ac,bc,&c);
    shuffle_mulnbp(CO,ar,b0,&t); mulnbp(CO,ah,t,&a1);
    shuffle_mulnbp(CO,a0,br,&t); mulnbp(CO,bh,t,&b1);
    addnbp(CO,a1,b1,&t); mulnbp(CO,(NBP)c,t,&u);
  }
  return u;
}

NBP harmonic_mul_nbm(NBM a,NBM b)
{
  NBP u,a0,ah,ar,b0,bh,br,a1,b1,t,s,abk,ab1;
  P ac,bc,c;

  if ( !a->d || !b->d )
    u = nbmtonbp(mul_nbm(a,b));
  else {
    mulp(CO,a->c,b->c,&c);
    ac = separate_xky_nbm(a,&a0,&ah,&ar);
    bc = separate_xky_nbm(b,&b0,&bh,&br);
    mulp(CO,ac,bc,&c);
    harmonic_mulnbp(CO,ar,b0,&t); mulnbp(CO,ah,t,&a1);
    harmonic_mulnbp(CO,a0,br,&t); mulnbp(CO,bh,t,&b1);
    abk = make_xky(((NBM)BDY(BDY(ah)))->d+((NBM)BDY(BDY(bh)))->d);
    harmonic_mulnbp(CO,ar,br,&t); mulnbp(CO,abk,t,&ab1);
    addnbp(CO,a1,b1,&t); addnbp(CO,t,ab1,&s); mulnbp(CO,(NBP)c,s,&u);
  }
  return u;

}

void addnbp(VL vl,NBP p1,NBP p2, NBP *rp)
{
  NODE b1,b2,br=0,br0;
  NBM m1,m2,m;
  P c;

  if ( !p1 )
    *rp = p2;
  else if ( !p2 )
    *rp = p1;
  else {
    for ( b1 = BDY(p1), b2 = BDY(p2), br0 = 0; b1 && b2; ) {
      m1 = (NBM)BDY(b1); m2 = (NBM)BDY(b2);
      switch ( comp_nbm(m1,m2) ) {
        case 0:
          addp(CO,m1->c,m2->c,&c);
          if ( c ) {
            NEXTNODE(br0,br);
            NEWNBM(m); m->d = m1->d; m->c = c; m->b = m1->b;
            BDY(br) = (pointer)m;
          }
          b1 = NEXT(b1); b2 = NEXT(b2); break;
        case 1:
          NEXTNODE(br0,br); BDY(br) = BDY(b1);
          b1 = NEXT(b1); break;
        case -1:
          NEXTNODE(br0,br); BDY(br) = BDY(b2);
          b2 = NEXT(b2); break;
      }
    }
    if ( !br0 )
      if ( b1 )
        br0 = b1;
      else if ( b2 )
        br0 = b2;
      else {
        *rp = 0;
        return;
      }
    else if ( b1 )
      NEXT(br) = b1;
    else if ( b2 )
        NEXT(br) = b2;
    else
      NEXT(br) = 0;
    MKNBP(*rp,br0);
  }
}

void subnbp(VL vl,NBP p1,NBP p2, NBP *rp)
{
  NBP t;

  chsgnnbp(p2,&t);
  addnbp(vl,p1,t,rp);
}

void chsgnnbp(NBP p,NBP *rp)
{
  NODE r0,r=0,b;
  NBM m,m1;

  for ( r0 = 0, b = BDY(p); b; b = NEXT(b) ) {
    NEXTNODE(r0,r);
    m = (NBM)BDY(b);
    NEWNBM(m1); m1->d = m->d; m1->b = m->b; chsgnp(m->c,&m1->c);
    BDY(r) = m1;
  }
  if ( r0 ) NEXT(r) = 0;
  MKNBP(*rp,r0);
}

void mulnbp(VL vl,NBP p1,NBP p2, NBP *rp)
{
  NODE b,n;
  NBP r,t,s;
  NBM m;

