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

Revision 1.2, Fri Sep 28 08:20:28 2018 UTC (4 years, 2 months ago) by noro
Branch: MAIN
CVS Tags: HEAD
Changes since 1.1: +7 -7 lines

Changed macros : QTOS->ZTOS, STOQ->STOZ etc.

/* $OpenXM: OpenXM_contrib2/asir2018/engine/Fgfs.c,v 1.2 2018/09/28 08:20:28 noro Exp $ */

#include "ca.h"

void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp);
void gcdsf_main(VL vl,P *pa,int m,P *r);
void ugcdsf(P *pa,int m,P *r);
void head_monomial(VL vl,V v,P p,P *coef,P *term);
void sqfrsfmain(VL vl,P f,DCP *dcp);
void pthrootsf(P f,Z m,P *r);
void partial_sqfrsf(VL vl,V v,P f,P *r,DCP *dcp);
void gcdsf(VL vl,P *pa,int k,P *r);
void mfctrsfmain(VL vl, P f, DCP *dcp);
void next_evaluation_point(int *mev,int n);
void estimatelc_sf(VL vl,VL rvl,P c,DCP dc,int *mev,P *lcp);
void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P lcu,P lcv,int *mev,P *up);
void substvp_sf(VL vl,VL rvl,P f,int *mev,P *r);
void shift_sf(VL vl, VL rvl, P f, int *mev, int sgn, P *r);
void adjust_coef_sf(VL vl,VL rvl,P lcu,P u0,int *mev,P *r);
void extended_gcd_modyk(P u0,P v0,V x,V y,int dy,P *cu,P *cv);
void poly_to_gfsn_poly(VL vl,P f,V v,P *r);
void gfsn_poly_to_poly(VL vl,P f,V v,P *r);
void poly_to_gfsn_poly_main(P f,V v,P *r);
void gfsn_poly_to_poly_main(P f,V v,P *r);
void gfsn_univariate_to_sfbm(P f,int dy,BM *r);
void sfbm_to_gfsn_univariate(BM f,V x,V y,P *r);

void monomialfctr_sf(VL vl,P p,P *pr,DCP *dcp)
{
  VL nvl,avl;
  Z d;
  P f,t,s;
  DCP dc0,dc;
  Obj obj;

  clctv(vl,p,&nvl);
  for ( dc0 = 0, avl = nvl, f = p; avl; avl = NEXT(avl) ) {
    getmindeg(avl->v,f,&d);
    if ( d ) {
      MKV(avl->v,t); 
      simp_ff((Obj)t,&obj); t = (P)obj;
      NEXTDC(dc0,dc); DEG(dc) = d; COEF(dc) = t;
      pwrp(vl,t,d,&s); divsp(vl,f,s,&t); f = t;
    }
  }
  if ( dc0 )
    NEXT(dc) = 0;
  *pr = f; *dcp = dc0;
}

void lex_lc(P f,P *c)
{
  if ( !f || NUM(f) )
    *c = f;
  else
    lex_lc(COEF(DC(f)),c);
}

DCP append_dc(DCP dc,DCP dct)
{
  DCP dcs;

  if ( !dc )
    return dct;
  else {
    for ( dcs = dc; NEXT(dcs); dcs = NEXT(dcs) );
    NEXT (dcs) = dct;
    return dc;
  }
}

void sqfrsf(VL vl, P f, DCP *dcp)
{
  DCP dc,dct;
  Obj obj;
  P t,s,c,cont;
  VL tvl,onevl;

  simp_ff((Obj)f,&obj); f = (P)obj;
  lex_lc(f,&c); divsp(vl,f,c,&t); f = t;
  monomialfctr_sf(vl,f,&t,&dc); f = t;
  clctv(vl,f,&tvl); vl = tvl;
  NEWVL(onevl); NEXT(onevl)=0;
  if ( !vl )
    ;
  else if ( !NEXT(vl) ) {
    sfusqfr(f,&dct);
    dc = append_dc(dc,NEXT(dct));
  } else {
    t = f;
    for ( tvl = vl; tvl; tvl = NEXT(tvl) ) {
      onevl->v = tvl->v;
      cont_pp_mv_sf(vl,onevl,t,&cont,&s); t = s;
      sqfrsf(vl,cont,&dct);
      dc = append_dc(dc,NEXT(dct));
    }
    sqfrsfmain(vl,t,&dct);
    dc = append_dc(dc,dct);
  }
  NEWDC(dct); DEG(dct) = ONE; COEF(dct) = (P)c; NEXT(dct) = dc;
  *dcp = dct;
}

void sqfrsfmain(VL vl,P f,DCP *dcp)
{
  VL tvl;
  DCP dc,dct,dcs;
  P t,s;
  Z m,m1;
  V v;

  clctv(vl,f,&tvl); vl = tvl;
  dc = 0;
  t = f;
  for ( tvl = vl; tvl; tvl = NEXT(tvl) ) {
    v = tvl->v;
    partial_sqfrsf(vl,v,t,&s,&dct); t = s;
    dc = append_dc(dc,dct);
  }
  if ( !NUM(t) ) {
    STOZ(characteristic_sf(),m);
    pthrootsf(t,m,&s);
    sqfrsfmain(vl,s,&dct);
    for ( dcs = dct; dcs; dcs = NEXT(dcs) ) {
      mulz(DEG(dcs),m,&m1); DEG(dcs) = m1;
    }
    dc = append_dc(dc,dct);
  }
  *dcp = dc;
}