  if ( !p1 || !p2 ) {
    *rp = 0; return;
  }
  if ( OID(p1) != O_NBP ) {
    if ( !POLY(p1) )
      error("mulnbp : invalid argument");
    NEWNBM(m); m->d = 0; m->b = 0; m->c = (P)p1;  
    MKNODE(n,m,0); MKNBP(p1,n);
  }
  if ( OID(p2) != O_NBP ) {
    if ( !POLY(p2) )
      error("mulnbp : invalid argument");
    NEWNBM(m); m->d = 0; m->b = 0; m->c = (P)p2;  
    MKNODE(n,m,0); MKNBP(p2,n);
  }
  if ( length(BDY(p1)) < length(BDY(p2)) ) {
    for ( r = 0, b = BDY(p1); b; b = NEXT(b) ) {
      mulnbmnbp(vl,(NBM)BDY(b),p2,&t);
      addnbp(vl,r,t,&s); r = s;
    }
    *rp = r;
  } else {
    for ( r = 0, b = BDY(p2); b; b = NEXT(b) ) {
      mulnbpnbm(vl,p1,(NBM)BDY(b),&t);
      addnbp(vl,r,t,&s); r = s;
    }
    *rp = r;
  }
}

void mulnbmnbp(VL vl,NBM m,NBP p, NBP *rp)
{
  NODE b,r0,r=0;

  if ( !p ) *rp = 0;
  else {
    for ( r0 = 0, b = BDY(p); b; b = NEXT(b) ) {
      NEXTNODE(r0,r);
      BDY(r) = mul_nbm(m,(NBM)BDY(b));
    }
    if ( r0 ) NEXT(r) = 0;
    MKNBP(*rp,r0);
  }
}

void mulnbpnbm(VL vl,NBP p,NBM m, NBP *rp)
{
  NODE b,r0,r=0;

  if ( !p ) *rp = 0;
  else {
    for ( r0 = 0, b = BDY(p); b; b = NEXT(b) ) {
      NEXTNODE(r0,r);
      BDY(r) = mul_nbm((NBM)BDY(b),m);
    }
    if ( r0 ) NEXT(r) = 0;
    MKNBP(*rp,r0);
  }
}

void pwrnbp(VL vl,NBP a,Z q,NBP *c)
{
  NBP a1,a2;
  Z q1,r1,two;
  NBM m;
  NODE r;

  if ( !q ) {
     NEWNBM(m); m->d = 0; m->c = (P)ONE; m->b = 0;
     MKNODE(r,m,0); MKNBP(*c,r);
  } else if ( !a )
    *c = 0;
  else if ( UNIQ(q) )
    *c = a;
  else {
    STOQ(2,two);
    divqrz(q,two,&q1,&r1);
    pwrnbp(vl,a,q1,&a1);
    mulnbp(vl,a1,a1,&a2);
    if ( r1 )
      mulnbp(vl,a2,a,c);
    else
      *c = a2;
  }
}

int compnbp(VL vl,NBP p1,NBP p2)
{
  NODE n1,n2;
  NBM m1,m2;
  int t;

  if ( !p1 )
    return p2 ? -1 : 0;
  else if ( !p2 )
    return 1;
  else {
    for ( n1 = BDY(p1), n2 = BDY(p2);
      n1 && n2; n1 = NEXT(n1), n2 = NEXT(n2) ) {
      m1 = (NBM)BDY(n1); m2 = (NBM)BDY(n2);
      if ( (t = comp_nbm(m1,m2)) || (t = compp(CO,m1->c,m2->c) ) )
        return t;
    }
    if ( n1 )
      return 1;
    else if ( n2 )
      return -1;
    else
      return 0;
  }
}

void shuffle_mulnbp(VL vl,NBP p1,NBP p2, NBP *rp)
{
  NODE b1,b2,n;
  NBP r,t,s;
  NBM m;

  if ( !p1 || !p2 ) {
    *rp = 0; return;
  }
  if ( OID(p1) != O_NBP ) {
    if ( !POLY(p1) )
      error("shuffle_mulnbp : invalid argument");
    NEWNBM(m); m->d = 0; m->b = 0; m->c = (P)p1;  
    MKNODE(n,m,0); MKNBP(p1,n);
  }
  if ( OID(p2) != O_NBP ) {
    if ( !POLY(p2) )
      error("shuffle_mulnbp : invalid argument");
    NEWNBM(m); m->d = 0; m->b = 0; m->c = (P)p2;  
    MKNODE(n,m,0); MKNBP(p2,n);
  }
  for ( r = 0, b1 = BDY(p1); b1; b1 = NEXT(b1) )
    for ( m = BDY(b1), b2 = BDY(p2); b2; b2 = NEXT(b2) ) {
      t = shuffle_mul_nbm(m,(NBM)BDY(b2));
      addnbp(vl,r,t,&s); r = s;
    }
  *rp = r;
}

void harmonic_mulnbp(VL vl,NBP p1,NBP p2, NBP *rp)
{
  NODE b1,b2,n;
  NBP r,t,s;
  NBM m;

  if ( !p1 || !p2 ) {
    *rp = 0; return;
  }
  if ( OID(p1) != O_NBP ) {
    if ( !POLY(p1) )
      error("harmonic_mulnbp : invalid argument");
    NEWNBM(m); m->d = 0; m->b = 0; m->c = (P)p1;  
    MKNODE(n,m,0); MKNBP(p1,n);
  }
  if ( OID(p2) != O_NBP ) {
    if ( !POLY(p2) )
      error("harmonic_mulnbp : invalid argument");
    NEWNBM(m); m->d = 0; m->b = 0; m->c = (P)p2;  
    MKNODE(n,m,0); MKNBP(p2,n);
  }
  for ( r = 0, b1 = BDY(p1); b1; b1 = NEXT(b1) )
    for ( m = BDY(b1), b2 = BDY(p2); b2; b2 = NEXT(b2) ) {
      t = harmonic_mul_nbm(m,(NBM)BDY(b2));
      addnbp(vl,r,t,&s); r = s;
    }
  *rp = r;
}

#if 0
NBP shuffle_mul_nbm(NBM a,NBM b)
{
  int ad,bd,d,i,ai,bi,bit,s;
  int *ab,*bb,*wmb,*w;
  NBM wm,tm;
  P c,c1;
  NODE r,t,t1,p;
  NBP u;

  ad = a->d; bd = b->d; ab = a->b; bb = b->b;
  d = ad + bd;
  w = (int *)ALLOCA(d*sizeof(int));
  NEWNBM(wm); NEWNBMBDY(wm,d); wmb = wm->b;
  for ( i = 0; i < ad; i++ ) w[i] = 1;
  for ( ; i < d; i++ ) w[i] = 0;
  mulp(CO,a->c,b->c,&c);
  r = 0;
  do {
    wm->d = d; wm->c = c;
    ai = 0; bi = 0;
    for ( i = 0; i < d; i++ ) {
      if ( w[i] ) { bit = NBM_GET(ab,ai); ai++; }
      else { bit = NBM_GET(bb,bi); bi++; }
      if ( bit ) NBM_SET(wmb,i);
      else NBM_CLR(wmb,i);
    }
    for ( p = 0, t = r; t; p = t, t = NEXT(t) ) {
      tm = (NBM)BDY(t);
      s = comp_nbm(tm,wm);
      if ( s < 0 ) {
        /* insert */
        MKNODE(t1,wm,t);
        if ( !p ) r = t1;
        else NEXT(p) = t1;
        NEWNBM(wm); NEWNBMBDY(wm,d); wmb = wm->b;
        break;
      } else if ( s == 0 ) {
        /* add coefs */
        addp(CO,tm->c,c,&c1);
        if ( c1 ) tm->c = c1;
        else NEXT(p) = NEXT(t);
        break;
      }
    }
    if ( !t ) {
      /* append */
      MKNODE(t1,wm,t);
      if ( !p ) r = t1;
      else NEXT(p) = t1;
      NEWNBM(wm); NEWNBMBDY(wm,d); wmb = wm->b;
    }
  } while ( ni_next(w,d) );
  MKNBP(u,r);
  return u;
}