void pthrootsf(P f,Z m,P *r)
{
  DCP dc,dc0,dct;
  Z qn,rn;

  if ( NUM(f) )
    pthrootgfs((GFS)f,(GFS *)r);
  else {
    dc = DC(f);
    dc0 = 0;
    for ( dc0 = 0; dc; dc = NEXT(dc) ) {
      NEXTDC(dc0,dct);
      pthrootsf(COEF(dc),m,&COEF(dct));
      if ( DEG(dc) ) {
        divqrz(DEG(dc),m,&qn,&rn);
        if ( rn )
          error("pthrootsf : cannot happen");
        DEG(dct) = qn;
      } else
        DEG(dct) = 0;
    }
    NEXT(dct) = 0;
    MKP(VR(f),dc0,*r);
  }
}

void partial_sqfrsf(VL vl,V v,P f,P *r,DCP *dcp)
{
  P ps[2];
  DCP dc0,dc;
  int m;
  P t,flat,flat1,g,df,q;

  diffp(vl,f,v,&df);
  if ( !df ) {
    *dcp = 0;
    *r = f;
    return;
  }
  ps[0] = f; ps[1] = df;
  gcdsf(vl,ps,2,&g);  
  divsp(vl,f,g,&flat);
  m = 0;
  t = f;
  dc0 = 0;
  while ( !NUM(flat) ) {
    while ( divtp(vl,t,flat,&q) ) {
      t = q; m++;
    }
    ps[0] = t; ps[1] = flat;
    gcdsf(vl,ps,2,&flat1);
    divsp(vl,flat,flat1,&g);
    flat = flat1;
    NEXTDC(dc0,dc);
    COEF(dc) = g;
    STOZ(m,DEG(dc));
  }
  NEXT(dc) = 0;
  *dcp = dc0;
  *r = t;
}

void gcdsf(VL vl,P *pa,int k,P *r)
{
  P *ps,*pl,*pm;
  P **cp;
  int *cn;
  DCP *ml;
  Obj obj;
  int i,j,l,m;
  P mg,mgsf,t;
  VL avl,nvl,tvl,svl;

  ps = (P *)ALLOCA(k*sizeof(P));
  for ( i = 0, m = 0; i < k; i++ ) {
    simp_ff((Obj)pa[i],&obj);
    if ( obj )
      ps[m++] = (P)obj;
  }
  if ( !m ) {
    *r = 0;
    return;
  }
  if ( m == 1 ) {
    *r = ps[0];
    return;
  }
  pl = (P *)ALLOCA(m*sizeof(P));
  ml = (DCP *)ALLOCA(m*sizeof(DCP));
  for ( i = 0; i < m; i++ )
    monomialfctr(vl,ps[i],&pl[i],&ml[i]);
  gcdmonomial(vl,ml,m,&mg); simp_ff((Obj)mg,&obj); mgsf = (P)obj;
  for ( i = 0, nvl = vl, avl = 0; nvl && i < m; i++ ) {
    clctv(vl,pl[i],&tvl);
    intersectv(nvl,tvl,&svl); nvl = svl;
    mergev(vl,avl,tvl,&svl); avl = svl;
  }
  if ( !nvl ) {
    *r = mgsf;  
    return;
  }
  if ( !NEXT(avl) ) {
    ugcdsf(pl,m,&t);
    mulp(vl,mgsf,t,r);  
    return;
  }
  for ( tvl = nvl, i = 0; tvl; tvl = NEXT(tvl), i++ );
  for ( tvl = avl, j = 0; tvl; tvl = NEXT(tvl), j++ );
  if ( i == j ) {
    /* all the pl[i]'s have the same variables */
    gcdsf_main(avl,pl,m,&t);
  } else {
    cp = (P **)ALLOCA(m*sizeof(P *));
    cn = (int *)ALLOCA(m*sizeof(int));
    for ( i = 0; i < m; i++ ) {
      cp[i] = (P *)ALLOCA(lengthp(pl[i])*sizeof(P));
      cn[i] = pcoef(vl,nvl,pl[i],cp[i]);
    }
    for ( i = j = 0; i < m; i++ )
      j += cn[i];
    pm = (P *)ALLOCA(j*sizeof(P));
    for ( i = l = 0; i < m; i++ )
      for ( j = 0; j < cn[i]; j++ )
        pm[l++] = cp[i][j];
    gcdsf(vl,pm,l,&t);
  }
  mulp(vl,mgsf,t,r);  
}

/* univariate gcd */

void ugcdsf(P *pa,int m,P *r)
{
  P *ps;
  int i;
  UM w1,w2,w3,w;
  int d;
  V v;

  if ( m == 1 ) {
    *r = pa[0];
    return;
  }
  for ( i = 0; i < m; i++ )
    if ( NUM(pa[i]) ) {
      itogfs(1,(GFS *)r);
      return;
    }
  ps = (P *)ALLOCA(m*sizeof(P));
  sort_by_deg(m,pa,ps);
  v = VR(ps[m-1]);
  d = getdeg(v,ps[m-1]);
  w1 = W_UMALLOC(d);
  w2 = W_UMALLOC(d);
  w3 = W_UMALLOC(d);
  ptosfum(ps[0],w1);
  for ( i = 1; i < m; i++ ) {
    ptosfum(ps[i],w2);
    gcdsfum(w1,w2,w3); 
    w = w1; w1 = w3; w3 = w;
    if ( !DEG(w1) ) {
      itogfs(1,(GFS *)r);
      return;
    }
  }
  sfumtop(v,w1,r);
}

/* deg(HT(p),v), where p is considered as distributed poly over F[v] */
int gethdeg(VL vl,V v,P p)
{
  DCP dc;
  Z dmax;
  P cmax;

  if ( !p )
    return -1;
  else if ( NUM(p) )
    return 0;
  else if ( VR(p) != v )
    /* HT(p) = HT(lc(p))*x^D */
    return gethdeg(vl,v,COEF(DC(p)));
  else {
    /* VR(p) = v */
    dc = DC(p); dmax = DEG(dc); cmax = COEF(dc);
    for ( dc = NEXT(dc); dc; dc = NEXT(dc) )
      if ( compp(vl,COEF(dc),cmax) > 0 ) {
        dmax = DEG(dc); cmax = COEF(dc);
      }
    return ZTOS(dmax);
  }
}

/* all the pa[i]'s have the same variables (=vl) */

void gcdsf_main(VL vl,P *pa,int m,P *r)
{
  int nv,i,i0,imin,d,d0,d1,d2,dmin,index;
  V v,v0,vmin;
  VL tvl,nvl,rvl,nvl0,rvl0;
  P *pc, *ps, *ph,*lps;
  P x,t,cont,hg,g,hm,mod,s;
  P hge,ge,ce,he,u,cof1e,mode,mod1,adj,cof1,coadj,q;
  GFS sf;

  for ( nv = 0, tvl = vl; tvl; tvl = NEXT(tvl), nv++);
  if ( nv == 1 ) {
    ugcdsf(pa,m,r);
    return;
  }
  /* find v s.t. min(deg(pa[i],v)+gethdeg(pa[i],v)) is minimal */
  tvl = vl;
  do {
    v = tvl->v;
    i = 0;
    do {
      d = getdeg(v,pa[i])+gethdeg(vl,v,pa[i]);
      if ( i == 0 || (d < d0) ) {
        d0 = d; i0 = i; v0 = v;
      }
    } while ( ++i < m );
    if ( tvl == vl || (d0 < dmin) ) {
      dmin = d0; imin = i0; vmin = v0;
    }
  } while ( (tvl = NEXT(tvl)) != 0 );

  /* reorder variables so that vmin is the last variable */
  for ( nvl0 = 0, rvl0 = 0, tvl = vl; tvl; tvl = NEXT(tvl) )
    if ( tvl->v != vmin ) {
      NEXTVL(nvl0,nvl); nvl->v = tvl->v;
      NEXTVL(rvl0,rvl); rvl->v = tvl->v;
    }
  /* rvl = remaining variables */
  NEXT(rvl) = 0; rvl = rvl0;
  /* nvl = ...,vmin */
  NEXTVL(nvl0,nvl); nvl->v = vmin; NEXT(nvl) = 0; nvl = nvl0;
  MKV(vmin,x);

  /* for content and primitive part */
  pc = (P *)ALLOCA(m*sizeof(P));
  ps = (P *)ALLOCA(m*sizeof(P));
  ph = (P *)ALLOCA(m*sizeof(P));
  /* separate the contents */
  for ( i = 0; i < m; i++ ) {
    reorderp(nvl,vl,pa[i],&t);
    cont_pp_mv_sf(nvl,rvl,t,&pc[i],&ps[i]);
    head_monomial(nvl,vmin,ps[i],&ph[i],&t);
  }
  ugcdsf(pc,m,&cont);
  ugcdsf(ph,m,&hg);

  /* for hg*pp (used in check phase) */
  lps = (P *)ALLOCA(m*sizeof(P));
  for ( i = 0; i < m; i++ )
    mulp(nvl,hg,ps[i],&lps[i]);

  while ( 1 ) {
    g = 0;
    cof1 = 0;
    hm = 0;
    itogfs(1,(GFS *)&mod);
    index = 0;
    for ( index = 0; getdeg(vmin,mod) <= d+1; index++ ) {
      /* evaluation pt */
      indextogfs(index,(GFS *)&s);
      substp(nvl,hg,vmin,s,&hge);
      if ( !hge )
        continue;
      for ( i = 0; i < m; i++ )
        substp(nvl,ps[i],vmin,s,&ph[i]);
      /* ge = GCD(ps[0]|x=s,...,ps[m-1]|x=s) */
      gcdsf(nvl,ph,m,&ge);
      head_monomial(nvl,vmin,ge,&ce,&he);
      if ( NUM(he) ) {
        *r = cont;
        return;
      }
      divgfs((GFS)hge,(GFS)ce,&sf); t = (P)sf;
      mulp(nvl,t,ge,&u); ge = u;
      divsp(nvl,ph[imin],ge,&t); mulp(nvl,hge,t,&cof1e);
      /* hm=0 : reset; he==hm : lucky */
      if ( !hm || !compp(nvl,he,hm) ) {
        substp(nvl,mod,vmin,s,&mode); divsp(nvl,mod,mode,&mod1); 
        /* adj = mod/(mod|x=s)*(ge-g|x=s) */
        substp(nvl,g,vmin,s,&t);
        subp(nvl,ge,t,&u); mulp(nvl,mod1,u,&adj);
        /* coadj = mod/(mod|vmin=s)*(cof1e-cof1e|vmin=s) */
        substp(nvl,cof1,vmin,s,&t);
        subp(nvl,cof1e,t,&u); mulp(nvl,mod1,u,&coadj);
        if ( !adj ) {
          /* adj == gcd ? */
          for ( i = 0; i < m; i++ )
            if ( !divtp(nvl,lps[i],g,&t) )
              break;
          if ( i == m ) {
            cont_pp_mv_sf(nvl,rvl,g,&t,&u);
            mulp(nvl,cont,u,&t);
            reorderp(vl,nvl,t,r);
            return;
          }
        } else if ( !coadj ) {
          /* ps[imin]/coadj == gcd ? */
          if ( divtp(nvl,lps[imin],cof1,&q) ) {
            for ( i = 0; i < m; i++ )
              if ( !divtp(nvl,lps[i],q,&t) )
                break;
            if ( i == m ) {
              cont_pp_mv_sf(nvl,rvl,q,&t,&u);
              mulp(nvl,cont,u,&t);
              reorderp(vl,nvl,t,r);
              return;
            }
          }
        }
        addp(nvl,g,adj,&t); g = t;
        addp(nvl,cof1,coadj,&t); cof1 = t;
        subp(nvl,x,s,&t); mulp(nvl,mod,t,&u); mod = u;
        hm = he;
      } else {
        d1 = homdeg(hm); d2 = homdeg(he);
        if ( d1 < d2 ) /* we use current hm */
          continue;
        else if ( d1 > d2 ) {
          /* use he */
          g = ge;
          cof1 = cof1e;
          hm = he;
          subp(nvl,x,s,&mod);
        } else { 
          /* d1==d2, but hm!=he => both are unlucky */
          g = 0;
          cof1 = 0;
          itogfs(1,(GFS *)&mod);
        }
      }
    }
  }
}