int nbmtoxky(NBM a,int *b)
{
  int d,i,j,k;
  int *p;

  d = a->d; p = a->b;
  for ( i = j = 0, k = 1; i < d; i++ ) {
    if ( !NBM_GET(p,i) ) {
      b[j++] = k;
      k = 1;
    } else k++;
  }
  return j;
}

NBP harmonic_mul_nbm(NBM a,NBM b)
{
  int da,db,d,la,lb,lmax,lmin,l,lab,la1,lb1,lab1;
  int i,j,k,ia,ib,s;
  int *wa,*wb,*w,*wab,*wa1,*wmb;
  P c,c1;
  NBM wm,tm;
  NODE r,t1,t,p;
  NBP u;

  da = a->d; db = b->d; d = da+db;
  wa = (int *)ALLOCA(da*sizeof(int));
  wb = (int *)ALLOCA(db*sizeof(int));
  la = nbmtoxky(a,wa);
  lb = nbmtoxky(b,wb);
  mulp(CO,a->c,b->c,&c);
  /* wa[0],..,wa[la-1] <-> x^wa[0]y x^wa[1]y .. */  
  /* lmax : total length */
  lmax = la+lb;
  lmin = la>lb?la:lb;  
  w = (int *)ALLOCA(lmax*sizeof(int));
  /* position of a+b */
  wab = (int *)ALLOCA(lmax*sizeof(int));
  /* position of a */
  wa1 = (int *)ALLOCA(lmax*sizeof(int));
  NEWNBM(wm); NEWNBMBDY(wm,d); wmb = wm->b;
  for ( l = lmin, r = 0; l <= lmax; l++ ) {
    lab = lmax - l;
    la1 = la - lab;
    lb1 = lb - lab;
    lab1 = l-lab;
    /* partion l into three parts: a, b, a+b */
    /* initialize wab */
    for ( i = 0; i < lab; i++ ) wab[i] = 1;
    for ( ; i < l; i++ ) wab[i] = 0;
    do {
      /* initialize wa1 */
      for ( i = 0; i < la1; i++ ) wa1[i] = 1;
      for ( ; i < lab1; i++ ) wa1[i] = 0;
      do {
        ia = 0; ib = 0;
        for ( i = j = 0; i < l; i++ )
          if ( wab[i] ) w[i] = wa[ia++]+wb[ib++];
          else if ( wa1[j++] ) w[i] = wa[ia++];
          else w[i] = wb[ib++];
        for ( i = j = 0; i < l; i++ ) {
          for ( k = w[i]-1; k > 0; k--, j++ ) NBM_SET(wmb,j);
          NBM_CLR(wmb,j); j++;
        }
        wm->d = j; wm->c = c;
        for ( p = 0, t = r; t; p = t, t = NEXT(t) ) {
          tm = (NBM)BDY(t);
          s = comp_nbm(tm,wm);
          if ( s < 0 ) {
            /* insert */
            MKNODE(t1,wm,t);
            if ( !p ) r = t1;
            else NEXT(p) = t1;
            NEWNBM(wm); NEWNBMBDY(wm,d); wmb = wm->b;
            break;
          } else if ( s == 0 ) {
            /* add coefs */
            addp(CO,tm->c,c,&c1);
            if ( c1 ) tm->c = c1;
            else NEXT(p) = NEXT(t);
            break;
          }
        }
        if ( !t ) {
          /* append */
          MKNODE(t1,wm,t);
          if ( !p ) r = t1;
          else NEXT(p) = t1;
          NEWNBM(wm); NEWNBMBDY(wm,d); wmb = wm->b;
        }
      } while ( ni_next(wa1,lab1) );
    } while ( ni_next(wab,l) );
  }
  MKNBP(u,r);
  return u;
}
#endif