void head_monomial(VL vl,V v,P p,P *coef,P *term)
{
  P t,s,u;
  DCP dc;
  GFS one;

  itogfs(1,&one);
  t = (P)one;
  while ( 1 ) {
    if ( NUM(p) || VR(p) == v ) {
      *coef = p;
      *term = t;
      return;
    } else {
      NEWDC(dc); 
      COEF(dc) = (P)one; DEG(dc) = DEG(DC(p));
      MKP(VR(p),dc,s);
      mulp(vl,t,s,&u); t = u;
      p = COEF(DC(p));
    }
  }
}

void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp)
{
  DP dp;
  MP t;
  int i,m;
  P *ps;
  struct order_spec *spec, *currentspec;
  extern struct order_spec *dp_current_spec;

  currentspec = dp_current_spec;
  create_order_spec(0,0,&spec);
  initd(spec);
  ptod(vl,rvl,p,&dp);
  for ( t = BDY(dp), m = 0; t; t = NEXT(t), m++ );
  ps = (P *)ALLOCA(m*sizeof(P));
  for ( t = BDY(dp), i = 0; t; t = NEXT(t), i++ )
    ps[i] = (P)C(t);
  gcdsf(vl,ps,m,c);
  divsp(vl,p,*c,pp);
  initd(currentspec);
}

void mfctrsf(VL vl, P f, DCP *dcp)
{
  DCP dc0,dc,dct,dcs,dcr;
  Obj obj;

  simp_ff((Obj)f,&obj); f = (P)obj;
  sqfrsf(vl,f,&dct);
  dc = dc0 = dct; dct = NEXT(dct); NEXT(dc) = 0;
  for ( ; dct; dct = NEXT(dct) ) {
    mfctrsfmain(vl,COEF(dct),&dcs);
    for ( dcr = dcs; dcr; dcr = NEXT(dcr) )
      DEG(dcr) = DEG(dct);
    for ( ; NEXT(dc); dc = NEXT(dc) );
    NEXT(dc) = dcs;
  }
  *dcp = dc0;
}

/* f : sqfr, non const */

void mfctrsfmain(VL vl, P f, DCP *dcp)
{
  VL tvl,nvl,rvl;
  DCP dc,dc0,dc1,dc2,dct,lcfdc,dcs;
  int imin,inext,i,j,n,k,np;
  int *da;
  V vx,vy;
  V *va;
  P *l,*tl;
  P gcd,g,df,dfmin;
  P pa[2];
  P f0,pp0,spp0,c,c0,x,y,u,v,lcf,lcu,lcv,u0,v0,t,s;
  P ype,yme,fin;
  GFS ev,evy;
  P *fp0;
  int *mev,*win;

  clctv(vl,f,&tvl); vl = tvl;
  if ( !vl )
    error("mfctrsfmain : cannot happen");
  if ( !NEXT(vl) ) {
    /* univariate */
    ufctrsf(f,&dc);
    /* remove lc */
    *dcp = NEXT(dc);
    return;
  }
  for ( n = 0, tvl = vl; tvl; tvl = NEXT(tvl), n++ );
  va = (V *)ALLOCA(n*sizeof(V));
  da = (int *)ALLOCA(n*sizeof(int));
  /* find v s.t. diff(f,v) is nonzero and deg(f,v) is minimal */
  imin = -1;
  for ( i = 0, tvl = vl; i < n; tvl = NEXT(tvl), i++ ) {
    va[i] = tvl->v;  
    da[i] = getdeg(va[i],f);
    diffp(vl,f,va[i],&df);
    if ( !df )
      continue;
    if ( imin < 0 || da[i] < da[imin] ) {
      dfmin = df;
      imin = i;
    }
  }
  /* find v1 neq v s.t. deg(f,v) is minimal */
  inext = -1;
  for ( i = 0; i < n; i++ ) {
    if ( i == imin )
      continue;
    if ( inext < 0 || da[i] < da[inext] )
      inext = i;
  }
  pa[0] = f;
  pa[1] = dfmin;
  gcdsf(vl,pa,2,&gcd);
  if ( !NUM(gcd) ) {
    /* f = gcd * f/gcd */  
    mfctrsfmain(vl,gcd,&dc1);
    divsp(vl,f,gcd,&g);
    mfctrsfmain(vl,g,&dc2);
    for ( dct = dc1; NEXT(dct); dct = NEXT(dct) );
    NEXT(dct) = dc2;
    *dcp = dc1;
    return;
  }
  /* create vl s.t. vl[0] = va[imin], vl[1] = va[inext] */
  nvl = 0;
  NEXTVL(nvl,tvl); tvl->v = va[imin];
  NEXTVL(nvl,tvl); tvl->v = va[inext];
  for ( i = 0; i < n; i++ ) {
    if ( i == imin || i == inext )
      continue;
    NEXTVL(nvl,tvl); tvl->v = va[i];
  }
  NEXT(tvl) = 0;

  fin = f;
  reorderp(nvl,vl,f,&g); f = g;
  vx = nvl->v;
  vy = NEXT(nvl)->v;
  MKV(vx,x);
  MKV(vy,y);
  /* remaining variables */
  rvl = NEXT(NEXT(nvl));
  if ( !rvl ) {
    /* bivariate */
    sfbfctr(f,vx,vy,getdeg(vx,f),&dc1);
    for ( dc0 = 0; dc1; dc1 = NEXT(dc1) ) {
      NEXTDC(dc0,dc);
      DEG(dc) = ONE;
      reorderp(vl,nvl,COEF(dc1),&COEF(dc));
    }
    NEXT(dc) = 0;
    *dcp = dc0;
    return;
  }
  /* n >= 3;  nvl = (vx,vy,X) */
  /* find good evaluation pt for X */
  mev = (int *)CALLOC(n-2,sizeof(int));
  while ( 1 ) {
    /* lcf(mev)=0 => invalid */
    substvp_sf(nvl,rvl,COEF(DC(f)),mev,&t);
    if ( t ) {
      substvp_sf(nvl,rvl,f,mev,&f0);
      pa[0] = f0;
      diffp(nvl,f0,vx,&pa[1]);
      if ( pa[1] ) {
        gcdsf(nvl,pa,2,&gcd);
      /* XXX maybe we have to accept the case where gcd is a poly of y */
        if ( NUM(gcd) )
          break;
      }
    }
    /* XXX if generated indices exceed q of GF(q) => error in indextogfs */
    next_evaluation_point(mev,n-2);
  }
  /* f0 = f(x,y,mev) */
  /* separate content; f0 may have the content wrt x */
  cont_pp_sfp(nvl,f0,&c0,&pp0);

  /* factorize pp0; pp0 = pp0(x,y+evy) = prod dc */
  sfbfctr_shift(pp0,vx,vy,getdeg(vx,pp0),&evy,&spp0,&dc); pp0 = spp0;

  if ( !NEXT(dc) ) {
    /* f is irreducible */
    NEWDC(dc); DEG(dc) = ONE; COEF(dc) = fin; NEXT(dc) = 0;
    *dcp = dc;
    return;
  }
  /* ype = y+evy, yme = y-evy */
  addp(nvl,y,(P)evy,&ype); subp(nvl,y,(P)evy,&yme);

  /* shift c0; c0 <- c0(y+evy) */
  substp(nvl,c0,vy,ype,&s); c0 = s;

  /* shift f; f <- f(y+evy) */
  substp(nvl,f,vy,ype,&s); f = s;

  /* now f(x,0,mev) = c0 * prod dc */

  /* factorize lc_x(f) */
  lcf = COEF(DC(f));
  mfctrsf(nvl,lcf,&dct); 
  /* skip the first element (= a number) */
  lcfdc = NEXT(dct);

  /* np = number of bivariate factors */
  for ( np = 0, dct = dc; dct; dct = NEXT(dct), np++ );
  fp0 = (P *)ALLOCA((np+1)*sizeof(P));
  for ( i = 0, dct = dc; i < np; dct = NEXT(dct), i++ )
    fp0[i] = COEF(dct);
  fp0[np] = 0;
  l = tl = (P *)ALLOCA((np+1)*sizeof(P));
  win = W_ALLOC(np+1);

  for ( k = 1, win[0] = 1, --np; ; ) {
    itogfs(1,(GFS *)&u0);
    /* u0 = product of selected factors */
    for ( i = 0; i < k; i++ ) {
      mulp(nvl,u0,fp0[win[i]],&t); u0 = t;
    }
    /* we have to consider the content */
    /* f0 = c0*u0*v0 */
    mulp(nvl,LC(u0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,mev,&lcu);
    divsp(nvl,pp0,u0,&v0);
    mulp(nvl,LC(v0),c0,&c); estimatelc_sf(nvl,rvl,c,lcfdc,mev,&lcv);
    mfctrsf_hensel(nvl,rvl,f,pp0,u0,v0,lcu,lcv,mev,&u);
    if ( u ) {
      /* save the factor */
      reorderp(vl,nvl,u,&t);
      /* y -> y-evy */
      substp(vl,t,vy,yme,tl++);