/* DPM functions */

int compdmm(int n,DMM m1,DMM m2)
{
  int t;

  if ( dpm_ispot ) {
    if ( m1->pos < m2->pos ) return 1;
    else if ( m1->pos > m2->pos ) return -1;
    else return (*cmpdl)(n,m1->dl,m2->dl);
  } else {
    t = (*cmpdl)(n,m1->dl,m2->dl);
    if ( t ) return t;
    else if ( m1->pos < m2->pos ) return 1;
    else if ( m1->pos > m2->pos ) return -1;
    else return 0;
  }
}

void adddpm(VL vl,DPM p1,DPM p2,DPM *pr)
{
  int n;
  DMM m1,m2,mr=0,mr0;
  Obj t;
  DL d;

  if ( !p1 )
    *pr = p2;
  else if ( !p2 )
    *pr = p1;
  else {
    for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; )
      switch ( compdmm(n,m1,m2) ) {
        case 0:
          arf_add(vl,C(m1),C(m2),&t);
          if ( t ) {
            NEXTDMM(mr0,mr); mr->pos = m1->pos; mr->dl = m1->dl; C(mr) = t;
          }
          m1 = NEXT(m1); m2 = NEXT(m2); break;
        case 1:
          NEXTDMM(mr0,mr); mr->pos = m1->pos; mr->dl = m1->dl; C(mr) = C(m1);
          m1 = NEXT(m1); break;
        case -1:
          NEXTDMM(mr0,mr); mr->pos = m2->pos; mr->dl = m2->dl; C(mr) = C(m2);
          m2 = NEXT(m2); break;
      }
    if ( !mr0 )
      if ( m1 )
        mr0 = m1;
      else if ( m2 )
        mr0 = m2;
      else {
        *pr = 0;
        return;
      }
    else if ( m1 )
      NEXT(mr) = m1;
    else if ( m2 )
      NEXT(mr) = m2;
    else
      NEXT(mr) = 0;
    MKDPM(NV(p1),mr0,*pr);
    if ( *pr )
      (*pr)->sugar = MAX(p1->sugar,p2->sugar);
  }
}

void subdpm(VL vl,DPM p1,DPM p2,DPM *pr)
{
  DPM t;

  if ( !p2 )
    *pr = p1;
  else {
    chsgndpm(p2,&t); adddpm(vl,p1,t,pr);
  }
}

void chsgndpm(DPM p,DPM *pr)
{
  DMM m,mr=0,mr0;
  Obj r;

  if ( !p )
    *pr = 0;
  else {
    for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
      NEXTDMM(mr0,mr); arf_chsgn(C(m),&C(mr)); mr->pos = m->pos; mr->dl = m->dl;
    }
    NEXT(mr) = 0; MKDPM(NV(p),mr0,*pr);
    if ( *pr )
      (*pr)->sugar = p->sugar;
  }
}

void mulcdpm(VL vl,Obj c,DPM p,DPM *pr)
{
  DMM m,mr=0,mr0;

  if ( !p || !c )
    *pr = 0;
  else if ( NUM(c) && UNIQ((Q)c) )
    *pr = p;
  else if ( NUM(c) && MUNIQ((Q)c) )
    chsgndpm(p,pr);
  else {
    for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
      NEXTDMM(mr0,mr);
      arf_mul(vl,C(m),c,&C(mr));
      mr->pos = m->pos;
      mr->dl = m->dl;
    }
    NEXT(mr) = 0; MKDPM(NV(p),mr0,*pr);
    if ( *pr )
      (*pr)->sugar = p->sugar;
  }
}

void comm_mulmpdpm(VL vl,MP m0,DPM p,DPM *pr)
{
  DMM m,mr=0,mr0;
  DL d;
  Obj c;
  int n;