      /* update f,pp0 */
      divsp(nvl,f,u,&t); f = t;
      divsp(nvl,pp0,u0,&t); pp0 = t;
      /* update win, fp0 */
      for ( i = 0; i < k-1; i++ )
      for ( j = win[i]+1; j < win[i+1]; j++ )
        fp0[j-i-1] = fp0[j];
      for ( j = win[k-1]+1; j <= np; j++ )
          fp0[j-k] = fp0[j];
      if ( ( np -= k ) < k ) break;
      if ( np-win[0]+1 < k )
        if ( ++k <= np ) {
          for ( i = 0; i < k; i++ ) 
            win[i] = i + 1;
          continue;
        } else
          break;
      else 
        for ( i = 1; i < k; i++ ) 
          win[i] = win[0] + i;
    } else {
      if ( ncombi(1,np,k,win) == 0 ) {
        if ( k == np ) break;
        else 
          for ( i = 0, ++k; i < k; i++ ) 
            win[i] = i + 1;
      }
    }
  }
  reorderp(vl,nvl,f,&t);
  /* y -> y-evy */
  substp(vl,t,vy,yme,tl++);
  *tl = 0;
  for ( dc0 = 0, i = 0; l[i]; i++ ) {
    NEXTDC(dc0,dc); DEG(dc) = ONE; COEF(dc) = l[i];
  }
  NEXT(dc) = 0; *dcp = dc0;
}

void next_evaluation_point(int *e,int n)
{
  int i,t,j;

  for ( i = n-1; i >= 0; i-- )
    if ( e[i] ) break;
  if ( i < 0 ) e[n-1] = 1;
  else if ( i == 0 ) {
    t = e[0]; e[0] = 0; e[n-1] = t+1;
  } else {
    e[i-1]++; t = e[i];
    for ( j = i; j < n-1; j++ )
      e[j] = 0;
    e[n-1] = t-1;
  }
}

/* 
 * dc : f1^E1*...*fk^Ek
 * find e1,...,ek s.t. fi(mev)^ei | c 
 * and return f1^e1*...*fk^ek
 * vl = (vx,vy,rvl)
 */

void estimatelc_sf(VL vl,VL rvl,P c,DCP dc,int *mev,P *lcp)
{
  DCP dct;
  P r,c1,c2,t,s,f;
  int i,d;
  Z q;

  for ( dct = dc, r = (P)ONE; dct; dct = NEXT(dct) ) {
    if ( NUM(COEF(dct)) )
      continue;
    /* constant part */
    substvp_sf(vl,rvl,COEF(dct),mev,&f);
    d = ZTOS(DEG(dct));
    for ( i = 0, c1 = c; i < d; i++ )
      if ( !divtp(vl,c1,f,&c2) )
        break;
      else
        c1 = c2;
    if ( i ) {
      STOZ(i,q);
      pwrp(vl,COEF(dct),q,&s); mulp(vl,r,s,&t); r = t;
    }
  }
  *lcp = r;
}

void substvp_sf(VL vl,VL rvl,P f,int *mev,P *r)
{
  int i;
  VL tvl;
  P g,t;
  GFS ev;

  for ( g = f, i = 0, tvl = rvl; tvl; tvl = NEXT(tvl), i++ ) {
    if ( !mev )
      ev = 0;
    else
      indextogfs(mev[i],&ev);
    substp(vl,g,tvl->v,(P)ev,&t); g = t;
  }
  *r = g;
}

/*
 * f <- f(X+sgn*mev)
 */

void shift_sf(VL vl, VL rvl, P f, int *mev, int sgn, P *r)
{
  VL tvl;
  int i;
  P x,g,t,s;
  GFS ev;

  for ( g = f, tvl = rvl, i = 0; tvl; tvl = NEXT(tvl), i++ ) {
    if ( !mev[i] )
      continue;
    indextogfs(mev[i],&ev);
    MKV(tvl->v,x);
    if ( sgn > 0 )
      addp(vl,x,(P)ev,&t);
    else
      subp(vl,x,(P)ev,&t);
    substp(vl,g,tvl->v,t,&s); g = s;
  }
  *r = g;
}

/*
 * pp(f(0)) = u0*v0
 */

void mfctrsf_hensel(VL vl,VL rvl,P f,P pp0,P u0,P v0,P lcu,P lcv,int *mev,P *up)
{
  VL tvl,onevl;
  P t,s,w,u,v,ff,si,wu,wv,fj,cont;
  UM ydy;
  V vx,vy;
  int dy,n,i,dbd,nv,j;
  int *md;
  P *uh,*vh;
  P x,du0,dv0,m,q,r,fin;
  P *cu,*cv;
  GFSN inv;

  /* check the validity of lc's and adjust coeffs */
  /* f                -> lcu*lcv*x^(m+l)+... */
  mulp(vl,lcu,lcv,&t); 
  if ( !divtp(vl,t,LC(f),&m) ) {
    *up = 0; return;
  }
  mulp(vl,m,f,&t); f = t;
  /* u0 = am x^m+ ... -> lcu*x^m + a(m-1)*(lcu(mev)/am)*x^(m-1)+... */
  /* v0 = bm x^l+ ... -> lcv*x^l + b(l-1)*(lcv(mev)/bl)*x^(l-1)+... */
  adjust_coef_sf(vl,rvl,lcu,u0,mev,&u);
  adjust_coef_sf(vl,rvl,lcv,v0,mev,&v);

  /* f <- f(X+mev), u <- u(X+mev), v <- v(X+mev) */
  fin = f;
  shift_sf(vl,rvl,f,mev,1,&s); f = s;
  shift_sf(vl,rvl,u,mev,1,&s); u = s;
  shift_sf(vl,rvl,v,mev,1,&s); v = s;

  vx = vl->v; vy = NEXT(vl)->v;
  n = getdeg(vx,f);
  dy = getdeg(vy,f)+1;
  MKV(vx,x);
  cu = (P *)ALLOCA((n+1)*sizeof(P));
  cv = (P *)ALLOCA((n+1)*sizeof(P));

  /* ydy = y^dy */
  ydy = C_UMALLOC(dy); DEG(ydy) = dy; COEF(ydy)[dy] = _onesf();
  setmod_gfsn(ydy);

  /* (R[y]/(y^dy))[x,X] */
  poly_to_gfsn_poly(vl,f,vy,&ff);
  poly_to_gfsn_poly(vl,u,vy,&t); u = t;
  poly_to_gfsn_poly(vl,v,vy,&t); v = t;
  substvp_sf(vl,rvl,u,0,&u0);
  substvp_sf(vl,rvl,v,0,&v0);

  /* compute a(x,y), b(x,y) s.t. a*u0+b*v0 = 1 mod y^dy */
  extended_gcd_modyk(u0,v0,vx,vy,dy,&cu[0],&cv[0]);

  /* dv0 = LC(v0)^(-1)*v0 mod y^dy */
  invgfsn((GFSN)LC(v0),&inv); mulp(vl,v0,(P)inv,&dv0);

  /* cu[i]*u0+cv[i]*v0 = x^i mod y^dy */
  /* (x*cu[i])*u0+(x*cv[i])*v0 = x^(i+1) */
  /* x*cu[i] = q*dv0+r => cu[i+1] = r */
  /* cv[i+1]*v0 = x*cv[i]*v0+q*u0*dv0 = (x*cv[i]+q*u0*inv)*v0 */
  for ( i = 1; i <= n; i++ ) {
    mulp(vl,x,cu[i-1],&m); divsrp(vl,m,dv0,&q,&cu[i]);
    mulp(vl,x,cv[i-1],&m); mulp(vl,q,(P)inv,&t);
    mulp(vl,t,u0,&s);
    addp(vl,m,s,&cv[i]);
  }

#if 0
  /* XXX : check */
  for ( i = 0; i <= n; i++ ) {
    mulp(vl,cu[i],u0,&m); mulp(vl,cv[i],v0,&s);
    addp(vl,m,s,&w);
    printexpr(vl,w);
    fprintf(asir_out,"\n");
  }
#endif

  dbd = dbound(vx,f)+1;  

  /* extract homogeneous parts */
  W_CALLOC(dbd,P,uh); W_CALLOC(dbd,P,vh);
  for ( i = 0; i <= dbd; i++ ) {
    exthpc(vl,vx,u,i,&uh[i]); exthpc(vl,vx,v,i,&vh[i]);
  }

  /* register degrees in each variables */
  for ( nv = 0, tvl = rvl; tvl; tvl = NEXT(tvl), nv++ );
  md = (int *)ALLOCA(nv*sizeof(int));
  for ( i = 0, tvl = rvl; i < nv; tvl = NEXT(tvl), i++ )
    md[i] = getdeg(tvl->v,f);

  /* XXX for removing content of factor wrt vx */
  NEWVL(onevl); onevl->v = vx; NEXT(onevl) = 0;

  for ( j = 1; j <= dbd; j++ ) {
    for ( i = 0, tvl = rvl; i < nv; tvl = NEXT(tvl), i++ )
      if ( getdeg(tvl->v,u)+getdeg(tvl->v,v) > md[i] ) {
        *up = 0;
        return;
      }
    for ( i = 0, t = 0; i <= j; i++ ) {
      mulp(vl,uh[i],vh[j-i],&s); addp(vl,s,t,&w); t = w;
    }

    /* s = degree j part of (f-uv) */
    exthpc(vl,vx,ff,j,&fj); subp(vl,fj,t,&s);
    for ( i = 0, wu = 0, wv = 0; i <= n; i++ ) {
      if ( !s )
        si = 0;
      else if ( VR(s) == vx )
        coefp(s,i,&si);
      else if ( i == 0 )
        si = s;
      else
        si = 0;
      if ( si ) {
        mulp(vl,si,cv[i],&m); addp(vl,wu,m,&t); wu = t;
        mulp(vl,si,cu[i],&m); addp(vl,wv,m,&t); wv = t;
      }
    }
    if ( !wu ) {
      gfsn_poly_to_poly(vl,u,vy,&t);
      shift_sf(vl,rvl,t,mev,-1,&s);
      if ( divtp(vl,fin,s,&q) ) {
        cont_pp_mv_sf(vl,onevl,s,&cont,up);
        return;
      }
    }
    if ( !wv ) {
      gfsn_poly_to_poly(vl,v,vy,&t);
      shift_sf(vl,rvl,t,mev,-1,&s);
      if ( divtp(vl,fin,s,&q) ) {
        cont_pp_mv_sf(vl,onevl,q,&cont,up);
        return;
      }
    }
    addp(vl,u,wu,&t); u = t;
    addp(vl,uh[j],wu,&t); uh[j] = t;
    addp(vl,v,wv,&t); v = t;
    addp(vl,vh[j],wv,&t); vh[j] = t;
  }
  gfsn_poly_to_poly(vl,u,vy,&t);
  shift_sf(vl,rvl,t,mev,-1,&s);
  if ( divtp(vl,fin,s,&q) )
    cont_pp_mv_sf(vl,onevl,s,&cont,up);
  else
    *up = 0;
}

void adjust_coef_sf(VL vl,VL rvl,P lcu,P u0,int *mev,P *r)
{
  P lcu0,cu;
  DCP dc0,dcu,dc;