  if ( !p )
    *pr = 0;
  else {
    n = NV(p);
    d = m0->dl;
    c = C(m0);
    for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
      NEXTDMM(mr0,mr);
      arf_mul(vl,C(m),c,&C(mr));
      mr->pos = m->pos;
      adddl(n,m->dl,d,&mr->dl);
    }
    NEXT(mr) = 0; MKDPM(NV(p),mr0,*pr);
    if ( *pr )
      (*pr)->sugar = p->sugar;
  }
}

void weyl_mulmpdpm(VL vl,MP m0,DPM p,DPM *pr)
{
  DPM r,t,t1;
  DMM m;
  DL d0;
  int n,n2,l,i,j,tlen;
  struct oMP mp;
  static DMM *w,*psum;
  static struct cdl *tab;
  static int wlen;
  static int rtlen;

  if ( !p )
    *pr = 0;
  else {
    for ( m = BDY(p), l = 0; m; m = NEXT(m), l++ );
    if ( l > wlen ) {
      if ( w ) GCFREE(w);
      w = (DMM *)MALLOC(l*sizeof(DMM));
      wlen = l;
    }
    for ( m = BDY(p), i = 0; i < l; m = NEXT(m), i++ )
      w[i] = m;

    n = NV(p); n2 = n>>1;
    d0 = m0->dl;
    for ( i = 0, tlen = 1; i < n2; i++ )
      tlen *= d0->d[n2+i]+1;
    if ( tlen > rtlen ) {
      if ( tab ) GCFREE(tab);
      if ( psum ) GCFREE(psum);
      rtlen = tlen;
      tab = (struct cdl *)MALLOC(rtlen*sizeof(struct cdl));
      psum = (DMM *)MALLOC(rtlen*sizeof(DMM));
    }
    bzero(psum,tlen*sizeof(DMM));
    for ( i = l-1; i >= 0; i-- ) {
      bzero(tab,tlen*sizeof(struct cdl));
      mp.dl = w[i]->dl; mp.c = C(w[i]); mp.next = 0;
      weyl_mulmm(vl,m0,&mp,n,tab,tlen);
      for ( j = 0; j < tlen; j++ ) {
        if ( tab[j].c ) {
          NEWDMM(m); m->dl = tab[j].d; m->pos = w[i]->pos; C(m) = (Obj)tab[j].c; NEXT(m) = psum[j];
          psum[j] = m;
        }
      }
    }
    for ( j = tlen-1, r = 0; j >= 0; j-- ) 
      if ( psum[j] ) {
        MKDPM(n,psum[j],t); adddpm(vl,r,t,&t1); r = t1;
      }
    if ( r )
      r->sugar = p->sugar + m0->dl->td;
    *pr = r;
  }
}

void mulobjdpm(VL vl,Obj p1,DPM p2,DPM *pr)
{
  MP m;
  DPM s,t,u;

  if ( !p1 || !p2 )
    *pr = 0;
  else if ( OID(p1) != O_DP )
    mulcdpm(vl,p1,p2,pr);
  else {
    s = 0;
    for ( m = BDY((DP)p1); m; m = NEXT(m) ) {
      if ( do_weyl )
        weyl_mulmpdpm(vl,m,p2,&t);
      else
        comm_mulmpdpm(vl,m,p2,&t);
      adddpm(vl,s,t,&u); s = u;
    }
    *pr = s;
  }
}

int compdpm(VL vl,DPM p1,DPM p2)
{
  int n,t;
  DMM m1,m2;

  if ( !p1 )
    return p2 ? -1 : 0;
  else if ( !p2 )
    return 1;
  else if ( NV(p1) != NV(p2) ) {
    error("compdpm : size mismatch");
    return 0; /* XXX */
  } else {
    for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2);
      m1 && m2; m1 = NEXT(m1), m2 = NEXT(m2) )
      if ( (t = compdmm(n,m1,m2)) ||
        (t = arf_comp(vl,C(m1),C(m2)) ) )
        return t;
    if ( m1 )
      return 1;
    else if ( m2 )
      return -1;
    else
      return 0;
  }
}