  substvp_sf(vl,rvl,lcu,mev,&lcu0);
  divsp(vl,lcu0,LC(u0),&cu);
  for ( dc0 = 0, dcu = DC(u0); dcu; dcu = NEXT(dcu) ) {
    if ( !dc0 ) {
      NEXTDC(dc0,dc);
      COEF(dc) = lcu;
    } else {
      NEXTDC(dc0,dc);
      mulp(vl,cu,COEF(dcu),&COEF(dc));
    }
    DEG(dc) = DEG(dcu);
  }
  NEXT(dc) = 0;
  MKP(VR(u0),dc0,*r);
}

void extended_gcd_modyk(P u0,P v0,V x,V y,int dy,P *cu,P *cv)
{
  BM g,h,a,b;

  gfsn_univariate_to_sfbm(u0,dy,&g);  
  gfsn_univariate_to_sfbm(v0,dy,&h);  
  sfexgcd_by_hensel(g,h,dy,&a,&b);
  sfbm_to_gfsn_univariate(a,x,y,cu);
  sfbm_to_gfsn_univariate(b,x,y,cv);
}

/* (F[y])[x] -> F[x][y] */

void gfsn_univariate_to_sfbm(P f,int dy,BM *r)
{
  int dx,d,i;
  BM b;
  UM cy;
  DCP dc;

  dx = getdeg(VR(f),f);  
  b = BMALLOC(dx,dy);
  DEG(b) = dy;
  for ( dc = DC(f); dc; dc = NEXT(dc) ) {
    /* d : degree in x, cy : poly in y */
    d = ZTOS(DEG(dc));
    cy = BDY((GFSN)COEF(dc));
    for ( i = DEG(cy); i >= 0; i-- )
      COEF(COEF(b)[i])[d] = COEF(cy)[i];
  }
  for ( i = 0; i <= dy; i++ )
    degum(COEF(b)[i],dx);
  *r = b;
}

void sfbm_to_gfsn_univariate(BM f,V x,V y,P *r)
{
  P g;
  VL vl;

  sfbmtop(f,x,y,&g);
  NEWVL(vl); vl->v = x;
  NEWVL(NEXT(vl)); NEXT(vl)->v = y;
  NEXT(NEXT(vl)) = 0;
  poly_to_gfsn_poly(vl,g,y,r);
}

void poly_to_gfsn_poly(VL vl,P f,V v,P *r)
{
  VL tvl,nvl0,nvl;
  P g;

  /* (x,y,...,v,...) -> (x,y,...,v) */
  for ( nvl0 = 0, tvl = vl; tvl; tvl = NEXT(tvl) ) {
    if ( tvl->v != v ) {
      NEXTVL(nvl0,nvl);
      nvl->v = tvl->v;
    }
  }
  NEXTVL(nvl0,nvl);
  nvl->v = v;
  NEXT(nvl) = 0;
  reorderp(nvl0,vl,f,&g);
  poly_to_gfsn_poly_main(g,v,r);
}

void poly_to_gfsn_poly_main(P f,V v,P *r)
{
  int d;
  UM u;
  GFSN g;
  DCP dc,dct,dc0;

  if ( !f )
    *r = f;
  else if ( NUM(f) || VR(f) == v ) {
    d = getdeg(v,f);
    u = UMALLOC(d);
    ptosfum(f,u);    
    MKGFSN(u,g);
    *r = (P)g;
  } else {
    for ( dc0 = 0, dct = DC(f); dct; dct = NEXT(dct) ) {
      NEXTDC(dc0,dc);
      DEG(dc) = DEG(dct);
      poly_to_gfsn_poly_main(COEF(dct),v,&COEF(dc));
    }
    NEXT(dc) = 0;
    MKP(VR(f),dc0,*r);
  }
}

void gfsn_poly_to_poly(VL vl,P f,V v,P *r)
{
  VL tvl,nvl0,nvl;
  P g;

  gfsn_poly_to_poly_main(f,v,&g);
  /* (x,y,...,v,...) -> (x,y,...,v) */
  for ( nvl0 = 0, tvl = vl; tvl; tvl = NEXT(tvl) ) {
    if ( tvl->v != v ) {
      NEXTVL(nvl0,nvl);
      nvl->v = tvl->v;
    }
  }
  NEXTVL(nvl0,nvl);
  nvl->v = v;
  NEXT(nvl) = 0;
  reorderp(vl,nvl0,g,r);
}

void gfsn_poly_to_poly_main(P f,V v,P *r)
{
  DCP dc,dc0,dct;

  if ( !f )
    *r = f;
  else if ( NUM(f) ) {
    if ( NID((Num)f) == N_GFSN )
      sfumtop(v,BDY((GFSN)f),r);
    else
      *r = f;
  } else {
    for ( dc0 = 0, dct = DC(f); dct; dct = NEXT(dct) ) {
      NEXTDC(dc0,dc);
      DEG(dc) = DEG(dct);
      gfsn_poly_to_poly_main(COEF(dct),v,&COEF(dc));
    }
    NEXT(dc) = 0;
    MKP(VR(f),dc0,*r);
  }
}

void printsfum(UM f)
{
  int i;

  for ( i = DEG(f); i >= 0; i-- ) {
    printf("+(");
    printf("%d",IFTOF(COEF(f)[i])); 
    printf(")*y^%d",i);
  }
}

void printsfbm(BM f)
{
  int i;

  for ( i = DEG(f); i >= 0; i-- ) {
    printf("+(");
    printsfum(COEF(f)[i]); 
    printf(")*y^%d",i);
  }
}